.

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 30

CONTRIBUTORS TO THIS VOLUME

Ralph S . Keen Jifi Komrska C . K. McLane Milorad S . MladjenoviC George L. Schnable R. TornoviC Hardy W. Trolander James H. Veghte L. Vodovnik

Advances in Electronics and

Electron Physics

EDITED BY

L. MARTON Smithsonian Institution, Washington, D.C.

Assistant Editor CLAIRE MARTON

EDITORIAL BOARD

T. E. Allibone H. B. G. Casimir W. G. Dow A. Rose A. 0. C. Nier

E. R. Piore M. Ponte

L. P. Smith F. K. Willenbrock

VOLUME 30

1971

ACADEMIC PRESS New York and London

COPYRIGHT 0 1971, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY PHOTOSTAT, MICROFILM, RETRIEVAL SYSTEM, OR ANY OTHER MEANS, WITHOUT WRITTEN PERMISSION FROM THE PUBLISHERS.

ACADEMIC PRESS, INC. 111 Fifth Avenue, New York, New York 10003

United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London NWI IDD

LIBRARY OF CONGRESS CATALOG CARD NUMBER: 49-7504

PRINTED IN THE UNITED STATES OF AMERICA

Contents

CONTRIBUTORS TO VOLUME 30 . . . . . . . . . . . . . . . . vii

FOREWORD . . . . . . . . . . . . . . . . . . . . . ix

Experimental Plasma Turbulence

C . K . MCLANE

I . Introduction . . . . . . . . . . . . . . . . . . . 1 I1 . Diffusion . . . . . . . . . . . . . . . . . . . . 3

111 . Positive Column Instability and Turbulence . . . . . . . . . . 7 IV . Drift Waves and Transition to Turbulence . . . . . . . . . . 11 V . Feedback Suppression of Low Frequency Plasma Instabilities . . . . . 17

VI . Convection Cells . . . . . . . . . . . . . . . . . . 22 VII . Other Experimental Studies of Turbulent Plasmas . . . . . . . . 23

VIII . Conclusion . . . . . . . . . . . . . . . . . . . 36 References . . . . . . . . . . . . . . . . . . . 38

Recent Advances in Design of Magnetic Beta-Ray Spectrometers

MILORAD S . MLADJENOVIC

I . Introduction . . . . . . . . . . . . . . . . . . . 43 I1 . Flat Spectrometers. with Cylindrical Field . . . . . . . . . . 46

111 . Sector Spectrometers . . . . . . . . . . . . . . . . 53 IV . Toroidal (" Orange ") Spectrometers . . . . . . . . . . . . 56 V.Lenses. . . . . . . . . . . . . . . . . . . . . 57

VI . Trochoidal Spectrometers . . . . . . . . . . . . . . . 58 VII . Optical Analogy Spectrometer . . . . . . . . . . . . . . 64

VIII . Correctors . . . . . . . . . . . . . . . . . . . 67 IX . Azimuthally Varying Field . . . . . . . . . . . . . . . 71 X . Comparison Table . . . . . . . . . . . . . . . . . 73

References . . . . . . . . . . . . . . . . . . . 75

On Failure Mechanisms in Large-Scale Integrated Circuits

GEORGE L . SCHNABLE AND RALPH S . KEEN

I . Relationship between Types of Integrated Circuits and Failure Mechanisms . 80 I1 . Bipolar Failure Mechanisms . . . . . . . . . . . . . . 86

I11 . MOS Failure Mechanisms . . . . . . . . . . . . . . . 98 IV . Multilevel Metallization . . . . . . . . . . . . . . . . 107 V . Integrated Circuit Assembly . . . . . . . . . . . . . . 118

VI . Integrated Circuit Reliability . . . . . . . . . . . . . . 122 References . . . . . . . . . . . . . . . . . . . 133

V

vi CONTENTS

Scalar Diffraction Theory in Electron Optics JIkf KOMRSKA

I . Introduction . . . . . . . . . . . . . . . . . . . 139 I1 . The Diffraction Integral . . . . . . . . . . . . . . . . 142

I11 . Electron Diffraction by Uncharged Obstacles . . . . . . . . . . 165 IV . Scattering of Electrons by Charged Obstacles . . . . . . . . . . 210

V . Summary . . . . . . . . . . . . . . . . . . . . 232 References . . . . . . . . . . . . . . . . . . . . 232

Recent Advances in Biological Temperature Measurements

HARDY W . TROLANDER AND JAMES H . VEGHTE

I . Conductive Electric Thermometry . . . . . . . . . . . . . 235 I1 . Radiation Thermometry . . . . . . . . . . . . . . . 261

References . . . . . . . . . . . . . . . . . . . 270

Systems Approach to Skeletal Control: Concept of the System

R . TOMOVIC

I . Introduction . . . . . . . . . . . . . . . . . . . 273 I1 . Rehabilitation of Amputees and Paralyzed Persons . . . . . . . . 274

111 . Systems Approach to Muscle Control . . . . . . . . . . . . 276 IV . Multifunctional Hand Prosthesis . . . . . . . . . . . . . 278 V . ArmControl . . . . . . . . . . . . . . . . . . . 279

VI . Robots for Physical Rehabilitation . . . . . . . . . . . . . 280 References . . . . . . . . . . . . . . . . . . . 281

Functional Electrical Stimulation of Extremities

L . VODOVNIK

I . Introduction . . . . . . . . . . . . . . . . . . . 283 I1 . Classification of FESE . . . . . . . . . . . . . . . . 284 111 . Motoric FESE . . . . . . . . . . . . . . . . . . 285 IV . Implanted Systems . . . . . . . . . . . . . . . . . 288 V . Examples of New Systems . . . . . . . . . . . . . . . 289

References . . . . . . . . . . . . . . . . . . . 296

AUTHOR INDEX . . . . . . . . . . . . . . . . . . . 299 SUBJECT INDEX . . . . . . . . . . . . . . . . . . . 310 CUMULATIVE AUTHOR INDEX. VOLUMES 1-30 . . . . . . . . . . . 315 CUMULATIVE SUBJECT INDEX. VOLIJMES 1-30 . . . . . . . . . . . 333

CONTRIBUTORS TO VOLUME 30

RALPH S. KEEN,* Microelectronics Division, Philco-Ford Corporation, Blue

JIkf KOMRSKA, Institute of Instrument Technology, Czechoslovak Academy

C. K. MCLANE, Department of Aerospace Engineering Sciences, University

MILORAD S . MLADJENOVI~,~ B. Kidrii: Institute of Nuclear Sciences, Belgrade,

GEORGE L. SCHNABLE,* Microelectronics Division, Philco-Ford Corpora-

R. TOMOVIC, Department of Electrical Engineering, University of Belgrade,

HARDY W. TROLANDER, Yellow Springs Instrument Company, Inc., Yellow

JAMES H. VEGHTE, Aerospace Medical Research Laboratory, Wright-

L. VODOVNIK, Faculty for Electrical Engineering, University of Ljubljana,

Bell, Pennsylvania

of Sciences, Brno, Czechoslovakia

of Colorado, Boulder, Colorado

Yugoslavia

tion, Blue Bell, Pennsylvania

Belgrade, Yugoslavia

Springs, Ohio

Patterson Air Force Base, Ohio

Ljubljana, Yugoslavia

Present address: Inselek, 743 Alexander Road, Princeton, New Jersey 08540. ' Present address: 2410 California Street, N.W., Washington, D.C. 20008. * Present address: RCA Laboratories, David Sarnoff Research Center, Princeton, New

Jersey 08540.

vii

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FOREWORD

This thirtieth volume of Advances in Electronics and Electron Physics appears roughly 25 years after the inception of the series. The intervening period has seen great changes in both science and technology; we have attempted to cover in our reviews a significant part of these changes. If we have succeeded it is largely due to the helpful collaboration of many people: our excellent contributors and the publishers. l t is appropriate now to express our thanks to all of them.

In this volume we present an interesting mixture of plasma physics, particle spectroscopy and diffraction phenomena, failures in electronic components, and, last but not least, three papers on bioelectronic engineering. C . K. McLane’s review is important because of the large-scale efforts, in this country and abroad, to harness nuclear fusion. Better understanding of turbulence effects will help to produce the conditions necessary for the controlled operation of dense plasmas. M. S. Mladjenovif. covers recent work on the subject of P-ray spectrography, which was treated in an early review in this series by R. Hayward. The intervening years have witnessed a vast improvement in the design of these instruments, requiring an up-dating of the earlier review. Failure mechanisms in integrated circuits have been the subject of many investigations. G . L. Schnable and R. S . Keen review over 170 references ranging from very generalized considerations on the possible mechanisms to detailed investigations of the components or processes employed in the production and use of large-scale integrated circuits.

J. Komrska’s review is an important contribution to the role of contrast in electron optical image formation. Originally scattering was considered to be the most important factor; the role played by diffraction was not recognized until relatively recently. The present review focuses mostly on diffraction.

Biological temperature measurements are the subject of the review by H. W. Trolander and J. H. Veghte. Biomedical engineering practitioners follow quite assiduously the advances in electronics, and a compact view of this subject may appeal to many of our readers.

The last two reviews belong together. R. TomoviC discusses the general subject of “ Systems Approach to Skeletal Control,” while his colleague, L. Vodovnik, gives a specific illustration of it in “Functional Electrical Stimulation of Extremities.” With advances in the engineering of prosthetic devices, it appears desirable to call them to the attention of a wider audience than the specialists.

ix

X FOREWORD

As in the past, we include a list of future reviews together with the prospec- tive authors:

Electron Polarization Recent Advances in Field Emission

Microfabrication Using Electron Beams The Effects of Radiation in MIS Structures Small Angle Deflection Fields for Cathode Ray Tubes

Sputtering Interpretation of Electron Microscope Images of Defects in

Galactic and Extragalactic Radio Astronomy

Electromagnetic Scattering by Plasma Turbulence

Crystals

Optical Communication through Scattering Channels Trends in Communications Satellites

Single Photoelectron Detection and Timing Current Saturation Mechanisms of Field Effect Transistors Wave Interactions in Solids Hollow Cathode Arcs Gas Discharge Display Devices Chemical Lasers

Electronic Engineering in Ocean Technology Channelling in Solids

Thermal Energy Ion Molecule Reactions Physics and Applications of MIS Varactors

Ion Implantation in Semiconductors

Image formation in the Electron Microscope with Particular Reference to the Defects in Electron Optical Images

Self-scanned Solid State Image Sensors

Stephen 3. Smith Lynwood Swanson and

Francis Charbonnier A. N. Broers Karl Zaininger R. G. E. Hutter and

H. Dressel M. W. Thompson M. J. Whelan

F. J. Kerr and Wm. C. Erickson

David L. Feinstein and Victor L. Granatstein

Robert S . Kennedy P. L. Bargellini and

E. S. Rittner Sherman K. Poultney Edward S. Yang Morris Ettenberg J. L. Delcroix B. Kazan and John Hall Peter H. Dawson and

G. H. Kimbell Richard 0. Rowlands R. Sizmann and

Constantin Varelas Eldon E. Ferguson W. Harth and

H. G. Unger S. Namba and

Kohzoh Masuda D. L. Misell

Paul K. Weimer

Suggestions for coverage of other subjects and for suitable authors are

A cumulative index of the 30 volumes published, as well as of the supple- most welcome.

ments, is given at the end of this volume.

L. MARTON CLAIRE MARTON

May 1971

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS

VOLUME 30


Experimental Plasma Turbulence

C . K. McLANE

Department of Aerospace Engineering Sciences, University of Colorado,

Boulder, Colorado

........................................................................... 11. Diffusion ..........................................................................................

111. Positive Column Instability and Turbulence ............................................. IV. Drift Waves and Transition to Turbulenc V. Feedback Suppression of Low Frequency

VI. Convection Cells. ................................. VII. Other Experiment Plasmas.. .....................................

A. Linear Turbulent Heating Experiments.. .............................................. B. Toroidal Experiments ................................................ ............. C. Collisionless Shocks ........................................................................ D. Wind Driven Plasma Turbulen

VIlI. Conclusion .................... ............................. References .................... .............................

..................................

1 3 7

11 17 22 23 23 29 33 35 36 38

1. INTRODUCTION

A turbulent fluid possesses a random velocity field extending to a scale much larger than the mean free path or charged particle magnetic gyroradius, but smaller than the characteristic dimensions of the flow field. The magnitude of this intermediate scale random velocity field is of the same order as the macroscopic flow velocity. If the fluid is electrically conducting (for example, a plasma), there may be electric and magnetic fields present, and these will possess fluctuating components of the same dimensional scale as the random velocity, and coupled thereto.

The importance of turbulence in fluids and plasmas is that it modifies greatly the magnitude of such transport processes as diffusion, electrical conductivity, heat conductivity, and viscosity. Fluid elements subjected to the turbulent velocity or electromagnetic field are scattered coherently with an effect which is similar to that of a much increased collision frequency. Vis- cosity is enhanced because the mean step of the random walk of momentum is increased from the mean free path to a mean scale length of turbulence. Diffusion and thermal conductivity are increased because of a similar increase

1

2 C. K. MCLANE

in the transport of mass and energy. The increase of pressure drop in fluid flow channels when transition from laminar to turbulent flow occurs is well known, as are the rapidity of turbulent mixing, the increased magnitude of turbulent heat transfer, and the increased electrical resistivity of turbulent plasmas.

Transport of momentum, mass, and energy may also be affected greatly by the occurrence of convective instability in the fluid. In such a case, convective cells become established, and result in a completely determinate flow field whose time and space dependences can be exactly described. Such a state is exemplified by the von Karman vortex street in the wake of a bluff body (body of nonstreamlined shape) in fluid dynamics, and by the Kadomtsev-Nedospa- sov helical instability of the positive column of a glow discharge in a magnetic field parallel to the discharge current (see Section 111). A convectively unstable flow field of this sort is not turbulent because it does not possess the randomly fluctuating velocity, electric and magnetic fields characteristic of turbulence. Transport occurs by determinate, rather than a random walk process, and therefore cannot be described in terms of transport coefficients which have any general significance. Convectively unstable fluid and plasma flows do, however, become turbulent for sufficiently large driving forces, which, in the examples cited, are Reynolds number for the vortex street, and magnetic field for the helical plasma instability.

It is to these terminal, turbulent states of plasmas that we direct our principal attention in this chapter. Identification of the sorts of plasma turbulence which are of importance to confinement and heating of plasmas will require discussion of some of the experiments on plasma instabilities which lead to turbulence. No attempt at completeness will be made, for a rather comprehensive review of experiments on plasma instabilities has been given by Lehnert ( I ) and reviews of the theory of magnetohydrodynamic and microscopic plasma instabilities have been given by Jukes (2). Theory of the turbulent plasma and experiments on turbulent plasma were reviewed in depth by Kadomtsev (3) in 1965, and a review of turbulence in toroidal plasma confinement systems was published by Kadomtsev and Pogutse (4) in 1970. Experimental work on plasma turbulence has appeared at a much increased rate during the last four years. Much of the work reports new observations which are not yet fully interpreted, and there has certainly been insufficient time for the subject to mature to the point where a critical review would be justifiable, or even possible. The present chapter should be viewed as a survey of some of the recent literature on plasma turbulence and closely related phenomena. References are far from complete; citations are given to work which seems particularly useful in understanding the properties of turbulent plasmas and appreciating the meaning of the term turbulence as applied to plasmas. Similarities and differences between turbulence in plasmas and that in nonconducting fluids have been discussed in a particularly lucid way by Dupree (5). Few references

EXPERIMENTAL PLASMA TURBULENCE 3

will be made to the study of transition to turbulence and the turbulent state in reflex (or Penning) discharges. For these, the reader is referred to a recent review by Hooper (Su). Figures showing apparatus are simplified for clarity. For details, dimensions, and measurement techniques employed, the reader is referred to the references cited.

11. DIFFUSION

We consider first the diffusion of plasma through a neutral gas in a magnetic field. I t was in the experimental study of this phenomenon that an enhanced, or anomalously rapid diffusion of the plasma across the magnetic field was found and attributed to a new kind of turbulence in the plasma which could be created by the effect of electric and magnetic fields. For reference, then, we present first a brief survey of classical, or purely collisional, diffusion in a magnetic field.

Classical diffusion is described by the coefficients of the density gradient in the solutions of the following set of equations, of which Eqs. (la) and (lb) are equations of continuity, Eqs. (2a) and (2b)stateconservationofmornentum, and Eq. (3) is Poisson’s equation.

(anelat) + v n,v, = 0, ( 1 4

(ani/&) + V * nivi = 0, (1 b)

[a(ne me ve)latl+ Ve * V(ne me Ve) = - kTeVn, + eneVp - en,(v, x B) - n, me v, v,, , (2a)

[d(ni mi vi)/at] + vi - V(ni mi vi)

= - kTiVni - ZeniVq + Zeni(vi x B) - ni mi vi vin , (2b)

Vzp = -(e/eo)(Zni - n,). (3)

Here, n, and ni , v, and vi, me and m i , Te and Ti, and v,, and vin are the number density, mean (drift) velocity, mass, temperature, and frequency of collisions with neutrals of the electrons and ions, respectively. The Boltzmann constant is k , the electrostatic potential is cp, the magnetic field is B, and e0 is the permittivity of free space. Mks units are used, and e is the elementary charge (taken to be positive). Solutions of these equations are customarily discussed in terms of the following parameters :

pe = elm, ven, pi = Ze/mi V i n , ( 4 0 )

D, = kT,/m, v,, , Di = kTi/mi v in , ( 5 0 )

wbe = &/me, obi = ZeB/mi. (6a,b)

4 C. K . MCLANE

The p’s are the charged particle mobilities, the D’s the diffusion coefficients, and the LO<S the gyrofrequencies of electrons and ions respectively. Except in a sheath very near the wall, the diffusion velocities ve and vi are small enough that the inertial effects represented by the time derivatives and (nonlinear) convective terms on the left in Eqs. (2a) and (2b) may be neglected. [These were included in an analysis of wall effects by Persson (6)].

The following solutions of Eqs. (1)-(3) are of interest here: Case I. Free particle diffusion. Very low charged particle density-such

that the electric field (and Poisson’s equation, Eq. 3) can be neglected; B = 0. The mobilities and diffusion coeficients are the single particle values, given by Eqs. (4) and (5).

Case II. Free particle rlffrsion. Density as in case I. B # 0. The diffusion coefficients and mobilities now become tensor quantities. In Cartesian coordinates, and with B = Bd, the diagonal elements of the diffusion tensor are as follows :

(7)

(8)

D,, = D l l = kT/mv,

D,, = D,, = D , = (kT/mv)[l/(l + p2B2)] .

In Eqs. (7) and (8), the quantities T, m, v , and p (from Eqs. 4a and 4b) can be given the subscript e or i depending upon the coefficient desired. The only two nonzero off-diagonal elements of the diffusion tensor are Dx, and D,, , which are known as the Hall terms. The charged particle flux which they produce is perpendicular to the density gradient, and provides the diamagnetic current necessary to magnetohydrostatic equilibrium.

Case ZZZ. Ambipolar dzffusion. Density appreciable, so that Eq. (3) (Poisson equation) and the electric field terms must be included. B = 0. In this case, quasineutrality must obtain, n, z Z n , , and it follows from the continuity .equations (Eqs. 1 and 2) that the divergence of the total current density must vanish. Further progress with the problem will depend upon the boundary conditions specified. If these are such as to preclude current flow in the plasma, the effect of the V q terms in Eqs. (2a) and (2b) is to couple the ion and electron fluxes together in such a way as to satisfy a zero current condition, and the coefficient of the density gradient will be found to be the ambipolar diffusion coefficient, D , .

D, = ( t i e Di + pi De)/(Pe + Pi). (9)

This is the applicable diffusion coefficient for calculating plasma decay by diffusion to the walls. The potential gradient and the density gradient are related as follows in this case.

D, - ZDi

P e +Pi vq = V In n.


Ambipolar diffusion is the predominant decay process in late time afterglows. Case ZV. Ambipolar difusion with B # 0. This would appear to be possible

only under a very restricted set of conditions. In particular, ambipolar diffusion should be possible if there is no gradient of the density or temperature parallel to the magnetic field. In this case, the perpendicular component of the diffusion tensor, Da, is

D a , = ~ a [ l / ( l + ~le~liB*)I. (1 1)

The inverse B2 dependence (for p e pi B2 % 1) of the perpendicular diffusion coefficient given by Eq. (1 1) was responsible for early optimism on the prospects for using magnetic fields to confine hot plasmas for the purpose of achieving controlled thermonuclear fusion. (Strictly speaking, Eq. (1 1) applies to a weakly ionized plasma. A similar magnetic field dependence holds for the collision dominated fully ionized plasma.)

Case V. Simon dzflusion; B # 0. The opposite extreme from the ambipolar assumption, which holds that plasma currents are zero, is the assumption that conducting boundaries or the equivalent will cause the potential gradient within the plasma to be zero. Simon (7) showed that in this case, diffusion perpendicular to the magnetic field will proceed at the free ion rate as given by Eq. (8) applied to ions. The rate of Simon diffusion is much greater than the ambipolar rate because the ion mobility is much less than the electron mobility.

Simon diffusion was probably first encountered, though not recognized, in ion source research for Calutron isotope separators during World War 11. Diffusion of plasma to the walls (which were of graphite) was much faster than could be accounted for classically (Eq. 11). Bohm (8) attributed the phenomenon to what was in effect turbulent diffusion, and obtained the perpendicular diffusion coefficient since denoted &ohm

DBohrn =T$(kT/eB). (12)

It now seems much more likely that the rapid diffusion was due to the mechanism provided by Simon (7); the ambipolar electric field would be expected to have been shorted out by the flow of electrons between the conducting graphite walls and the plasma.

There seems little doubt that the ambipolar condition can be satisfied in a magnetoplasma. Most laboratory experiments, however, are done in finite apparatus with a part, at least, of the walls conducting. Geissler (9) reports very careful experiments which show that intermediate cases between ambipolar and Simon, or short-circuit, diffusion occur, and gives references to previous work.

The work of Bohm, leading to the diffusion coefficient given in Eq. (12) was ahead of its time. While the experimental situation which stimulated his

6 C. K. MCLANE

work did not require, nor perhaps even involve, a turbulent mechanism, subsequent experiments to be described in Sections 111, IV, and VII can only be explained on the assumption of turbulence. The essential nature of turbulent diffusion is most easily seen in an early contribution of Spitzer (lo), which contains the essential physics of the process. Cross field transport is caused by a random walk of charged particles in the fluctuating transverse component of the electric fleld, E L , due to whatever waves or instabilities constitute the turbulence. The velocity is that of the guiding center drift, EJB. Relating the electric field to the thermal energy of the plasma, and the coherence time of the electric field to the electron gyroperiod, Spitzer obtained a diffusion coefficient of the Bohm form. Experimental parameters of Stellarator plasmas gave a value of the numerical coefficient about three times Bohm’s 1/16 (Eq. 12). This was remarkably close to what was observed.

Assuming a cross field drift mechanism, Taylor (11) has employed thermo- dynamic reasoning to set an upper bound on the fluctuating electric field, and thereby an upper bound on the transverse diffusion coefficient. His result,

DL = $(kT/eB), (1 3)

is just four times the Bohm value (Eq. 12). Fowler (12) has drawn somewhat closer limits on the diffusion rate, taking account of parameters specific to several experiments in which an anomalous diffusion coefficient was measured.

It is interesting to note, if only as a mnemonic, that the ion and electron collision frequencies which (if regarded as independent variables) maximize the perpendicular ambipolar diffusion coefficient (Eq. 11) are just the respective gyrofrequencies. The maximum diffusion coefficient so obtained is just the upper bound given by Taylor (Eq. 13).

Porkolab and Kino (13) reported a study of transverse diffusion of a potassium plasma produced by surface ionization on hot tantalum in a vapor pressure mode (Fig. 1). The diffusion coefficient was determined from radial

FIG. 1 . Schematic drawing of Porkolab and Kino ( I S ) potassium plasma device with qualitative graph of plasma density distribution, n(r), superposed. Tantalum buttons, B-B, are heated by electron bombardment from the rear, using heated filaments, F-F. G-G are guard rings.


density profiles, which were governed by competition between end-plate recombination and radial diffusion. An inverse BZ dependence identified the diffusion as collision dominated, or classical. Enhancement of diffusion, and transition to an inverse B dependence occurred when either (1) a coherent, sinusoidal current or (2) a broad band noise current was drawn between the two heated end plates by application of a root mean square potential difference of a few volts [from 0 to 2.5 (noise) or 6 (8 kHz sinusoidal) volts].

The diffusion coefficient in this artificially stimulated turbulent state was proportidnal to the root mean square driving potential and to B-'. Since it may be expected that

v,, = kT,le, (14)

this dependence corresponds to a Bohm-type diffusion coefficient. When a sinusoidal current was employed, the potential on a floating probe showed the presence of harmonics of the driving frequency up to the fifth, and the resulting diffusion rate was frequency independent. Continuous wave and broad band noise, exceeding a threshold in frequency and amplitude, both produced diffusion at the Bohm rate, but this result is subject to a factor of ten uncertainty because of the accuracy limitation on plasma potential measurements. The occurrence of anomalous diffusion for continuous wave injected signals has also been found in experiments on drift waves (Section 11); however, the character of the plasma mode giving rise to Bohm diffusion in the Porkolab and Kino work was not identified.

The frequent occurrence of diffusion at the Bohm rate in strongly turbulent plasmas was associated by Dupree (5) with the expected equivalence between the period of the dominant instability mode and the nonlinear coherence time.

111. POSITIVE COLUMN INSTABILITY AND TURBULENCE

While it is quite possible that the ion source experiments described by Bohm et al. (8) were correctly explained by the short circuit diffusion described by Simon (7), experiments carefully designed to eliminate this effect were later carried out by Lehnert (14, and Hoh and Lehnert (15). These experiments (Fig. 2) were conducted on the positive column of discharges in helium, argon, krypton, and hydrogen in discharge tubes of radii from 0.535 to 1.00 cm. Three and one half meters of the tubes were in a solenoid, and 0.25 m of each end projected through the fringing field region. The magnetic lines of force therefore terminated on the insulating glass tube wall. A measure of the plasma loss rate, and hence of the transverse diffusion coefficient, was provided by the longitudinal electric field required to maintain constant discharge current. At small magnetic fields, the electric field decreased as expected from the decrease in transverse ambipolar diffusion (Eq. 11). In each case,

8 C . K. MCLANE

U

\ C

\

FIG. 2. Discharge configuration used by Lehnert (14) and Hoh and Lehnert (15). C , cathode; A, anode; S, solenoid.

however, a critical magnetic field was found above which the noise level of the discharge increased, as did the electric field, and hence transverse plasma transport.

The correct theoretical description of this experiment was given by Kadomtsev and Nedospasov (16). The plasma becomes unstable toward growth of a helical density perturbation when the physical parameters are such as to satisfy the following instability criterion, which thus determines the critical field observed by Lehnert.

(1 5 ) X2ky2 y p e ukyx k4 1 + y pi D,k3

~ 4 + ( 2 + ~ ) x ~ + 1 +Y+-- <- -y - X.

Here :

and k is the wave number of the perturbation, with components ky and k , . The mobilities pi, and electron diffusion coefficient, D, , are defined in Eqs. (4a), (4b), and (5a). The magnetic field and applied electric field are in the z-direction, and the electron drift velocity u = p, E, .

An heuristic derivation of a stability criterion very similar to Eq. (15) was later given by Hoh (17), who also gave a very clear physical picture of the development of the instability. If a helical density perturbation of the right sense appears on the plasma, the applied electric field causes space charge to appear in regions where the helix has a longitudinal density gradient (Fig. 3). The sign of the charge depends on the sign of the gradient, and its helical distribution in space leads to an azimuthal electric field. The latter gives rise to a radial plasma drift which reinforces the original helical perturbation when the magnetic field is strong enough that the drift is not compensated by transverse diffusion. Toader (18) presents experimental measurements of positive column critical fields in helium and neon at pressures from 0.5 to 4 torr, which


Fro. 3. The Kadomtsev-Nedospasov helical instability (16). Illustrated is an (originally cylindrical) surface of equal density with a helical perturbation superposed. Discharge electric field E causes charge separation as shown, leading to field perturbation,E', indirec- tion shown. Cross field drift (velocity, VD = El x B/ IBI ') causes helical density perturbation to grow.

show that the Kadomtsev-Nedospasov theory (16) deteriorates somewhat for pressures above 1.5 torr, and that the Hoh theory (17) becomes totally un- acceptable above 1.5 torr.

From the work just described to the present, effort on the positive column in the magnetic field has been devoted by many, including Artsimovich and Nedospasov (19), Kadomtsev (20), Woehler (21), Sheffield (22), and Halseth and Pyle (23 , to determine the extent to which a turbulent plasma couId be produced by this means. Artsimovich and Nedospasov (19) experimentally studied the macroscopic properties of the turbulent plasma (electric field and diffusive loss) up to the point at which the losses were comparable to magnetic field free losses, but they did not characterize the structure of the fluctuating velocity field. The density distribution (time average as a function of radius) agreed with that expected from the Kadomtsev theory (20).

Woehler (21) reports measurements of radial density dependence of an argon positive column in a magnetic field. Well below the critical field for the helical instability the density distribution follows the expected J,, Bessel function (curve A, Fig. 4). The theory of Kadomtsev (20) predicts a more sharply peaked distribution with flat wings near the wall (curve C, Fig. 4). Measure- ments well above the critical field showed a somewhat similar profile to that of Kadomtsev, with the exception that the density at the wall was nearly 40 % of the axial value, rather than zero (curve B, Fig. 4). Woehler also measured density fluctuation correlation length along and across the field; however, since he used straight probes inserted across the magnetic field, the experience of Sheffield (22) would suggest that his radial correlation length is overesti- mated.

Sheffield (22) studied the evolution at supercritical fields of the helical instability in helium. He found that spatial density correlation measurements

10 C. K. MCLANE

FIG. 4. Radial density profiles in experiments of Woehler (21). Curve A, 0.18 T; curve B, 0.6 T; curve C, theory of Kadomtsev (20).

revealed that the helical perturbation persisted up to ten times the critical field. He therefore found his data in better agreement with the theory of Holter and Johnson (24) who assumed a helical perturbation, than with Kadomtsev (20). However, Sheffield did agree with Artsimovich and Nedospasov (19) and Woehler (21) that there was a finite density discontinuity very near the wall at high magnetic fields. He therefore patterned a solution of the fluid equations somewhat after Holter and Johnson, but used experimental data on pressure, electron temperature, magnetic and electric fields, current, tube dimensions, and radial density profile to calculate frequency, time constant for growth of the perturbation amplitude (growth rate), wavenumber, and phase difference between perturbed density and electric field. Agreement between experiment and theory is to within 25 to 50 % on wavelength and frequency. No data were available on growth rate. The calculated growth rates were essentially zero up to four times the critical field and positive from 4 to about 10 times B, ,which Sheffield interprets as a relaxation oscillation growing into a turbulent state. The evidence for the latter is a broadening of the frequency spectrum of the helical oscillation as the magnetic field is increased to high values. Loss of plasma was found essentially due to drift, measured by the density-electric field cross-correlation ( C E O ) . Evidence was provided by agreement of calculated loss based on measurement of the correlation with experimental loss rate measurements.

The first experiments actually to be done in what could properly be called a fully turbulent positive column are those of Halseth and Pyle (23). These were done in a 3 m long discharge tube similar to that shown in Fig. 2, 5.5 cm in diameter, of which the central 2 m were in a solenoid which could produce a


magnetic field up to 1.2 T (Tesla; 1 tesla = 10,000 G). Currents of 200 and 400 mA were drawn through a hot cathode glow discharge in helium at pressures from 20 to 400 mtorr. For the lower magnetic fields, up to fifteen times critical, the loss was dominated by convection in the transverse electric field of the helical instability mode, and the semiempirical theory of Sheffield (22) gave a satisfactory representation of the transverse plasma loss. For higher fields, the transverse diffusion coefficient was in agreement with that calculated from both the theories of Kadomtsev (25) and Dupree (26). The Kadomtsev theory does not give the fluctuation amplitude correctly as a function of the radius. The observed amplitude is as great on the axis as elsewhere, while the mixing length theory of Kadomtsev gives n" = Idn/dr, where 1 is a constant fraction (about 0.1) of the tube radius everywhere, and this gives n" = 0 on axis. In addition, this theory does not give a satisfactory interpretation of the sharp decrease in density which occurs near the wall, and is in error by a factor of two on the high side in providing the frequency peak of the noise spectrum.

As the magnetic field increases, the experiments of Halseth and Pyle show the radial density profile to change from the J , Bessel function characteristic of diffusion with a constant coefficient to a flattened profile characteristic of convective transport. Finally, at high fields, the profile becomes sharply peaked on axis and exhibits broad, gently sloping wings in the outer regions as predicted by Kadomtsev. Under the high field condition, the spatial density correlation function no longer shows the damped cosine shape which would be characteristic of a persisting oscillatory mode. It decays exponentially, both transversely and longitudinally to the field. For example, at 1.2 T and 200 mtorr, where the critical field is 0.071 T, the axial correlation length is about 20 cm and the radial value is about 0.6 cm.

It may be concluded, therefore, that positive column turbulence is analogous to the wake of a bluff body in that the magnetic field (Reynolds number) required to produce the helical instability (Karman vortex street) must be exceeded by a large factor in order to produce a fully turbulent state.

Iv. DRIFT WAVES AND TRANSITION TO TURBULENCE

The Kadomtsev-Nedospasov, helical, or current convective instability as it is variously called, may be regarded as one of a class known as drift instabilities. In these, space charge is produced in regions where there is a density gradient by a variety of mechanisms, including current flow, diffusive particle flux, centrifugal force, and ambipolar electric field (taking advantage of the disparity in electron and ion mobility). The space charge gives rise to an electric field which, via the cross-field drift imparted to ions and electrons alike, enhances the density gradient which produced the original space charge,

12 C . K. MCLANE

and, incidentally, transports plasma across the magnetic field. The drift instability has been termed universal, for it may occur in any plasma possessing gradient in density, temperature, magnetic field, or other physical parameter. The variety of instabilities and waves properly classified in the drift category is so large as to preclude giving reference here to more than a few illustrative or particularly important experiments. A review of drift wave theory has been given recently by Krall (27).

Because of the wide variety of drift or driftlike waves which can occur due to gradients of various plasma state parameters, the literature on drift waves is long and confusing. Waves driven by temperature gradients, or the potential gradients arising therefrom, in surface ionized alkali-metal vapor plasmas [Q-machine (28) plasmas] have often been misinterpreted as density gradient drift waves.

The first careful isolation and identification of a pure density-gradient drift wave in an isothermal plasma was done by Hendel, Chu, and Politzer (28a) at Princeton, using the Q-1 alkali vapor plasma device (Fig. 5). The region of

FIG. 5. The Princeton Q-1 alkali vapor plasma device used in Hendel et al. (28a). Tungsten plates, E, are heated by electron bombardment from behind using hot cathodes, F. Cs or K vapor is directed in an axisymmetric pattern on the central regions of the plates by sources S. The plasma, P, has a radius of maximum density gradient, R., which is less than the radius of maximum temperature gradient, RT .

the temperature gradient was well separated from the density gradient by illuminating each of the hot end plates with an axisymmetric array of four metal vapor atomic beams. The radial intensity distribution was such that the intensity at the edges of the 3 cm diameter plates was only one tenth that at the center. A substantial part of the density gradient was thus confined to a region in which the logarithmic temperature gradient was less than or equal to 0.05 cm-', as compared with greater than or equal to 1 cm-' at the plasma column edges. I t was therefore possible to distinguish clearly the density


gradient drift oscillations in the first (nearly isothermal) region from the edge oscillations in the region of strong temperature gradient.

The azimuthal phase velocity of the density gradient drift waves was found to agree well with that predicted by the linear theory when corrected for the Doppler shift engendered by the plasma drift rotation under the influence of the radial electric field (azimuthal drift velocity, Eor/B). The radial electric field arose from the combined influence of the plasma density gradient and end plate temperature gradient; the value calculated from measured gradients equaled that obtained from plasma potential measurements.

Drift waves with azimuthal wavenumbers up to m = 7 were found, and their respective amplitudes were greatest at the magnetic fields for which the theoretically predicted growth rate was largest. Radial wave number, frequency, and azimuthal phase velocity were found to agree with theory in their dependence on magnetic field, plasma density, and mean ion mass (which was varied by using mixtures of cesium and potassium).

Radial transport was, of course, convective. I t was found to be an order of magnitude larger than classical diffusion, and an order of magnitude less than Bohm diffusion would have been under the conditions of the experiment. The wave-induced plasma loss rate was determined by the cross-correlation between density and azimuthal electric field, (iiE,), and depended on the phase difference between these quantities as it should.

The edge oscillations in alkali-metal plasmas have since been identified with the Kelvin-Helmholtz instability by Kent, Jen, and Chen (29). The instability is driven by a sheared azimuthal drift velocity which results from the steep temperature gradient found at the column edge.

Lisitano, DeDionigi, and Fontanesi (30) found that a plasma produced in a mirror field by a 3 GHz slow wave structure at one end was unstable, but quiescent if a second similar structure were used for heating at the other end. The quiescent plasma had a flatter radial temperature distribution than the unstable plasma. Broad band low frequency noise was suppressed as well as the primary instability (termed a drift instability by the authors) when the symmetric configuration was used.

Having, as it does, a transverse electric field associated with it, and being of low frequency so that it affects ion motions, the drift wave is a particularly effective agent in transporting plasma across the magnetic field. This practical concern with its effects has stimulated a very large amount of work on drift wave dispersion (31) and damping (32) and its role in transporting plasma (33). Not only are drift waves frequently unstable, but it appears that other unstable modes may couple to drift waves, thus exciting them and producing plasma losses. Clarke (34) found that this was the case in the Oak Ridge thermonuclear experiment DCX-2, where a cyclotron frequency modified negative mass instability coupled to a low frequency drift wave and caused

14 C . K. MCLANE

enhanced cross-field plasma flux. Hasegawa (35) showed that strong coupling of modulated plasma waves (such as ion or electron cyclotron waves) could occur if the Cerenkov condition

is satisfied, where ups is the phase velocity of the slow wave, ugf the group velocity of the fast wave, and 8 the angle between their propagation vectors (Fig. 6).

Slowwave

FIG. 6. Coupling between modulated fast wave and slow wave (35).

An important contribution to the systematic investigation of the nonlinear properties of drift waves was the recognition by Lashinsky (36) that they were very well represented by solutions of the van der Pol equation:

(d2x/dt2) - E ( 1 - j?x2)wo(dx/dt> + wo2x = 0, (20) where x is the “displacement” (6 or E l , for example), E is a small parameter, and /? measures the ratio of the linear growth rate to the strength of the nonlinear saturation mechanism. The characteristics necessary for a mode to be represented by Eq. (20) are: (1) Its amplitude must increase with finite slope monotonically and reversibly from some critical value of the parameter (magnetic field, for example) which governs the strength of the mode. That is, the excitation must be “ soft” (Fig. 7a). (2) The instability must grow to a finite limit cycle of constant amplitude.

It should be noted that the first characteristic does not usually hold for the Kadomtsev-Nedospasov instability of the positive column. This may show a “hard” excitation, that is, one in which the amplitude is not a single valued function of the magnetic fieId. In this case, a hysteresis-like behavior (Fig. 7b) is seen when the magnetic field is cycled through and above the critical, or onset value, as shown by Robertson and Currie (364 .

Mode interaction, as well as application of an external drive signal to the plasma mode as described by the van der Pol equation, may be represented as in Eq. (21).

(dZx/dt2) - E ( l - px2)wo(dx/dt) + wo2x = W o 2 E cos wi t, (21)


A

FIG. 7. Dependence of amplitude of instability, A , and magnetic field, B, for “soft” (a) and “hard” (b) excitation of an instability mode, after Kadomtsev (3).

where E is the amplitude and wi the frequency of the interacting mode or injected signal. The properties of this equation were studied by Lashinsky in a discussion of the transition to turbulence of the drift unstable plasma (37). Depending on the strength of the nonlinearity parameter E and the ratio of driving amplitude E to limit cycle amplitude, A , there exists a frequency range about coo, dw, , within which the free running frequency, wo , will be pulled into synchronism with the driving frequency, wi . [This phenomenon is well discussed by Keen and Fletcher (341 (Fig.8). Just outside this range, a phenomenon termed “periodic pulling” occurs (37), in which the mode which occurred undisturbed at wo is amplitude and frequency modulated on the time scale of the beat between the “pulled” signal and the injected signal. By this means, a naturally occurring mode may be broadened, and frequencies incommensurate with the original mode structure are introduced into the

FIG. 8. Synchronization behavior of Van der Pol oscillator (38). Amplitude of driven wave, P, and perturbing wave, D. Beat frequency, B, between driven and perturbing wave. wo is unperturbed resonant frequency, and 6w is half-width of synchronization band.

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plasma. Lashinsky shows an example of the transition of a discrete mode spectrum of drift waves (produced with a potential on the end plates resulting in an electron sheath, which suppresses the drift instability) to a spectrum in which the modes are hardly discernible above a strong background continuum (produced with an ion sheath, which enhances the drift instability). Periodic pulling results in a characteristic unilaterial broadening of the affected mode spectrum which has been reported for drift waves affected by an injected audio signal in a potassium plasma by Abrams, Yadlowski, and Lashinsky (39). Broadening occurs on the side of the mode spectrum remote from the perturbing signal. The effect is strong: a substantial broadening (factor of two or greater) of the drift wave can be caused by an injected signal 20 dB in amplitude below the drift mode.

Another mechanism for the introduction of new frequencies incommensurate with the mode structure of a drift unstable plasma is parametric mode- mode coupling, discussed by Hai and Wong (40). The linearity of the dispersion relation for drift waves makes possible a three wave interaction for which

wo = w, + w, and k , = k , + k 2 . (22)

In this case (w,, k,) is a drift wave denoted the pump which interacts with two waves (a,, k , ) and (a,, k,) from the thermal excitation spectrum. Among the cases examined experimentally in the linearly stable regime of a potassium plasma by Hai and Wong is the degenerate case in which the pump mode has azimuthal wave number m = 2 and the excited modes are both of m = 1.

Having noted at least two mechanisms by means of which the fluctuation spectrum in an unstable plasma can become broadened and extended in frequency, it is of interest to consider an experiment showing how turbulent transport can arise in a plasma having a rather simple mode spectrum. Buchel’nikova and Salimov (41) used a single ended potassium plasma device, having a hot contact ionizing plate of 20 mm radius at one end, and an assembly of cold electrodes at the other end of a 36 cm long column (Fig 9). A symmetric group of seven separate, 1 cm diameter electrodes was arranged in hexagonal close packed array at the cold end, thus dividing the plasma column into seven flux tubes, along each of which current could be made to flow independently. The diffusion coefficient could be estimated from measurement of radial flux, and, independently, from decay of density with distance from the hot plate.

It was found that an ion cyclotron wave instability could be driven by an electron drift velocity of 40 times the ion thermal speed in any flux tube (the cold electrodes in the other flux tubes being allowed to float). If these waves were excited in two adjacent flux tubes, they were found uncorrelated in phase, and strong density fluctuations were induced by the drift resulting from the stochastic transverse electric field between the tubes. When the plasma in all


J FIG. 9. Potassium plasma device used by Buchel'nikova and Salimov (41) for study of

enhanced diffusion. P, contact ionization plate heated by electron bombardment from filamentary cathode (not shown); S , potassium vapor source; C, collecting electrodes; A, ammeter; M, magnetic field coils.

seven tubes was excited, the ion gyro-frequency (40 kHz under conditions of experiment) was no longer observed; instead a low frequency (5-10 kHz) relaxation oscillation was seen. This was interpreted as the result of enhanced diffusion periodically reducing the density below the unstable regime.

It is interesting to note that, although the mean random walk step (flux tube size) was 1 cm, and the plasma radius was only 2 cm, the Bohm diffusion coefficient was found to hold. A diffusion coefficient calculated from experimental field measurements by means of Spitzer's theory (10) was in almost exact agreement with the experimental determination.

Though the ion temperature of the plasma was initially 0.2 eV (determined by the hot end plate temperature), fast ions (1-2 eV) were foundwhen the ion cyclotron instability was excited. A stochastic acceleration mechanism was shown to provide the most likely explanation of these results.

v. FEEDBACK SUPPRESSION OF LOW FREQUENCY PLASMA INSTABILITIES

Low frequency modes, such as drift waves and ion acoustic waves, are important contributors to the transport of plasma across the confining magnetic field. Attention has therefore been given to the possibility of a feedback suppression system external to the plasma to limit their growth.

The report of a first successful attempt to stabilize drift-type waves by this means was probably that of Parker and Thomassen (42). They utilized a hot cathode reflex discharge (Fig. 10) in 1/2-2 mTorr hydrogen with a magnetic field of 75-1 50 G. With a plasma density of the order 10" cm-3 and electron temperature of 5 to 8 eV, drift modes with azimuth wave numbers m = 1, 2, and 3 travelled around the tube in the electron diamagnetic drift direction with a frequency in the range 10-100 KHz. The wavenumber parallel to the

18 C. K. MCLANE

A

c €4

FIG. 10. Reflex discharge used by Parker and Thomassen for feedback suppression experiments (42), C, C, cathodes; A, A, anodes; PI-P4, plates for introduction of feedback signal.

tube axis was essentially zero. Electrodes subtending 45" angles were affixed to the interior wall of the tube (radius, 5 cm) at 90" intervals, and extended the full 60 cm length of the discharge. With these an azimuthal field interacting with modes m = 1 and/or 2 could be applied to the plasma. When the plates were driven by the properly phase shifted and amplified plasma potential signal picked up by a radially inserted Langmuir probe, the drift wave could be suppressed. Under these circumstances, discharge current and plasma density increases of 20 to 30 % indicate reduced loss to the wall. Frequency shift and amplitude changes of the drift modes depend on gain and phase shift of the feedback loop in the way expected from a root-locus diagram derived from a feedback control-system analysis.

Successful feedback suppression of drift type instabilities in a plasma of approximately two orders of magnitude higher density was achieved by Keen and Aldridge (43). These authors used one to four plates driven by separate feedback loops from probes biased to collect ion saturation current. The spatial arrangement and signal phasing on these plates was chosen to facilitate driving the plasma in m = 0, -t. 1, and +2 modes. The plasma was that of a hollow cathode discharge in argon operating in a 1,kG magnetic field. The cylindrical plasma column had a peak density of the order l O " ~ m - ~ and electron temperature of 5 eV. The density gradient scale length was 1.4 cm. As an example, a predominantly m = + 1 mode occuring at 5.5 kHz with optimum phase shift (-90") and gain of the feedback loop could be suppressed in amplitude by a factor of about ten. Regenerative feedback (phase shift + 90" or -270") enhanced the original signal by a factor of about two. Increasing feedback loop gain substantially beyond the optimum for suppression resulted in an instability level above-that of the undisturbed plasma. A reduction in cross field transport flux could be inferred from the change in radial density profile of the stabilized plasma, but no diffusion coefficients were actually measured.

Simonen, Chu, and Hendel (44) demonstrated feedback control of the amplitude of a well-identified density gradient drift wave. A signal picked up by a Langmuir probe (presumably measuring ion or electron density) was amplified and phase shifted, then fed to a magnetic field aligned wire probe


having fifty times the area of the Langmuir probe sensor. The driven probe acted as a modulated electron sink. The behavior of the system was in agreement with a modified stability criterion derived from a two fluid drift wave theory in which the sink term was included in the electron fluid continuity equation. Drift wave amplitude and plasma density depended on feedback loop phase shift and gain in the way the theory predicted. Instability-induced plasma loss could be completely suppressed up to 1.2 times the critical field for the m = 3 drift mode at which point the m = 2 mode destabilized.

In contrast to the experiments of Parker andThomassen (42) and Keen and Aldridge (43), no stabilization of the drift wave could be achieved by Simonen, Chu, and Hendel with suppressor electrodes external to the plasma, This suggests that the former authors were not observing density gradient drift waves, but possibly edge oscillations more like the Kelvin-Helmholtz instability identified by Kent, Jen, and Chen (29).

Hendel, Chu, Perkins, and Simonen (45) were able to effect remote stabilization of density gradient drift waves by irradiating the plasma with feedback signal modulated microwaves at the upper hybrid frequency. Heating was localized in a small region by introducing a magnetic field gradient which was small enough not to effect the drift wave behavior (grad In B z 0.03 cm-' with grad In no z 1 cm-I). The heat introduction was shown to behave in the theory like the electron sink term in the continuity equation of the previous work (44). Instability amplitude and frequency and plasma density depended on feedback phase shift and gain in the expected way.

Keen (46) utilized the van der Pol oscillator as a purely phenomenological model for feedback stabilization of the " collisional type drift waves " studied by Keen and Aldridge (43) in an argon hollow-cathode discharge plasma. The dependence of amplitude and frequency shift of the instability on gain and phase shift in the feedback loop is in very good agreement with the functional relationship predicted by the van der Pol model. The linear growth rate, u, was deduced from dependence of frequency shift, Am, on phase shift, ip, as predicted by the van der Pol model:

2Ao = a cos cp.

The result, u/mo = 0.12 k 0.02, was in very good agreement with the values of 0.13 k 0.02 from rise time and 0.15 & 0.03 from decay time when the feedback signal was gated off and on, respectively.

Thus the van der Pol oscillator model for the collisional drift wave is found to give a nicely self-consistent phenomenological description, though it remains without a firm basis in the physics of the phenomenon. Stix (47) has also pointed out the analogy between the behavior of the van der Pol oscillator and collisional drift waves in his nonlinear theory.

20 C . K. MCLANE

Still left open in the foregoing discussion of drift wave stabilization is the question of whether more than one mode could simultaneously be stabilized. That this, too, can be done was demonstrated by Lindgren and Birdsall (48) by means of experiments on a collisionless potassium plasma in a mirror magnetic field. Three tuned ( Q = 7) and phased feedback loops were used to suppress drift waves of azimuthaI mode number m = 2, 3, and 4 simultaneously. This was accomplished with only slight enhancement of modes m = 1 and 5 (Fig. 11). The marked destabilization of modes other than the one suppressed that is often seen when broad band feedback systems are used (44) was not present.

m = l 2 3 4 5

FIG. 11. Multimode feedback suppression experiments of Lindgren and Birdsall (48). (a) Schematic representation of amplitudes of modes m = 1 to 5 without, and (b) with feedback control of modes 2, 3, and 4.

Experiments on feedback stabilization of the ion sound instability are also of importance from the standpoint of cross field plasma transport and turbulence reduction. For these, the van der Pol oscillator model stands on a somewhat more physical basis.

Keen and Fletcher (38) showed that a two fluid theory of the ion-sound instability could produce an equation of van der Pol type if the ion-neutral collision frequency were well below the wave frequency. An anharmonic oscillator equation resulted for higher ion-neutral collision frequency. The condition for obtaining these results was that the continuity equation contain a source term, Si, accounting for ionization by electron impact, and recombination or other unspecified loss mechanisms:

Si = an, - pn12 - pi3. (24) Here, a, p, and y are constants, and n, is the density perturbation. The equation representing the oscillations of the system when driven externally by a term A sin ot in the collision dominated case is


(d2nl/dt2) + wo2nl = -(dn,/dt)[(v - a) + 2pn, + 3yn12]

- vpn,’ - vyn, + wo2A sin wt. (25)

The dependence of the reson.ance shape described by this equation for varying drive amplitude was exactly that found for the response of the plasma of a neon arc positive column driven by four coils equally spaced around the tube, oriented and phased such as to produce an in-phase azimuthal magnetic field, &. At a low amplitude of the driving field, a symmetric resonant response is found ; intermediate amplitude produces an asymmetric resonance with the peak shifted up in frequency; and high amplitude produces an asymmetric peak with hysteresis on the high frequency side of the peak characteristic of the behavior of Eq. (25). This predicts a triple root (with the middle one unstable) for the amplitude of the driven oscillator as a function of frequency on the high side of the peak response for a sufficiently strong driving field (Fig. 12).

W WO

FIG. 12. Resonance shape of nonlinear ion-sound instability as found by Keen and Fletcher (38). A , amplitude; w, frequency; w o , small amplitude resonance.

For very small collision frequency, the system is described by an equation

(d2nl/dt2) - (dn,/dt)[cx - 2pn, - 3ynI2] + aOZnl = Aoo2 sin a t . (26)

Keen and Fletcher show that the solutions of this equation are in good agreement with the response of the neon arc plasma at lower neutral pressure where the ion-neutral collision frequency is small. The synchronization phenomenon described in Section IV, as well as quenching of the instability outside the frequency range of synchronization were observed.

The behavior to be expected of a van der Pol oscillator when driven at a frequency well above its free running frequency is not yet agreed upon. Keen and Fletcher (49) show by means of experiments on the positive column plasma of a neon arc with a mercury pool cathode that the ionwave instabilityshows the asynchronous quenching phenomenon described by Bogolyubov (SO). The quenching signal was introduced by means of a short coil wound around the discharge tube. Dependence of oscillation amplitude and frequency shift on quenching signal amplitude and of critical amplitude of quenching signal (for

of the van der Pol type.

22 C. K. MCLANE

complete quenching) on quenching signal frequency were in agreement with the Bogolyubov theory, while the oscillation amplitude did not show the theoretically expected dependence on quenching signal frequency.

Remote stabilization of the ion acoustic wave instability was also demonstrated by Keen and Fletcher (51). The sensor for the feedback signal was a photodiode located outside the neon arc discharge tube used for the previous work. The appropriately phase shifted and amplified signal was used to modu- late an ultrahigh frequency source tuned to the electron cyclotron resonance frequency (500 MHz at 0.018T) and coupled to the plasma by a resonant structure outside the discharge tube. The ion wave amplitude depended on the rf power introduced and the phase angle of the modulation in the way expected of the van der Pol oscillator (46).

Efficient coupling of energy from an amplitude modulated microwave at the upper hybrid frequency to density gradient drift waves [see also Hendel et al. (45)], edge oscillations, and electrostatic ion cyclotron waves was reported by Wong, Baker, and Booth (52). A potassium plasma was used, and microwave power of 0.3 mW/cm2 could excite ion waves with amplitude n/no = 0.05. This is comparable to the power required of a probe inserted in the plasma. Depending on choice of phase, and plasma state, the modulated 2-4 GHz signal could be used either to excite ion waves or to suppress an ion wave instability.

VI. CONVECTION CELLS

Some of the experiments confirming convective transport of plasma by instabilities of the drift type have already been discussed. Among these were the Kadomtsev-Nedospasov instability of the positive column, and the density driven drift waves which have been studied principally in alkali-metal vapor plasmas produced by surface ionization. Convective transport can also occur by other means. To discuss it completely is beyond the scope of this chapter, and in advance of the time of writing. The purpose of this section is to point out a few other types of convective transport which have proven, or may prove to be important. While the literature on convective cells in plasmas is long, this discussion will be limited to a few very recent references.

An example of convective cells set up by support members passing through the plasma confinement region in a toroidal octupole is provided by Schmidt and Schmidt (53). Such cells produce plasma loss above what is expected from fluctuation levels. Regions of steep potential and density gradients are localized near the obstacles. The flow caused by these may serve to carry plasma from regions of stable confinement to unstable regions.

Chen and Etievant (54) find that significant particle drifts can arise from plasma waves (particularly standing waves) in an inhomogeneous plasma.


They calculate corrections to homogeneous medium wave propagation in the case that the wavelength is large compared to the density gradient scalelength. Ordinary and extraordinary electromagnetic waves and ion cyclotron waves are considered.

Mosher and Chen (55) estimated particle loss in an alkali plasma device due to drift in the potential gradient engendered by nonuniformity of end plate temperature. The loss took place in the absence of fluctuations in a magnetic field with shear produced by a current carrying conductor passing axially through the plasma confinement region.

A convective cell structure associated with the spatial nonuniformity in heat input to the plasma during ionization and heating in a linear quadrupole device was reported by Harries (56). Variations of density and potential, but not of electron temperature, occurred in the cells. Maximum potential variation was of the order of kTJe. Drift kinetic energy up to 30 % of the electron thermal energy density was found in the cell structure in the stable part of the plasma confinement volume. The cells persisted long into the afterglow period of the discharge with a time constant of about 300 psec. It is not known whether they were effective in transporting plasma from stable to unstable regions, or whether they affected the confinement time.

VII. OTHER EXPERIMENTAL STUDIES OF TURBULENT PLASMAS

The purpose of this section is to review some of the experiments which have produced turbulent plasmas. The list would be very long, if exhaustive; therefore, a selection is presented on the basis of the insight provided by the experiment toward the nature and properties of the turbulent plasma. The diversity of manifestations of turbulence in plasmas exceeds even that in nonconducting fluids.

A . Linear Turbulent Heating Experiments

Because the cross section for electron-ion collisions decreases with the three-halves power of the electron energy, the use of ohmic heating to produce a hot plasma is limited to a few tens or hundreds of electron volts. Above that the energy supplied by the applied electric field is delivered to a small group of runaway electrons which, because of their high energy, are ineffective in heating the rest of the plasma. There remain three principal means of heating: adiabatic compression, resonance heating, and turbulent heating. It is to the last that this section is devoted.

Very early in the pursuit of the controlled thermonuclear reaction, the linear pinch which is essentially a very high current spark of very short duration was studied intensively. I t was thought that the plasma was heated to

24 C. K. MCLANE

thermonuclear temperature by the high current of the discharge. The evidence was that neutrons were produced when the experiment was done in deuterium gas.Anderson et a/. (57) showed that thiswas not the case, but thatdeuterons were accelerated to the necessary energy for the D D reaction in the high electric fields produced by magnetohydrodynamic instabilities of the pinch discharge. Not only was the number of deuterons so accelerated a small part of the total, but their chance of undergoing the fusion reaction was so small in the lifetime of the discharge that a net energy producing plasma could not be based on the linear pinch. The same is true of the plasma focus. This is a capacitor discharge between coaxial rod and tube electrodes. The rod is shorter than the tube, so that the current sheet, traveling away from the end at which power is fed, collapses to a concentrated linear pinch at the end of the rod. Very high neutron yields are obtained. These are not of thermonuclear origin, but result from acceleration of deuterons by the electric and magnetic fields of the discharge (58).

In some sense, the pinch experiments represent a midway point between ohmic heating by collisional processes and turbulent heating. A scale of fluid motion and potential fluctuation between the microscale and the laboratory scale is introduced, but it is not maintained long enough for stochastic heating, which is the dominant characteristic of the turbulent heating process, to occur.

An experiment which is not a turbulent plasma experiment, but which nicely illustrates the stochastic heating process, was reported by Puri, Dunn, and Thomassen (59). A sodium plasma of low density (10' crnd3) was confined in a magnetic mirror field of ratio 1.5. Heating was by the transverse electric field of an amplified broad band noise source applied by means of copper plates on opposite sides of the discharge tube which extended the length of the plasma and whose width subtended an angle of about 45" at the tube axis. The heating rate of the plasma, derived from Langmuir probe electron temperature measurements, was proportional to the mean square value of the applied electric field.

The stochastic field in most turbulent heating experiments is provided by one or more wave propagation modes of the plasma (such as electron plasma waves) excited to strongly nonlinear amplitudes. Thermalization may then follow by nonlinear mode interaction mechanisms like those discussed in Section IV, and by wave-particle interactions. Computer experiments may provide an insight into these processes, even though they treat an enormously simplified version of the real physical situation.

Heating a plasma by means of electron plasma waves driven to large amplitude was the subject of a numerical experiment done by Kruer, Kaw, Dawson, and Oberman (60). In such experiments, limitations posed by finite computer size and speed make necessary the assumption of an artificially small ion to electron mass ratio. A one-dimensional plasma of lo4 electrons and lo4


ions in a region 256 Debye lengths long was driven by an electric field at the electron plasma frequency. The ion mass was 100 times the electron mass and the initial ion temperature was 1/30 the electron temperature. The plasma wave energy is found to grow exponentially by two orders of magnitude in the first 200 plasma periods, and to saturate abruptly. During the wave energy growth, the heating of the plasma is slow, being determined classically by collisions. In this same time interval, ion-density fluctuations also build up. When these reach a sufficient level, the plasma resistivity is enhanced, and the plasma heats rapidly. The heating rate after the wave energy saturates corresponds to an effective electron collision frequency of about one fifth the electron plasma angular frequency and a resistivity 50 to 75 times the classical value.

Turbulent heating may be modeled after beam plasma experiments. Whether the heating is by means of a particle beam, or by a heavy current drawn through the plasma, a plasma instability first develops and grows into the nonlinear amplitude regime. For example, Yaremenko, Deev, Slabovik, and Kharchenko (61) studied residual gas ionization by a 10 kV, 2 to 4 A electron beam with a pulse length of 10 psec in a parallel magnetic field of 1000 to 1300 gauss. Ionization was produced not only by collisional processes directly involving the beam but by high frequency fields associated with development of turbulence in the plasma. The autocorrelation function for fluctuations developed first from an undamped sinusoid of varying amplitude to a damped sinusoid as the high frequency amplitude increased to a maximum during the beam pulse. The fact that the spectrum extended from 600 to 1600 MHz and that stationarity was reached in 50 to 100 nsec suggests that an electron plasma wave instability was responsible.

Degradation of beam energy is another source of information on the interaction. Shustin, Popovich, and Kharchenko (62) measured the distribution function of emergent beam electrons by a retarding potential method. Energy degradation was qualitatively as predicted by quasilinear theory. At higher gas pressures where the velocity distribution function was monotonically decreasing, it was found that low frequency oscillations still grew in the plasma. Even though f ’ (o ) 5 0, growth was possible because of the spatial nonuniformity of the beam.

Murakami and Lidsky (63) used a gated electron trap to measure the energy distribution function for a two delta function initial distribution at 1 kV. Broadening of the distribution function was found in agreement with the strong turbulence theory of Dupree (64).

An example of turbulent heating employing the two stream instability excited in the plasma by runaway electrons is to be seen in the work of Karchevskii, Averin, and Bezmel’nitsyn (65). A long (more than 3.5 m) uniform magnetic field region (0.05 to 0.2 T) with a mirror trap in the middle (Fig. 13) contains: ( I ) a linear discharge between a plate and a screen anode

26 C. K. MCLANE

1111111111111111 FIG. 13. Turbulent heating experiment of Karchevskii et al. (65). LD, linear discharge

source of runaway electron beam; P, plasma injector; S, solenoidal field coils; M, mirror field coils; AB, region in which beam attenuation is measured.

at one end, and (2) a coaxial plasma injector at the other end.Firsttheinjector (2) is fired, and then electron beam source (1). The electric field in (1) exceeds the Dreicer runaway limit, so at a plasma density of 2 x 1013 crn-’, 80% of the discharge energy of (1) and almost the entire current (10 to 15 kA)appears in runaway electrons. These interact with the plasma in the trap region (mirror ratio 2.5) between the injector (2) and the linear discharge (1). The 80% figure is measured one meter from the anode of discharge (I), and 25% is found 2.5 m from this screen anode .and close to injector gun (2). At 7 x 1013 cm-3 plasma density, these figures are 30 and 0 %, respectively. The plasma energy in the beam heated rtgion of the trap increases linearly with the magnetic field to 6 x l O I 5 eV/cm3 at 0.2 T. Beam heating efficiency in this case is 1.7 %.

The heating of ions by a turbulent beam plasma interaction is illustrated by Alexeff et al. (66) in the machine called Burnout V. Spectroscopic linewidths for the first three deuterium Balmer lines show a complex structure with the outer part dominated by the Doppler shifted emission from fast escaping neutrals. The width of the outer part of the spectral lines is consistent with velocity analysis of escaping neutrals, which gives a kinetic energy of 1-2 keV. This must be the ion energy of the discharge since the escaping neutrals are assumed to arise from fast ions by resonant charge exchange on excited atomic neutrals.

Turbulent heating of ions has also been observed by Hamberger et al. (67), who attributed the production of 700 eV ions to longitudinal plasma oscillations, and by Graybill and Uglam (68) who found 20 MeV ions produced in plasmas generated by electron beams of 1.6 MeV maximum energy.

Koidan et al. (69) heated a plasma produced in a reflex discharge with a capicitor discharge. When the electron drift velocity in the second discharge


exceeded the electron thermal velocity, oscillations were excited in the regions of electron and ion plasma frequencies. The latter seemed to be associated with anomalously high electron collision frequency [compare this with the numerical experiments of Kruer et al. (60)].

Babykin and his associates were among the first to report successful turbulent heating experiments. They have reported anomalous resistivity orders of magnitude higher than classical, and attribute the occurrence of enhanced diffusion to the same cause (70). It would appear from the theory of Weinstock (71), however, that an appropriate choice of excitation mechanism could lead to enhancement of resistivity without so great an effect on diffusion.

Berger et al. (72) attribute the appearance of enhanced resistivity to electron plasma waves in a paper which provides excellent experimental detail. A Pen- ning discharge is used for continuous injection of plasma into a one meter long mirror field (ratio, 2). A high current capacitor discharge is used for turbulent heating of this plasma. All plasma properties are found to depend sensitively on the ratio of discharge induced electron drift velocity to electron thermal velocity. When this ratio reaches and exceeds unity, there is a break in the trend of the heating current with time, and the discharge expands to fill the discharge tube cross section. This suggests association of enhanced diffusion with enhanced resistivity as was noted by Babykin et al. (70). The authors noted no enhancement of resistivity caused by the ion acoustic instability.

A very ingenious scheme for simultaneous measurement of plasma ion charge exchange neutral energy and momentum was developed by Zavoiskii, Nedoseev, and Rudakov (73). A capacitance microphone had a thin aluminum diaphragm coated with aluminum oxide on the back and lampblack on the front so that differential thermal expansion caused the capacitance 'to be temperature dependent. The momentum delivered to the diaphragm by the neutral flux during a pulsed experiment caused the diaphragm to oscillate at 640 Hz with an amplitude determined by the impulse. Superposed on this was the slow displacement due to temperature rise (thermal time constant 0.1 sec). The extent of this was a measure of the energy (Fig. 14). This device was used with a magnetic mirror trap device in which a plasma injected with a titanium hydride gun at each end could be heated with an axial current. Measurements of ion energy as a function of injection and heating times and injection energy led to the conclusion that ions could be heated by linear Landau damping of oscillations excited by the heating current; this mechanism would be stronger than the nonlinear mechanism of the usual turbulent heating.

Jensen and Scott (74) filled a large (180 cm long by 40 cm diameter) mirror trap (ratio, 2) with plasma from two hydrogen conical pinch guns (Fig: 15). By guiding the plasma along a curved hexapole field, the neutral effluent from the guns was not guided into the trap, and a higher degree of ionization

28 C. K. MCLANE

I

FIG. 14. Schematic response showing dependence on time, t , of capacitance, C, of microphone used by Zavoiskii ef al. (73). The oscillations (period greater than in the experiment for clarity of representation) are excited in the microphone diaphragm by momentum of impacting charge exchange neutrals. The slow drift of capacitance is a thermal effect due to energy imparted by impacting charge exchange neutrals.

resulted. Turbulent heating was by a 1 MHz current of 5000 A amplitude drawn along the axis.

A diamagnetic flux loop measured the perpendicular energy per electron ion pair when one gun was fired at 20 eV. When two guns were fired simultaneously, the result was 40 to 50 eV, and with the axial heating discharge, 500 eV per pair. Energy measurement of charge exchange neutrals gave a 500 eV Maxwell distribution for the ions alone; this left an uncertainty of a factor of two in the ion energy achieved. An energy balance gave 3 to 4 % conversion of energy stored in the heating capacitor into perpendicular ion energy. Since the latter is proportional to the square of the heating current, higher energy utilization in turbulent heating can be projected. Since there was 20 % confinement of perpendicular ion energy after 50 psec, the authors concluded that velocity space diffusion must slow down rapidly after heating.

Kalinin el al. (79, in an experiment similar in concept to thatofJensenand Scott, found that the efficiency of turbulent heating increased with the product

FIG. 15. Turbulent heating experiment of Jensen and Scott (74). P, P, plasma sources; G, one of two similar hexapole guide fields; E, one of two similar electrodes for 1 MHz heating discharge.


of density and temperature up to the maximum value they observed, which was 25 % at 4 x 10" eV/cm3. Note that this is about four times the PIT value at which Jensen and Scott found 3 to 4 % efficiency. One can therefore conclude that the two experiments are in accord. Kalinin et al. attribute the turbulent heating to the excitation of ion acoustic waves.

B. Toroidal Experiments

Linear mirror trap devices must always pay the penalty of plasma escape through the loss cone in velocity space. When the attempt is made to avoid this loss by use of toroidal confinement systems, a way must be found to eliminate the magnetic field gradient drift. If this is not done, a polarization electric field will develop in the direction parallel to the axis, and this will cause a cross-field drift to the outer wall. Elimination of this is usually accomplished by applying a rotational transform to the toroidal magnetic field. The rotational transform produces a shear in field direction as one proceeds through the nested toroidal field surfaces along a minor radius (Fig. 16).

FIG. 16. Illustration of shear (rotational transform) in magnetic field surfaces of current carrying toroidal plasma. Sections of two surfaces are shown.

In stellarators, this is done by helical windings of small pitch applied to the outside of the torus. Tokamaks employ a toroidal current in the plasma to provide the rotational transform.

In this section, a few representative results on Tokamak plasma confinement (Fig. 17) will first be examined together with some attempts at interpreting these, preliminary as they are because of the paucity of data. Two toroidal turbulent plasma heating experiments will be described, and the section will conclude with a brief discussion of toroidal confinement times.

Kuznetsov (76) reported particle lifetimes of 2 to 6 msec in Tokamak TM-3. These were greater than the energy confinement lifetime, thus demon- strating that conduction and/or radiation losses were significant. They were considerably longer than confinement times which had been realized in other toroidal confinement systems.

30 C. K. MCLANE

FIG. 17. Schematic cross section of Tokamak toroidal plasma device. W, windings to produce poloidal magnetic field and induce toroidal plasma current; T, windings to produce toroidal magnetic field ; C, heavy copper liner to suppress magnetohydrodynamic instabilities (having a cut in a major radial plane so that it does not short out the toroidal electric field induced in the plasma by the changing poloidal magnetic flux); S, stainless steel vacuum wall; P, plasma.

Bobrovskii et al. (77) attempted to resolve energy loss from TM-3 into three categories: (1) loss of charged particles by diffusion; (2) loss of energy through heat conduction by electrons and ions; and (3) loss by radiation in both discrete and continuous spectra, and by charge exchange. The authors considered the most uncertainty to reside in loss by conduction, and deduced this by correcting the experimental energy confinement times for loss by diffusion, radiation, and charge exchange. There was no agreement between experimental and theoretical conduction loss data. Some as yet unrecognized, possibly collective, heat transfer mechanism is operative.

Artsimovich et al. (78) reported successful ion heating in the T-3 Tokamak, which has a major radius of 100 cm and a minor radius of the plasma cross section of 12 to 15 cm. The toroidal plasma current flowed for 30 to 70 msec, and the charged particle lifetime exceeded 100 msec. For an experiment in which a toroidal magnetic field of 3.6 T was maintained while a current of 120 kA flowed in the deuterium plasma, energy analysis of charge exchange neutrals showed an ion temperature of 390 eV with a distribution which was Maxwellian out to 3 keV. The neutron yield extended from 20 to 60 msec with a maximum at 45 msec, and had an intensity which yielded an ion temperature


agreeing with the charge exchange data to within 25 %. The plasma appeared to be stable throughout the experiment. Gorbunov et al. (79) conclude that the energy confinement time in the T-3 is 20 to 30 times the “Bohm time”- that is, the time the decay would take if Bohm diffusion (Eq. 12) were the only loss process.

The improved confinement time of Tokamak over stellarators is not fully understood. Galeev et al. (80) calculate the effect small asymmetry in field configuration has in increasing the rate of collisional diffusion. The conclusion is that these effects cannot produce diffusion at the Bohm rate, as is seen in stellarators, and that losses of the Bohm order in some axisymmetric torus experiments provide additional support for the postulate that another diffusion mechanism must be operative. They suggest that small irregularities in electrostatic potential due to a variety of causes could cause collisional diffusion to be enhanced by the requisite amount.

A possible explanation of the alternative mechanism may be found in a two fluid theory of anomalous diffusion presented by Yoshikawa (81). The density and electric field perturbations are Fourier analyzed in space. With the assumption that in product series such as terms representing electrostatic force, only products of like wavenumbers 1 k I contribute, it is possible to solve for the k = 0 components of the fluxes and hence derive the diffusion coefficient. The result is dependent on aspect ratio and rotational transform in such a way as to predict the observed ratio of confinement times for stellarators and Tokamaks.

Grad and Hogan (82) have analyzed the process of resistive diffusion in a Tokamak. They point out that plasma diffusion is, in general, a complicated phenomenon in which field diffusion, plasma diffusion and convection, and geometric factors are coupled together in a nonlinear way. Scaling on the basis of present information is not possible on any simple basis, because Tokamak operation has been in a highly transient region in which the ratio of plasma kinetic energy to magnetic field energy (p) is an order of magnitude higher than that corresponding to the diffusional equilibrium field profile. Transport by convection is tentatively advanced as the dominant Tokamak loss mechanism.

Coppi (83) has given a discussion of the anomalous resistivity deduced from electric field and toroidal current measurements in Tokamaks. This appears to be large (thirty times classical in TM-3 and five or ten times in T-3) and suggests the presence of collective modes which might be termed plasma turbulence.

Tokamak is not primarily a research device. It could be called a preproto- type thermonuclear fusion reactor. I t is not designed to isolate a particular physical phenomenon and provide unambiguous information on it. Therefore, it is not surprising that the results are not amenable to a satisfying analysis at

32 C. K. MCLANE

this early stage in its history, However, it does provide a significant step toward turbulent heating of a plasma of moderately high density with a rather impressive confinement time.

Much earlier experiments established the feasibility of turbulent heating in a toroidal system. Fanchenko et al. (84) applied a toroidal electric field of 150 V/cm at 2.5 MHz to plasmas of various densities (of order 1013 crn-’) in a toroidal, 0.1 T magnetic field. They found that while a plasma current started to flow in phase with the applied field-characteristic of pure resistive impedance-this current decayed much faster than the applied electric field. Resistivity deduced from current density and field measurements was interpreted as an effective collision frequency of lo9 sec-’. This was lo4 times larger than the coulomb collision frequency and lo3 times larger than the frequency of electron collisions with neutrals.

Balakhanov et al. (85) recently reported an experiment on turbulent heating in a toroidal experiment similar to a Tokamak. A plasma of density l O I 3 to lOI4 cm-3 was produced by an inductively coupled discharge in the torus. A heavy copper jacket with a gap cut in a plane containing the major radius and toroidal axis served the double purpose of stabilizing the plasma, and acting as a one turn coupling coil for the rf turbulent heating discharge (30 kV, 1 MHz). For the first two or three half cycles of the rf discharge, current and voltage were in phase, and the ratio of their values was determined by an effective plasma resistance of 6 ohms. This was a hundred times the expected ohmic resistance. Of the energy stored in the heating circuit capacitor (80 J), 22 J were absorbed by the plasma, and 4 J appeared as thermal plasma energy. The ratio of the last two numbers was quoted as an 18% turbulent heating efficiency.

A “bumpy” toroidal confining field was used by Fanchenko et al. (86) for a turbulent heating experiment in which enhancement of resistivity pre- dominated over enhancement of diffusive loss. The field was produced by ten strong field coils wound in one sense alternating with ten weaker coils wound in the opposite sense. The field on the minor toroidal axis was unidirectional and corrugated with a ratio of 20 : 1 (maximum, 1.5 T). At the outside of the torus the field was cusped. The heating field of 250 V/cm exceeded the Dreicer runaway field of 10 V/cm at an electron temperature of 1 eV and density of 1013 cm-3. This current flowed for 1 psec; plasmalifetime was 5 psec, probably limited by charge exchange for which the lifetime would be 10 pec. The decay time was at least ten times the toroidal magnetic field gradient drift time.

Ohkawa and Voorhies (87) also report a toroidal experiment (Doublet I) of Tokamak type, in which the rotational transform is produced by a current in the plasma induced by a capacitor discharge through a carefully shaped copper wall. The energy confinement time was 10 psec, which was 5 to 10 times the magnetohydrodynamic characteristic growth times, indicating magnetohydrodynamic stability. The plasma current persisted for 100 psec and


then was damped by impurity influx. This time was not long enough to determine whether turbulent transport would be encountered.

Meade et al. (88) suggest that a drift (E x B/ I B J 2, convective model fits particle confinement times in low$ toroidal containment experiments better than the Bohm diffusion model. For the twelve experiments they cite, which include stellarators, multipoles, and a levitron, confinement times range from 4 to 100 times that expected in the Bohm diffusion model. If a convective model assumes an electric field proportional to electron temperature divided by toroidal minor radius, and the distance the plasma must move across the magnetic field to escape in the particular experiment is A , the confinement time is given by

The constant C for eight of the twelve experiments cited is within 30 % of its mean value over the twelve. For the ratio of confinement time to Bohm time, only two experiments have a ratio within 30% of the mean ratio for the twelve experiments. Tokamak experiments were not included by Meade et al. because of uncertainty in particle confinement time as distinguished from energy confinement time, and an uncertainty which then existed in the electron temperature values.

z w CBaAIT,. (27)

C. Collisionless Shocks

The subject of collisionless shocks would be a suitable one for a rather extensive monograph. A review to the date of the 1968 Novosibirsk Conference was written by Drummond (W. E.) and Kolb (89). Reference to the subject here must be brief, but is appropriate because the entropy production mechanism in a collisionless shock is necessarily some form of plasma turbulence. The study of these shocks will contribute to an understanding of turbulence as it has in the past. Reference will be made to a few recent observations and experiments in which the physical conditions (plasma and neutral density, and physical dimensions) are such as to give reasonable assurance that shocks observed were indeed collisionless. In some cases, the experimental facts are indicative of the probable mechanism of the turbulence. No discussion of the theory will be given.

When doubt still existed as to whether collisionless shocks had been produced in the laboratory, there could be no doubt that the earth’s bow shock was indeed collisionless. The thickness of the shock which was observed was very much less than the relevant mean free paths. Fredricks et al. (90) found with the OGO-5 satellite probe that a low frequency spectrum of electric field fluctuations occurred simultaneousIy with change in the magnetic field in the bow shock. Further analysis of the spectral data from OGO-5 (91) yielded power density spectra over a 1 kHz passband (of the 21 kHz bandwidth available from the original data) at 12.5 msec intervals (Fig. 18). This

34 C. K. MCLANE

FIG. 18. Frequency spectra of turbulent plasma in magnetopause due to Fredricks et at. (91).

time resolution corresponds to 4 Debye lengths in spacecraft motion, or 20 Debye lengths in shock motion. The spectrum is discrete-beginning with a few frequencies with frequent splitting of single peaks into two or more peaks. They appear to be electrostatic waves excited by the diamagnetic current within the shock. Proton thermalization is found always to occur after a region of strong " turbulence " as defined by strong excitation of the electrostatic fluctuation spectrum.

Typical of collisionless shock experiments is the observation by Keilhacker et al. (92) that the effective electron collision frequency to explain the electron heating rate was about a hundred times the coulomb collision frequency. This was of the order of the ion plasma frequency-but no mechanism for the anomalous dissipation was proposed.

Patrick and Pugh (92a) studied the stationary " bow shock " created when a highly ionized plasma flow passed a magnetic dipole. The shock satisfied the magnetohydrodynamic Rankine Hugoniot relations (momentum and energy conservation laws) as shown by density and magnetic field measurements. The shock thickness was 2 to 4 ion gyroradii, and the spectra of electric and magnetic field fluctuations were consistent with the standing whistler wave model proposed by Robson. A wave-particle interaction mechanism, rather than particle fluctuating field mechanism, appeared necessary to account for the energy dissipation rate found.

Taylor, Baker, and Ikezi (93) gave a beautiful demonstration of the propagation of collisionless electrostatic shocks in a quiescent argon plasma. Two plasmas of differing density are separated by a negatively biased grid, and the potential of the more dense plasma is slightly negative with respect to the less dense one. When a positive potential step function or ramp is applied to the more dense plasma, a compression travels from the grid into the less dense plasma, and a rarefaction in the opposite direction. Propagation of the compression is at the ion acoustic speed, and when a ramp is employed, the steepening into a shock characteristic of the Riemann solution is seen. Oscillations develop behind the shock, and ions are seen to stream in front of the shock.


Daughney, Holmes, and Paul (94) have succeeded in measuring the spectrum of ion wave turbulence within a collisionless shock by light scattering. The shock is produced by a linear z pinch in preionized hydrogen. A Fabry Perot interferometer with a bandwidth of 20 mA is used to obtain the spectrum of the incident ruby laser beam (spectral width also 20 m a ) and of the light scattered at 3.3" to 6.9" (spectral width 55 ma). Shot by shot scanning of the profiles is accomplished using variation of the gas pressure in the interferometer for spectral tuning. The turbulence is identified as ion wave turbulence by scaling experiments in which density, and hence, ion plasma frequency, and magnetic field, and hence, electron gyrofrequency, are varied. The spectrum agrees with the prediction of Kadomtsev (95) as to shape, and cutoff at

Another very promising measurement technique is illustrated by the work of Kunze et al. (96) on a very fast, high voltage, low density theta pinch. The experiment is based on a prediction of Baranger and Mozer that electric fields due to plasma oscillations would cause satellites to appear on forbidden spectral lines. The satellites would be displaced by the frequency of the plasma oscillations, and their intensity would be related to the energy density in the oscillating field. Kunze et al. develop the necessary modifications of the small amplitude Baranger-Mozer theory to allow application to their experiments, in which the field amplitude is not small. The measurements of the satellite strength give a fluctuating electric field amplitude of 7 kV/cm which would give an effective electron collision frequency of one fourth the ion plasma frequency, essentially in agreement with Daughney, Holmes, and Paul (94). Identification of the responsible plasma mode is made difficult by the limited accuracy of measurements of satellite displacement (about 0.2 a ) , and of correcting the measured frequency for the expected Doppler shift. The authors are inclined to favor ion sound wave turbulence. Since the magnetic piston and compression wave do not separate in this experiment, it does not relate to a fully developed collisionless shock.

kr2, R 1.

D . Wind Driven Plasma Turbulence

Another class of laboratory experiments is that in which a plasma is rendered turbulent by collisional coupling with a turbulent gas. In such experiments, the large scale motions are usually dominated by the aerodynamic turbulence, and may exhibit a spectrum of energy density as a function of wavenumber obeying the Kolmogorov-Heisenberg power law for which E(k) K k - 5 / 3 . The plasma turbulence will thus have the same structure as the gas turbulence except for the large wavenumber end of the spectrum, in which viscous dissipation becomes important for the gas and loss by ambipolar diffusion for the plasma component.

36 C. K. MCLANE

Such an experiment was performed by Rothman, Guthart, and Morita (97) and Guthart, Weissman, and Morita (98). An ethylene-oxygen flame seed- ed with potassium chloride, and burning at 32 torr pressure was expanded through a nozzle into a large chamber at 16 torr pressure. Power spectral density of ion and electron fluctuations were found to be the same, and ion density correlation measurements show that the flow on the axis of the jet is approximately isotropic and frozen. Microwave scattering studies made on this same plasma (99) show that the Born approximation is valid for electron densities up to one percent of critical. The frequency employed was in the X-band.

Granatstein (100) used continuum probes (extension of the Langmuir probe to the collision dominated case) to measure the spectrum of density fluctuations in weakly ionized argon in a tube in which a discharge was maintained parallel to a rapid axial flow of argon. A small (less than one half decade in wavenumber, k ) inertial range ( I c - ” ~ ) was found in the energy spectrum obtained at a Reynolds number of 8000, and none at 4000. The author argued that fluctuations in the density of energetic electrons will be rapidly damped, and that therefore the fluctuation spectrumof the emitted light will be governed primarily by fluctuations in neutral density. The fluctuation spectrum of emitted light does show a slower decay at higher frequencies than is the case with probe spectra, and this is more pronounced at a Reynolds number of 4000 than at 6000. This observation appears to confirm that ambipolar diffusion is a more effective dissipation mechanism cutting off the plasma spectrum than viscosity is for the neutral spectrum. The fact that the spectrum was dependent on Reynolds number, and not on pressure (density) and velocity separately, was used to verify the frozen flow assumption on which transformation from frequency to wavenumber was made.

Garosi, Bekefi, and Schulz (101) utilized a gas flow discharge very similar to that of Granatstein for a study of anomalous diffusion and enhanced resistivity. The plasma loss increased for Reynolds numbers above 1500 by a factor which increased to fifteen at a Reynolds number of 6300.

VIII. CONCLUSION

Seldom is a laboratory plasma encountered which is not rather far from an equilibrium state in some respect. When the departure is in the form of a density gradient normal to a magnetic field, when particle beams or drifts are present, or when some other gradients are present-gradients in temperature, potential, magnetic field, velocity, or even impurity content, the plasma is likely to be unstable toward some form of collective excitation. Such instabilities may even be present when the degree of ionization is as small as a part per million, as is the case for the Kadomtsev-Nedospasov helical instability


of the positive column (26). The phenomenon of turbulence in plasmas is then almost as widely distributed as is the plasma state itself.

The most straightforward experimental problem might seem to be temperature determination, until the influence of turbulence is considered. Dimock and Mazzucato (102) utilized the Thomsen scattering of light to get a true electron temperature measurement in the C stellarator. Electrical conductivity was commonly used as a measure of temperature until anomalously low conductivity was encountered when the electron drift velocity exceeded the ion acoustic speed. This would lead to an anomalously low value of the “conductivity temperature ” when compared with measurements of plasma diamagnetism, a fact which was noted both in C stellarator and in Tokamak devices. The Thomsen scattering data support the plasma diamagnetism measurements as giving better temperatures than the conductivity.

Reduction of the electrical conductivity by nearly a factor of 100 in the presence of strong electron plasma wave excitation was shown by Hamberger and Friedman (103). An electric field up to 500 V/cm was inductively applied to a toroidal plasma in resistivity measurements which corroborated Bune- man’s expectation :

rJ = +(M/rn)”3wp,. (28) It is not necessary to go to fully developed turbulence, if by that term we

mean that no appreciable coherent remnant of the original instability is present, to get a substantial increase in resistivity. A tenfold enhancement of microwave measured resistivity of a positive column was found by Tsukishima, Mase, and Takeda (104) at a magnetic field less than twice the onset field for the helical instability. The effect on the dc conductivity was a factor of four smaller, and this is not understood.

A good plasma turbulence experiment should provide two independent measures of some sensitive parameter of the turbulence-for in this way an internal consistency check is provided. A good example would be the experiment on magneto-acoustic wave damping (Fig. 19) by Maksimov, Smirnov, and Utyugov (105). The object was to compare the effective collision frequency from the wave damping experiment with the same parameter determined from a dc conductivity measurement. The two measurements were made simultaneously on the same plasma and the same result was obtained.

A wide range of measurement techniques which are well suited to the characterization of turbulent plasmas are coming to the fore. These extend all the way from light scattering (94), which requires a rather dense plasma for successful utilization, through emission spectroscopic methods (96), to a method which can only be described as exquisite in its sensitivity. At the suggestion of Su and Oberman (106), the dependence of the amplitude of electron plasma wave echoes upon the rate of electron diffusion in velocity

38 C. K. MCLANE

FIG. 19. Schematic of turbulent wave damping and electrical resistivity experiment of Maksimov et al. (105). E, E, electrodes for turbulent heating; S, S, solenoid and shim coils; P, P, theta pinch type plasma sources; W, coil to launch magnetoacoustic wave.

space was used by Jensen, Malmberg, and O”eil(107) to estimate a velocity space diffusion coefficient so small that it would have reduced the electron mean free path in their experiment from the several hundred kilometers determined by background noise to two kilometers, had apparatus dimensions not made such mean free paths meaningless.

Progress is occurring at a substantial rate in experimental plasma turbulence research. This is evident from the papers cited herein and from the many more which were not cited because of the limitation in scope and in length of this chapter.

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Recent Advances in Design of Magnetic Beta-Ray Spectrometers

MILORAD S . MLADJENOVIc*

B . KidriE Institute of Nuclear Sciences. Belgrade. Yugoslavia

I . Introduction .................................................................................... Performance Parameters .....................................................................

I1 . Flat Spectrometers. with Cylindrical Field ................................................ A . Semicircular Spectrometers ............................................................... B . &2 Spectrometers ........................................................................ C . (?r/2).1/13 Spectrometer .................................................................. D . ?r.1/10 Spectrometer ........................................................................

“Winding Field .. Spectrometer ......................................................... I11 . Sector Spectrometers ........................................................................... IV . Toroidal (“Orange”) Spectrometers ......................................................

Multiple Loop Spectrometer .................................................................. VII . Optical Analogy Spectrometer ...............................................................

- -

E .

V . Lenses ............................................................................................. VI . Trochoidal Spectrometers ..................................................................

A . Dispersion .................................................................................... B . Aberrations and Resolution ............................................................ C . Deflecting Magnet ........................................................................ D . Magnetic Lenses ...........................................................................

VIII . Correctors ....................................................................................... A . Multistrip Source ........................................................................... B . Second-Order Correctors ..................................................................

IX . Azimuthally Varying Field .................................................................... X . Comparison Table ..............................................................................

References .......................................................................................

43 45 46 47 48 51 52 53 53 56 57 58 61 64 65 65 66 66 67 67 69 71 13 75

I . INTRODUCTION

The last review paper on beta-ray spectrometers in this series. written by Hayward (I). appeared at the time when the first large double-focusing spectrometer was constructed by Hedgran. Siegbahn. and Svartholm in Stockholm (2). marking the beginning of a new generation of electron spectrometers .

* Present address: 2410 California Street. N.W., Washington. D.C. 20008 . 43

44 ,MILORAD s. MLADJENOVIC

The distinguishing marks of the new generation were the large size and more sophisticated field forms with much improved focusing characteristics. Incidentally, that first Stockholm's large double-focusing spectrometer had perhaps a longer life than any design made afterwards, since several copies were delivered to other laboratories, including one recently to Orsay.

The development which followed brought forth new spectrometer types and new features and its general characteristics could be briefly summarized in the following way:

1. The size kept increasing and reached a limit at ro = 100 cm, (ro being the mean orbit radius), A further increase would require embarassingly low fields and the total cost would become relatively high.

2. The development of multichannel data handling stimulated the introduction of multidetector systems, placed along extended focal planes. The full and widespread use of arrays of detectors is yet to come.

3. Several specialized types of spectrometers were devised for measurements of Compton and photoelectrons ejected by gamma rays either from a radioactive source or from (n, y ) reactions. Recently these spectrometers had to be abandoned in most cases and replaced by Ge (Li) detectors. We shall not review them, referring the reader to the review papers of Bartolomew et al. (3), MladjenoviC (4), and Demidov (5).

4. Following a well established pattern, according to which the spectroscopic methods initiated in atomic and nuclear physics migrate to chemistry and other fields of science, beta-ray spectrometers became a new tool for the study of systems of atoms. A most important development was made by Siegbahn and his collaborators in Uppsala (6).

5. The impact of the computer is important in this field of instrument design also. I t is used in theoretical field shape analysis, for the design of magnets and for testing and correcting the magnets and beam geometry, once the instrument is built. Recent illustrations of computer use can be found in the work of the Uppsala computer group (7a, b, c). The main result is that we now have magnets producing more precisely the required field shapes and thus improving their performances.

6 . The development of spectrometers took place principally in the following directions:

(a) Increase of dispersion-A typical example is a flat spectrometer with a cylindrically symmetric field, where dispersion improves with an increase in the radial focusing angle. The earliest spectrometers of semicircular type had a focusing angle of 180", then came the much improved Siegbahn-Svartholm double-focusing spectrometers with focusing angles of 255", while recently spectrometers were built with focusing angles up to 500". I n these spectro-

DESIGN OF MAGNETIC BETA-RAY SPECTROMETERS 45

meters the transmission is usually less than 1%, and increased dispersion serves mainly for high resolution work with relatively larger sources.

(b) Increase of transmission (T)-High transmission can be obtained with a lens and an “ orange.” While the former never reached T = 10 %, the latter has successfully reached transmissions of 20%. In these types of spectrometers the resolution is practically never higher than about 0.1 %.

(c) Correctors-The performances of a spectrometer can be improved by eliminating the aberrations of the first and second order. The most important first order contribution to the line width is due to the source size; a way has been found to correct for it. We shall call “correctors” the additional devices eliminating or reducing the aberrations of various orders.

Since the corrector essentially changes the cylindrical symmetry of the field, a more general approach to the elimination of the aberrations is to start with a nonsymmetric field and thus dispose of more degrees of freedom. This approach has so far been -only theoretically explored, as will be seen in Section IX.

In the following we shall briefly review the most important developments, starting from the simplest types of spectrometers. A comprehensive review was written by Siegbahn ( B ) , and a more recent one was given by Lee- Whiting at the Herceg-Novi Meeting (9). This review includes some of the topics discussed by the author at the Nashville Meeting (10).

Performance Parameters

Before starting the review itself it would be useful to define the performance parameters, since the accepted terminology is not always precisely used. Sometimes, a distinction is not made between the transmission and the solid angle, while some authors do not show how they have measured the transmission, especially when the detector slit is of the same size as the source, in which case a fraction of the transmitted beam is not accepted by the slit.

A more precise definition of the passage of the beam from source to detector could be obtained with the help of the following parameters:

Solid angle R, expressed in percentage of 4n, describes what fraction of isotropically emitted monokinetic electrons are accepted by the entrance baffles.

Transmission T, represents the percentage of the emitted monokinetic electrons reaching the image plane and forming the image. In the case where no beam is lost between the entrance baffle and the image position, the transmission would be equal to the solid angle. Numerically, the transmitted beam can be measured by having the slit larger than the image. A curve with a flat top is then obtained.

46 MILORAD s. MLADJENOVIC

Acceptance factor F, measures the ratio between the beam accepted by a given detector slit and the beam transmitted to the image position. Numeric- ally, it is the ratio between the peak height of a line and the height of the flat top line defining the transmission.

Effective transmission FT represents the percentage of all monokinetic electrons leaving the source, counted in the detector at a given slit size.

Luminosity can be defined by multiplying the parameters defined above with the source surface A : Geometric luminosity L , = A a, Luminosity L = AT, Efective Luminosity L F = ATF.

Dispersion D is sometimes defined as

D = (Ax/Ap)p = Ax[(Br)/A(Br)],

where the dimension x along which the dispersion is measured often represents the radius of electron orbits, so that D can be written

D = Ar[(Br)/A(Br)].

Another measure of dispersion is obtained by dividing D by the orbit radius r . We shall denote it by D, . It has the form

D, = (Ar/r"r)/A@r)J.

Resolution R is defined by

R = Apfp = A(Br)f(Br),

= Ax/D,

where A(&) is the width of the half maximum of a line having a momentum

Information density measures the number of points on the spectrum which ( B d .

can be simultaneously measured.

11. FLAT SPECTROMETERS, WITH CYLINDRICAL FIELD

Cylindrically symmetric fields are used for the large majority of beta-ray spectrometers. Most of them have the source and the detector in a median plane perpendicular to the axis of cylindrical symmetry. The whole field can be then defined by the field in the median plane Bz(r, 0), expressed in the form of a series

where ro is the radius of the circle containing the centers of the source and the detector, called the optic circle, and B, is the field at the optic circle.


The first expansion coefficient a, is connected with the radial focusing angle CP,, and the axial focusing angle CPz by the relations

CP, = n/( 1 - a1)1'Z, oz = n/( - a1)1'2. (2) The increase of one focusing angle is accompanied by the decrease of

another, and double-focusing (DF) is obtained when

wheren=O, 1 , 2 , 3 ,.... For half integers n = 1/2, 3/2, 5/2, . . . the focus is extended (EF), but

some aberration terms can be cancelled, as first pointed out by Daniel (11). The dispersion D, increases with C P r , I u1 1 , and n as

CP, = nCPz (3)

D, = (2/nZ)CP,2 = 2/(1 - al) = 2(1 + n2). (4)

The values of al, CP, , and D, for n < 3, are given in Table I.

TABLE I

VARIATION OF DISPERSION D WITH RADIAL FOCUSING ANGLE @,

n a1

Type of @r Dr focusing

0 0 2 1/2 -0.2 (7T/2)43 = 202" 2.5

1 -0.5 d i = 2.55" 4

2 -0.8 7743 = 402" 10

3 -0.9 rrdE = 569" 20

312 -0.69 ( 4 2 ) d E = 325" 6.5

512 -0.86 ( 4 2 ) d i G = 485" 14

~~

Semicircular EF

Siegbahn- Svartholm DF

EF DF EF DF

The dispersion increases rapidly with focusing angle, but when CP, > 360" the beam hits the source and the detector, seriously reducing the transmission.

The spectrometers with n = 0, 1/2, 1, 3/2, and 3 have been built so far. We shall consider them in turn, with less emphasis on semicircular and

spectrometers which are fully covered in previous reviews.

A . Semicircular Spectrometers

The interest seems to be declining for this modest veteran, which does not require much effort for construction, but in return does not offer much of a performance either. Its main advantage is that it presents a relatively large focal plane allowing simultaneous measurement of a substantial part of


the spectrum. Quite a few of the large permanent magnet spectrographs built in the 1950's (12-17) serve often for a quick look at a newly prepared source or when sufficient intensity is available even for high resolution work. Sets of three or four permanent magnet spectrographs with field values chosen to cover the spectrum up to 2-3 MeV (18,19) are used in laboratories concerned with the discovery and study of new radioactive isotopes.

The largest semicircular spectrograph was recently built by 1116s (20), having a maximum orbit radius of 75 cm. The performances of this spectrometer are included in the Comparison Table, given at the end of the chapter.

A field boundary corrector for focusing collimated beams was developed by Prokofiev and collaborators (21). An iron cylinder is introduced partially between the pole pieces, serving as a magnetic shield (Fig. 1) and the inner

FIG. 1. Cylindrical magnetic shield with the inner profile curved to improve the focusing of a parallel beam.

end is so profiled as to improve the focusing of a parallel beam. The spectrograph serves for the measurement of internal conversion electrons from (n, y ) reactions.

B. nJZ Spectrometers

The n& spectrometer has probably been the most useful type of spectrometer in the last two decades. Many laboratories have built one or two of them and the design is constantly improving. The main problem in the develop-


ment of this type of spectrometer has been the design of the magnets which would produce the required field form with high accuracy. The latest iron-free spectrometers (22) have the fields very close to optimum.

Iron-core and iron-free magnets were almost equally in favor. We shall consider them in turn.

In the iron-cored magnet the excitation coils can be either in the center or surrounding the working gap. The coil-in-the center type is more economical, but the edge effects may be serious, while the inside-out type costs more, the accessibility is reduced, but the flux leakage is eliminated and edge effects reduced.

Experience with the more than twenty iron-core n& spectrometers of both types built so far (2,23-36), some of them being copies of the same design, shows that it is almost impossible to obtain the exact field form predicted by the theoretical design of the pole-piece profiles. Often the field shapes vary with the field intensity. Sometimes an up-down asymmetry is found. In the majority of cases the large space intended for high transmission is of no use, because the field shape deteriorates so much at relatively larger distances from the equilibrium orbit that at larger apertures the line width increases prohibitively.

The field form can be corrected by iron shimming or coils. It appears that the empirical correction is easier when coils or shims are added on both sides of the working gap. In the coil-in-the center type iron rings can be distributed inside and outside the working gap, as was done by Samoilov (27). Perlman (364 uses only an iron cylinder on the outside, reducing the fringing. Kovrigin, Kolesnikov, and Latishev (29) added two flat coils and obtained a field form fit within 0.03%. In the inside-out type, Bartlett, Ristinen, and Bird (35) divided the excitation coil into seven sections and placed three inside coils, and determined empirically the current distribution.

While for the case of iron-cored spectrometers no author claims to have been able to fit precisely more than three coefficients of the field development, the iron-free types have been fitted up to the fifth coefficient, obtaining generally better performances.

Two kinds of geometry were used in the design of coils for iron-free spectrometers. One approach is to start with pairs of current loops, symmetric with respect to the median plane, while the other uses current sheets, and in both cases corrections are made for the finite size of the coils.

The two-current sheet approach was used by Siegbahn (37) for the design of the first iron-free spectrometer, and the same geometry was essentially adopted later by several authors (38-40). It was again Siegbahn, with collaborators (41), who introduced four sheet geometry and produced a low energy electron spectrometer with a field form very closely fitting the optimum.

The current-loop type was first built by Moussa and Belliccard (42) using


four pairs of coils. The most important spectrometer in this class was designed by Graham, Ewan, and Geiger (43), based on the calculations of Lee-Whiting and Taylor (44). It is the largest (ro = 100 cm) and one of the best beta-ray spectrometers ever built. Scaled down versions of this spectrometer were later built in five laboratories (45-48).

A novel design of the iron-free spectrometer for low energy electrons was recently proposed by Fadley, Miner, and Hollander (48a). One main coil, with four pairs of smaller coils wound on it, all have smaller radii than the inside wall of the vacuum chamber (Fig. 2). The access to the chamber is then

FIG. 2. A view of the inner-coil ndz low energy spectrometer.

easy and allows the use of various auxiliary equipment around the source and the detector.

The discussion has been going on for some time as to which of the two approaches-sheet or loop-was better, and even some of those who built one considered that the other type might be more convenient. The prevailing opinion now is that precision of design is much more important than the type of design. The performances of both types are comparable for the same amount of effort.

In special cases when background is very important, the twofold focusing spectrometer developed by Shestopalova (49) might be useful. The detector is transparent to electrons, having very thin double windows, so that the beam after passing through the focus makes another 255" angle and hits the second detector. Placing the source above the median plane, the first detector is located below and the second above the median plane. Both detectors are in coincidence. This arrangement is primarily intended for higher energies.


C. (n/2)J13 Spectrometer

In this type of spectrometer the beam has the maximum axial extension at the position of radial focus. The exit slit is high and can be curved radially and azimuthally. By choosing proper curvatures, two aberration terms in the angular opening can be eIiminated. In order to eliminate the remaining aberrations of the second order, the projection of the exit slit in the radial plane has to be a parabola, while the third order term is eliminated by azimuthal curvature. The fourth order term can be reduced by making a diamond shaped entrance baffle. In principle, therefore, very high order focusing can be achieved. But, the price is also high. The detector is very large and has to fit a complicated shape of the exit slit.

A (n/2)@ spectrometer was designed by Daniel, Jahn, Kuntze, and Spannagel (50). The basic parameters of the spectrometer (Fig. 3) are the following :

Field shape B = Bo(l - 0.692308 q + 0.461538 q2 - 0.31656 q3

+ 0.22965 q4) q = (r - ro/ro),

radial focusing angle = 342.5",

dispersion D, = 6.5,

radius of equilibrium orbit: ro = 30 cm.

FIG. 3. Heidelberg (7r/2)dfi spectrometer. (a) Beam geometry; (b) coil geometry.


The magnet is iron-free, the field being produced by ten coils. The field was first found using the current-loop approximation, and then corrections for finite size were made. The coils were L ,.ide with a mechanical precision of 0.1 mm. In the symmetry plane the deviations of the real field from the theoretical are 1-2 x Two counte,rs are'csed, one 10 cm high for transmission up to 0.7 % and another 20 cm high for transmissions up to 1.5 %.

Theoretically, this type of spectrometer should give high transmission, with a very high resolution (for instance T = 2.7% with R = 0.04%). The measured performances, given in the Comparison Table (Section X), fall below the theoretical expectations, althougn they are still very good. Since the first spectrometers of a new type usually serve to test the main features, it can be expected that later ones will come closer to the theoretical predictions.

The main advantages of the ( n l 2 ) d type are the higher order focusing and the possibility of using extended sources. The serious disadvantages are the great detector size and the practical impossibility of using an extended focal plane.

D. nJl0 Spectrometer

Lee-Whiting (51) has shown that among the spectrometers with integer values of n, and n > 1, those with odd n have the focus further away from the source, and for n = 3 the problem of premature encounters of the beam with the source and the detector is less severe.

The only spectrometer with n = 3 so far reported was designed by Baranov and collaborators, and a very brief report was published (52). The basic parameters of the spectrometer are the following :

field shape B = B,, (1 - 0.9 r] + 0.825 qz - 0.767 q3),

radius of equilibrium orbit ro = 40 cm,

dispersion D, = 20,

radial focusing angle = 570".

The authors do not mention the kind of magnet used and one gathers that it is probably of an iron-yoke type, from the last sentence in the paper: "It has to be mentioned, however, that the requirements of magnetic field shape fitting are much more stringent in the given case and, probably, full use of the advantages of this type of instrument is only possible in an iron-free spectrometer."

The beam is prevented from entering the detector, before completing 570", by two apertures. One of them placed at 285" cuts the central part of


the beam, and another, placed in front of the source, limits its radial angular opening angle. In such a way two-thirds of the horizontal opening of the beam is lost.

The performance data, quoted in the Comparison Table, show that for R = 0.04%, the source is quite 1; .ge, as-expected in the case of large disper- sions, but the solid angle is very small. Tnere is no doubt that with an iron-free design better performances could be achieved.

E. '' Winding Field '' Spectrometer

Daniel and collaborators (53) have made calculations of the focusing properties of a spectrometer with a helicoidal field in which the beam describes a spiral path for 910" before reaching the focus. It is a modification of a flat spectrometer, which would have the radial focusing angle equal to 910". To prevent multiple crossing of the detector and the source, the beam is "pulled out" and the optic circle changed into a helicoidal beam axis. Very high dispersion, characteristic for large radial focusing angles, is conserved.

The authors have calculated the first five series expansion coefficients CI and the slope k of the field with respect to a constant 2 plane; this field simultaneously eliminates both second order aberration terms which arise from the opening angles. They also achieved a focusing which is independent of the third, fourth, and fifth order aberration terms from the radial opening angle.

For a radial focusing angle of 910" the dispersion is D, = 47, which is an order of magnitude better than the dispersion of z,/z spectrometers. Calcula- tions were made only for solid angles smaller than 0.3%. No discussion of magnet design was yet made. It would be no doubt interesting to pursue the study of this type of spectrometer.

111. SECTOR SPECTROMETERS

The advantage of sector magnetic spectrometers is that the source and the detector are in a field-free region, allowing easy access and use of the auxilliary apparatus. The main design problem is the fringing field, which in most cases cannot be accurately calculated. Since the disturbance due to fringing is smallest for a narrow beam, confined to the median plane and entering per- pendicularly to the sector boundary, the sectors were mostly used for the analysis of narrow beams, somewhat less for flat but wide beams close to the median plane, and even less again for beams having large axial apertures.

The study of sectors can be roughly divided in four categories:

1. Uniform field, straight boundaries, fringing field effects neglected, motion in median plane (54-57). Second order focusing can be obtained for oblique entrance (58).


2. Uniform field, curved boundaries, fringing field neglected, motion i n median plane (59,60).

3. Uniform field, straight boundaries, double focusing produced by the fringing field (61, 62).

4. Cylindrically symmetric field, radially decreasing as r -", straight boundaries, double focusing produced by the sector field (6365). Fringing field effects can be included (66).

The powerful matrix method technique introduced by Penner (67), appropriate for narrow beams, is generally of less interest for beta-ray spectroscopy.

The sector spectrometers were mostly developed for mass spectroscopy and accelerator beam guiding and analysis, which usually deal with relatively narrow beams.

An oblique entrance, uniform field beta-ray spectrometer was designed by Paris (68), while Berlovich (69) described two uniform field-shaped boundary spectrometers, which he used mostly for coincidence work.

A most important development in magnetic sectors for beta-ray measurements took place in Tokyo, where Sakai, Ikegami, and collaborators built a series of double-focusing spectrometers with sector angle z 180" (70-72). An extensive description of the latest model was given by Yamamoto, Takuni, and Ikegami (73). Ikegami also considered theoretically the case of curved boundaries (74). Kaminskii and Kaganskii (75) built a spectrometer similar to those in Tokyo.

The characteristic parameters of the spectrometer described by Yama- mot0 et al. (73) are the following:

B = Bo(1 - 0.5 v + ( $ 1 ~ ~ - (41~~1 , ro = 34 cm,

distance between poles at ro , 22, = 24 cm,

sector angle 0 = 194",

source distance 1, = 44.7 cm,

magnification M = 0.733,

dispersion D, = 3.47.

The geometry is shown in Fig. 4. The source is outside the field to facilitate the coincidence work, while the focus is inside the field, to avoid the distor- sions due to fringing flux and to leave enough space for a second instrument. The field shape is determined by the empirical current distribution in the six coils inside and another six outside the vacuum chamber. Iron shims are


y-ray Detector

F I ~ . 4. A cross section of Tokyo sector double-focusing spectrometer.

placed symmetrically between the coils. The authors describe in detail how they handled the fringing field.

A convenient feature of this spectrometer is that a focal line exists, covering 15 % of the momentum range. The resolution varies over the focal line by about 15%. The performances, quoted in the Comparison Table, are comparable with good n,/i spectrometers of similar size.


An electron double-focusing spectrometer used for scattering experiments with the 85 MeV linear electron accelerator was recently described by de Jager, Douma, Bruinsma, and de Vries (76).

The “ orange ” spectrometers, which we shall consider separately, can also be considered as sectors.

IV. TOROIDAL ((‘ ORANGE”) SPECTROMETERS

Orange spectrometers have a much higher transmission than any other type of spectrometer, the values of T ranging between 10 and 20% for well designed instruments. For a given T, the resolution is an order of magnitude better than in the high transmission lens spectrometers. The fringing field effects have, however, imposed a limit on the resolution, the highest reached so far being about 0.1 %.

The transmission through the toroid depends on the gaps, but they distort the field inside and create the field outside, which’impair both the resolution and the transmission. Most of the development of orange spectrometers concentrated on the study of the gap effect and the search for improved profiles. The empirical investigations of profiles are easier, when they are identical on both sides. For that reason almost all reported orange spectrometers are symmetrical with respect to a plane perpendicular to the source-detector axis.

As the effect of the gap increases with its relative width, it is preferable to have a larger number of relatively narrow gaps. The construction is simpler in the case of iron-free coils, since the production of magnetically identical iron sectors requires great care. The iron-cored spectrometers usually have up to 8 gaps, while the iron-free may have up to 100.

Bisgird (77) has given a detailed description of the gap properties of an iron-core six-gap spectrometer, the design of which closely followed the first iron-cored spectrometer built by Nielsen and Kofoed-Hansen (78). After adjusting empirically the profiles for optimum resolution he found the following gap properties: (1) The field near the pole pieces is 0.4% stronger than in the median plane. This is due to the nonnegligible radial opening of the gap. (2) The transmission and resolution are both maximum in the median plane, the main reason being the defocusing action ((‘lens effect”) of the fringing field. (3) When all six gaps &re open the resolution is worse than with a single gap (0.85%, instead of 0.5% for a single gap). That indicates the seriousness of the problem of the magnetic identity of sectors.

In the 100-gap iron-free spectrometer built at Argonne by Freedman, Wagner, Porter, Terandy, and Day (78), the resolution is 0.39 % for a transmission of 19%. By reducing the transmission by a factor of 12, and the source diameter from 0.3 to 0.1 cm, the resolution improves by only a factor of three. Such a gain in resolution is really not worth a luminosity decrease of two orders of magnitude.


Two spectrometers more or less similar to the Argonne design, with comparable performances, were built later by Gasior (79) and Moll (80). No studies of sector profiles have been reported lately, and it would be interesting to see if modern computers could help to overcome the resolution barrier of

Quite a few single gap iron-cored spectrometers have been made, based on the sector boundary shape of the multigap instrument (81-85). They are considered to be convenient for coincidence work.

0.1 %.

V. LENSES

Very few lenses have been constructed lately, mainly those for beta- gamma coincidence studies (86). An important contribution to our understanding of focusing properties of various lens geometries was made by Lindgren et al. (87-89). They studied theoretically 37 different field shapes, ranging from bell shaped, which have the highest spherical aberrations, to U-shaped (Fig. 5 ) fields which have the lowest spherical aberrations.

In order to reduce the computer time, the contribution of the source diameter 2s and of the beam opening angle to the resolution were calculated separately. Their sum R, + R, represents the total resolution (at the basis of the line). Since the point source resolution R, is roughly proportional to the square of the solid angle a, and R, to s, the convenient magnitudes for comparison purposes are R, /02 and RJs. For each set of field and geometry parameters, a number of trajectories were computed. At the detector end side, the beam was supposed to be defined by Hubert baffles (90).

We shall summarize briefly only some of the results:

1. Both partial resolutions depend very much on the field form. For instance, R,/Q2 varies by two orders of magnitude between the optimum field and the ones with very large spherical aberrations.

2. While R,/R2 is smallest, R,/s is largest for fields with the smallest spherical aberrations. The opposite behavior of partial resolutions does not permit a straightforward selection of the “ best” field shape.

3. The focusing properties of some fields, like the short lens, appear inferior even without further, more complex investigations.

4. Maximum luminosity is obtained for a homogeneous field, and for the U-shaped field which decreases in the middle to 75 % of the value at the source and the detector.

5 . When specific activity is so high that a small source size can be tolerated and large solid angles are needed, the U-shaped field with 25-50 % depression becomes more adequate.

The performances of some of the best lens spectrometers (91-94) are included in the Comparison Table in Section X.

cm-' 0 1

0 1

01 0 Of OR

00'

o m 0 0'

OL

00

0 0

00

MILORAD S. MLADJENOVIC

* = ?p/&

1 loo POINT SOURCE 10 -

RESOLUTION

A 12' EMISSION ANGLE 0 20' 0 28' 36'

B 12. I 11. 1 18' x 56' 8 61'

FIG. 5. Disk source resolution at the ring focus for a point source versus the point source resolution for some typical magnetic fields and for different emission angles. Since the total resolution is roughly composed of point and disk source contributions, the best field shapes are generally those having both of them small.

VI. TROCHOIDAL SPECTROMETERS

Although the idea of trochoidal electron paths was introduced by Thibaud 35 years ago, it is only now that the first trochoidal beta spectrometers with good performances are being planned and made. One of the main reasons for such a delay is that the powerful analytical techniques, developed to deal with electron trajectories close to a circular equilibrium orbit, cannot be fully used in this case. It is relatively easy to deal with trochoidal paths in the symmetry plane, but skew paths, especially if the departure angle is large, have to be numerically computed. Much computer work is needed not only for the study of electron optical properties but also for the design of the magnet. These studies were undertaken recently by two groups, one in Lyon


and another in Zurich. In Lyon, where Thibaud pioneered in this field, LafoucriBre and his collaborators studied in detail the properties of the trochoidal spectrometer (95,96), built one which gave modest performances (97), and are now designing a much more ambitious one (98-100). In Zurich, Hofman (ZOZ) developed the theory of a multiple trochoid spectrometer and with Baker, Bharucha, and Heinrich (102) designed and constructed such a spectrometer. We shall attempt to present the main features of these two approaches and comment on them. Earlier work in this field was summarized by Siegbahn (8) and later by Lee-Whiting (9) who has himself explored in a very elegant manner the trochoidal spectrometer and made valuable contributions (Z03).

Most of the properties of the trochoidal spectrometer can be expressed using the parameter k defined as

where B, is the field at the source radius r , , while Bo is the homogeneous field which would force an electron of momentum p to circle along ro . The field itself can be represented in the symmetry plane by

k = Bo r,/p = B,/Bo, (5 )

Bz(r, 0) = Borer-'. (6)

The trajectories in the symmetry plane are shown in Fig. 6 . Laufou- criBre (95) was the first to show that particles leaving the source at any angle with respect to the tangent are all focused at a point having the same radius ro , and at the focusing angle given by

S = [k/(k2 - 1)”2] - 1. (7)

FIG. 6. The parameters defining the radial and the axial extension of trochoids, in the median plane.


Besides the source circle radius r,,, there are two other significant radii r - and r + defining circles, enveloping trajectories from the inner and outer side, respectively. It is between r - and r + that the field has to follow l/r dependence. They are connected with k by the relation

r f / r - = [(k + l ) / (k - l ) ] [ ( k + sin e)/(k - sin E)] , (8)

where + E is the semiaperture angle.

defined as The dispersion for the trajectories confined to the symmetry plane may be

D = d6/dk = 2/(k2 - l )3i2 (9)

for one trochoid loop, and increases linearly with the number of loops. We reproduce in Fig. 7 graphs prepared by Lee-Whiting (103) showing the

r+/r-

14

m 8

6

4

2

I 1.2 f.4 f.6 4.8 2 0 0

FIG. 7. Lee-Whiting's calculations of the focusing angle 8, dispersion D , , and the enveloping circles ratio r+ / r - as a function of k , for trochoidal spectrometers.

focusing angle, ratio r + / r - , and dispersion D, as a function of k . One can see that large dispersion requires large focusing angles and high r f / r - ratio. A focusing angle larger than 271 is not very convenient, but more serious difficulties can be expected from the requirement to produce high r + / r - . This is why up to now only the values of k greater than 1.25 were seriously considered.

The focusing in the symmetry plane is quite simple, which is not at all the


case with skew orbits where numerical integrations have to be made. Lee- Whiting calculated aberrations, resolution, transmission, and the luminosity of a trochoidal spectrometer with k = 1.25. He found that for a point source, such a spectrometer should have a transmission of 2.3% at a resolution of 0.01 %, which is about 20 times greater than the transmission of the n& spectrometer, at the same resolution. Unfortunately, the luminosity turned out to be five times lower than in the case of 7~(2)'/~ spectrometer.

More recently, the group in Lyon, especially Mugnier (98-100), extended the computation of skew orbits with large departure angles, greater sources, and a range of k-values. Their results for two values of k are summarized in Table 11.

The theoretical performances of a spectrometer with k = 1.288 and tangential emission appear to be outstanding. Unfortunately, the difficulties encountered in producing the magnet are just as outstanding. The large ratio of r + / r - requires the field to fit the l/r gradient over a very wide range of values of r . The weight of the iron pole pieces is estimated at 100 tons, which is 20 times greater than the weight of the first large double focusing instrument (ro = 50 cm) made at the Nobel Institute. The Lyon group is now considering an iron-free design, developing further the idea of conical windings first proposed by Lee-Whiting (103). Mugnier recently found the geometry needed for r + / r - = 10, and the remaining problem appears to be the current feeding.

Multiple h o p Spectrometer

The Zurich group built a spectrometer with six trochoidal loops (Z02). The reasons for increasing the number of loops are: (1) Dispersion increases linearly with the number of loops, and (2) Hofman (101) found that when the number of loops is larger than one, double focusing can be achieved for certain (" stable ") values of k. First and second order aberrations with respect to the opening angle then vanish, and the third order aberrations do not lie in the direction of momentum discrimination.

We reproduce in Table 111 the relevant parameters for three " stable " values of k. For values of k = 1.3, which give high dispersion, the total focusing angle becomes even for two loops larger than 2n. The data in the last row correspond to the spectrometer which was built. Its r + / r - ratio is not excessive and the focusing angle is not large, but the dispersion is still an order of magnitude smaller than that of a spectrometer with k = 1.3 and

The 6-loop spectrometer built in Zurich has a source orbit radius ro = 14 cm and rmar = 25 cm. The cross section of the vacuum chamber in the symmetry plane is shown in Fig. 8. The price paid for the increase of the dispersion is an elaborate system of slits which together with the source have to be

3 loops.

TABLE JI

THEORETTCAL PERFORMANCES OF TROCHOIDAL SPECTROMETER (MUGNIER) ~ g Direction Source Exit slit Magnet

k of r+/r- Width Length Width Length T L R Diam Weight F

F 10 g

2

emission (-1 (-) (cm) (m) (tons)

2.25 tangential 2.60 0.2 5 0.1 5 4.7 0.047 1.2 x 10-3 1.7 2.15 radial 2.74 0.2 5 0.1 3 0.6 0.004 10-3 1.288 tangential 7.94 0.2 5 0.1 7 4.8 0.068 1.3 x 3 100

radial 0.2 5 0.1 2 0.22 0.0005 1.3 x ch

DESIGN OF MAGNETIC BETA-RAY SPECTROMETERS

TABLE I11

PARAMETER FOR " STABLE " k VALUES (HOFMAN)

Number Total Disper- k of loops, focusing sion r + / r -

n angle,& nD

3.227 2 370" 17' 1.4 1.9 1.329 2 373" 32' 25 7.1 1.309 3 594" 22' 41 7.5

3.227 6 111" 50' 4.2 1.9

63

FIG. 8. The beam geometry of the Zurich 6-loop trochoidal spectrometer.

accurately adjusted. The source position is not easily reached and in the present design the whole geometry defining system has to be removed from the magnet when a new source is introduced.

The theoretical performances of the spectrometer are very good, the most


interesting property being a rather flat T-R curve. The transmission and luminosity are several times higher than that of a 7cJZ spectrometer of similar size. Unfortunately, the actual performances of the spectrometer itself fall below theoretical expectations. At very high resolutions the transmission is several times smaller than theoretically predicted and the source size contribution is also more important than expected. The probable reasons for the unexpected luminosity drop are the field imperfections. It would be worthwhile trying to improve the field shape. Another possibility, not as difficult, is to develop an iron-free multiloop spectrometer.

Two limitations of the multiloop spectrometer should be mentioned: It cannot be used as a spectograph, and it is almost impossible to use it for coincidence work.

VII. OPTICAL ANALOGY SPECTROMETER

Kelman and collaborators (104-106) developed an electron spectrometer analogous to the optical spectrometer, in which focusing and dispersion are separated and performed by different electron-optical elements. The spectrometer consists of two lenses and a dispersive prism in-between (Fig. 9). The first lens collimates electrons into a parallel beam, which is deflected by the

FIG. 9. The geometry of the Kelman spectrometer with symmetrical lenses.


prism and focused by the second lens. Most of the spectrometers of this type are of the large size, each of the two arms being 2-4 m long. This offers the possibility of achieving large dispersion.

A . Dispersion

The magnetic prism consists of a central part with a homogeneous field, and two fringing fields which act as cylindrical lenses. A beam parallel to the pole faces, entering at an angle cxl, is focused by the first cylindrical lens into a line focus lying in the median plane, midway between the sides of the magnet. The action of the second lens is symmetrical, so that a parallel beam leaves the magnet at the same angle L Y ~ . The angle a, is determined uniquely and is equal to 58".

The dispersion is given by the expression

D = 2fr tan a,,

= 3.2&

wheref, is the focal length of the focusing lens. For focal lengths of about 100 cm, the dispersion is over 300 cm.

B. Aberrations and Resolution

The expression for resolution R can be written as

R = (Aim + 4 1 ) / 2 D ,

Aim = ( S + d,)M + 4 + A",

(10)

(1 1)

where AsI is the exit slit width, and Aim is given by

where M = -fr/' is the magnification and d , , df are the diameters of the confusion disks in the collimating and focusing lens, respectively, s is the source width,

Av = 2b(AIf/If + MAIc/Ic)

is the aberration produced when the currents in the lenses differ by AIf and Arc from the values required to focus the electrons deflected by the prism, and b is the width of the collimated beam.

The relation (1 1) expresses the usual contribution of lens aberrations, measured by the diameters of the disks of confusion. The contribution resulting from mismatching the fields can be serious, since AIf/If = is equivalent to adding 1 mm to the width of the source, which is itself 1 mm wide in the high resolution work.


C. Deflecting Magnet

The ideal field of a deflecting magnet can be defined by the following requirements: (1) The field should be two-dimensional, not depending on the x coordinate. (2) The left and right fringing flux distributions, which act as cylindrical lenses, should be identical. (3) The inside field should be homogeneous, without local variations. (4) Symmetry with respect to the median plane is required. (5 ) The field should be everywhere perpendicular to the x axis. (6) The field geometry should be independent of field strength or of previous field history. (7) There should be no stray fields.

Although some of these requirements can be relaxed somewhat, the development of a satisfactory deflecting magnet has probably taken more time and effort than any other component of the spectrometer.

D. Magnetic Lenses

The lenses can be made. with constant or variable geometry. The operating disadvantage of the constant geometry lenses is that in

order to change the solid angle, one has to move the source. This requires a readjustment of the lens current and of the source rotation angle. In one of the latest types of constant geometry lenses the focal length could be changed from 127 to 28 cm, thereby changing the solid angle from 0.04 % to 0.8 % of 4n.

The variable geometry lenses (Fig. 10) were recently developed by Peregud and collaborators (107). They considered that fixed geometry lenses had two important disadvantages: (1) The increase of solid angle is limited by the requirement that the focal length of the collimating lens cannot be made shorter than the halfwidth (at half-height) of the bell-shaped field distribution.

FIO. 10. Asymmetrical lenses with variable focal length for optical analogy spectrometer.


Making the lens shorter does not pay, because spherical aberrations increase. (2) If the focal length of the collimator lens is decreased, while& remains the same, the magnification j J f , increases prohibitively, for large solid angles.

The variable geometry lens is shown in Fig. 10 with corresponding field distributions. The source is placed in the center of the lens, so that only one half is used. The unused half of the lens is cut at 10 cm from the center and the field is not symmetrical. By switching in various parts of the coil, the focal length can be set at various values, changing the solid angle from 0.06 to 3.6 % of 471. The lens is 240 cm long.

The focusing lens is identical to the collimating one. This offers two advantages: magnification can be kept equal to 1, and for high resolution, lenses with wide field distribution are used, which have smaller spherical aberrations. The contribution of aberrations to the line width then becomes negligible. The performances of both variations are given in the Comparison Table (Section X).

VIII. CORRECTORS

New degrees of freedom, needed to reduce the aberrations, can be obtained by giving up the rotational symmetry. This can be achieved either by adding a new electron optical device, magnetic or electrostatic, to a cylindrically symmetric field, or by using a single magnet with nonsymmetrical field. The additional devices, which we call correctors, have often been conceived and designed after the spectrometer has been in use. We shall first consider the correctors, and in the next section the nonsymmetric fields.

The correctors can be classified, according to the order of magnitude they correct, into first and higher order correctors. The most important first order magnitude contribution to the aberrations is the source width. The corresponding corrector is better known as the multistrip source.

A . Multistrip Source

One of the most interesting innovations in beta spectroscopy technique during the last decade has probably been the development of the multjstrip source by Bergkvist (108, 109). The principle is simple (Fig. 11). Each strip is held at the electrostatic potential needed to correct for the distance from the optic axis. The momenta of electrons emitted from each strip are changed by the amount necessary to bring them all into focus. The potential varies with the momentum of electrons, and at 1 MeV it may amount to 10 kV.

There is no need to give a description of the multistrip source since it has already appeared in review papers (8), but we shall comment on its merits and present limitations.


,central circle

/ momentum pa orbits far nominal

v (90) source patentiat detector slit

FIG. 11. The principle of the multistrip source.

The luminosity gain is between one and two orders of magnitude. This is such a vast improvement that some previously impossible experiments might now become possible.

The principle is applicable to many types of spectrometers. It was initially developed by Bergkvist for large n,/z spectrometers. Later, Jahn (50) made a multistrip source for the (n/2),/% spectrometer, while Peregud and collaborators (107) designed one for the optical analogy spectrometer.

Its present limitations appear to be the following: (1) The multistrip source is not simple to make, nor simple to use. (2) The best resolutions so far achieved were about 0.04 %. Inherent aberrations and imperfections of source geometry make it very hard to approach resolutions of 0.01 %. The appropriate linewidths for use with a multistrip source appear at present to be those above 0.05 %. (3) Limitations on energies are not so serious. Still, it is less convenient to work at very high and very low energies. Very high energies require larger electric fields, while at low energies scattering may become appreciable.

The multistrip source is not convenient for use in spectrographs or with multidetector systems. Aberrations become nonnegligible at distances from the optic axis equivalent to a 1 % change in momentum. It is true though that at high resolutions there may be many points measured within 1 % of the momentum range.


B. Second-Order Correctors

The aberrations of the second and some higher orders can be reduced or eliminated by a separate electron-optical device. Such a corrector can use either an electrostatic or a magnetic field. Magnetic correctors had been earlier developed for lenses (110, 111). Bergkvist was the first to develop second order correctors for spectrometers, using an electrostatic field produced by properly shaped wires. On the other hand, a magnetic field can be produced either by iron-free coils or by using iron pole pieces. The choice between various possibilities can be made by taking the following factors into account.

1. In the ideal case, one would like to be able to calculate the correcting field and theoretically design the corrector. A precise knowledge of the main field is then required. The procedure is simpler when the main field can be expressed analytically.

2. Since it happens in practice that a precise analytical expression for the main field is not available, or that some asymmetries exist, it is convenient if the geometry of the corrector coils or electrodes can be varied. Optimization can be done by ray-tracing with the help of a computer and finally in the spectrometer itself.

3. The corrector should produce the desired field without disturbing the main field.

4. It is desirable not to have separate power supplies and controls for the corrector.

5. Since coils or electrodes can be in the space where the beam is passing, it is desirable that no appreciable part of the beam be cut away.

Various corrector types are summarized in Table IV, which also contains

TABLE IV

POSSIBLE CORRECTOR TYPES ~ ~~ ~~~ ~

Spectrometer

Corrector Iron-cored Iron-free type

Electrostatic Made by Bergkvist (109) Calculated by Lee-Whiting (112) General theory by Shpalek (114)

Mag- netic

Iron-free

Iron

Made by Shibata et al. (113)

Not reported Not convenient (Field disturbed)


the names of the authors who made or calculated such devices for ~ ( 2 ) ” ~ spectrometers.

The semiempirical development of the corrector is simpler in the electrostatic case; it is relatively easy to shape the wires and determine the right potentials. This is the main reason why Bergkvist chose the electrostatic type for the iron-cored n@ spectrometer (209). The corrector is shown in Fig. 12.

\ central circle

FIG. 12. The principle of the electrostatic corrector of aberrations produced by the final beam aperture.

It consists of two pairs of curved grids, the outer pair being at the potential of the spectrometer, while the inner ones are at a negative potential. The electrons are first decelerated and then accelerated for about the same amount, but a deflecting component of the electric field increases the radius of the electron orbit for an amount necessary to bring it into point focus on the optic circle. The correcting potential is - 3.2 kV for electrons of 330 keV. The installation of the corrector improved the resolution-transmission characteristics by a factor of four.

Lee-Whiting (212) calculated a cylindrical electrostatic corrector for an iron-free n f i spectrometer, which should improve the transmission by a


factor of two. This figure could be increased with a noncylindrical corrector, which would work over the whole of the available aperture. The electrostatic type does not fulfill requirement number 4, since it represents a separate device which has to be matched to the magnet and needs separate control and power supplies.

The advantage of magnetic correctors is that in principle they do not represent a separate device. Coils could be connected in series with the main coils, or iron pieces could be added to the main pole pieces. The only magnet- tic corrector reported so far was made by Shibata et al. (113). They developed an iron-free corrector for an iron-cored n$ spectrometer. There is no problem with the return circuit then, but there is a possibility that the coil disturbs the main field. The intensity of the correcting field is 6 % of the main field and the authors found that the main field is not disturbed. The shape of the coils, which were determined by simplified calculations, is shown in Fig. 13. They cut out 10% of the beam. The presence of iron introduces a nonlinear relationship between the current in the main and the correcting coils.

FIG. 13. The corrector coil for the magnetic correction of aberrations produced by the final beam aperture in an iron-cored magnet.

This effect was found not to be serious and the coils were connected in series. The performance was improved by a factor of three.

A general approach to iron-free correctors for iron-free spectrometers was developed by Shpalek (114). A practical problem is the returncircuit.Thecoi1 has to be either infinitely long or a large thorus.

An iron corrector for an iron-clad spectrometer has not yet been reported. The difficulty is that the correcting field cannot be sharply confined.

IX. AZIMUTHALLY VARYING FIELD

New degree of freedom can be obtained by destroying the rotational symmetry and having an azimuthally varying field. The change is somewhat analogous to the introduction of strong focusing in the accelerator design. The proposal originated in Berkeley where Sessler (115) formulated the basic


approach, and later with Bergkvist (226) calculated the parameters and performance of such a spectrometer. The idea was taken up by Schmutzler and Daniel (217) who have made extensive calculations.

The calculations performed by both groups demonstrated theoretically that interesting performances can be obtained with azimuthally varying fields. The main difficulty appears at present to be the design of a magnet producing the desired field. It seems that, at least in the beginning, one should start with some si.mpler magnet design having some adjustable parameters, and then try to find the combination for which the aberration coefficients vanish. No such magnet design has yet been published. For that reason, we shall only very briefly mention the theoretical approach.

The field, which for the sake of simplicity, can be taken as constant along the optic circle, may be described in the median plane by

B&, 0) = Bo(1 + a,? + a,q2 + a3 q3 + = * - ) , (12)

where the coefficients a,(@ depend on the azimuthal angle 0 in the following way :

a,(e) = D,, + D,, sin e + D,, cos e + D,, sin 2e + D~,, cos 2e

+ D,, sin 30 + D,, cos 38. (13)

For a point source on the optic circle the radial coordinate q* of the image point is expressed by

Authors have searched by means of digital computation for values of D,, which cancel the aberration coefficients A,, . The parameters obtained by two groups are reproduced in Table V. Since these are the results of initial exploratory calculations, they can be considered as encouraging for further work.

TABLE V

THEORETICAL PARAMETERS FOR AVF SPECTROMETER

Point source Finite source (Berkeley) (Heidelberg)

Radial focusing angle 3.50" 402"

Source size 0 0.25 x 25 mmz Radius of optic

circle, ro 50 cm

Dispersion 10 10

Resolution, % 0.01 0.012 Solid angle, % 0.9 0.38


X. COMPARISON TABLE

Many papers reporting new spectrometers end with a diagram showing luminosity-resolution characteristics, compared with some other instruments. There is no doubt that authors should study these important performance parameters, along with quite a few others. In this review paper, however, we will not end with a diagram. We feel that when one works with and studies such a large and diversified family of spectrometers, one becomes involved with them on an almost human level. Each has its merits and shortcomings, large or small, visible or hidden. Instead of a two-dimensional diagram, then, we prefer to give a table, emphasizing that it should be considered as an illustration of the capabilities of different instruments.

Only one or two spectrometers of each type were chosen to illustrate a specific performance. No attempt was made to cover all possible types and their variations, especially the older ones.

COMPAR~SON TABLE

Performances

Type of spectrometer Size ro Source and or B or

Authors 2s0 Width Length R T Ln o r L (cm) (cm) (cm) (%) (%)

Semicircular Geoffrion and Giroux 35 0.1 5.3 0.25 0.075 4 x (118) 0.1 5.3 0.19 0.06 3.2 x

Ifles and Berenyi rmax (20) 75 0.02 2 0.04 0.08 3.2 x

- Antman et al. (119) 50 0.08

0.2 0.4

Bartlett et d., (35) 50 0.05 0.3

Graham et al., (43) 100 0.02 0.08 0.15

Helmer (48) 35 0.0037 0.015 0.75

2 2 2

2 3.8

1.25 I .25 1.25

1 1 2

0.04 0.14

0.06 0.33

0.013 0.05 0.1

0.008 0.01 8 0.08

0.032 0.12 0.24

0.08 2.0

0.07 0.2 0.3

0.007 0.04 0.08

3.2 x 10-5 4.8 x 10-4

8 x 2.3 x

1.75 x 10-5 2.4 x 10-4 5.6 x 10-4

3 x 10-7

1.2 x 10-4 6 x

(continued)

COMPARISON TABLE-Continued

Performances

Size ro Source Type of spectrometer or

and 2 sn Width Length R R o r T LR orL Authors (cm) (cm) (cm) (%I (%) (cm2)

(id21413 Daniel et al. (50)

w 4 l o - Baranov et al. (52)

Sector Yamamoto et al. (73) -

Orange Bisglrd (77)

Friedman et al. (78)

Lens J G e r m a n ef al. (93)

DuMond (91)

Trochoidal Balzer et al. (102)

Optical analogy Kelman et al. (104)

Gumenyuk et al. (107)

30

40

34

3 - d 34

s - d

67

s - d 228

s - d

63

14

0.02 0.02 0.02 0.02

0.15

0.1 0.1

0.12 0.12

0.008 0.054

0.04 0.04 0.1 0.15

0.1

1 0.048 1.0 1 0.03 0.6 0.25 0.022 0.6 0.25 0.013 0.15

4 0.038 0.03

1 0.08 0.01 1.5 0.2 0.2

0.5 0.2 1.0 0.5 1.4 1.0

Radius 0.2 0.2 0.2 0.05 0.05

0.22 0.11 0.055

0.93 0.4 0.21 0.3 0.3

0.044 0.024 0.02

19 16 2 3 13 16

0.5 0.24 0.12

0.0045 0.02 0.5 0.018 0.08 1.0 0.072 0.32 2.0 0.16 0.73 3.0 0.29 1.3 4.0 0.45 2.0 5.0

3 0.045 0.4 3 0.13 1.4

1.5 0.014 0.045 1.5 0.022 0.012 1.5 0.036 0.04 1.5 0.014 0.37

0.06 0.06 0.09 0.17

1.5 0.14 0.34 0.25 1.1 0.77 3.6

2 x 10-4 1.2 x 10-4 3 x 10-5 7.5 x 10-6

1.8 x 10-4

8 x 3 x 10-4

6 x 6 x

2.4 x 2 x 10-2 3.5 x 10-3 1 x 10-3

7.5 x 10-4

9 x 1 0 - 5 1.1 x 10-5

3 x 10-7 1 x 10-5 3 x 10-4 2.5 x 10-3

1.2 x lo-&

1 x 10-2 3 x 10-2

1.2 x 10-4 2.2 x 10-3

3 x 10-6 7 x 6 x 8 x

9 x 10-5 2.6 x 10-4 5.1 x 10-4 1.7 x 10-3 5.4 x 10-3


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On Failure Mechanisms in Large-Scale Integrated Circuits

GEORGE L . SCHNABLE* AND RALPH S . KEENt

Microelectronics Division. Philco-Ford Corporation. Blue Bell. Pennsylvania

I . Relationship between Types of Integrated Circuits and Failure Mechanisms .............................................................................. 80 A . Introduction .................................................................................... 80 B . Definition of Large-Scale Integration ................................................... 80 C . Failure Modes and Mechanisms ......................................................... 82 D . Types of LSI Devices ........................................................................ 83 E . Categories of Failure Mechanisms ...................................................... 85 F . Types of Bipolar Integrated Circuits ...................................................... 85 G . Types of MOS Integrated Circuits ...................................................... 86

I1 . Bipolar Failure Mechanisms ...... ....................................................... 86 A . Introduction .................................................................................... 86 B . Electromigration .............................................................................. 86 C . Open Metal at Oxide Steps .................................................................. 89 D . Aluminum Penetration ..................................................................... 92 E . Metallization Systems Based on Gold ................................................... 94 F . Bulk Failure Mechanisms .................................................................. 94 G . Oxide Shorts ................................................................................. 95 H . Surface Effects ................................................................................. 95 I . AI-Si Contacts ................................................................................. 97 J . Radiation-Hardened Integrated Circuits ................................................ 97 K . Reliability of Other Circuit Elements ................................................... 97

111 . MOS Failure Mechanisms . ................................................................ 98 A . Introduction ................ ................................................................ 98 B . Oxideshorts .................................................................................... 98 C . Gate Oxide Breakdown ..................................................................... 98 D . Static Electricity Effects ..................................................................... 101 E . Surface Potential and Fast States ......................................................... 102 F . Gate Threshold Voltage Drift ....................................................... G . Field Inversion Voltage ................................................................ H . Surface-Ion Migration ..................................................................... 103 I . Failures Due to Surface-Ion Migration Plus Localized Defects .................. 104 J . Conductive Particles ........................................................................ 106 K . Failure Mechanisms of Other Types of MOS Devices .............................. 106

IV . Multilevel Metallization ........................................................................ 107 A . Introduction .................................................................................... 107 B . Surface Effects ..................... ................................................. 108

* Present address: RCA Laboratories, David Sarnoff Research Center, Princeton, New

t Present address; Inselek, 743 Alexander Road, Princeton, New Jersey 08540 . Jersey 08540 .

79

80 GEORGE L . SCHNABLE AND RALPH S . KEEN

C . Oxide Shorts between Metallization Layers ............................................. D . Contact Resistance between Layers of Metallization in Vias ..................... E . Metallization over Integrated Circuit Topography F . Discretionary Wiring ........................................................................

V . Integrated Circuit Assembly .................................................................. A . Introduction .................................................................................... B . Chip-to-Package Bonds ..................................................................... C . Gold Wire Bonds .............................................................................. D . Aluminum Wire Bonds ..... E . Assembly Systems Based on iques Other than Wire Bonding ............... F . Testing .......................................................................................... G . Packages .......................................................................................

VI . Integrated Circuit Reliability .................................................................. A . Introduction .................................................................................... B . Integrated Circuit Failure Rates ......................................................... C . Quality Assurance ........................................................................... D . Test Structures .............................................................................. E . Failure Analysis .............................................................................. F . Effect of LSI Trends on Reliability . ................................................. G . Reliability versus Chip Complexity ...................................................... H . Reliability Tradeoffs and Limitations ................................................... I . Accelerated Stress Testing ................................................... J . Attainment of LSI Reliability ............................................................ K . Effect of Complexity on Reliability ...................................................... References ..........................................................................................

.................................

........................................................

109 110 1 1 1 115 118 118 118 119 120 120 121 121 122 122 123 124 124 127 128 128 129 131 131 133 133

I . RELATIONSHIP BETWEEN TYPES OF INTEGRATED CIRCUITS AND FAILURE MECHANISMS

A . Introduction

A substantial and increasing portion of the electronic functions in new electronic systems are being performed by very complex planar silicon integrated circuits. which offer the possiblity of simultaneously increasing system reliability and decreasing system costs . The increased complexity of comnier- cially available integrated circuits is being achieved by the use of new processes. materials. and structures. as well as by many evolutionary trends and refinements in integrated circuit design and manufacturing technology . The dominant failure mechanisms in the most important types of large-scale integrated circuits being manufactured are reviewed in subsequent sections of this chapter. and the reliability implications of various types of complex circuits are discussed .

B . Definition of Large-Scale Integration

Although a number of definitions of large-scale integration (LSI) have been advanced. none has been universally accepted . Among the more widely accepted definitions are: 100 or more logic gates per chip. multilevel metalliz-

ON FAILURE MECHANISMS IN INTEGRATED CIRCUITS 81

ation, or the performance of a subsystem rather than a circuit function on a single chip (2-4). Medium-scale integration (MSI) is more complex than conventional integrated circuitry and less complex than LSI but has some of the attributes of LSI. Integrated circuits of conventional complexity are termed small-scale integration (SSI).

The various degrees of complexity of monolithic circuits are perhaps best illustrated by the integrated circuits shown in Figs. 1 to 4. The properties of these devices are listed in Table I, and are compared with those of a discrete transistor. Figure 1 illustrates a typical SSI product, a bipolar integrated circuit of relatively low complexity. Figure 2 illustrates a single-level metallized bipolar circuit which would be classified as MSI. Figures 3 and 4 illustrate

FIG. 1 . PL9962 SSI integrated circuit with typical A1 metal linewidth of 0.5 mil.

82 GEORGE L. SCHNABLE AND RALPH S. KEEN

FIG. 2. PD9300 MSI integrated circuit with typical A1 metal linewidth of 0.25 mil.

LSI products which are typical of the complexity attainable today in LSI devices.

C. Failure Modes and Mechanisms

Failure mode relates to the cause for rejection of the failed device in terms of the requirement the device failed to meet (5). Thus no failure analysis is required to identify the failure mode. Most failed devices are analyzed at least to the point of defining broad categories of failure modes, such as bulk effects, surface effects, chip-to-header bonds, wire bonds, and package failures. A failure mechanism relates to the specific defect or physical process which results in degradation and eventual catastrophic failure of the device. In some cases microscopic examination of failed devices permits identification of processing defects or of physical mechanisms of failure. In other cases very detailed and sophisticated analytical techniques are required (6) to determine the exact location of the failure on the chip and/or the exact cause of the


FIG. 3. SP0199A MSI integrated circuit with two levels of A1 metallization. The typical metal linewidth is 0.5 mil.

failure. This is particularly true of oxide shorts and of surface-related failure mechanisms.

D. Types of LSI Devices

Currently-available MSI and LSI arrays are principally based on two types of active silicon planar devices : double-diffused npn bipolar transistors and p-channel enhancement-mode MOS transistors.

In the case of bipolar integrated circuits, a variety of single-level-metallized MSI arrays and some singIe-level-metallized LSI arrays are available. Multi- level-metallized bipolar arrays containing two or three levels of metallization are available in limited quantities.


FIG. 4. PM1024C LSI MOS integrated circuit having a typical A1 metal linewidth of 0.4 mil.

TABLE I

COMPLEXITY CHARACTERISTICS OF TRANSISTOR AND INTEGRATED CIRCUIT DEVICES

Num- Number of Number ber of Circuit Area

number active of size (transistors, circuit devices metal- resistors, element

lization or diodes)

Description Device of layers Chip elements Per

(milz) (mi12)

Discrete transistor SN5020 1 1 150 1 150 Triple 3-input

gate PL9962 18 1 1369 30 46 Digital crosspoint

quad SP0199A 74 2 6080 132 46 4-Bit universal

shift register PD9300 104 1 7544 185 40 Dynamic read-only

memory PM1024C 1300 1 7400 1340 6


A variety of MOS LSI arrays is available with only a single level of metallization. The existing techniques for obtaining two or more levels of metallization have not yet been applied to MOS arrays, other than developmental types. Available silicon-gate MOS arrays, however, may be considered to have more than one level of metallization (7). Other types of MSI and LSI products include complementary MOS (8) and n-channel MOS integrated circuits.

There are, as indicated in the following sections, a number of variations in the materials, designs, structures, and processes used to fabricate both bipolar and MOS LSI circuits (9). These variations can significantly influence the incidence of certain failure mechanisms.

E. Categories of Failure Mechanisms

Bipolar and MOS circuits have a number of failure mechanisms in common. They also have unique failure mechanisms, and differ significantly in the relative incidence of certain types of failure modes and mechanisms. Multilevel metallization results in some possible new failure modes, as well as some changes in the relative significance of previously identified mechanisms. It is thus appropriate to separately discuss bipolar failure mechanisms, MOS failure mechanisms, and multilevel metallization failure mechanisms, and to then discuss common failure mechanisms such as those related to wire bonds and packaging. The subsequent sections of this chapter are arranged on this basis, and are followed by a general discussion of the effects of large-scale integration on reliability of electronic systems.

F. Types of Bipolar Integrated Circuits

By far the largest number of bipolar circuits contain only npn transistors, diffused resistors, and p-n junction diodes, with electrical isolation obtained by reverse-biased p-n junctions.

Most bipolar circuits employ aluminum metallization. Other metallization systems in use for bipolar circuits include the Mo-Au system (ZO), which was developed specifically to avoid the possiblity of Au-A1 interaction at wire bonds, and the Ti-Pt-Au system, which is the basis for the beam-lead sealed- junction technology (ZZ, 12).

Oxide-isolated integrated circuits with thin-film resistors such as Ta or Ni-Cr alloy are used for radiation-hardened applications and for other specialized requirements.

High-speed TTL circuits containing AI-Si Schottky barrier diodes (13) are available from several manufacturers.

Specialized circuits containing complementary bipolar transistors pr junction field-effect transistors are available in developmental quantities. Limited


use is also being made of simplified bipolar techniques which are capable of high functional'density (14).

G. Types of MOS Integrated Circuits

Most of the MOS integrated circuits in use are based on p-channel enhancement-mode transistors. Most processing uses ( I 11) silicon, and a single layer of thermally grown SiOz for the gate dielectric. A considerable number of process variations are in use. (100) Si is being used for low voltage devices, in some cases with a gate dielectric that includes a layer of silicon nitride (Si,N,) (15) or aluminum oxide (A1,OJ over a thin layer of S O z . Circuits with p-channel transistors are also being made by the silicon-gate process (16), and by several ion implantation techniques.

A number of other fabrication techniques such as silicon-on-sapphire or silicon-on-spinel have been described, but these are still developmental approaches.

11. BIPOLAR FAILURE MECHANISMS

A . Introduction

Substantial quantities of bipolar integrated circuits were first manufactured in 1964. Studies of the reliability of integrated circuits, and of failure mechanisms have constituted a very considerable effort since that time. These efforts, while very successful in permitting substantial improvements in integrated circuit reliability, are by no means complete (17). Much work remains to be done, even to more fully understand the known failure mechanisms.

Principal categories of bipolar failure mechanisms are wire bond failures, metallization opens at oxide steps, and disappearing metal due to Kirkendall effect or to electromigration of metal, with some failures also due to metal scratches, photolithographic defects, nonhermetic packages, oxide shorts, contamination, surface effects, and chip-to-package bonds (18, 19). Both the failure rate and the relative incidence of the various failure mechanisms change with the level of stress, manufacturer (20-27), type of circuit package, and other factors. Table I1 shows the relative incidence of failures for bipolar integrated circuits at rated stress levels (20).

B. Electrornigration Electromigration, the mass transport of metal atoms by momentum ex-

change with conducting electrons, has been shown to be a significant cause of failure of integrated circuits in which a high current density occurs in delineated


TABLE I1

BIPOLAR FAILURES UNDER RATED STRESS LEVELS OFOPERATINGLIFE AT 1 2 5 ' C ~ m ENVIRONMENTAL TESTING OF METAL-BOTTOM 14-LEAD FLAT PACK

Category of Percentage of failure failures

Open metal at oxide steps Bonds Photolithographic defects Contact cut resistance Hermeticity Wire defects Channeling Contamination Miscellaneous

25 19 19 13 10

5 4 4 1

metal lines (28,29). In electromigration, metal atoms move toward the positive end of the conductor, and lattice vacancies move toward the negative end. In general, with aluminum metallization, reliability problems occur only when current density exceeds lo5 A/cmZ and the chip temperature exceeds 100°C (30). The most common result of electromigration is to produce disappearance of aluminum in certain regions and, ultimately, open metallization, Figure 5 shows a metal stripe in which an opening occurred as a result of electromigra- Zion. Electromigration can also result in the formation of whiskers, in fractur- ing of an overlying glass layer, or in problems at AI-Si contacts (30).

The mean-time-to-failure (MTF) of a metal stripe in an integrated circuit depends not only on the temperature and the current density, but also on the temperature gradient (30), impurity content of the metal (31), grain size of the metal (32), metal layer thickness (30), linewidth (30, 31), whether the metal is overcoated with a glass (30), the properties of overcoating glass (3, 33, 34), and other factors.

Aluminum-metallized structures subjected to high current density at elevated temperature generally exhibit a temperature dependence for MTF which follows the Arrhenius equation, k = s exp( - EJRT), where k is the rate con- tant of reaction, s is a constant, E, is the activation energy for electromigration failure, R is the gas constant, and T is the absolute temperature.

The activation energy, determined from the MTF of metal stripes, is higher for films in which the rate-determining process is diffusion of lattice vacancies in the bulk, rather than diffusion at grain boundaries or surfaces.

A number of investigators have found that MTF is inversely proportional to the square of the current density, J (3, 30, 32). This point is, however,


FIG. 5. Electromigration open in A1 metal 0.5 mil wide and 1 p thick. The arrow points to the open.

controversial, with other investigators (35, 36) indicating MTF is inversely proportional to J, or to J 3 , or J4.

The effect of temperature and current density on MTF due to electromigration is shown in Fig. 6, which is based on an assumed effective activation energy of 20 kcal/mole (0.87 eV) and a J-’ relationship between current density and MTF.

In circuits in which design rules are chosen to limit the current density not to exceed lo5 A/cmZ, electromigration may still be the ultimate cause of failure at localized constrictions in the cross-sectional area of the metal conductor. Such constrictions may result from photolithographic defects, metal scratches, poor metal coverage of oxide steps, inadequate contact cut areas, or similar deficiencies.

The phenomenon of electromigration occurs with a wide variety of metals, including gold, silver, copper, platinum, tungsten, and tin (21). The current density at which electromigration causes reliability problems in gold films is substantially higher (37-39) than that of ahminum films, and thus there has


300

280

260

240

220

200

2 180 a a

160 z 3 140 J a

a

120 4

w 4 100

+ 80

60

40 I 10 100 1,000

TIME TO FAILURE, ARBITRARY UNITS

30

FIG. 6. Plot of relationship between temperature and mean time to failure, in arbitrary units, for an activation energy of 20 kcal/mole.

been some tendency to use gold metallization systems for devices where designs require very high current densities (40, 41).

Figure 7 shows another A1 metallization line which opened due to electromigration. In this particular case the failure occurred at the corner, where current crowding significantly increased the current density at the inside edge and caused a current density gradient.

C. Open Metal at Oxide Steps

Open metal at oxide steps has been a significant cause of failure in single- level-metallized bipolar arrays. It is also a factor in multilevel-metallized arrays and is discussed in that context in a subsequent section.

There is a specific location in which metal at oxide steps is most likely to fail; this location is shown in Fig. 8. The microcrack occurs at the steep upper


FIG. 7. Electromigration open in A1 metal, under 1 t~ of deposited glass, due to current crowding at a corner. The arrow points to the open. The metal linewidth is 0.5 mil.

step produced by the photoengraving operation used to remove oxide from contact cut areas. This step is steep because the overlying phosphorus-containing glass from the emitter diffusion is considerably faster etching than the underlying pure thermally-grown SiO, . The probability of failures of the aluminum metal because of opens at this type of step is increased when the step is higher or steeper, when the angle of metal impingement during evaporation is not normal to the wafer surface, when the metal deposit is thin, when the linewidth over the step is small, when the photoengraving is not


EXPANDED CONTACl

"'7 CONTACT OUT 7

PHOSPHOSILICATE LAYER

FIG. 8. Schematic drawing of a microcrack at a contact cut.

adequately controlled, and when the circuit is subjected to high currents, high current pulses, or temperature cycling.

The phenomenon of microcrack formation at the upper step has been studied in some detail, and it has been shown that the effect occurs during evaporation (42, 43). Proposed solutions have been to remove all or part of the upper phosphosilicate glass layer produced by the emitter diffusion (44), to use line or multiple evaporation sources (4.9, to rotate substrates during evaporation, to use thicker layers of aluminum, and to use a substrate heater to maintain the silicon wafers at 300°C during evaporation (42,43).

The microcrack phenomenon' has been observed to occur with the Mo-Au metallization system as well as with A1 metal (37).

Microcracks are generally not detectable by conventional optical microscopy techniques, even at high magnification. One reason they are difficult to observe is that the crack is not normal to the surface. Scanning electron microscopy has been very effectively used in the study of the microcrack phenomenon (42, 43, 46, 47).

Another type of metallization failure mechanism can occur when excessive time or temperature or a combination of these is used during the contact alloying (sintering) operation used to form ohmic contacts between the aluminum and the silicon. Contact alloying is generally performed at below the A1-Si eutectic (48) temperature of 577"C, and thus a liquid phase is not formed (49). Solid-state dissolution of Si in Al does occur, particularly at the edges of the contact cut (50), and the Al-Si interface thus moves downward, as shown in Fig. 8. If overalloying has occurred, a discontinuity in the A1 is produced between A1 over SO, and Al at the edge of the contact region, causing a constriction in the cross-sectional area of the conductor stripe. In


contrast to microcracks, serious overalloying is readily evident from optical microscopy studies.

Figure 9 is a photomicrograph of a cross section of overalloyed A], and

FIG. 9. Photograph of a 90" rnetaIIurgica1 cross section of 1-p thick A1 metal that has penetrated the Si at the edge of the contact cut. The arrow points to the penetration into the silicon.

shows a penetration of the Al-Si interface of approximately 1 p. The overalloying type failure mechanism is particularly severe when metal stripes into the contact cut region are narrow rather than extending around all sides of the cut. This particular cause of failure has been discussed by a number of authors (46,47,50-52), and has been shown to be a result of overalloying or of excessive heat treatment at subsequent processing steps.

D. Aluminum Penetration

A failure mechanism that is related to overalloying arises from the tendency of A1 to spread laterally under the thermally grown SiOz during contact alloying (50, 52, 53).

In Fig. 10 the A 1 can be observedunder the thermally grownoxide alongside the A1 metallization as viewed from the top. This lateral spreading of the A1 as drawn in cross section in Fig. 1 1 has penetrated almost to the point of shorting the emitter-base junction. The crystallographic orientation of the surface of the device shown is (1 1 1 ) . Since the solid-state dissolution of Si in Al proceeds less rapidly along (1 1 1 ) planes, the limiting edges of the spreading A1 tend to be (1 1 1) planes, three sets of which intersect the wafer


FIG. 10. Top view of overalloying of Al-Si. The A1 has moved under the SiOz and is visible at the emitter contact cut. The arrow points to the overalloying under the oxide.

OXIDE

1 2 N SILICON

FIG. 11. Schematic drawing of overalloying of AI-Si under the oxide.

surface at 60" angles from each other. Shallow diffused devices are particularly susceptible to problems due to this lateral spreading effect (54).

Circuits in which excessive lateral spreading occurs are frequently susceptible to subsequent failure as a result of high localized current density at high field regions in devices.


Several techniques are being used to avoid lateral spreading problems, including more effective removal of Si02 from contact cut areas to permit successful alloying at lower temperatures, more conservative design rules and geometries, and the use of an Al-Si alloy instead of pure A1 for the metallization material (SZ).

If a device is operated under high stress or pulse conditions which produce localized temperatures in excess of the Al-Si eutectic temperature, 577°C dissolution of Si may destroy the device (55).

E. Metallization Systems Based on Gold

Considerable information is available on the reliability of the Mo-Au metallization system. The Mo-Au system has potential reliability problems due to the delineation techniques for this bimetal system (56). Undercutting of the Mo layer can occur, causing the possibility of solutionentrapmentand thus galvanic corrosion. This corrosion produces salts that have been observed to grow dendritically causing shorting between metallic conductors (57). The bimetal system in itself is a problem even when the undercutting is under control since with any nonhermetic packaging technique or with any hermetic package which leaks, galvanic corrosion, which could be enhanced during device operation, could cause shorts or open metallization.

Information has also been published on the reliability of the beam-lead metallization system Ti-Pt-Au (58) and on other systems which use a gold layer as the conductor (10, 38, 39, 57, 59).

Devices with gold-containing metallization can have localized formation of Au-Si eutectic (melting point 370°C) in regions where the barrier metal is not continuous. Such penetration of the Au degrades the electrical properties of the devices (57, 59).

F. Bulk Failure Mechanisms

Bulk effects, that is, phenomena occurring inside of the silicon, are sometimes cited as the cause of integrated circuit failures. There is considerable published evidence to substantiate that bulk defects can be a very significant factor affecting the yield of integrated circuits. Crystallographic defects can be a factor in the reliability of silicon devices which operate in the avalanche mode, or which are susceptible to second breakdown effects, but these possibilities do not pertain to typical commercially available integrated circuits.

Available evidence on failure mechanisms and their distribution at both normal and elevated stress levels does not support the conclusion that bulk defects of any kind, other than cracked chips, are a significant reliability factor in integrated circuits, whether SSI, MSI, or LSI. Published results


clearly show yield effects (60-62), but reliability effects, if any, must be inferred. This is not to imply that bulk defects are unimportant, but only to indicate that other failure mechanisms predominate in currently available integrated circuits.

One type of defect which may be classified as a bulk defect would be silicon cracks. Cracks in the chip, which primarily result during scribing, are a cause of integrated circuit failures (59).

G. Oxide Shorts

Some failures are attributable to shorts through the thermally grown oxide between the circuit metallization and the silicon. In general such shorts arise because of photolithographic problems which result in the formation of localized thin spots or very small pinholes in the oxide during the etching of contact cuts. Other causes may be mechanical damage to the oxide, and impurity- caused devitrification of local areas of SiO, . Oxide shorting may be aggravated by the tendency of aluminum to react to some extent with SiO, at temperatures of 400°C and above (55 ,6346) . The possibility of this reaction occurring is particularly important in MOS devices, and is discussed in additional detail in the section on MOS failure modes.

H. Surface Efects

Surface-related failure mechanisms arise because ofchanges in the electrical properties of the Si-Si02 interface. These changes may be due to ion migration in the thermally-grown oxide, ion migration along the oxide surface, dipole polarization effects, or charge-trapping effects. The most widely used types of digital bipolar integrated circuits, including typical RTL, DTL, TTL, and ECL circuits, are based on dopant densities of atoms/cm3 or higher (0.5 ohm-cm n-type or less), and are thus less susceptible to surface effects than are devices which employ higher resistivities or operate at higher voltages (such as MOS integrated circuits and some analog integrated circuits).

Figure 12 shows the relationship between substrate dopant density and the effective oxide charge density necessary to invert the silicon surface (67). Resistivity values are based on published mobility data (68).

Alkali ions are known to have a high mobility in thermally grown (amorphous) SiOz in an electric field (69), and thus alkali ion migration can cause reliability problems when integrated circuits are operated under conditions which produce elevated chip temperature plus an electrical field. In the absence of bias, the ion migration effects quickly anneal at elevated temperatures, and thus are not observed in some cases in which room temperature measurements are made on devices which were not allowed to cool under bias.


SPECIFIC RESISTIVITY, OHM-cm AT 25OC

LL 0

a m f 3 2

w

BULK DONOR DENSITY

FIG. 12. Plot of resistivity versus number of charges needed to invert n-type silicon.

Bipolar integrated circuits benefit from the fact that the phosphosilicate glass surface layer which is formed during emitter diffusion effectively getters alkali ions. Device reliability problems can occur if too much of the phosyho- silicate layer is removed during subsequent processing, or if an unusually large amount of alkali contamination is introduced on the device surface.

The advent of MOS integrated circuits has been accompanied by very in- tensive studies of the electrical properties of the Si-SiO, interface. It has been estimated that over 1500 pertinent published articles have appeared in the last ten years. Fortunately much of this information has been reviewed, and extensive review articles and bibliographies are available (70-74).

Surface-related device failures are frequently only partially characterized when the analysis of defective devices is made. They may be termed surface leakage, excess leakage, channeling, beta degradation, or recoverable failures. Usually devices can be restored to operating condition by baking at 200°C for several hours without bias. Sometimes recovery occurs at room temperature in a few days. The specific types of charge motion which can result in surface- related failures are reviewed in detail in the section on MOS failure mechanisms.


I. AI-Si Contacts

Some failures are caused by high resistance contacts between the A1 metallization and the silicon. The high resistance contact may be caused by contact windows which are too small, failure to remove all of the silicon dioxide from the contact cut area, or inadequate alloying time or temperature.

J . Radiation- Hardened Integrated Circuits

Radiation constitutes a special type of environmental stress to which integrated circuits are sometimes subjected. Radiation hardened bipolar integrated circuits are constructed by special techniques, including dielectric isolation, small geometry transistors, narrow basewidths, thin-film resistors, and special circuits (75, 76). Most of the oxide isolated circuits have been used for high reliability applications, and their reliability has been assessed in detail (77-79). A number of studies have been made to determine whether any new failure mechanisms exist in dielectrically isolated circuits of the type designed for radiation-hardened applications, and a number of reports are now available detailing the observed failure rates for SSI components. One new failure mechanism which has been observed in several studies (77, 78) is related to the occurrence of open metallization at the regions where metal conductors cross a trench at the edge of single-crystal regions. Failures occurred when wafer processing was not properly controlled, resulting in formation of a trench in those regions where the oxide isolation walls intersected the upper surface of the wafer.

MOS circuits are considerably more susceptible than bipolar circuits to radiation effects because of the susceptibility of MOS transistors to charge trapping effects in the SiO, when subjected to ionizing radiation. While a number of exploratory investigations of dielectrics which are less susceptible to radiation effects have been performed (80, Sl), radiation-hardened MOS integrated circuits are not now available, even in developmental quantities.

K. Reliability of Other Circuit Elements

The reliability of LSI arrays containing Al-Si Schottky barrier diodes has recently been evaluated experimentally. Based on stressing of devices at 1 50°C, it was concluded that the use of Al-Si Schottky barrier devices in LSI arrays poses no reliability problems (82).

The reliability of thin-film resistors of various types has been studied (83-85). Reported failure mechanisms include oxidation effects, contact effects, and surface ion migration effects.


111. MOS FAILURE MECHANISMS

A . Introduction

Since MOS integrated circuits have not been commercially available as long as bipolar integrated circuits, the amount of information on MOS failure mechanisms is less extensive than that on bipolar failure mechanisms. More- over, bipolar integrated circuits have been widely used for military and space applications which required high reliability and extensive testing and documen- tation. By contrast a considerably greater portion of MOS circuits are being used for commercial applications such as desk top calculators, small computers, and electronic organs. Considerable MOS reliability data is, however, available, including data on large numbers of LSI devices (86-88). The principal categories of failure are those attributable to oxide shorts and to surface effects. The predominance of these two types of failure mechanisms in MOS is not unexpected since MOS circuits contain substantial areas of thin oxide covered by metal, and since the resistivity of silicon substrates used for MOS circuits is high and the operating voltages are high.

B. Oxide Shorts

Life test data on MOS integrated circuits fabricated by a number of manufacturers show that oxide shorts are a significant cause of MOS integrated circuit failure (86, 87). The observed shorts can be divided into two distinct types: (1) shorts occurring as a result of electrical overstress, and (2) shorts occurring during operation within rated conditions. of voltage, temperature, and power dissipation. Those shorts which occur within rated conditions are caused by localized oxide defects. Devices which contain such localized defects can to a large extent be electrically screened at voltages higher than ratings to eliminate those devices which contain regions of oxide of marginal quality. On certain types of circuits, dynamic screening is necessary to attain voltage at internal circuit nodes.

C. Gate Oxide Breakdown

The gate oxide thickness in typical MOS integrated circuits ranges from approximately 0.1 p to 0.15 p (1000 to 1500 A), substrate dopant density is on the order of 10'' atoms/cm3, and applied potentials range up to 30 V (clock voltage). In contrast, the thinnest oxide in bipolar integrated circuits is the emitter glass, typically 0.5 p thick, substrate dopant density is on the order of 10l6 atoms/cm3, and applied potential is usually less than 10 V (Vcc).

ON FAILURE MECHANISMS IN INTEGRATED ClRCUlTS 99

The dielectric strength (89, 90) of amorphous S i 0 2 is on the order of lo7 V/cm, and thus the maximum applied voltage in MOS circuits corresponds to approximately one-fifth of that which would exceed the dielectric strength.

Localized regions in MOS circuits may be substantially thinner than the average gate oxide thickness, or may have a lower dielectric strength because of impurities and/or structural defects. Such regions will break down at voltages which are significantly lower than the 100 to 150 V required for breakdown of a high quality MOS gate oxide (92).

Any thin spots in the oxide may be made thinner bythereactionofAlmetal- lization with Si02 during alloying or during subsequent processing steps which are performed at temperatures greater than 400°C. It has been shown that the quality of the oxide is an important determinant of the rateat whichthesolid- state reaction of A1 with SiOz causes local penetration (65).

An example of the effect of localized gate oxide defects is provided by the data (91) shown in Fig. 13, where the distribution of devices which break down

30

t N I

0

10.0 mil n 1

FIG. 13. Plot of oxide -breakdown of varying area versus voltage.

at various voltages is shown for structures having areas of 0.1, 1, 10, and 100 mils' (6.5 x cm'). An area of 0.1 mil2 corresponds to the gate overlap area of both the source and drain regions in a single MOS transistor of the type typically used in MOS LSI arrays. In any reasonable process this area has low defect density, and the median breakdown voltage is approximately 120 V.

to 6.5 x


It can be seen in Fig. 13 that as the area of the structure increases to 1 mil2, and more particularly to 10 mil2, the distribution becomes bimodal, with breakdown at localized defects occurring at approximately 60 V in about half of the devices. At an area of 100 mils2, which corresponds to the total gate overlap area which may exist in an LSI product, a certain percentage of the devices break down below 30 V, and would constitute yield losses. Another percentage breaks down at 30 to 40 V; these represent potential reliability hazards. This type of information on oxide defects, which is most readily obtained using test patterns, has been used in the industry to improve fabrication procedures and to maintain process control (91).

Examination of devices which have been broken down by electrical stressing indicate, as shown in the photomicrograph in Fig. 14, that breakdown predictably occurs at the highest field regions (corners in this case).

Defects in the gate oxide, if present, will cause a random breakdown of the thin gate oxide as shown in Fig. 15.

FIG. 14. Oxide breakdown at high electric field points on MOS thin gate oxides as shown by the arrows. The A1 metal is 0.5 mil wide.


FIG. 15. Oxide breakdown at defects in the thin MOS gate oxide as shown by the arrows. A number of breakdowns have occurred. The A1 metal is 0.5 mil wide.

D. Static Electricity Eflects

MOS devices, because of very high input impedance and thin gate oxides, are susceptible to damage due to static electricity effects, voltage transient effects, and other conditions which may cause the voltage applied to the circuit to temporarily exceed the device maximum rating and break down the thin oxide between the gate metal and p + silicon. This effect has been termed “ zapping.”

Most commercially available MOS circuits include some form of input protection device on the circuit inputs. The input protection devices can provide a considerably increased resistance to static electricity effects. However, even the better input protection devices do not afford total protection against mishandling of devices which results in grossly exceeding the rated voltage levels, and thus handling precautions are advisable (92).

One type of input protection device which is widely used is a surface avalanche diode type structure which is designed to pass current by avalanche breakdown when applied potential exceeds a value on the order of 40 V. The


current-voltage characteristics of surface avalanche diodes have a tendency to “walk out ” to higher breakdown voltages during electrical testing at voltages above the avalanche breakdown voltage, or as a result of the effects of static electricity discharges. As a result the avalanche breakdown voltage of such devices may “ walk out ” to appreciably higher values, such that the device no longer offers the desired input protection. The drift effect occurs because the avaianche results in injection and trapping of electrons in the thermally grown SiOz near the Si-SiO, interface (93).

One type of input protection device which has a substantially lower resistance in the on condition and which is not susceptible to drift effects is based on a punchthrough-limited lateral pnp bipolar transistor specifically designed to have the appropriate p-to-p spacing to begin to pass current at approximately 40 V.

E. Surface Potential and Fast States

. The electrical properties of the Si-SiO, interface in MOS circuits are of critical importance in determining the performance and reliability of devices. Both the initial value of and the stability of the surface potential are the most important determinants of susceptibility of an integrated circuit to degradation or failure due to surface effects. The surface potential determines whether or not a channel exists, influences the carrier generation or recombination rate, influences the threshold voltage of MOS transistors, and influences the width of the depletion layer at the edge of a p-n junction (67). Changes in the junction depletion layer width result in changes in: (1) source-to-drain punchthrough voltage of MOS transistors, (2) diode breakdown voltage of p-n junctions, ( 3 ) lateral punchthrough voltage between adjacent parts of a complex microcircuit structure, and (4) transconductance of MOS transistors (67).

Fast states at the Si-Si02 interface are important because they influence the surface generation and recombination rates, the surface potential, and the temperature coefficient of the surface potential.

F, Gate Threshold Voltage Drift

Historically, surface-related planar silicon device instability, such as channel formation, was initially attributed to migration of ions along the surface of the silicon dioxide (at the Si0,-ambient interface) (94).

In early MOS transistors severe changes in threshold voltages were observed which could not be attributed to surface-ion migration effects. It was learned (95, 96) that sodium-ion migration in the oxide at elevated temperatures in an electrical field was the cause of the observed MOS threshold voltage instability. The migration of sodium ions in an electric field has a high activation energy (96) (32 kcal/mole), and threshold voltage drift due to


mobile ions can thus be accelerated very considerably by increasing the temperature. Tests of threshold voltage stability can be performed in minutes at 300°C.

It is also possible for mobile hydrogen ions to exist in thermally grown oxides, and to produce instability in MOS devices at room temperature (25°C) (97).

The industry now produces p-channel MOS integrated circuits which are essentially free of sodium ion drift effects in the gate oxide and thus have stable values of gate threshold voltage. This is accomplished either by using MOS manufacturing techniques which avoid introduction of alkali-ion contamination, or by keeping alkali-ion contamination at a low level and then employing a P,O, deposition step to getter the sodium. Silicon nitride (15) or aluminum oxide (98) has been used as a barrier to avoid the effects of alkali-ion contamination of completed devices.

G . Field Inversion Voltage

In p-channel MOS devices, where normal biasing makes the metal lines negative relative to the silicon substrate, the migration of alkali ions would be expected to increase the field inversion voltage and thus not cause reliability problems unless alkali-ion contamination were present in very large amounts. Anions do not have appreciable mobility in amorphous SiOz at temperatures up to 300"C, and have thus not been a factor in reliability of MOS devices. It has recently been shown (99) that p-channel MOS circuits can exhibit a field inversion voltage decrease as a result of high-temperature reverse-bias aging, even though the gate inversion voltage on the same device is quite stable. This instability, which might be termed a negative-ion-type instability, has been investigated in detail. A proposed model for the effect involves immobile negative ions such as chloride in the SiOz near the Si-SiOz interface, plus mobile sodium-ion countercharges in the same vicinity. Application of a negative potential to the metal at an elevated temperature, for example 150"C, causes the sodium ions to move toward the metal, thereby decreasing the surface potential and lowering the field inversion voltage (99).

Techniques exist for preparing MOS field oxides inp-channel MOS circuits in which the negative-ion-type instability effect does not exist or is insignificant in magnitude. Such techniques have not, however, been used for all MOS devices presently being used in electronic equipment.

H. Surjiace-fon Migration

The migration of ions along the surface of an oxide can affect the electrical properties of the underlying Si-SiOz interface in all types of planar silicon devices. In general the importance of surface-ion effects is increased in devices


with thinner insulator layers (loo), higher resistivity silicon substrates, lower immobile charge density (&) in the oxide, or with insulator materials of higher dielectric constant (101). Figure 16 shows a cross-sectional view of a p-n junction with a channel formed.

A- SURFACE IONS - - - - - - DIELECTRIC

I I

N-TYPE SILICON

-DEPLETION LAYER

- F A S T STATES INVOLVED I N GENERATION OR RECOMBINATION O F CARRIERS

FIG. 16. Schematic drawing of device with leakage due to surface carrier generation.

Surface-ion migration effects have also been shown to be a factor in metallization corrosion effects, metallic transport by electrolytic migration (102- 204), and the instability of thin-film resistors (83, 84).

I. Failures Due to Surface-Ion Migration Plus Localized Defects

The activation, during device life, of localized defects as a result of surface- ion migration is one possible cause of failure of integrated circuits. Certain types of localized defects, if present within the depletion layer of thep-n junction of any active device, will prevent the device from operating at rated conditions. The same types of localized defects in areas beyond the depletion layers would have no immediate effect on the electrical performance of the circuit. As a result of surface-ion migration, the depletion layer will ultimately widen at the surface in unmetallized areas. There is then a certain probability that a localized defect will be present in the additional area which became


electrically active, and will cause excessive leakage current to flow. This condition is illustrated in Fig. 17. The dotted line shows the initial location of the intersection of the outer edge of the depletion layer of a reverse-biased p-n junction with the Si-Si02 interface. As manufactured, the p-n junction area is defined by the area of the cuts during thep-type diffusion and by the amount of lateral diffusion out from the cuts during processing. The process also results in an immobile positive charge in the oxide which causes the depletion layer at the surface to be slightly narrower than the depletion layer in the bulk. When negative bias is applied to the metallization during circuit operation, there is a slow buildup of negative charge over unmetallized regions of the oxide adjacent to metal lines. With time the potential at the surface in unmetallized areas can asymptotically approach that of the negative potential of metallization lines. As a result the depletion layer at the surface on the

s HIGHER IN UNMETALLIZED AREAS

\ s LOW - UNDER METALLIZATION

-CONTACT CUT

-METALLIZATION

FIG. 17. Schematic drawing of depletion layer motion causing a failure when it contacts the silicon defect.


n-type side of p-n junctions widens somewhat. If a localized defect occurs in this incremental area, it can create a problem during the operating life of the device as a result of the interaction of surface-ion migration effects with localized defects beyond the junction. The probability of a defect occurring somewhere in an array within the incremental areas is higher for LSI than for SSI. Possible categories of localized defects include localized thin spots in the dielectric, localized regions of higher or lower Qss or N,, and localized minority carrier genereration sites.

J. Conductive Particles

The high impedance of MOS devices makes them more susceptible to failure as a result of electrical leakage between adjacent metal lines caused by conductive particles or contaminants. Glass passivation which covers all areas of the chip except the bonding pad areas has been very effective in eliminating this problem (49). Not all commercially available MOS circuits, however, have continuous glass passivation.

K. Failure Mechanisms of Other Types of MOS Devices

A room temperature threshold shift has been observed in silicon-gate MOS devices fabricated by certain types of processing sequences (105).

Under certain temperature cycling conditions in early manufactured devices, opens have been observed in the polycrystalline silicon conductor lines of silicon-gate devices where those lines cross oxide steps. Silicon has a much higher linear thermal coefficient of expansion than silicon dioxide, and thus polycrystalline silicon conductor lines crossing the edge of an oxide step are in tension at low temperatures. This effect may be insidious in that the electrical open may only exist at temperatures below room temperature. The reliability of polycrystalline silicon conductors over oxide steps is currently being investigated in the industry. One approach to the problem which has been implemented in developmental devices is to use a tapering process (91, 106- 108) to obtain a beveled edge in the photolithographically delineated thermally grown SiOz.

Metal-nitride-oxide-silicon (MNOS) transistors have been reported to have unstable threshold voltage, due to the possibility of charge transport and storage in the two layer dielectric system, unless the fabrication process is controlled to insure that the deposited silicon nitride conductivity is low (109). The maximum applied voltage should also be kept low to insure device stability (109).


IV. MULTILEVEL METALLIZATION

A . Introduction

A number of integrated circuits products containing two and three levels of metallization are now commercially available.

Most of the multilevel-metallized arrays available to date have employed aluminum for all levels. Products based on the Mo-Au metallization system, and using Mo-Au-Mo for the first-level metallization are also available (37, 110). Beam-lead crossovers have been shown to be feasible ( 2 2 1 , 222), but are not used in currently available beam-lead products.

The deposited dielectric between levels of metallization is typically silicon dioxide (37, 206, 207) or phosphosilicate glass (113).

The sequence of steps used to prepare multilevel arrays typically consists (86, 123, 214) of the following steps after delineation and contact alloying of the first-level metal: deposition of a dielectric layer by chemical vapor plating or rf sputtering, photolithographic delineation of openings (vias) where contacts are desired to first-level metal, and deposition and delineation of second- level metal. If an additional layer of metallization is desired, the steps of dielectric deposition, delineation, metal deposition, and delineation are repeated.

The dielectric deposition process, which must be compatible with the properties and temperature limitations of the underlying metallized and al- loyed circuit, is generally performed at a temperature of less than 500°C. A typical process used is the oxidation of silane at 400°C to form an amorphous silicon dioxide layer (3, 86). The second-level metal deposition temperature or subsequent heat treatment temperature is usually also under 500°C. A passivation glass layer is frequently deposited over the upper metallization layer.

Because of the widespread interest in multilevel metallization and the realization of its increasing importance, a considerable number of studies have been made, and are continuing, to develop multilevel processes and to assess their reliability (92, 207, 210). The use of test patterns, as discussed in a subsequent section, has accelerated the development and evaluation of multilevel designs, structures, materials, and processes.

All presently available multilevel-metallized integrated circuit arrays are based on bipolar integrated circuits. A number of silicon-gate MOS arrays are also available, and these are sometimes considered to be equivalent to multilevel arrays in that they can contain three levels of interconnections (the pattern of diffused interconnections in the single-crystal silicon, the pattern in the delineated and doped polycrystalline silicon layer over thermally grown


silicon dioxide, and the A1 metallization pattern, separated from the polycrystalline silicon by chemical vapor-deposited silicon dioxide). The silicon gate process as presently implemented, while providing two conducting layers one of which has a relatively high sheet resitsance plus one metal layer, does not provide low resistance metal-over-metal crossovers.

A number of other types of multilevel metalkation systems and process sequences are under development (37,110-112,115), but reliability data is not yet available on these processes.

The additional processing steps required to manufacture multilevel-metallized large-scale arrays can introduce a number of new failure mechanisms, and may also increase or reduce the significance of known failure mechanisms

The effects of multilevel metallization processes on the reliability of LSI arrays may be separated into three broad categories: (1) surface effects, (2) shorts or increased leakage through or along dielectrics, and (3) opens or increased series resistance in conductors (86).

(86).

B. Surface Efects

The deposited second layer of insulator material must cover the first layer of metal interconnections, and thus its formation requires a technique other than thermal oxidation (which is used for all first- or single-insulator layers in microcircuits). It is essential that the materials and processes used to deposit and photolithographically delineate the deposited dielectric do not adversely affect the properties of the Si-Si02 interface either because of a decrease in stability or b cause of a parameter shift which reduces the tolerance to in-

Figure 18 shows a model of charge distribution in a planar structure with two insulator and two metal layers (67), and indicates the possible complexity of surface effects.

The effects of the deposited dielectric in LSI on the electrical properties of the Si-Si02 interface are quite similar to those which occur when dielectrics are deposited for other reasons, most notably, for glass passivation of single- level-metallized integrated circuits. Accordingly, there is a considerable a- mount of available information on the effects of deposited dielectrics which can be used to make certain judgements relative to their effects on LSI reliability (3, 113, 116).

Specific LSI failure mechanisms due to surface effects caused by the dielectric deposition process include a substantial shift in surface potential as a result of the effect of glass deposition processing conditions on the immobile charge density, Q,,, and a severe decrease in the stability of the surface potential under bias at elevated temperatures, due to alkali ion contamination

stability (67). 9


TRAPS AT OXIDE

INTERFACE MOBILE CHARGES THE OXIDE-SILICON OF INACTIVATING IONS IONS OXIDE INTERFACE FAST STATES

OTHER FACTORS SCALES

= LOMICRON Cl0,WOi) I METAL- SEMICDNOUCTOR WORK FUNCTION

INSULATOR ~ INSULATOR CONTACT POTENTIAL

DIFFERENCE VERTICAL.. . . . .

HORIZONTAL." - ~ 6 . 0 MICRONS (0.25MILI

FIG. 18. Charge types and their distribution in the oxides utilized in a two-level A1 metal system.

introduced during glass deposition (67). Phosphosilicate glass, which has the ability to getter or immobilize alkali ions, has been used to insure against sodium ion contamination effects (113).

C. Oxide Shorts between Metallization Layers

Shorts or leakage paths through the deposited dielectric layer can be a mechanism of failure in multilevel-metallized integrated circuits (86). The ability of deposited dielectrics to completely cover the surface, including the edges of delineated first-level metal lines, and to be free of pinholes and localized thin spots, depends on the properties of the dielectric and the substrate cleaning (3), the process used for deposition, the degree of roughness of the metal, the height of the underlying steps (3), contour of the edge of the steps (91, 106, 107), freedom from dust particles, substrate properties (3), the mechanical stress in the deposited film, and the extent of metal-dielectric interaction which occurs by solid-state reaction at elevated temperatures during processing.

Many dielectric films are in tension as deposited (113, 117-119). If the tensile stress is too great the film will crack as deposited or during a subsequent processing step which is performed at a temperature greater than the deposition temperature. Figure 19 shows a deposited dielectric film in a multilevel- metallization structure which cracked because of tensile stress. It is possible to obtain low stress, chemical vapor-deposited films by the adjustment of deposition conditions or film composition (108, 113, 119).


FIG. 19. Cracked interlevel dielectric between two levels of A1 metal. The narrowest metal linewidth is 0.5 mil.

D. Contact Resistance between Layers of Metallization in Vias

If multilevel-metallization processes are not properly controlled, a high contact resistance will occur in some of the vias between the first and second levels of metallization (49, 120). This high resistance can be attributed, in the case of an A1 metallization system, to the presence of a layer of A1,0, over


much of the area of first-level A1 at the bottom of the via cut, and thus a reduced cross-sectional area of metal-metal contact. During device operation this type of contact could be noisy and would be particularly susceptible to failure due to localized Joule heating or electromigration effects. Because of the mismatch in thermal coefficient of expansion between A1 and Si or S O z , the vias, if not properly fabricated, may also tend to become open when the device is cycled to lower temperatures.

E. Metallization over Integrated Circuit Topography

Metal-metal crossovers in multilevel arrays must be properly designed and fabricated to insure good yields as well as high reliability. Localized constrictions in the cross-sectional area of second-level metal lines where they cross oxide steps have been a major concern in selecting processes and designs for multilevel-metallized integrated circuits. Two specific regions of particular concern are the regions where metal conductor stripes cross the edges of photolithographically delineated vias in the deposited dielectric, and regions where the second-level conductor stripes cross the steps due to the edges ofdelineated first-level metallization lines. Also, other steps result from various diffusion and oxide cuts in the surface of the substrate.

The problem of obtaining adequate metal coverage of steep steps is very similar to the effect which can occur in first-level metallization at the edge of contact cuts. This microcrack effect was discussed in Section I1 C in regard to open metal at oxide steps. The step created by delineated first-level metal tends to be rather steep, and is sometimes increased in steepness by the deposited dielectric (106, 114). For example, Fig. 20 shows a cross-sectional view of vapor-plated dielectric coverage of the edges of steps. As might be expected,

FIG. 20. Photograph of a 90" metallurgical cross section of two levels of A1 metal. The top level is 2 p thick. The lack of taper of the first-level metal caused an open in the second- level metal at the points indicated by the arrows.


steep steps are difficult to cover with a continuous metallization film which will not have reliability problems. In Fig. 20 a 2-p thick, second-level metallization layer is crossing a delineated I-p thick first-level metal line. While the A1 film may be continuous over steps, the thin cross-sectional area and presence of cracks could adversely affect device reliability, especially under conditions of high current density or temperature cycling over a wide range.

Figure 21 is a scanning electron micrograph of a three-level metallized

FIG. 21. Microcrack in the A1 metal at a step in the topography where third-level metal crosses delineated second-level metal and the interlevel dielectric.


integrated circuit structure. The increased thickness of the vapor-deposited dielectric along the edge of the second-level metal line is evident. The third- level metal line clearly has a very severe crack at the edge of the step. The constriction in metal area at the edge of the step can take a number of forms, such as notching, perforation, or tunnel formation.

One very effective technique for avoiding the problems of open metallization at crossovers is to use a process which produces a low-angle tapered

FIG. 22. Top view of tapered first-level A1 metal lines. The metal linewidth is 0.5 mil at the base.

114 GEORGE L

. SCH

NA

BL

E A

ND

RA

LPH

S. KEEN

a e k FIG. 23. Two levels of A1 metal on a SPO199A MSI integrated circuit having the first-level metal tapered. The

narrowest metal linewidth is 0.5 mil at the base. The arrow points to tapered first-level metal.


FIG. 24. Photograph of a 90" metallurgical cross section of tapered first-level A1 metal 1 p thick. The second-level metal and the interlevel dielectric are each 1 p thick. The arrow points to a tapered first-level metal line.

edge in the delineated underlying metal. This type of process has been reported by a number of investigators (91,106-108), and is being used by several manufacturers in fabrication of multilevel-metallized integrated circuits (106, 108). Figure 22 shows an optical micrograph of a tapered A1 metal pattern. Figure 23 is a top view of a completed multilevel-metallized structure with tapered first-level metal. Figure 24 is a cross-sectional view of metal-metal crossovers in a structure where the first-level metal had a low-angle taper.

A number of techniques have been used to obtain better coverage of the edges of via cuts (91, 110). The most effective means to insure good coverage of the oxide edge of via cuts is to use a technique which produces a taper of the edge of the delineated dielectric layer. Figure 25 shows the edge of a 1-p thick SiOz layer delineated by conventional techniques. Figure 26 shows the edge of an oxide layer delineated by a special technique which produces a low angle relative to the plane of the substrate. The photographs in Figs.25and26 were both taken using monochromatic light (Na,).

F. Discretionary Wiring

Discretionary wiring or discretionary routing is a multilevel metallization technique which involves preparation of a unique metallization pattern to interconnect only those logic cells which previously were shown by dynamic and static testing to be functional. The technique involves probe testing of


F I ~ . 25. Top-view photograph of a typical photolithographically delineated oxide. The oxide is 1 p thick and 10 mils on each side.

each logic cell on each wafer after the first-level metal is delineated, computer aided preparation of unique interconnection masks, and fabrication of the multilevel-metallized structure using the unique masks which were designed for use with each particular wafer. In contrast to this approach, most of the integrated circuit industry uses the " 100 % yield " approach for fabrication of complex arrays, with each array made using the same via and metallization masks, and testing performed only after delineation of the uppermost metallization layer.

Discretionary wiring provides an approach by which more complex multilevel arrays can be manufactured by currently attainable component or gate yields. There are, however, several economic and reliability limitations in discretionary wiring (3). Since the test probes gouge the test pads in the first


FIG. 26. Top-view photograph of a photolithographically delineated tapered oxide taken in 5890 A light (Nan). The oxide is 1 p thick and has a 5" taper.

level, it is necessary to avoid potential shorts between the first and second levels by using design rules which prohibit running second-level metal over first-level pads. Another limitation is that the completed device has an interconnection pattern and gate usage different from any other device, and thus, because of different interconnection path lengths, the chip may not necessarily have the same reliability characteristics as other devices since the parasitic resistance and capacitance and the magnitude of thermal gradients depend on the interconnection path length.


V. INTEGRATED CIRCUIT ASSEMBLY

A . Introduction

Most LSI array chips are assembled by the same sequence as SSI circuits. The sequence involves scribing, chip-to-package bonding, wire bonding, and then hermetic sealing of the package. While wire bonds are most widely used to make the interconnection between the chip and package in integrated circuits, other techniques are also extensively used. In particular, flip chip (face down bonding ) techniques are used by a number of manufacturers (122), and have been very effectively employed by one large manufacturer. The beam- lead sealed-junction approach (I1,12) is being used by several manufacturers.

Wire bonds are almost all made by thermocompression bonding of gold wires to Al-metallized chips (or to Mo-Au metallized chips) or by ultrasonic bonding of aluminum wire to Al-metallized chips (21).

Wire bond failure constitutes one of the principal causes of failure of integrated circuits of conventional complexity.

B. Chip-to-Package Bonds

The chip-to-package bond provides mechanical support for the silicon chip, and provide; the principal path for heat flow out of the silicon chip. In many cases the chip-to-package bond also provides the electrical contact to the substrate. Integrated circuit failures may be caused by deficiencies in any of these bond functions (21).

Chip-to-package bonds are almost always formed at elevated temperatures which result in melting of a fusable material. Most commonly Au-Si alloy, which forms a eutectic melting at 370°C, is the material which forms the chip bond. Other materials which may be used include the eutectics of Au-Ge, Au-Sn, Sn-Pb, and Al-Ge (75, 122) and low melting glasses and epoxy materials (21).

Low strength chip-to-leader bonds have in some cases been a significant cause of integrated circuit failure. In general these failures can be attributed to lack of adequate process controls during parts preparation or during the bonding operation.

Voids, which can occur in the solder of the chip-to-package bond as a result of unsatisfactory chip bonding conditions, can cause significantly increased thermal resistance and therefore degrade device reliability. The trend in LSI toward greater power densities makes it more important to reproduc- ibly achieve chip-to-package bonds which are free of voids. Visual inspection of the solder fillet at the edge of the chip, x-ray scanning techniques, and infrared emission plotters have been used to insure high quality chip-to-package


bonds. Thermal resistance measurements could also be used where high reliability is required.

Failures have also been attributed to cracked chips and to the presence of solder balls which formed during chip-to-package bonding.

The incidence of chip-to-package bond failures is generally much lower than that of wire bond failures. The use of increasingly large chip sizes in LSI will, however, require greater attention to the possibility of detrimental stress arising from mismatch in linear thermal coefficient of expansion of the chip relative to that of the substrate.

C. Gold Wire Bonds

The failure mechanisms in Au wire bonds to Al-metallized chips have been the subject of a rather large number of studies during the past ten years (21, 49, 123, 124). Most of these studies have been concerned with the interaction of Au and A1 at wire bond interfaces to form intermetallic compounds. The interaction was termed “purple plague” in early work because one of the compounds formed is the purple phase AuAI, . The loss of strength and increase in resistance of Au wire bonds to A1 was initially attributed to the presence of brittle intermetallic compounds. Subsequently it was shown that Au-A1 interaction was accompanied by void formation due to the Kirkendall effect (123, 125, 226). The solid-state diffusion of Au and A1 to form Au-A1 intermetallic compounds can produce voids in three locations : between the Au and the Au-rich phases (126-128), in the area immediately beyond the area of Au-to-A1 contact, and in the A1 well beyond the actual bond (21, 129). In multilevel-metallized arrays, opens due to the Kirkendall effect have been observed in A1 in vias (86).

It has generally been concluded that Au to A1 thermocompression bonds can be strong and reliable if completed devices are not subjected to storage or operating temperature in excess of 150°C. Considerable data is available on the activation energy for Au-AI interaction (127, 130). Recent data has permitted a better understanding of some observed phenomena (131) such as the effects of ambients (128). It has been reported that when 0, or water vapor is present in the ambient of the chip, an oxidation of the A1 will occur and limit the surface diffusion of the A1 to the Au wire bond (128). The activation energy for surface diffusion and grain boundary diffusion in small-grain films of A1 is 11 kcal/mole, while the bulk or self-diffusion of A1 is 34 kcal/mole (30). Thus, when surface diffusion is limited the rate of Au-A1 compound formation will also be retarded.

Some data is available on the reliability of Au bonds to metallization systems other than A1 (56).


D. Aluminum Wire Bonds

The wire used for ultrasonic wire bonding of integrated circuits is an alloy containing 1 % Si in Al. The purpose of the Si is to increase wire hardness.

The reliability of A1 wire bonds has been compared to that of Au wire bonds, and it has been shown that with proper controls, A1 wire bonds can be at least as reliable as Au wire bonds.

Most Al-to-A1 wire bond failures can be attributed to overbonding, underbonding (122), cracks at the heel of the bond, misalignment, or contamination (132). Much progress has been made in understanding the factors which are the underlying causes of the failure of ultrasonic bonds. In particular, the importance of controlling wire bonding conditions and wire properties has been demonstrated in recent work (122, 132-136).

Some failures of A1 wire bonds to Au-plated Kovar (Fe-Ni-Co alloy) posts or pads of hermetic packages have also been observed (77). The failure mechanism in this case can be due to application of excessive temperatures or to a combination of underbonding and voids at or near the interface of the Au-rich phases due to Kirkendall effect.

The specific failure rates of A1 wire bonds have been compiled in a number of publications. Failure rate depends on the stress applied, thetype ofpackage, device manufacturer, and many other factors. Failure rates ranging from 0.001 to 0.0001 % per thousand hours per wire have been reported (137, 138).

Other mechanisms of wire failure include precipitation of excessively large silicon crystallites at grain boundaries in the A l - l x Si wire (132, 133, 135), and fatigue due to localized bending caused by current pulses which cause Joule heating and thus thermal expansion of the wire (139).

An A1 wire bond system in which the hardening agent in the wire is 1 % Mg has been studied recently, and bonds made with this system have been reported (140) to be mechanically superior to those made with that of the A1-Si wire after 1000 hr of aging at 300°C.

E. Assembly Systems Based on Techniques Other than Wire Bonding

While wire bonding constitutes the principal means for assembly of integrated circuits of various degrees of complexity, a number of other techniques are used in volume production of integrated circuits. Most notable of these are a number of flip chip techniques (face-down bonding) (121), beam-lead techniques, and " spider " techniques.

Information is available on the basic beam-lead sealed-junction technology (11, 12), and also on a number of variations in technology such as beam-lead substrates, crossover techniques, and A1 beam-lead techniques, and techniques which are applicable to MOS devices (141).


Accelerated stress tests of beam-lead sealed-junction devices have shown a failure mechanism due to penetration of the silicon by platinum, causing shorting of the junctions (58). This process has an activation energy of 41 kcal/mole. Extrapolation of test data can be performed to predict that a failure rate of 0.001 %/lo00 hr can be achieved for beam-lead sealed-junction devices at even higher junction temperatures than with hermetically sealed devices (58). A number of other possible beam-lead failure mechanisms have also been described in the literature (142).

Beam-lead devices have been reported to be comparable to high reliability devices having wire leads in overall ability to withstand shock (143).

Very good reliability has been reported for three-terminal transistor chips which are face-down bonded by the copper ball chip-joining technique, with a failure rate of about 0.00004 %/lo00 hr at a 90 % confidence level (144). Laboratory tests have predicted a considerably better reliability for chips bonded by the controlled collapse technique, with a chip failure rate due to solder fatigue of the interconnections predicted to be lo-’ %/lo00 hr (144).

The “ spider’’ bonding system uses an aluminum lead frame which is ultra- sonically bonded to the pads on the chip (145). The chip is then held by the lead frame, which is designed so that the leads can be welded into a package and sealed. The package lead frame is Au clad. While specific reliability figures have not been published, the system contains no new metallurgical couples which have not previously been investigated.

F. Testing

The electrical testing of LSI circuits with many pins or leads presents some formidable problems (146, 147). One problem is that in complex logic circuits it is not always possible to completely functional test all parts of the circuit in a reasonable period of time (9). Computer aided techniques have been used to establish test sequences which have a high probability of detecting circuits with defective gates. To a large extent LSI circuits have been designed and partitioned withlittle consideration given to testing or to reliability assessment. One approach which can be used is to provide additional pins or leads to bring out certain internal portions of the circuit specifically to facilitate functional testing or to permit reliability evaluations.

G. Packages

Most LSI circuits are being assembled in packages which are hermetically sealed. The most widely used packages are TO-5, various types of flat and of dual in-line packages. Plastic encapsulation, which has been widely used for bipolar integrated circuits of conventional complexity (including flip chip and


beam-lead devices as well as wire bonded SSI products), has not been widely used for LSI products.

Failure mechanisms attributable to conventional hermetically sealed packages include package leakage, presence of corrosive or ionic contaminants, presence of loose particles, poor adhesion of package plating (typically gold) to the underlying Fe-Ni or Fe-Ni-Co alloy, broken leads, and electrical leakage across the surface of the package dielectric.

Failure mechanisms known to exist in plastic encapsulated SSI products (Z48-15Z), such as wires damaged due to mechanical stresses applied by the plastic, and corrosion and ion migration effects due to lack of hermeticity and ionic impurities in the plastic, are at least as serious with LSI chips.

Packages specifically designed for LSI products, and containing in some cases more than 50 or 100 pins, have been designed and produced in limited quantities. Some of the initially offered LSI packages have had reliability problems of various types (151, Z52). To a large extent these problems will be overcome with increased manufacturing experience.

VI. INTEGRATED CIRCUIT RELIABILITY

A . Introduction

The rate of failure of integrated circuits depends on a large number of factors such as the type of device; the design, materials, and process used; the manufacturer and date and lot; the nature and conditions of the stress applied, and the definition of failure. Accordingly, any reported failure rates must be accompanied by a substantial amount of other information to permit assessment of their applicability to a given situation or to compare them with other reliability information. An example of the differences in failure rate for electrically similar devices obtained from five different manufacturers is shown in Table 111, which is based on recently published data (22).

TABLE 111

ELECTRICALLY SIMILAR

DIFFERENT VENDORS (22)

V e n d o r F a i l u r e r a t e

FAILURE RATES OF

INTEGRATED CIRCUITS FROM

A 18.3 B 1.3 C 0.1 D 3.1 E 1.1


B. Integrated Circuit Failure Rates

The effect of temperature on the failure rate also varies with a number of factors. The activation energy for many failure mechanisms is known, but it is necessary to know which mechanism is the principal determinant of the failure rate under the conditions of interest. An overall activation energy of 4.6 kcal/mole has been reported to be applicable to bipolar silicon integrated circuits (153). A bipolar integrated circuit failure rate of 0.03 %/lo00 hr was recently reported for 28,000 devices with an accumulated 147 million device hours of operation at an ambient temperature of 125°C (154).

Table IV illustrates the observed effect (22) of bipolar integrated circuit

TABLE IV

EFFECT OF INCREASING INTEGRATED CIRCUIT (22) COMPLEXITY ON FAILURE RATE

Integrated Number Total ofcatas- number % complexity Quan- circuit

factor tested failures failures ( T o )

Failed tity description trophic of Device

8-input positive

Quad 2-input positive

Quad-2 AND-OR-INVERT

Dual master/slave flip-

NAND gate 658 0 1 0.15 1

NAND gate 501 5 4 25 0.5 2

gate with expanders 814 1 10 1.2 3

flop 3556 1 1 67 1.9 4

complexity on failure rates, for circuits with a coniplexity factor (n,) (22, 153) ranging up to 4.

Available data on failure rates of complex MOS integrated (86-88, 155) circuits indicate failure rates ranging from on the order of 0.01 to 1 % per thousand hours. Recent high-stress life tests by one MOS manufacturer have accumulated over 2.8 million device hours with a demonstrated functional failure rate of less than 0.4%/1000 hr on LSI MOS devices of a complexity of 200 gates/chip (156).

Plastic encapsulated complementary MOS devices have been reported to have a failure rate of 0.3 %/lo00 hr at a 55°C case temperature (152).

Several investigators have concluded that the reliability of MOS integrated circuits is approximately equal to that of bipolar integrated circuits of equal complexity (23, 88).


C. Quality Assurance

The integrated circuit manufacturing industry has employed many techniques to improve the quality of integrated circuits. These techniques have ranged from sophisticated in-process controls to brute force " torture tests " on the finished product. The increasing importance of MSI and LSI has necessitated the development of improved means for product assurance, and has led to many processing improvements which were specifically motivated by the requirement for greater reliability. The reliability requirements of LSI have led to increasing dependence on advanced instrumental analytical techniques, and the increased usage of test patterns (91, 157).

D . Test Structures

Test structures are made using patterns specifically designed to provide information about various aspects of integrated circuit processes and the results they accomplish (86, 91, 101, 113, 158). The use of test structures to assess possible LSI failure mechanisms, to evaluate and control materials and processes, and to determine product reliability is now well established in the industry (86,159). In some cases, test structures are used on every chip, and in other cases several test patterns are used on every wafer. In some processes an occasional wafer containing test vehicles only is processed.

Test structures are commonly used on MOS circuit chips, but infrequently on bipolar chips. Figure 27 shows an MOS LSI chip with several test transistors along the edge.

The information obtainable from test patterns includes information about bulk effects (that is, effects in the silicon), information about surface effects (phenomena at the Si-Si02 interface), dielectric effects (effects in SiOz or in other insulators); and metallization effects (phenomena in aluminum or other metallization systems).

There are two general types of information obtainable from test structures. One is the average properties of the semiconductor, oxide, and metal regions on the wafers; the other is information about properties dependent on the incidence of localized defects (91). Average properties, which can be obtained from relatively small area test vehicles, include doping density (ND), sheet resistivity of diffused regions (p,) , oxide charge (Q,,), oxide charge stability ( Q J , surface recombination velocity (s), and discrete device parameters (Z, , V,, , p, VGsT). Test vehicles can also provide information about oxide breakdown voltage, metallization sheet resistivity, via resistance, and related parameters. The yield and reliability of complex integrated circuits is also determined or limited, to a large extent, by the presence of localized defects. Larger area test vehicles can provide information about oxide defect density,


FIG. 27. A pL5R100 dual 50-bit MOS shift register. The arrows point to test vehicles which are located at the chip periphery. The narrowest A1 metal linewidth is 0.4 mil.

localized variations in Q,, , localized avalanche or high generation regions, or localized areas of open or constricted metal at steps.

Figures 28 and 29 illustrate two examples of test vehicles that were designed for use in MOS processing. For the test vehicle in Fig. 28 the tests are designed


FIG. 28. Test vehicle for monitoring physical properties such as metal-to-silicon contact resistance, metal thickness, oxide thickness, and dielectric breakdown.

to provide information about material properties such as oxide breakdown strength, conductor and diffused layer resistivity, contact resistance, and film thickness (147, 159). For the test vehicle in Fig. 29, the tests are designed to provide information about surface phenomena such as mobile and immobile charge density, fast state density and surface ions, and the effect that those


FIG. 29. Test vehicle for monitoring the MOS characteristics of silicon-oxide interfaces.

phenomena have on device parameters such as threshold voltage and surface breakdown voltage (113, 159).

E. Failure Analysis

The analyses of devices which fail life tests, screening tests, and incom- ing inspections, and those which fail during equipment usage provide an important source of information which can be the basis for substantial product


improvement (160-162). To obtain maximum benefits and to avoid misleading conclusions, the failed devices must be handled very carefully (92).

F. E e c t of LSI Trends on Reliability

In addition to multilevel metallization, the trends in LSI technology include a number of changes which, if not properly implemented, would tend to decrease reliability. Trends in this category might include new materials, new processes, deposited dielectrics, smaller geometry, higher functional packing density, larger chip size, new assembly and packaging techniques, advanced circuitry, greater power density, less complete visual inspection, new circuit forms, less complete functional testing, and lower completed device unit volume production (3, 86,91, 157). These trends can introduce new failure mechanisms or increase susceptibility to known failure mechanisms. Proper in-process controls, screens, and tests are necessary to insure that reliability per gate on the chip is not adversely affected by any of the changes made to attain LSI.

The reliability benefits of early LSI products have been largely attained by a reduction in the number of interconnections in the system (interconnections external to the chip). The reliability improvement is attained because wire bonds are one of the principal causes of failure of conventional integrated circuits. To the extent that the system can be partitioned to significantly increase the gate-to-pin ratio of the monolithic chips, the number of wire bonds and external soldered interconnections in a system can both be significantly reduced.

The LSI approach also offers the economic possibility of more stringent process controls and screens and greater redundancy (91). For some system applications now being served by plastic encapsulated integrated circuits, it will also be economically possible to use hermetically packaged LSI circuits.

LSI also offers the possibility of improved chip reliability. Examples of this are the use of conservative design margins and more stringent in-process controls to attain high yields of very complex chips, which in turn reduces the probability of localized chip defects which may be reliability hazards.

G. Reliability versus Chip Complexity

As previously indicated, localized defects are a factor in both yield and reliability. If localized defects occurred randomly over the area of a wafer, then yield would decrease exponentially with increase in the area occupied by active devices. It has been shown that for the vast majority of integrated circuits, yield falls off at less than an exponential rate as active area increases, indicating that defects are clustered on the wafer rather than distributed at


random (7, 163, 164). If it is assumed that the localized defects which cause reliability problems are also clustered rather than random, then an increase in chip complexity will provide a decrease in the relative incidence, per gate, of defects which cause reliability problems.

The close interrelationship between yields and localized defects which can cause reliability problems can thus result in improved reliability per function accomplished in LSI arrays, since complex arrays would tend to contain a lower density of localized defects per gate. The necessity for reasonable yields in very complex arrays containing thousands of transistors has led to the implementation of many design, material, structure, and process improvements and refinements to reduce the density or the importance of localized defects, and will provide a powerful incentive for further design and manufacturing improvements which will benefit both yield and reliability.

H. Reliability Tradeofs and Limitations

While reliability is of great importance, it must also be realized that there are necessary tradeoffs between reliability and cost and between reliability and performance. There is a substantial amount of available infomation that can be applied to improve integrated circuit reliability. There are, however, various factors which limit the applicability of available knowledge. These factors include the cost of high reliability device production, the credibility gap, the question of value added, the cost of changeovers, and information exchange limitations. Some customers consider reliability data to be simply a numbers game in which the manufacturers supply extremely impressive but irrelevant data on the great reliability of products. There have even been papers in which high-stress reliability data was extrapolated to indicate that at normal device stresses the product would have a life somewhat in excess of that predicted for our sun. On the other hand, customers are aware of numerous cases in which deliveries included a substantial percentage of parts which did not meet the specifications. The cost of the additional testing necessary to supply high reliability parts is well documented and in fact has been cited frequently as one of the limitations of MIL-STD-883 (165).

It is also true that many customers would prefer, in view of lack of confidence in the vendor, to perform screening and burn-in type tests in their own facility and to thus gain the value added to the product and also the confidence of having control over such operations. While this may be desirable or even necessary in many cases, it has the effect of putting the emphasis and the available funds into screening of the final product rather than on the control of the manufacturing process.

It should also be pointed out that in many cases new information results


in process changes, design changes, or other changes which could be implemented in production of new products. However, many of these changes are not readily implemented, and of course many do not result in the immediate discarding of all existing inventory and replacement with devices made by new processes. One example of this would be the use of gold thermocompression bonds to aluminum metallization. Even after investigations had shown potential problems with this system at high storage temperature, it was physically impossible for large manufacturers to immediately discard all thermocompression bonders and implement aluminum ultrasonic bonding. Another example is afforded by electromigration, where reliability studies indicated that a maximum current density of lo5 A/cmZ should be employed in aluminum metallization if electromigration-type failure mechanisms are to be avoided. Many products at that time had employed designs which resulted in current densities somewhat in excess of lo5 A/cm2, for example 3 x lo5 A/cm2, at maximum device ratings. Again, it was not possible to immediately discard all inventory and redesign all masks to comply with new design rules which limit the current density.

It should also be pointed out that profits in the integrated circuit industry also are frequently small or nonexistent and this in turn limits the investment in engineering or in new equipment, even when it is known that such investment would improve reliability.

There are also limitations in information exchange. Many manufacturers are keenly aware of process problems and reliability limitations. Many manufacturers issue reliability brochures of various types. Some are amply illustrated with colored photographs but are almost devoid of data or contain only selective data which might most charitably be termed optimistic. It is better to consider at least some of this information as feasibility data which indicates how good the product might be under optimum fabrication conditions, and demonstrates that reliability is not limited by the design or by the inherent properties of the silicon, silicon dioxide, or aluminum metallization. A substantial number of failures continue to be attributable to manufacturing errors (20-27), and in general the brochures are more likely to give data on samples which did not have such manufacturing errors.

Governmental agencies and electronic equipment manufacturers who purchase integrated circuits are a valuable source of information relative to failure modes and mechanisms in semiconductor products, since they have a positive incentive to call attention to reliability problems. Customer data are, however, sometimes excessively pessimistic, including failures due to incorrect testing and even mechanically damaged parts. Furthermore, interpretation of customer data can be complicated by the fact that devices are frequently purchased to electrical specifications which differ from those listed on the standard data sheets.


I . Accelerated Stress Testing

Much of the available information on integrated circuit failure mechanisms and their relative importance has been obtained by accelerated stress testing, with levels of stress frequently far in excess of device maximum ratings. Accelerated stress testing is an extremely valuable technique in that it permits information about possible failure mechanisms to be obtained very rapidly, and permits obtaining meaningful data from relatively small groups of devices. To the extent that the failure mechanisms studied at high stress levels are the principal determinant of failure rates at usage conditions, and that the Arrhen- ius equation pertains, data obtained at high stress levels can be extrapolated to predict failure rates at any desired operating temperature.

One serious limitation of the extrapolation of high stress data lies in the fact that a failure mechanism other than the one studied at high stress levels may be the dominant factor in determining failure rates at low stress levels, but because of a lower activation energy, would be undetectable at higher stress levels. This possibility is illustrated in Fig. 30 where failure mechanism A, with an activation energy of 1.5 eV, determines device reliability in the temperature range from 200 to 350°C. Failure mechanism B, with an activation energy of 0.5 eV is the dominant mechanism at usage conditions. In this case, reliability predictions based on extrapolation of high stress data would be overly optimistic, predicting failure rates that are substantially lower than actual rates.

J. Attainment of LSI Reliability

There are two possible ways of viewing the reliability achievements of the integrated circuit manufacturing industry. On the one hand, reliability of integrated circuits has improved in spite of a trend toward increased circuit complexity and lower packaged device costs (23). On the other hand, most of the observed failures of devices under usage conditions are a result of manufacturing or design inadequacies rather than the inherent physical and chemical limitations of the basic materials used (Si, SiOz, Al). These errors have been variously attributed to reasons ranging from the need for more fundamental information about lattice defects to immaturity in management in the semiconductor industry.

Integrated circuit manufacturers can point to customers who discuss reliability requirements in terms of failure rates characteristic of carefully screened parts for aerospace requirements, but then purchase integrated circuits for less than 20# each. Customers can cite manufacturers who mention 0.001 %/lo00 hr failure rates in their brochures and press releases, but then make deliveries containing an excessive percentage of inoperable devices.


TEMPERATURE, CENTIGRADE c FAILURE RATE \e DUE TO MECHANISM A

\

\ISM FAILURE RATE B

\ \ \

1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1 3.3 3.5 1

TEMPERATURE 103 x -+ 7

FIG. 30. The possible activation energies for different failure mechanisms within a device at different temperatures.

A number of standard methods exist which are employed to insure the reliability of conventional integrated circuits. These include reliability physics studies, in-process quality controls, line qualification (166), captive assembly lines (167), preseal visual inspection (1629, burn-in (169), environmental tests, and life tests (170).

With LSI, the philosophy of designing and building the reliability into the product instead of attempting to screen or burn-in the completed device to obtain the desired reliability is attaining increasing acceptance (91, 172, 172). At the present time this approach, while having produced very impressive results, is only partially successful, and the most reliable products are those which have not only been manufactured by a mature, well controlled process,


but have also passed a complete series of electrical, environmental, and other tests.

K. Efect of Complexity on Reliability

The reliability of conventional bipolar circuits has been improving with time, Not only is failure rate in percent per thousand hours improving but the product mix has been changing to include an increasingly large proportion of more complex circuits. As a result, failure rate per gate has been decreasing more than the data might seem to indicate. The rate of improvement in reliability per average packaged device, however, is not necessarily occurring rapidly enough to mean better reliability per packaged device even for LSI, though it does mean substantially better reliability per gate.

The usage of LSI will result in a shift in the relative distribution of various types of failure mechanisms. This is somewhat similar to the shift in distribution of failure mechanisms which can be observed when conventional integrated circuits are subjected to two levels of stress. At high stresses, such as 300°C storage, one type of failure mechanism predominates; this may be typically associated with metallization failures or with wire bond failures. At lower stresses other types of failure mechanisms occur. Each of these failure mechanisms has an activation energy. At low stresses surface-related failure mechanisms are relatively more important. Surface-ion migration, for example, has been shown to have a very low activation energy (101). With LSI the relative incidence of wire bond and package related failures would be expected to decrease, and the relative incidence of failure mechanisms related to localized defects such as oxide defects would be expected to increase.

It can be concluded that the reliability of LSI circuits is significantly better, per function accomplished, than that of SSI circuits, and that further improvements in LSI reliability will continue to be made in the next decade.

ACKNOWLEGMENTS

The authors wish to thank E. S. Schlegel, M. M. Schlacter, R. C. Musa, P. V. Gott, and J. B. Kons for helpful comments concerning the text, and D. M. Schmechel, D. A. Diehl, and D. B. Hobson for assistance in preparation of the manuscript.

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Scalar Diffraction Theory in Electron Optics

J l R f KOMRSKA

Institute of Instrument Technology, Czechoslovak Academy of Sciences,

Brno, Czechoslovakia

I. Introduction ....................................................................................... 11. The Diffraction Integral ........................................................................

B. The Diffraction Integral for Space Waves . ...................................... C. The Diffraction Integral for Two-Dimensional Waves.. ............................

111. Electron Diffraction by Uncharged Obstacles.. ........................................... A. Babinet's Theorem ........................................................................... B. Diffraction at Screens with Axial Symmetry .......................................... C. Diffraction by a Screen the Parts of Which Are Separated by Mutually

D. More Complicated Diffraction Phenomena.. ........................................... IV. Scattering of Electrons by Charged Obstacles .............................................

A. Scattering of Electrons by a Charged Dielectric Sphere Lying on a Conductive Supporting Film ............................................................

B. Electron Interference Phenomena Produced by Electrostatic Biprism.. .......... V. Summary ..........................................................................................

References ..........................................................................................

A. The Wavefunction in the Specimen Plane ................................................

Perpendicular Systems of Straight Lines ................................................

139 142 143 147 159 165 166 167

186 208 210

21 1 218 232 232

I. INTRODUCTION

As a result of the interaction of electrons with the specimen, various scattering phenomena become evident. In transmission electron microscopy two kinds of phenomena may be distinguished. The most frequent is that caused by the interaction of electrons with the inner-i.e., atomic or molecular-structure of the specimen. The study of this interaction is the subject of electron diffraction. Another type of scattering phenomena is that by opaque or partially transparent obstacles whose linear dimensions are large in comparison with the atomic scale. Then the observed scattering phenomena are not immediately influenced by the atomic structure of the specimen and in the simple cases they resemble Fresnel diffraction in light optics. The patterns obtained by shadow electron microscopy serve as an example. The interpretation of the phenomena appearing as a result of the electron scattering by these macroscopic obstacles is the subject of this paper.

139

1 40 JIkf KOMRSKA

From the historical point of view it is interesting to note that this sort of electron scattering played a definite role in the experimental verification of de Broglie’s postulate on the wave nature of particles. The consequences of de Broglie’s postulate have in fact been quantitatively confirmed by experiments of Davisson and Germer ( I ) and Thomson and Reid (2, 3) on the diffraction of electrons by crystal lattices of solids. Diffraction by crystal lattices, however, does not have the convincing simplicity of the classical diffraction experiments of Young and Fresnel, which were so important for the development of the wave theory in light optics. Here we may quote von Laue ( 4 ) : “A sceptic could still object that atoms may deflect particles in a way not yet understood.” From this standpoint Rupp’s experiments (5) are noteworthy. In 1928 he demonstrated the diffraction of slow electrons (70-310 eV) from a ruled grating at angles of incidence of rad. The angles related to the diffraction maxima were of the same order and permitted the wavelength to be measured with an accuracy of 5 % , and in the best case of 2%. The diffraction patterns are, however, not very distinct and the intensity distribution in the patterns can hardly be interpreted in detail.

The invention of the electron microscope made it possible in principle to obtain perfect electron diffraction patterns by macroscopic obstacles. But only after a further eight years of technical development of the electron microscope was sufficient magnification and resolution available to observe Fresnel diffraction phenomena. The first pattern of this type was published by Boersch in 1940 (6). It represents the diffraction of electrons at the edge of an opaque half-plane (cf. Fig. 25 in Section lII.C.3). At the same time Boersch (7) and Hillier (8) drew attention to the fact that Fresnel diffraction phenomena may be observed in a defocused electron microscope image, Since then Fresnel diffraction phenomena have been used for the focusing of the image, correction of the axial astigmatism, and generally for the estimation of operational properties of the electron microscope.

The most convincing demonstration of the wave nature of free electrons are electron interference phenomena produced by apparatus analogous to interferometers in light optics. The first interferometers were suggested by Marton (9) in 1951. They belong to the group of interferometers in which the amplitude is divided. The electron beams are split by the diffraction from thin (x 150 A) epitaxial crystals of gold. Using one of these interferometers Marton, Simpson, and Suddeth (ZO) obtained interference patterns at a path difference between the two branches of the interferometer of 276 A, which corresponds to 5.8 x lo3 wavelengths of the electrons accelerated by 50 kV (11). At the same time similar interference phenomena were published that occur only occasionally while observing suitable objects in the electron microscope. In 1951 Mitsuishi, Nagasaki, and Uyeda (12) observed equidistant dark bands in the images of graphite flakes and interpreted them as

SCALAR DIFFRACTION THEORY IN ELECTRON OPTICS 141

interference fringes produced by wedge-shaped flaking off of the graphite crystals. In 1952 Mollenstedt (23) and Rang (24) published interference phenomena observed in electronmicroscope images of cavities in the single- crystal foils. Equidistant dark lines have been produced by the interference of the beams divided by the front and back walls of the cavity.

The development of nonconventional techniques of electron microscopy has given further impulse to the study of the diffraction and scattering phenomena from macroscopic objects. The scattering obstacles are sometimes charged so that the diffraction pattern due to the obstacle geometry is influenced also by the electrostatic field produced by the charges. A good example is the interference of electrons produced by the electrostatic biprism, first described by Mollenstedt and Duker in 1955 (15, 26) (cf. Section 1V.B). The electrostatic biprism is an interferometer dividing the wavefront. From the point of view evoked by the above quotation from von Laue (4) the electron interferences produced by the electrostatic biprism are of particular interest because the splitting and the superposition of the electron beams is achieved without any interaction of electrons with the material.

Another example of electron scattering by macroscopic obstacles is the shadow electron microscopy of dielectric particles. These when irradiated by the electron beam become charged, so that the diffraction phenomena are influenced by scattering in the electrostatic field (cf. Section 1V.A).

The charges on the scattering objects are small and consequently the corresponding potential energy U(r) is everywhere small (x 10 eV) in comparison with the kinetic energy T of the electrons (x lo5 eV). Then it may be assumed that the condition for the applicability of the quasiclassical approximation of quantum mechanics p 3 $- hmJVUJ [see, e.g., (27)] is satisfied. Here p = [2mr]'/2 is the momentum and m the mass of the electron. This condition expresses the assumption that the potential energy U(r) is a slowly varying function of the position r. Moreover, we shall suppose that V(r) + 0 as r + 00. Thus, the potential energy U should satisfy the following conditions :

U(r) 4 T(r), Am I VU(r) I 4 p3(r), lim U(r) = 0. (1) r+ m

Under these conditions it is possible to express the wavefunction in terms of a diffraction integral which adequately describes the electron beam behind the weakly charged objects. We shall see in Section I1 that its derivation is, in fact, an application of the scalar theory of optical diffraction to a medium with a slightly varying refractive index. Section 111 describes particular diffraction phenomena by uncharged obstacles and gives their detailed interpretation. In Section IV the detailed interpretation of several scattering phenomena by charged obstacles is discussed. The paper as a whole deals with electron scattering by weak electrostatic fields only and omits the

1 42 JIfif KOMRSKA

scattering by magnetic fields [magnetostatic biprism (18), Lorentz micros- COPY (1911.

11. THE DIFFRACTION INTEGRAL

The scalar theory of optical diffraction is based on the idea that the wavefunction $(P) at the point of observation P is determined by the wavefunction $ ( M ) at points in the plane of the diffraction screen. As $ is a solution of the wave equation, it is evident that the diffraction problem, i.e., the problem of finding the wavefunction $(P) at the point of observation P, is a boundary value problem of the wave equation. The solution of this boundary value problem is the diffraction integral.

For the case of diffraction in a uniform medium Sommerfeld (20) has found its form by the method of Green’s function. In specifying the boundary values $(M) it is necessary to refer to experiment. In most cases a good agreement with experiment is achieved for the boundary values $ ( M ) in the form of the product of two factors: (i) the wavefunction $&4) characterizing the unperturbed wave which would be at points M in the absence of any obstacles whatever, and (ii) the transmission function specifying the diffracting obstacles.

In solving the problem of the scattering of electrons by charged obstacles we shall proceed in a similar way. As the potential energy U is a function of position r, the problem concerns a nonuniform medium. The conditions (1) guarantee, however, that the medium is only slightly nonuniform. To find the wavefunction $(P) at the point of observation P means, in the non- relativistic approach, to solve the boundary value problem of the Schrodinger equation

V’$(r) + k2(r)$(r) = 0, (2)

k(r) = p(r)/ti, p(r) = [2m1T(r)]’/~, T(r) = E - U(r), (3)

where

E being the energy of the electrons.

vides the diffraction integral of the form (cf. Sections II.B.3-5) The method of Green’s function is successful in this case as well. It pro-

where K is the plane of the specimen (or of the diffraction screen), i.e., the plane on which the boundary values $(M) are prescribed. The function B(P, M ) is simply related to the Green’s function used.


We assume the boundary values $ ( M ) to have the form

$(MI = rc/"(M)!(M). (5 )

$"(M) is the solution of the Schrodinger equation (2) which characterizes the influence of the electrostatic field arising from the charges of the scattering objects, which does not include, however, the influence of the obstacles themselves. f ( M ) is the transmission function of uncharged obstacles.

The boundary values $(M) will be discussed in the next section, 1I.A. In subsequent parts of Section I1 the diffraction integral (4) for electrons scattered by charged obstacles will be derived. Its derivation differs slightly for the cases of spatial and two-dimensional (cylindrical) waves. Therefore, in addition to the detailed derivation of the diffraction integral for spatial waves given in Section II.B, the two-dimensional waves are briefly dealt with in Section 1I.C.

The diffraction integral as the solution of the general case of the Schrod- inger equation in the presence of both electric and magnetic fields has been found by Glaser and Schiske (21) [re-edited in (22) and (23)]. In comparison with their treatment the derivation of the diffraction integral given in this section is much less general because it is limited to the weak electrostatic fields. This restriction permits us, however, to follow the original Sommerfeld derivation (20) more closely and to generalize it in a very simple way. The resulting form of the diffraction integral is then much simpler and ready to be used for numerical calculations in Sections I11 and IV.

A . The Wavefunction in the Specimen Plane

The boundary values are supposed to have the form of (5). The solution I)" of the Schrodinger equation will be found in Section 1I.A.I with the use of the quasiclassical approximation. The transmission function f ( M ) will be introduced in Section II.A.2.

1 . The Quasiclassical Approximation

Let $o(r) denote the wavefunction of free electrons, i.e., of electrons moving in a space without any field. It must satisfy the special case of the Schrodinger equation (2) with potential energy U(r) = 0 (the Helmholtz equation) :

where

k* = po/h, po = [2mE]"2.

144 JIgf KOMRSKA

If the potential energy U(r) is not identically equal to zero but satisfies the conditions (1) we shall find the solution i,bu(r) of the Schrodinger equation (2) by means of the quasiclassical approximation. We assume it to be of the form [(20), p. 2071:

(7)

i,bu(r) is a rapidly varying function of position, because ko takes large values (for electrons with E = 100 keV it is ko = 1.7 x 10"m-'). On the other hand A(r) and S(r, E ) are supposed to be slowly varying functions of coordinates. Now our task is to find the functions A(r) and S(r, E).

i,bu(r) = 4r)exPWo S(r, Ell.

Substituting (7) into (2) and dividing by ko @(r) we obtain

(8) 1 V 2 A (t)' - (VS)2 +

With regard to the above properties of k , , A@), and S(r, E), Eq. (8) is satisfied approximately if

i.e., with respect to (3) and (6),

(k/kOl2 = (W2,

p2 = p02(VS)?

P W = povm, a, This equation is fulfilled if

and thus

C being an arbitrary curve with its terminal point at r. If C is a curve such that its element dr is parallel to the momentum vector p (classical trajectory) we denote it by I and the preceding integral takes the form

The ratio p(r)/po is the refractive index of the space without any magnetic field [see e.g. (22), Section 981. From (l), (3), and (6) we obtain

For the function S(r, E) we finally write


In the approximation to zero powers of l/ko the relation (8) does not provide any condition for the amplitude A(r). We obtain the amplitude from the requirement J/u(r) = J/o(r) if U(r) = 0:

4) = I + o w I - (9)

In the approximation to zero powers of Ilko in (8) the wavefunction of electrons in the potential field U(r) takes the form

We shall now specify the spatial region where this approximation adequately represents the influence of the electrostatic field U on the wavefunction. For this reason let us consider the geometry of the experimental arrangement in shadow electron microscopy (Fig. 1). The electrons are

P

FIG. 1. Diagrammatic representation of the experimental arrangement for observing the scattering of electrons by a charged object N. P o , the source of electrons; x , the plane of the specimen (the back side of the supporting carbon film); T, the plane of observation.

emitted from a source Po (crossover image) and travel along straight lines through the space, where the field is practically zero. Only in the proximity of the plane x of the specimen may the trajectories be curved when the specimen particles N are charged. Behind the specimen the electrons follow straight lines again. From the condition V(r) < T(r) we can conclude that the angle p of the straight line parts of the trajectory is small. Thus, for points Q in front of the specimen x, or behind it but in its proximity, the trajectory I between the source Po and the point Q differs only slightly from the segment PoQ. The integral along I in (9) may then be replaced by the integral along PoQ. Denoting rQ = PoQ, the wavefunction (10) takes the form

- - -

146 JIRf KOMRSKA

Now we want to know the number of electrons passing through unit area in the vicinity of point Q in unit time. This number is equal to the normal component of the probability current density vector j , . From (1 1) it follows that

and using (1) and (6) we obtain for the probability current density vector

Thus, we see that at points Q where the wavefunction (11) is useful for the description of the electron beam, the probability current density vector j is equal to the vector jo corresponding to U(r) = 0. In other words the intensity distribution in the specimen plane or in planes in its vicinity is not influenced by the weak potential field caused by the charges on the scattering obstacles. This agrees with the fact that small charges at the specimen do not become evident in focused or slightly defocused images taken in the electron microscope (24-27).

On the other hand, if we observe the scattering pattern in a plane n far behind the specimen, the intensity distribution (i.e.,j,,) in patterns from charged and uncharged particles differs substantially. This is obvious, for example, from the comparison of Figs. 12 and 38 and Figs. 41c and 41a, f given below. Therefore, at greater distances behind the plane x the wavefunction (1 1) does not describe adequately the electron beam which has passed through the electrostatic field U(r). It is caused by the fact that the wavefunction (10) is only an approximative solution of the equation (8). Moreover we have replaced the wavefunction (lo), the phase of which involves the integral along the classical trajectory 1, by the wavefunction (11) where this integral is related to the segment Px If the point Q is far behind the specimen this segment may deviate substantially from the trajectory (cf. Fig. 1).

2. The Transmission Function

Since @o(rQ) in (1 1) refers to the unperturbed illuminating beam, i.e., it describes the situation without any scattering objects whatever, it is evident that the wavefunction (11) characterizes only the influence of the field U on electrons and does not express the influence of the particles themselves. Thus, let us consider a specimen whose particles are not charged. Such a specimen


can be specified by a complex transmission function f ( M ) = z(M)exp[k(M)] defined at points M of a plane x close behind the specimen (cf. Fig. 1). In a formal way the transmission function can be introduced by the ratio f ( M ) = $(M)/$o(M) of the wavefunction $ characterizing the beam close behind the specimen and the unperturbed wave t,b0. The modulus z (M) then gives the relative decrease of the amplitude, 0 5 z (M) 5 1, and the phase E ( M ) is the phase of $ related to the phase of $ o .

In the case of charged, partially transparent, or opaque objects the wavefunction at points M of the plane x takes the form

1 ’ $(M) = I $o(M)lf(M) .XP( iko rg [ 1 - Jo w o + r&f 0 4). (13)

Then, for the calculation of $ ( M ) in a particular case we must know the wavefunction i,h0 characterizing the illuminating beam, the transmission function f ( M ) characterizing the specimen, and the electrostatic field U produced by charges on the specimen.

Finally, the plane x of the specimen, i.e., the plane to which the diffraction integral (4) is related, should be specified more precisely. We assume that the scattering objects are distributed approximately in a plane. In other words, we assume the deviations of the objects from the arrangement in this plane and the object dimensions in the direction of the incident electrons are small in comparison to the distances of the objects both from the source Po and from the point of observation P. Theoretically, we may choose the plane x anywhere in the specimen region. In particular cases we are guided in our choice by two requirements: (i) the wavefunction in the form of (13) must provide a correct description of the electrons at points M of the plane x , and (ii) the explicit form of the Green’s function G (see Section II.B.4) should be as simple as possible. With regard to these requirements it is advantageous to choose the plane x in such a way that (i) there are no partially transparent scattering objects behind it but (ii) that it is as close to these objects as possible. For example, let the scattering objects be dielectric particles which eventually become charged by the action of the illuminating beam. If the particles are distributed on a supporting film, the back side of the film is chosen as the plane x (see Fig. 2). In the case of a conductive supporting film the electrostatic field produced by charges on the particles is screened off (see Fig. 1) so that there is no field behind the plane x . In such a case the explicit form of the Green’s function is especially simple (cf. Section II.B.4).

B. The Diyraction Integral for Space Waves

The starting point for the derivation of the diffraction integral (4) is Green’s theorem which will now be presented.

148 JIfif KOMRSKA

1. Green’s Theorem

Let v be a finite volume surrounded by a piecewise smooth surface S; let n be the outward normal of the surface S and $(Q), $,(Q) be any scalar functions of positions with all their first derivatives continuous inside and on S and all their second derivatives continuous inside the surface S. Then

/jj($Wl - $lW do = fs($V$l - $1V$)n dS* U S

This theorem may be considered as a consequence of Gauss’ theorem and its proof is given, for example, in (28).

If, moreover, the functions $(Q) and $,(Q) are the solutions of the same Schrodinger equation (2),

[i.e., the kinetic energy of electrons (cf. Eq. 3) is the same in both equations for all the points Q inside S], we get by multiplying the first equation by $1, the second by $, and subtracting: $Vz$l - @lV2$ = 0. Then the Green’s formula takes the form

Vz$(Q> + k2(Q>$(Q) = 0, Vz$l(Q) + k2(Q)$1(Q> = 0

j/($V$l - $1V$>n dS = 0. (14) S

2. Green’s Function

Our aim is to express the wavefunction $(P) in terms of known values of the wavefunction $(M) in the plane x of the specimen. The plane x will be introduced into Green’s theorem (14) in such a way that one part of the surface Swill be identified with a certain part of the plane x . We denote this part by S1. The remaining part of the closed surface S will be formed by a portion S, of a sphere of large radius and centered at the point of observation P (see Fig. 2). A suitable choice of the auxiliary function $1 in (14) will cause (i) the

FIG. 2. The surface Sl U Sz U s‘.


integral over the portion S, on which the wavefunction $ is not known to be negligible, and (ii) show that it is not necessary to prescribe the normal derivative VI) n on the portion S , , i.e., in the plane x .

As did Sommerfeld (20), we substitute into (14) for the auxiliary function $,, the Green's function G(sQ) = G(P, Q) belonging to the plane x . Here sQ = PQ, Q being an inner point of the surface S , u S, . The Green's function is specified by the conditions

d

V$G(P, Q) + k2(Q)G(P, Q) = 0 (1 5a)

G(P, M ) = 0 ( 15b)

G(sQ) l/SQ (15c)

at points Q # P of the half-space ( x , P),

at points M of the plane x ,

as SQ + 0,

~sQG(sQ)I < const., s&"G(P, Q)n - ik(Q)G(P, Q) ] - t o (15d)

as SQ + CO.

The conditions (15d) must be satisfied uniformly with respect to all the space directions coming into consideration in the half-space ( x , P).

The reasons for such a choice of the requirements laid on the Green's functions are as follows: The condition (15a) says that G is the solution of Schrodinger equation which is necessary for its substitution into (14). The singularity (1%) prevents the immediate application of (14) with $, = G to the surface S, u S, , It permits us, however, to derive an integral theorem expressing $(P) in terms of $ at points of the surface S, u S, . The conditions (15d) called the condition of finiteness and the radiation condition ensure that the integral over S, goes to zero as the radius of S, increases to infinity. Finally, the condition (15b) makes it possible not to specify VI)n at points M € x .

The explicit form of the Green's function will be found in Section II.B.4. For the meantime we shall suppose that a function with properties (15a) to (1 5d) exists.

3. The Integral Theorem

The singularity of G(P, Q ) at the point Q = P is a typical property of Green's function. It permits us to express $(P) in terms of the wavefunction $ at points of the surface S , u S, .

To exclude this singularity from the interior of the surface S of (14) we circumscribe a small sphere around the point P and denote its surfaoe by S'

150 JIU KOMRSKA

(see pig, 2). The Green's theorem (14) with surface S, u S , v S'. We obtain

= G may be applied to the

jj ($VG - GV$)n dS + /j($VG - GV$)n dS = 0. (16) s1 us2 S

The first integral includes the wavefunction at points of the surface S , u S, . By calculating the limit of the second integral for the radius of S' going to zero we obtain the expression involving the required value of the wavefunction at the point P of observation.

Taking into account that on the sphere S' we may put n = -s/s, dS = s2 sin 9 d9 dx, x and 9 being the angles in spherical coordinates, we obtain for the limit of the second integral in (16)

2n n

[$VG * s - GV$ * s]s sin 9 d9 dx -:: lo lo lim $(P + s) lirn ssVG - lirn GssV$ sin 9 d9 dx.

Now we shall calculate the limits in the integrand of the right-hand side. Obviously, it is

lim $(P + s) = $(P).

1 = -s,'"s," [ 0 s+o S' 0 s+ 0

S+O

With respect to (1%) we obtain for the second and third limits:

1 lirn ssVG = lirn ssV - = - 1, s+o s+o s

lirn GssV$ = lim sV$ = 0, s+o s - r o

because lims+o I V$(P + s) I is the finite number I V$(P) I. Thus for the limit of the integral over the sphere S' in (16) we get

271 n

s+o 0 0 lirn JJ($VG - GV$)n dS = $(P) 1 1 sin 9 d9 dX = 471$(P).

S'

Then, it follows from (16) that

$(P) = - - Jj [$VG - GV$]n dS. 471

s1 u s2

Expressing $(P) in terms of $ and V$n at points of the closed surface S, US,, the integral theorem (17) is analogous to the Helmholtz integral theorem for the scalar waves in uniform media. It was derived with the use


1 2 4n I!jr V$ - iks$)sG dR VG - iksG)s$ dR

n

of (1 5a) and (1 5c) only, and, in fact, it holds for any closed surface bounding a finite volume and for the function $ satisfying the condition of the Green’s theorem (14).

Using (15b) the relation (17) takes the form

(19)

s1 S l

This equation holds for the inner point P of the finite volume bounded by surfaces S, and S, (cf. Fig. 2). Now we shall investigate the limit of the integral over the surface S, if the radius s of S,’ increases to infinity. For this purpose we estimate the absolute value of the integral. On the surface S, n dS = ss dR, where dR denotes an element of the solid angle. Hence,

i 1 = 471 I [j ($VG - GV$)ss df2

ksG$) - (Gs * V$ - iksG$)]s dR

1 1 I- jJ 1s * VG - iksGl I s$ l dR + - SJ’ 1s V$ - iks$l lsGl dR - 411 4n:

- I I S * VG - i k ~ G ~ , , , ~ ~ l ~ $ ~ , , , ~ ~ + I S * V$ - iks$Imax ISGI,, ,~~.

n n

By the suffix “ max ” we denote the maximum of the respective absoIute value on the surface S, . Now we use the conditions (15d) for the function G. More- over, we suppose that the function $ also satisfies the condition of finiteness and the radiation condition uniformly with respect to all the space directions coming into consideration :

(20) IsQ$(Q)I < const.,

Then it is evident from (19) that

sQ[V$(Q)n - WQ)$(Q)l-, 0 as SQ -, ~ 0 .

1

s + m 411 lim - JJ($VG - GV$)n dS = 0,

S l

i.e., in the limit for s + co the integral over S , does not contribute to the value of the wavefunction at P.

152 JIkf KOMRSKA

Hence, it follows from (18) that

x

The region of integration now involves the whole plane x , for the region S, spreads over the whole plane x if the radius s of the surface S2 increases without limit. The relation (21) gives the wavefunction $(P) at the point P in terms of the wavefunction $ ( M ) at points M of the plane x of the specimen. Thus, it has the form of the diffraction integral (4) with B(P, M ) = -(1/4n)VG(P, M)n. To calculate the normal derivative VGn, we must now find the explicit form of the Green’s function.

4 . The Explicit Form of the Green’s Function

When deriving the diffraction integral for diffraction in a uniform medium Sommerfeld [(20), Section 34.C] found the Green’s function by means of the method of images (Fig. 3) . Let P‘ be the mirror image of the point of observation P with respect to the plane x . The Cartesian reference frame 0, 5 , q, c

loio, 0, o i

FIG. 3. Construction of the Green’s function for the half-space (x , P).

is chosen in such a way that the plane O , c , q lies in the plane x and the axis c points to the half-space containing the point of observation P. The coordinates of P and P‘ are denoted P(x, y , z) and P’(x, y , -z) . For the general point Q((, q, c), ( 2 0 Sommerfeld has formed the Green’s function

exp(ik,sQ) - exp(ik, so’) W, Q) =

SQ’ 3

SQ where

sQ2 = (r - x)2 + (q - y)’ + (l - z)2,

s; = (t - x)’ + (q - y)2 + (c + z)’.

This form of the Green’s function is usable for us only if there is no field behind the plane x , i.e., U(5, q, c) = 0 if [ 2 0.


If the nature of the specimen makes it possible for a field induced by the charges on the particles to penetrate behind the plane x it is necessary to employ a more general form of the Green's function. To satisfy the condition (15b) we introduce the function U,(5, q, () defined by

Then the required Green's function has the form

(24) - 1 exp( iko s p ~ [ 1 - lo' u p ' + s i t ) d t ] ) .

S Q

We shall now verify that this function satisfies all the requirements placed on the function G(P, Q), especially the conditions (15a) to (15d). First of all it is evident that for all points Q(5, q, 0, 5 2 0, Q # P the function G(P, Q ) having the form (24) is continuous with all its first and second derivatives.

(a) As the function of coordinates of the point Q the function G(P, Q ) is the approximate solution of the Schrodinger equation with the potential energy U,. The wavefunction I) is the approximate solution of the Schrodinger equation with the potential energy U. For 5 2 0 it is U, = U and, therefore, G(P, Q) and Ic/ are approximate solutions of the same Schrodinger equation.

(b) At points M of the plane x of the specimen, G(P, M ) = 0. In order to satisfy this condition we have chosen the plane x in such a way that there are no particles behind it (cf. the end of Section II.A.2).

(c) If SQ + 0 the function G(P, Q ) --f l/sQ, because its first term approaches to 1/sQ while the second term remains finite.

(d) The condition of finiteness I sQG(sp) I < const. as sQ + oc) is obviously satisfied. The radiation condition is also satisfied as can be shown by direct calculation. If the point Q lies in the half-space (x , P) we obtain

154 JIl\f KOMRSKA

(In VQ[so’S~U,(P’ + s, l t)dt] it is not possible to change the order of operations, because the derivation of U, need not be continuous in the plane [ = 0, i.e., in x.) The outwardnormal n = at the points Q of the surface S2 and thus

sQ[VQ G * n - ikG]

The estimation of the absolute value of the investigated expression yields

For sQ -+ 00 obviously SQSQ’ /SQ’~ 1. With respect to (3) and (4) it follows from the condition U(Q) + 0 as Q + 00 (cf. Eq. l), that k/ko -+ 1. Disregard- ing the mathematical complications we may infer from the same condition that (sQ/so’). vQ[sQ‘jk U,(P‘ + s,’t)dt] -+ 0. Taking into account these limits we find that 1 sQ[VQGn - ikG] I + 0 as sQ -+ 00, which guarantees the satis- faction of the radiation condition (1 5d).

5. The Difraction Integral

Now we substitute the explicit form (24) of the Green’s function into the integral (21). Obviously, at points M of the plane x the following relations are iralid:

SM = sM’, sM’ * n = - SM * n, 1 1

0 jo u,(P’ + S M ’ t ) dt = 1 U(P + S M t ) dt ,


Substituting them into (25) we obtain

V G . n = 2iko 1 - - 1 - 9) %nexp(ikosMIL - &loi U(P +s , t ) d t ] ] .

( 1koSM 2E SM

For points P far enough from the plane x we can neglect l/(kosM)< 1. Further, in the space as a whole U/2E < 1 (cf. Eq. 1). Hence,

1 ' VG * n = 2iko exp( iko SM[ 1 - 2~ S, U(P + S y t) dt ] ) Kn

SM2

and the integral theorem (21) reads

If the electrons are emitted from a point source at Po we have in (13) I @&M) I = & / r M , rM = Po M and the substitution of (1 3) into (26) gives the diffraction integral in the form

+

X

To facilitate the numerical calculations in Sections I11 and IV this diffraction integral will be slightly modified in the following section.

6. Modifications of' the Diffraction Integral for Numerical Calculations

Suppose that the linear dimensions d of the region in the plane x where the transmission function f ( M ) differs from zero are small in comparison with the lengths rM and s, (cf. Fig. 4). Then the value of the diffraction

FIG. 4. Illustrating the conditions of applicability of the diffraction integral (29).

156 JIgf KOMRSKA

integral is determined just by this region; we denote it by S, . The factor sM*n/(rMsM2) changes only negligibly as the function of M. If the origin 0 of the reference frame 0, t, q, [ introduced in Section II.B.4 is chosen somewhere in the region S, , we may replace the factor by so * n/(roso2) where ro = Po 0, so = PO. The diffraction integral then takes the form

__+ 3

$(P) = - - iko - so n J'Sf(M)exp[ik,(r, + s,)] 2nr0 so so

S.

Usually ko(rM + s,) and ko~,!&+,U(P0 + r,t) + s,U(P + sMt)]dt/2E are very large numbers. Therefore, it is advantageous to relate the phase of the exponenkial expressions in (28) to the values taken by these numbers at the origin. Taking the complex unit with this reference phase in front of the integral (14) we finally obtain the following form of the diffraction integral

where

7. The Conditions of Applicability of the Diflraction Integral

We shall now recapitulate the assumptions under which the wavefunction $(P) may be calculated according to the diffraction integrals (28) and (29), respectively.

First of all there are the conditions (1) placed on the potential energy U due to the charges on the scattering obstacles. We must add three further conditions of optical diffraction:


The factor sM.n/ (rMsMZ) in the integrand of (27) may be brought outside the sign of integration only if all the linear dimensions d of the region of integration S, are small in comparison with rM and sM:

It is obvious that the diffraction screens having an infinitely large opening (disk, strip, slit, half-plane etc.) do not satisfy this condition. Fortunately, using the method of stationary phase [see, e.g., (29), pp. 386 and 7521 it can be shown that the integral (28) or (29) is useful in the case of the infinite region of integration as well. This may be elucidated by the fact that the main contribution to the value of $(P) comes from around the point M,, where the phase of the integrand is stationary and the dimensions of this surrounding satisfy the condition (33).

In particular cases we must find the explicit form of the transmission functionf(M), i.e., we must set up a model of the specimen or of the diffraction screen. It results usually in the decomposition of the plane x into several regions S, where the transmission function is approximately constant, i.e., f ( M ) i f,, if M E S , . The linear dimensions d, of these regions are large in comparison with the wavelength I , :

This condition is well satisfied in transmission electron microscopy, especially if the scattering obstacles are large in comparison with atomic dimensions. It follows, however (and also from Eq. l), that the scattering angles are small. Supposing that the incident beam is approximately perpendicular to the specimen plane x we have the conditions

rM/rM -n, s M / s M = n, (35)

the second one of which has been already used in (30). The transmission function f ( M ) is often chosen to be a piecewise contin-

uous function having finite discontinuities at the boundaries of the scattering objects. Consequently the boundary values $(M) in (13) are piecewise continuous too and, therefore, do not satisfy the assumption of Green’s theorem. Nevertheless, the diffraction integral is applicable in these cases as well : Mathematically it is possible to construct such a smooth function f i ( M ) to our piecewise continuous function , f ( M ) that the difference A(M) = f i ( M ) - f ( M ) differs from zero only in an arbitrarily narrow region bordering the discontinuities of f ( M ) . The boundary values I ) ~ ( M ) with the transmission functionf,(M) satisfy the conditions of the Green’s theorem. With the use of the relation fi(M) = f ( M ) + A(M) one immediately concludes that the wave-function t,bl(P), provided by the diffraction integral with the smooth

158 JIkf KOMRSKA

transmission function f , ( M ) , differs by an arbitrarily small value from the wave-function $(P) given by the diffraction integral with the piecewise continuous transmission functionf(A4).

8. The Intensity Distribution in the Diyraction Pattern

We are now interested in the intensity distribution in the plane of observation ( = z passing through the point P(x, y , z) . The term intensity is not always introduced unambiguously in electron niiscropy. Usually it is understood to be a quantity proportional to the brightness of the fluorescent screen, i.e., proportional to the normal component of the probability current density vector j(P). Nevertheless, in most cases the probability density $(P)$*(P) is the calculated quantity which is compared with the brightness of the fluorescent screen or with the density of the photographic plate. The aim of this section is to justify this apparent inconsistency.

In our nomenclature the probability current density vector is

ih i(P) = [$(P)Vp$*(p) - $*(P)Vp$(W

From (28) we calculate V,$(P). While differentiating under the integral sign we simplify V,s, G V,so = -so/so, and bring this unit vector outside the sign of integration. Neglecting the term U(P)/2E in the integrand in comparison with unity we obtain

SO V,$(P) = $ ( P ) E + 2--1 SO - i k o 3 ] , SO

el being the unit vector in the direction of the C-axis. Hence, the vector j can be written

We find that the probability current density vector is really proportional to the probability density and that the factor of proportionality is the velocity vector vo of free electrons

The same relation, however, holds between the vector j o and the probability density $o$o* of free electrons: In the absence of any scattering obstacles the wavefunction $o describing the electrons diverging from the

SCALAR DIFFRACTION THEORY IN ELECTRON OPTICS 159 - point source Po has the form +,(P) = A , exp(ik, R)/R, where R = Po P. The vector j,(P) then is

Thus, neglecting the difference in directions of - solso and R/R the relative intensity Z(P) defined by

may be calculated according to

This relative intensity is customarily the quantity used for the comparison of calculations and experiment. It will be the aim of our calculations in solving the particular scattering problems in Sections I11 and IV.

C. The Difraction Integral for Two- Dimensional Waves

A problem which is entirely independent of one Cartesian coordinate, say g, is called two-dimensional. The wavefunctions describing a two-dimensional scattering are called two-dimensional or cylindrical waves. In electron microscopy one meets the scattering..of two-dimensional waves when electrons pass out of a line source and the boundaries of the scattering objects are straight lines parallel to the source. For example, in the case of electron interference produced by the electrostatic biprism (see Section 1V.B) the line source of electrons formed, for example, by cylindrical optics is parallel to the biprism filament (26).

The derivation of the diffraction integral for the two-dimensional case is analogous to that for the space waves. The integration is, however, related to the straight line x lying in the specimen plane and perpendicular t p t h e straight line edges of the objects forming the specimen.

Green’s theorem for the two-dimensional case (30) has the form

where y is a closed, piecewise smooth curve surrounding the finite plane region S, +(Q) and I ,~~(Q) are scalar functions of position with continuous first derivatives inside and on y and continuous second derivatives inside y, and n is the outward normal of y.

160 JIRf KOMRSKA

If $ and t j l are the solutions of the same Schrodinger equation inside the curve y the integrand of the double integral is identically equal to zero and therefore

(37)

The curve y is composed of three parts y = y1 u y z u y’. As in the portions of the surface S in Fig. 2, y1 is a part of the straight line x , y z is a part of the circle with a large radius and centered at the point of observation P , and y’ is a circle of small radius and centered at P as well. For the auxiliary function $ I we substitute into (37) the Green’s function G(sQ) = G(P, Q) belonging to the straight line x and having the properties

V $ W , Q ) + k2(Q)W‘ , Q ) = 0 (384

at points Q # P of the half-plane (x, P),

G(P, M ) = 0 (38b)

at points M of the straight line x ,

as sQ+O, u = 1.781,

I s ~ ~ ’ ~ G ( s ~ ) I < const., SQ’”[VQ G(P, Q ) . n - ik(Q)G(P, Q)] + 0 (38d)

uniformly for all the directions as sQ + co. The relation (37) then becomes

($VG - GV$)n dy + / ($VG - GV$)n dy = 0. jYI Y 2 Y ‘ (39)

As in Section II.B.3 we find the limit of the integral along y’ if its radius s + 0. On y’ it follows that ndy = -sd9, where 9 is the angle of the polar coordinates.

lim j (JIVG - GVJI)n dy = -s [lim $(P +s) lim s * VG - lim Gs * VJt d9. s-ro y’ 0 s-10 s-ro s-ro

For the limits of the right-hand side we find

1 2 n

lim $(P + s) = +(PI,

2i lim(s - VG) = -. s-0 II

s-0


With the use of (38c),

s-ro x s-ro

Hence

liin ($VG - GV$)n dy = -4i$(P). s-ro J1 '

Using (38b) we have for the wavefunction $(P) at the point of observation,

(40) i i

$ ( P ) = - - 1 $VGn dy - 4 j y G - GV$)n dY. 4 Y1

We shall now investigate the limit of the integral along y 2 if the radius s of yz increases without limit. We estimate the absolute value of the integral. On yz we have ndy = s d9. By the use of the same manipulations as in (19) we obtain

The suffix max denotes the maximum of the respective absolute value on the curve y 2 . Using the properties (38d) of the Green's function and supposing that the function $ satisfies uniformly with respect to directions the conditions

IsQ1/2$(Q)I c const., so"2[V$(Q)n - ik(Q)$(Q)] -+ 0 as so + CO,

we find that the integral along yz in (40) is equal to zero if the radius s of the curve yz increases to infinity. The relation (40) then gives the wavefunction $(P) at the point P of observation in the form

(41) i

$(PI = - 4 J $(M)VG(P, M)n dy, x

To find the explicit form of the Green's function G(P, Q) we introduce the Cartesian reference frame 0, c, with the axis < identical with x and with the b-axis pointing to the half-plane containing the point P of observation. The coordinates of the general point Q are Q({, c), those of the point of observation we denote by P(x, z) . The point P'(x, - z ) is the mirror point of P with respect to the {-axis. Then the function

162 JIRf KOMRSKA

1 ikosb - H!?(k0 sp’lexp [- 2B jo U&P’ + s’& dt (42)

satisfies the conditions (38a)-(38d) and is consequently the Green’s function for the two-dimensional case. In (42) sQ’ = P‘Q, Ho(’) is the Hankel function, and Ug(& [) is the function defined by (23). That (38a) and (38b) are satisfied is evident. That (38c) is satisfied follows from the expansion of the Hankel function at the origin [cf., e.g., (30), p. 961

+

2i akos x 2

Hh1’(k0 s) = 1 + - In - + O(koZs2). (43)

With regard to (43) we see that if s -+ 0 the absolute value of the first term in (42) increases without limit as (38c) demands, whereas the second term remains finite. The satisfying of the conditions (38d) follows from the asymptotic properties of the Hankel function (31)

With the use of (44) it is obvious that G(P, Q) satisfies the condition of finiteness [ S ~ ” ~ G ( S ~ ) ~ < const. as sQ + co. It is more complicated to verify the satisfying of the radiation condition. Using [cf. (31), p. 741

and supposing that the point Q lies in the half-space ( x , P), we obtain


On the curve yz we have n = sQ/sQ and thus

From this it follows that for the absolute value of the expression being investigated,

NOW, S;SQ/(S~~SQ) + 1, U(Q) + 0, k/ko -+ 1, (sQ/sQ)VQSQI 5: Ug(P‘ + s,’t)dt + 0 as sQ + m. From the asymptotic relations (44) and (45) we find Ho(’)(z) - iH1(’)(z) = O ( ~ / Z ~ / ~ ) . Consequently, the investigated absolute value goes to zero if sQ + 00 and, therefore, the radiation condition in (38d) is satisfied.

The expression for VG*n at points M of the straight line x which is requisite for (41) can be obtained from (47) by the use of the same manipulation as in Section II.B.5:

VG(P, M) * n = -2k0H\”(ko sM)exp[ - 2~ Jb U(P + sM t ) dt ] ikoSM ’

. [I I U(fi1) Hh”(k0 s M ) ] s . 2E H\’)(ko sM) SM

ikosM 1 = -2ko H\”(k0 s,)exp [ - - 2E S, U(P + sM t ) dt] % * n.

SM

164 IIRf KOMRSKA

Substituting this into (41) the integral becomes

(48)

For q ( M ) we substitute from (13). If the electrons emerge from the line source passing through the point Po and if Po is far away from the straight line x (ix., korM B 1) we can write for the unperturbed wavefunction in (13)

+ - I $ o ( W I = I Ao Hb' '(ko TM) I = Ao[2/(nko rM)l''f rM = Po M

(cf. Eq. 44). Supposing that the point of observation is far behind x , so that ko sM B 1, we may substitute for ffl(')(k0 sM) in (48) its asymptotic expression (45). Then, the integral (48) takes the form

[rM U(P0 + rM t ) + SM U(P + SM t ) ] dt % * n d t . 1 sM

We assume that the length of the interval y x on x where the transmission functionf(M) differs from zero is small in comparison with the lengths r, and s,. We choose the origin 0 of the reference frame 0, 5 , [ somewhere in the interval y x and denote Po 0 = ro , PO = so. Putting n*s,/s, = 1, and using the same arrangements as in Section II.B.6, we find for the diffraction integral a form suitable for numerical calculations

__+ 3

where

1

* exp[ - 2 jo [ro U(Po + ro t ) + so U(P + so t ) ] d t ] (50)

and the expressions for q(M) and cpu(M) are the same as in (31) and (32). Also, the conditions of applicability of the integral (49) are the same as in the spatial case, namely, (l), (33), (34), and (35).

The interpretation of the electron interference given in Section 1V.B is based on the diffraction integral (49).


111. ELECTRON DIFFRACTION BY UNCHARGED OBSTACLES

In the introductory parts of books on quantum mechanics-usually while giving reasons for the necessity to abandon the classical concept of the particle-the behavior of particles which have passed through a slit, double- slit, or other opening is discussed. Inadequate attention is, however, paid to the results of the experiments carried out. In extreme cases experiments that have never been made are described, while at the same time hypothetical experiments are discussed even in cases when it would be possible to refer to actual diffraction experiments. Therefore, various electron diffraction patterns from uncharged screens will be given in this section and it will be shown what a detailed interpretation can be made.

If the scattering objects are uncharged, i.e., U = 0 within the whole space, the diffraction integral (29) takes the form

ik, A, 2n roso

= - --exp[iko(ro + so)] J/f(M)exp{ik,[r, + sM - ( ro + sO)l} dS. s x

For general diffraction screens the transmission function f ( M ) has no particular property and the diffraction integral (51) cannot be further simplified (except the expansion of the path difference in the expression for the phase of the integrand, cf. (58) and (91) in the following text). Therefore, the wavefunction must be computed according to (51). In most cases the computation is not very simple, because the integrand is a rapidly oscillating function of the position of M in the plane of the diffraction screen. In several particular cases, however, the transmission function f ( M ) enables us to express the double integral (51) by repeated evaluations of two ordinary integrals with constant limits of integration. Then, it may be possible to express the diffraction integral (51) in terms of special functions, at least for a particular position of the source Po. For example, in the case of the diffraction from axially symmetrical screens the diffraction integral can be expressed in terms of Lommel’s functions only if the source Po lies on the symmetry axis of the screen (see Section 1II.B). The screens formed by rectangles with parallel sides may serve as another example. In this case the diffraction integral can be expressed by Fresnel’s integrals even at the general position of the source Po (see Section 1II.C). Nevertheless, even in these particular cases it is necessary to use several artificial tricks for expressing the diffraction integral by special functions. Thus, a question arises, whether it would not be better to compute directly the diffraction integral (51) also in these particular cases. We suppose that it is worthwhile to express the diffraction integral by special functions whenever possible. Two reasons may support this opinion: (i) In view of the rapidly oscillating integrand the computation

1 66 JIkf KOMRSKA

of the wavefunction is much simpler with the use of the representation by special functions in comparison with the numerical integration. (ii) The representation of the diffraction integral by special functions enables us to take advantage of numerous relations among these functions, their asymptotic representations etc., for the discussion of the diffraction pattern (e.g., for the determination of intensity extremes, for the calculations of the wavefunction at significant points of observation etc.).

The aim of the discussion of the diffraction phenomena in this section is to obtain suitable expressions for the intensity, which is a directly measurable quantity. In addition to the intensity the expressions for the phase are also given even if the phase is not a directly measurable quantity. There are two reasons for presenting the phase value: (i) The knowledge of the expression for the phase completes the wavefunction from the mathematical point of view. (ii) The development of the holographic methods suggests new possibilities for the phase determination of the diffracted wave (32, 33).

From the diffraction integral (51) the Babinet’s theorem follows immediately.

A . Babinet’s Theorem

Let us consider an opaque screen with the aperture S, . The wavefunction $(P) at points P of observation is given by the diffraction integral (51). Now let us take any number n of opaque screens with apertures Swr, p = 1, 2, . . ., n satisfying the conditions

n

p = 1 u S,,=S,andS,,nS,,=(ZI, v = l , 2 ,..., p - l , p + l , ..., n.

(52)

Let $,(P) denote the value of the wavefunction at P for the diffraction by p’s screen. Then it follows from (51) and (52) that

n

As a special case let us consider a pair of complementary screens, i.e., a pair of such screens that the openings of one screen correspond to the opaque parts of the other screen and vice versa (e.g., disk and circular aperture, strip and slit, a pair of half-planes of opposite orientation which touch each other at the edges, etc.). Then $(P) in (53) is the nondisturbed wave and (53) represents a useful condition relating the values of the wavefunctions characterizing the diffraction from complementary screens.

A special consequence of (53) valid for Fraunhofer diffraction phenomena was known to Babinet (1837) a long time before the Kirchhoff-Sommerfeld


diffraction theory was built up. In the older literature this special consequence is called Babinet’s theorem or Babinet’s principle. In more recent books, however, Eq. (53) is referred to as Babinet’s theorem.

B. Diffraction at Screens with Axial Symmetry

1. The Diyraction Integral in Cylindrical Coordinates

Identifying the origin 0 of the Cartesian reference frame 0, 5, q, C from Section II.B.4 with the center of axial symmetry of the diffraction screen, the cylindrical coordinates may be introduced according to Fig. 5. The correspondence of the cylindrical coordinates of the source Po(ao, xo , zo), the point

n

FIG. 5. The cylindrical coordinates.

of observation P(a, x, z), and the general point in the plane of the diffraction screen M(p, 0, 0) with the respective Cartesian coordinates Po(xo , y o , zo), P(x, y , z), and M (5 , q, 0) is given by

xo = 0 0 cos xo,

y o = a. sin xo ,

x = d cos x, y = a sin x,

5 = p cos 0,

q = p sin 0.

The lengths r , and s, are given by

rM = [(xo - 5)’ + (yo - q)’ + z%]’/’

= [ro2 + p2 - 2a0p cos(0 - xO)l1/’

168 JI#f KOMRSKA

Referring to the conditions of optical diffraction (33) and (35), the second and third terms in the last expression in (54) and (55) are small with respect to unity and the expressions may be expanded into power series:

Thus, we have for rp(M)/ko of (31):

-- - r~ + SM - (ro + S O ) P(M)

k0

00 a

r0 SO = -p [- cos(0 - xo) + - cos(Q - 4

+ - 2 (- ro [1 - (2)2 cos2(0 - XO)] + [l - ( ~ ) ' C O S 2 ( 0 - x)]]

+ 3 cos(0 - x) [ 1 - (:)2 COS2(0 -

P 2 1

a + . * .. SO

With the use of (58) the diffraction integral (51) becomes

S 1

The relations (58) and (59) are suitable for classification of the diffraction phenomena. Generally speaking under the conditions of optical diffraction the terms of third and higher orders in p are always neglected. If it is necessary to use the first two terms in (58) for calculating the diffraction integral (59) the corresponding pattern is called Fresnel (or microscopic) diffraction. If it is sufficient to use only the first term in (58) one speaks of Fraunhofer (or telescopic) diffraction. For the discussion of the conditions under which the Fraunhofer or Fresnel diffraction is observed see, e.g., (29), pp. 383 and 384. In this paper only Fresnel diffraction is discussed.


2. Fresnel Diffraction at Screens with Axial Symmetry

In this section we shall derive the intensity and phase distribution in the diffraction pattern from a circular aperture in an opaque screen (Subsection a) and from an opaque circular disk (Subsection b). In these cases the wavefunction $(P) can be expressed in terms of the so-called Lommel’s functions of two variables introduced by Lommel in his memoir on diffraction by a circular aperture and disk (34). Therefore, a brief review of the necessary properties of Lommel’s functions and their graphs are given in Section III.B.2.c.

In order to be able to express the wavefunction $(P) in terms of special functions it is necessary to restrict the discussion to the case when the source Po lies on the symmetry axis of the screen, i.e., a. = 0. Further, we neglect in (58) the terms of the third and higher orders in p and to simplify the term with p2 we suppose that kopza2/2sO3 4 27t. Then, (58) reduces to

a. The circular aperture in an opaque screen. Denoting a as the aperture radius the transmission function has the formf(p) = 1 for p < a andf(p) = 0 for p =- a. The diffraction integral (59) may then be written

I * j: exp[iko(k + i) g ] p Io2n exp[ - i k o p - a cos(0 - x) dO d p .

SO

Using the integral P. 201

(61)

representation of Bessel’s functions [cf., e.g., (31),

the integral with respect to the angular variable in (61) can be expressed by the Bessel’s function Jo(ko ap/so) and (61) takes the form

170 J I I f KOMRSKA

This integral can be rewritten in the form of the integral representation of Lommel’s functions (see (82) in Subsection c). For this reason we introduce the substitution

and denote p = at (64)

u = k o -+-- a , (It, s 2

v = k, aa/so. (66)

Then the diffraction integral (63) takes the form

which, on using (65) and (82), gives

or, using (81),

+ ( P ) = -- exp[ iko(ro + so) + ro + so

* ( v0(u, v ) - iv1(u, u) - exp

Denoting R the distance from the source Po to the point of observation P (see Fig. 6) we may substitute ro + so = R in the denominators of (67a) and (67b). In the exponential function, however, it is necessary to use (cf. Fig. 6)

FIG. 6. Illustrating the derivation of relation (68).


R = {[ro + (so2 - 02)112]2 + a2}l/’

Then, the expressions (67a) and (67b) are

A0 $(P) = - exp[iko R + [U2(u, u) + iU,(u, u)],

Rewriting (69a) and (69b) in polar form, the resulting expression for the wavefunction is :

where $(P) = (A,/R) Z’/*(u, u)exp[iko R - i@(u, u)] , (70)

(7W Z(u, 0) = UI2(U, u) + UzZ(u, u),

The expressions Z1/’(u, u)Ao/R and koR - @(u, u) represent the amplitude and phase of the wavefunction in the point of observation P. The function Z(u, u) thus specifies the relative intensity, that is, the ratio of the intensity at the point of observation P in the presence of the diffraction screen and the intensity at the same point without any diffraction screen whatever (cf. Sec- tion II.B.8). The function @(u, u) specifies the phase difference of the wavefunction at the point P in the presence of the diffraction screen and the disturbance at the same point without the diffraction screen:

@ = (mot - koR + 0) - (mot - k,R).

It is evident that the functions Z(u, u) and O(u, u) give the intensity and phase distribution on the sphere centered at the source Po and having the

172 JI#f KOMRSKA

diameter R (only in the region of optical diffraction, of course, i.e., Q + so). The function Z(u, u) gives with a good approximation the intensity distribution in a plane of observation z = const. A similar statement about the function @(u, u) would, however, not be correct, for k, is very large and, therefore,

V- 0 5 I0 15

FIG. 7. The graph of the function Z(u, u) (71) giving the intensity of the diffraction patterns from the circular aperture in an opaque screen. The diagonal u = o (not plotted) corresponds to the boundary of the shadow region. Note the extreme values of the intensity at points u = Z n r of the u-axis (cf. Fig. 9).


even in the immediate vicinity of the axial point ko A is comparable with 2x (A is the gap between the plane of observation, z=const., and the sphere (Pol?); see Fig. 6). The graphs of the functions I(u, v ) and @(u, v ) are given in Figs. 7 and 8.

0 5 10 15 20 v-

FIG. 8. The graph of the function @(u, 0)/27~(72)characterizing the phase of the diffraction from the circular aperture in an opaque screen. The diagonal u = u (not plotted) corresponds to the boundary of the shadow region. From the comparison of Figs. 7 and 8 it can be seen that at points of zero intensity I the function @ is multiple-valued taking all the values in the interval ( - 4 2 , n/2).

174 JIRf KOMRSKA

In diffraction experiments with light perfect diffraction patterns may be obtained [see, e.g., (35)], the intensity distribution of which agrees with the calculations in all observed details (36). It is more difficult to obtain diffraction patterns from circular apertures in an opaque screen by electrons because the apertures must be extremely small (a = mm), which makes it difficult to achieve an axially symmetrical screen opaque even in the proximity of the edge of the aperture. The diffraction patterns obtained by electrons have been published by Faget and Fert (37, 44, 38) and are given in Fig. 9. A

FIG. 9. Fresnel diffraction patterns from circular apertures in an opaque screen obtained by electrons (37,44,38). The individual patterns correspond to the situations when the screen transmits from two up to seven Fresnel zones. For an even number of transmitted zones the intensity at the center of the pattern is zero; in the case of an odd number of transmitted zones there is the intensity maximum ( I = 4) at the center. (By courtesy of Professor Ch. Fert.)

detailed comparison of the experiment and theory has not been made, but perfect agreement may also be expected.

The agreement between theory and experiment is especially obvious in the special case when the point of observation lies on the optical axis. Then, o = 0, i.e., u = 0 (cf. Eq. 66) and using (84) and (85), respectively, we obtain from (71)

I(u, 0) = u,’(u, 0) + U~’(U, 0) = 2[1 - COS(U/~)] = 4 sin2(u/4).


The relative intensity at the axial points oscillates between 0 and 4 taking these extreme values if u/4 = n42, i.e., using (65)

The extreme relative intensities are observed if

112 a = a, = [x n~,] ,

ro + z

where n is the integer giving the number of Fresnel’s zones transmitted by the screen. If the radius of the aperture corresponds to the odd number of Fresnel’s zones the relative intensity 1(2nn, 0) = 4, if n is even 1(2nn, 0) = 0 (cf. Fig. 7). This agrees with Fresnel’s conclusions [cf., e.g., (29), Section 8.21 and Fig. 9 shows the experimental confirmation.

b. The opaque circular disk. The transmission function in this case has the form f (p) = 0 if p <a, and f (p) = 1 if p > a, a being the radius of the disk. It would be possible to derive the expression for the wavefunction in a way similar to the case of the circular aperture. The derivation based on Babinet’s theorem is, however, much simpler.

Denoting the unperturbed wave by $,(P) = A , exp(ik,R)/R, the wavefunction (69a) characterizing the diffraction from the circular aperture of the same radius as the disk by q1(P), and the wavefunction corresponding to the diffraction from the disk by 4b2(P), we obtain from Babinet’s theorem (53)

With a simple manipulation we have

JIRf KOMRSKA 176

or using @I),

[Vo(u, u ) - iV,(u, u)] . (74b)

Rewriting (74a) and (74b) in polar form, the following expression for the wavefunction is obtained :

I , 9z (~ ) = ( A ~ / R ) z ” ~ ( ~ , v)exp[ikoR - i@(u, 011,

where the relative intensity is

q u , u) = VO2(U, u) + V I Z ( U , u),

= 1 + Ul2(U, u) + U22(u, u) - 2U,(U, u)

and the phase

The physical meaning of the functions Z(u, u) and @(u, u) is analogous to the case of the diffraction by the circular aperture. The graphs of these functions are given in Figs. 10 and 11.

For the axial points of observation P (a = 0) the expression (76a) takes a very simple form (see Eqs. 66 and 85)

I(u, 0) = V02(u, 0) + V&, 0) = 1. (78)

In this way the explanation of the well-known FresneI-Arago bright spot which always appears at the center of the diffraction pattern from an opaque disk [see, e.g., (20), p. 2151 is obtained.

Figure 12 shows the diffraction patterns from opaque spherical particles screening off one and four Fresnel’s zones, respectively, and Fig. 13 shows


the calculated intensity distribution in the patterns of Fig. 12 (39). The comparison of the two figures indicates a good agreement between theory and experiment. Both figures show distinct Fresnel-Arago central spots.

c. Supplement on Lommel’s functions of two variables. Lommel’s functions Un(u, u), Vn(u, u) of two variables u, u and the integral order n are defined by Neumann’s series

Sometimes the functions Vn(u, u) are defined in such a way that for n odd they differ from the above definition by the factor ( - 1) [see, e.g., (32), p. 5371.

For u/u < 1 the series for Un is more convergent than the geometric series ~ ~ = o ( ~ / u ) z m + n . For u/u < 1 the series for Vn is more convergent than the geometric ser ies~~=o(u/u)Zm+n. With respect to (65) and (66) it follows that the functions Un are more convenient for the calculations of the outside part of the diffraction pattern and the functions V,, for the calculations of the inside part.

There exist a great number of relations among Lommel’s functions, They can be found in the original Lommel’s memoir (34) or in the monographs on Bessel’s functions [(JZ), p. 537; (441. While discussing the diffraction from a circular aperture and a disk we have used only four functions : U, , Uz , Vo , and V, . The graphs of these four functions are given in Figs. 14 to 17 and several of their properties follow below.

The functions U, and V, are related by

u,(u, u) + v,(u, u) = sin &[u + (uz/2)] (79)

and the functions Uz and Yo by

178 Jlkf KOMRSKA

0

i 5

10

15

20

25 0 5

5

10 15 20 V-

FIG. 10. The graph of the function I(u, u) (76) giving the intensity of the diffraction patterns from the opaque circular disk. The diagonal u = o (not plotted) corresponds to the boundary of the shadow region. Note the unit value along the u-axis corresponding to the unit relative intensity that always appears at the center of the diffraction pattern from an opaque disk (cf. relation (78) and Fig. 12).


0 5 10 20 v-

15

FIG. 1 1 . The graph of the function @(M, u) /Zn (77) characterizing the phase of the diffraction from the opaque circular disk. The diagonal u = u (not plotted) corresponds to the boundary of the shadow region.

180 JI#f KOMRSKA

A o ~ 0 . 5 p m I I

Fro. 12. Diffraction of electrons by spherical latex particles screening off one and four Fresnel's zones, respectively, (39). xo = 4.33 x mm; the sphere diameters 20 = 0.12 and 0.23 pm, respectively; the distance from the source to the specimen ro = 42.8 mm, and the distance from the specimen plane to the plane of observation I = 0.78 mm.

The Lommei's functions have the following integral representations :

1

U,(U, u) = u j J,(ut)cos - (1 - t ' ) t d t , 0 [: 1

1

iU,(u, u) = u JoJ,(ut)exp (1 - t')] t dt , (82)


If the variable u = 0, the following holds:

The tables of Lommel’s functions Ul(u, u) and Uz(u, u) over the range 0 5 u 5 39.8, 0 5 u S 12.0, and at the intervals Au = Av = 0.2 are given in (41). The detailed tables of all the four functions U,, U, , V, , and V, are given in (42); their range of tabulation is, however, somewhat complicated.

FIG. 13. Calculated intensity distribution corresponding to the diffraction patterns in Fig. 12 (39).

182 JIfif KOMRSKA

o

5

i

fS

20

-\

I I

2 15 ”- 0 5 lo

Fro. 14. The graph of Lommel’s function U,(u, u). With the use of the properties U,(u, v) = - Ul(-u, v ) and U,(u, v ) = Ul(u, -v), the graph provides the values of the function CJl(u, u) in the region -25 6 u 5 25, -20 5 v 6 20.

0

5

i

8

f5

20

25 0


5 10 20 ‘5 v-

FIG. 15. The graph of Lommel’s function Uz(u, u). With the use of the properties U2(u, u) = U2(-u, u) = Ut(u, -u), the graph provides the values of the function U2(u, u) in the region -25 5 u 6 25, -20 6 v 5 20.

184

0

5

10

.15

20

25 0

1 I I I

1 I I

1 I 1 I I I 1 I 1

t 5

JIki KOMRSKA

1 20

FIG. 16. The graph of Lornrnel's function V&, u). With the use of the properties Vo(u, v ) = Vo(-u, v ) = Vo(u, - v ) , the graph provides the values of the function V&, u) in the region -25 5 u 5 25, -20 5 u 5 20.


I I 5 -

10 -

r5 -

20 -

i v 25

0 10 !! 15

20 v-

FIG. 17. The graph of Lommel's function Vl(u, u). With the use of the properties V,(u, u ) = - Vl(-u, u), Vl(u, u) = V,(u, -u), the graph provides the values of the function Vl(u, u) in the region -25 5 u 5 25, -20 5 u 5 20.

186 Jldf KOMRSKA

C. Diffraction by a Screen the Parts of Which Are Separated by Mutually Perpendicular Systems of’ Straight Lines

Another type of diffraction screen where the diffraction integral can be expressed in terms of special functions is represented by screens formed by rectangles, all of them having parallel sides. Evidently, this type of diffraction screen involves half-planes, filaments etc., i.e., the screens at which the electron diffraction by macroscopic objects has been first observed.

1 . The Diffraction Integral in Cartesian Coordinates

Let us consider the Fresnel diffraction by a diffraction screen consisting of any number of regions separated by mutually perpendicular sets of parallel straight lines. Thus, the individual parts of the screen are formed by rectangles (see Fig. 18). Let the amplitude of the incident wave be decreased by

FIG. 18. Choice of the Cartesian reference frame 0, f, v, 5.

the factor zCv and the phase be shifted by E,, after passage through the pvth rectangular (the meaning of the indices p, v is specified below).

For the expression for the diffraction integral the Cartesian reference frame 0, 5 , q, t; from Section II.B.4 will be used (see Fig. 18). The plane 0, 5, q coincides with the plane x of the diffraction screen. The [-axis goes through the source P o , is perpendicular to the plane at the diffraction screen, and its positive direction is the direction of the propagation of electrons. The g- and q-axes are parallel to the straight lines bordering the parts of the diffraction screen and are chosen in such a way that the system 0, 5, q, ( is right-handed.

The coordinates of the source are Po(O, 0, zo), those of the point of observation P(x, y , z), and of the general point of the diffraction screen M(5, q, 0). The equations of the straight lines bordering the pvth part of the diffraction screen are5 = t,-l, 5 = tP, q = q v - l , q = qv, wherep = 1,2,. . . , Nl ; v = 1,


2, . . . , N z , to = qo = - 00, = qNz = co. The transmission function z(t, q)exp[k(& q)] is constant in each rectangular part:

~ ( 5 , 1 1 ) = r , v , & ( r , I f ) = & p v i f 5 E ( 5 p - 1 , 5 , ) l p = 1 , 2 , . . . , N l ,

q E ( q v - l , q v ) , v = 1 , 2 , . . . , N z . (86)

The conditions of optical diffraction (33), (34), (35) now have the following form: From the inequality (34) it follows that

2nlko = Jo 4 t p - t p - 1 , q v - uy-1 ~1 = 132, - . ., N 1 ,

V = 1,2 ,..., N2. (87)

From conditions (33) and (35) it follows that

I t N , - l J r I t 1 1 3 l~Nz-ll, 1?11 + IZOI, IZ I , (88)

i.e., the region where the transmission function of the diffraction screen may vary is not far from the origin 0 and its linear dimensions are small in comparison with the distances of the source Po and of the point of observation P, respectively, from the plane of the diffraction screen. Further, it follows from (35) that

1x1, IY I 4 IZOI, I 4 9 (89)

i.e., the wavefunction will be calculated only at those points of observation P which are not too far from the c-axis.

Denoting ro = -zo and referring to (88) we get for the length r, the expression

1 tz + qz

2 ro rM = [g2 + qz + rO2l1/’ = ro + - - + . - I .

From (88) and (89) it follows that the expression for s, may be expanded into the power series in ({ - x)/z, (q - y) /z :

sy = [ZZ + (g - x>2 + (q - y)2]”2 = z + (1/22)[(5 - x)2 + (q - y)2] + ..*. Hence, we have for the sum,

x 2 + y 2 b + q y tz 1 1 2z Z 2 ro

+- -+- +- -+ - + ...* rM + s, = ro + z + ~ - - ( I) (r: i) (90)

Now we rearrange this expression in such a way that both linear and quad- ratic terms in { and q occur only in terms of the square of differences (5 - ,&)z and (q - qP)’, where 5, = ro x/(ro + z), q p = roy/(ro + z) are the coordinates of the point of intersection M p of the straight line POP and of the plane

188 JIa KOMRSKA

of the diffraction screen (see Fig. 18). This rearrangement, typical for Fresnel diffraction phenomena of the type being investigated, makes it possible to introduce the substitutions (96) and (97), leading to the Fresnel's integrals (105). Thus, (90) takes the form

+?(q--)'($+;) 1 +.". (91)

Introducing the distance

(91) becomes

Using (93) the Cartesian form of the diffraction integral (51) is obtained:

2. The DifSraction Integral Expressed in Terms of Fresnel's Integrals

We shall now take advantage of the property (86) of the transmission function. We obtain


By using the substitutions

(the negative signs are chosen to ensure that u, and v, given by Eqs. 99 and 100 are increasing functions of coordinates x and y, if ro/(ro + z) > 0), the expression (95) for the wavefunction leads to

* juuw exp( i 5 u 2 ) du JOT- exp( i 5 u’) dv, (98) u- 1

where the limits of integrations are

ro + z

Writing ro + z G R in the denominator of (98) the following expression for the wavefunction $(P) is obtained :

$(PI = ( A o / W ” 2 ( u , , vv)expW0 R - i W p , u,>l, (101)

where

190 Jlf i f KOMRSKA

= nt2 ZtZ 1 C(c0) = S(c0) = -

0 2 0 2 2' C(a) = !" cos - dt, S(a) = I' sin - dt , (105)

The conditions under which the wavefunction (101) provides the proper description of the diffraction phenomenon are given by (87), ( 8 9 , and (89).

Again, the function Z is the relative intensity in the sense of Section II.B.8 and the function @ is the phase difference between the wavefunction $(P) in the presence of the diffraction screen and the wavefunction ICl0(P) (at the same point P without the diffraction screen).

Now, the way of obtaining the intensity and the phase distribution on the sphere (Po R) centered at Po and having a radius R (of course, in the proximity of the z-axis only) will be described. The functions u,(x) and v,(y) are linear functions of the coordinates x and y, respectively. These linear functions have the same coefficient {koro/[nz(ro + z)]}''~ (see Eqs. 99 and loo), and therefore the differences

Av, = v, - v1 = - [: (k + :)] "'(q, - ql),

are independent of coordinates x and y. The numbers u,, and v, can be expressed as

u,, = u1 + Au,,, V , = vl + Av,. (107)

The functions Z(ul, Auo, Au2, . .., AuN1, v l , Avo, A v z , ..., AvNJ, @(*. * ) depend on the coordinates x and y only in terms of the variables u l , vl , and therefore they represent the intensity and the phase distribution on the sphere (Po, R) in the vicinity of the z-axis.

In the same way as in Section III.B.2.a the function Z(ul, v l ) may be considered to give the intensity distribution in the plane of observation z = const., because it follows from (89) that the relative changes of R are very small. Again, a similar statement about the function @(ul , vl) would not be correct.


3. Special Cases of the Difraction Screen

The expressions for the intensity and the phase in several special diffraction phenomena will now be given. In the same way as in the discussion of the diffraction phenomena from axially symmetrical screens, the graphs of the functions I and CD will be presented only if they provide the intensity and the phase for all possible parameters of the experimental arrangement.

a. Right-angle boundary of the opaque screen. For the two screens drawn in Fig. 19 it is Nl = N2 = 2. The boundaries of the individual parts of the

I a ) ( b 1

FIG. 19. The right angle boundaries of the opaque screen.

screens are to = - 00, tl, t2 = 00, qo = - 00, ql, q2 = co. Then it follows from (106) that Auo = Auo = co, Au2 = Au2 = - co at all possible values of the experimental parameters ,lo, ro , z, tl, ql , and the functions I(#, , vl) and CD(ul, ul) give the intensity and the phase distribution for any experimental arrangement. The different values of experimental parameters cause only a change in the coefficient of the linear functions u1 = uI(x), u1 = vl(y). In view of this generality of the functions Z(ul , ul) and O(ul, ul) it is worthwhile giving their explicit forms and graphs here.

The transmission function of the rectangular aperture in an opaque screen (Fig. 19a) is given by 711 = 712 = T~~ = 0, 722 = 1, E~~ = 0. Then, the following expressions for the relative intensity and for the phase are obtained from (102), (103), (104):

I ( U 1 , 01) = t{[f + C(Ul)l2 + [f + s(u1>12>{[t + C(O,)l2 + rt + s(o1)I2>,

(108)

The graphs of these functions are given in Figs. 20 and 21.

192 JIRf KOMRSKA

The opaque screen bounded by the right angle in the form of Fig. 19b is specified by q1 = rlZ = rZ1 = 1, E~~ = E~~ = E~~ = 0, rZ2 = 0. Then it follows from (103) that

Using these expressions the intensity I and the phase CP can be calculated

0 -

1 -

i'

31'

6 I -1 0 2 J 4 5

- 4

FIG. 20. Intensity distribution I(ul, ul) (cf. Eq. 108) in the diffraction pattern from the screen shown in Fig. 19a. The region u1 > 0,01 > 0 corresponds to the illuminated area.


-1 -

0 -

1 -

2 -

3 -

4 -

5 -

6

according to (102). The graphs of the intensity I (u l , u l ) and of the phase @(ul, u l ) are given in Figs. 22 and 23.

The calculated intensity distribution in Figs. 20 and 22 can be compared with the pattern published by Boersch in 1943 (43) and reproduced in Fig. 24. The comparison shows good agreement.

b. Rectangular aperture and rectangular screen. In these two cases Nl = N2 = 3 and the coordinates of the boundaries of the individual parts of the screen are to = -a, t t , t 2 , t3 = a, vo = - m, VI vz tf3 = a.

0 1

-1 0 1 2 3 4 5 - "1 FIG. 21. The graph of the function @(ul , ul)/27r (cf. Eq. 109)for thediffraction from the

screen shown in Fig. 19a. The region uI > 0, u1 > 0 corresponds to the illuminated area.

194 JIfif KOMRSKA

-4 3 "f -- -3 -2 -1 0 1 2

FIG. 22. Intensity distribution I&, v I ) in the diffraction pattern from the screen shown in Fig. 19b. The region ul > 0, u1 > 0 corresponds to the geometrical shadow region.


-4 -3 -2 3 6 - -1 0 1 2

FIG. 23. The graph of the function @(u,, uJ27 for the diffraction from the screen shown in Fig. 19b. The region uI > 0, uI > 0 corresponds to the geometrical shadow region.

196 JI#f KOMRSKA

FIG. 24. Out-of-focus image of the MgO crystal [Boersch (43)J showing the diffraction patterns from the right-angled boundaries indicated in Fig. 19. Compare with the calculated intensity distribution in Figs. 20 and 22. (By courtesy of Professor H. Boersch.)

For an empty rectangular aperture in an opaque screen all the zlrv = 0 except zzz = 1, ez2 = 0. The relative intensity and the phase are given by

= ac[ccuz) - C(Ul)lZ + [S(uz) - S(U1)lZ1 -"(uz) - C(V1)lZ + [ m z ) - S(Vl)l21Y

II a=- 2

For an opaque rectangle in empty surroundings zlrv = 1, E~~ = 0 for all p, v except zz2 = 0. Then, the expressions X and Y in (103) take the form

x = - [C(UZ) - C(U,)l[C(~Z) - a41 + [S(UZ) - m,)l[S(uz) - S(U,)l,

y = 2 - [C(UZ) - C(U,)"(uz) - S(u1)l - [S(Uz) - S(U,)l[C(~Z) - C(U1)l.

The relative intensity and the phase is to be calculated according to (102). c. Screens consisting of parallel strips. The electron diffraction patterns

from filaments, half-planes etc., i.e., from screens the edges of which are formed by parallel straight lines, are most frequently published in the literature. Let the boundaries of the individual parts of the screen be parallel, for


example, to the q-axis (cf. Fig. 18). Then Nz = 1, i.e., qo = -00, ql = 00 and according to (100) uo = 00, u1 = - 00. The individual parts of the transmission

The relative intensity and the phase can be derived either from the diffraction integral (98) in the same way as in Section III.C.2 or directly from the relations (102), (103), and (104). In such a way simpler expressions are obtained

(1 11) where

function (86) can be denoted by symbols with a single index zpl = z, , E , ~ = % *

](up) = *[X,’ + y12], @(up) = n/4 - arctan (YJX,),

N,

Ni

,= 1 Y, = C z,,{[S(u,) - s(u,- l)]cos E, + [ ~ ( u , ) - c(u,- ,)]sin E,}.

As special cases these general expressions provide the intensity and the phase distributions in the diffraction phenomena from an opaque and a transparent half-plane, an opaque strip, and a slit in an opaque screen.

(i) Opaque half-plane. The first diffraction pattern from an opaque half- plane obtained with electrons was published by Boersch in 1940 (6) and is reproduced in Fig. 25.

FIG. 25. The first electron diffraction pattern from an opaque half-plane (amorphous aluminum oxide) published by Boersch in 1940 (6). rD = 0.35 mm, z = 313 mm, Xo = 6.6 x lo-’ mm (36 keV). (By courtesy of Professor H. Boersch.)

198 JIRf KOMRSKA

Let the points of the straight line edge of the half-plane have the coordinate rl and let the opaque half-plane cover the part t < t1 of the plane [ = 0 of the diffraction screen. Then N l = 2, to = - 00, r2 = co, z1 = 0, 72 = 1, E~ = 0. Again, from (106) it follows that Au,, = oc), Au2 = -00, independently of particular values of experimental parameters so that the curves I = I(u,) and @ = @(u,) give the intensity and the phase distribution for any experimental arrangement :

(113) w = tm + C(u,)I2 + [t + S(u1>I2>1

The term - nn appears in (1 14) as a result of considering only the principal value of the inverse tangent, n stands for a nonnegative integer. Its value corresponding to a certain value of the variable u1 can be determined from the requirement of the continuity of @(ul). For calculations, however, it is sufficient to know that n is even if t + C(ul) > 0, and odd if 3 + C(u,) c 0. The graphs of the functions I(ul) and @(u,) are given in Fig. 26. The detailed comparison of the theory and the experiment shows that the intensity extremes in Figs. 25 and 26 are in precise correspondence.

(ii) Non-absorbing half-plane shifting the phase by n. Probably the only diffraction patterns of this type obtained with electrons have been published by Faget and Fert (44, 45, 38). One of them is reproduced in Fig. 27. The half-plane was formed by a carbon film of thickness approximately 150 A, which only slightly absorbs the electrons and shifts the phase by n.

Again, let the half-plane cover the part 5 < t1 of the plane ( = 0. Then Nl = 2, go = -00, t2 = co, z1 = z2 = 1, E~ = n, E~ = 0. The expressions (1 11) for the intensity I(u,) and the phase CD(u,) take the form

I(uJ = 2[C2(u1) + S2(u1)], @(ul) = (i - n)n - arctan[S(u,)/C(u,>], (1 15)

where n = 0 if u1 > 0, n = 1 if u1 < 0. The graphs of these functions are given in Fig. 28.

The diffraction pattern from the nonabsorbing half-plane shifting the phase by n, obtained with light, was published by Kastler (1950) (46).

(iii) Slit in an opaque screen and an opaque strip. In both cases Nl = 3 and the coordinates t of the boundaries between the individual parts of the screen

For an empty slit in an opaque screen tl = z3 = 0, t2 = 1, E~ = 0. The are to = - 00, t l , t2, t3 = 00.

relative intensity and the phase are given by

I=t-{[C(u,) - C(ul)lZ + L W 2 ) - S(u1)I2>9 (1 16)


0 1 2 3 4 5 6 7 8 9 10 I l u ,

FIG. 26. Intensity Z(ul) and phase @(uI) for the diffraction from an opaque half-plane. Region u1 > 0 corresponds to the illuminated part of the plane of observation, region u1 < 0 corresponds to the geometrical shadow.

200 JIgf KOMRSKA

FIG. 27. Fresnel diffraction of electrons at the straight line edge of the carbon film (44, 45, 38). At the thickness of 150 A the carbon film is almost perfectly transparent and shifts the phase of electrons accelerated by 1 X 105V approximately by T. (By courtesy of Professor Ch. Fert.)

The graphs of these functions are shown in Figs. 29,30, and 31. The functions are plotted in the dependence on the variables

These variables have been chosen since (ul + u2)/2 is proportional to the distance in the direction of the x-axis from the center of the diffraction pattern, and (ul - u2)/2 is proportional to the width of the slit and does not depend on the coordinate x of the point of observation.

For an opaque strip in empty surroundings zI = z3 = 1, z2 = 0, E , = e3 = 0, and the expressions for the relative intensity and the phase are


x 1 - S(UJ + m,) 1 - C(U,) + C(U,) '

= - - arctan 4

The graphs of these functions are given in Figs. 32, 33, and 34. The diffraction patterns of this type are frequently observed in out-of-focus

images of needlelike particles [e.g., ZnO (43)] or in shadow microscopy of the filamentary, objects. The comparison of theory and the experiment for the diffraction from the opaque filament is shown in Fig. 35 (47).

FIG. 28. Intensity distribution I(ui) and phase @(ul) (cf. Eq. 115) in the diffraction pattern from a perfectly transparent half-plane shifting the phase by r. At the point u1 = 0 which corresponds to the projection of the half-plane edge, the intensity is zero and the phase is discontinuous with the jump of T.

202 JIa KOMRSKA

'0 25 1 -n7 -5 0 5 = _ 10

2

ui- u, 2 -

5

4 75

4 5

4 25

4

3 75

35

3 25

3

2 75

25

225

2

f 75

15

f 25

f

0 75

05

0 25

FIO. 29. Intensity distribution in the diffraction patterns from slits of various widths in opaque screens. The zeros indexed by the values of (ul - u2)/2 indicate the levels of zero intensity of the respective curve. The dots on the curves indicate the geometrical shadow of the slit edges.


0

1

2

3

4

5 1 2 3 5 6 7 w u I

2

F I ~ . 30. The graph of the function Z(116) giving the intensity of the diffraction patterns from the slit in an opaque screen. The curves of the previous figure represent the sections through the surface I by the planes (ul - u2)/2 = const. The geometrical shadow of the edge of the slit is given by the condition uz = 0, i.e., in the graph (ul + uJ2 = (u, - 1 4 2 .

204

0

u,-u, 2

2

3

JIki KOMRSKA

J 6 7 0 I 2 3 4 5 - __

2

FIG. 31. The graph of the function @/2n (1 17) characterizing the phase of the diffraction from the slit in an opaque screen. The geometrical shadow of the edge of the slit is given by the condition u2 = 0, i s . , in the graph (ul + u2)/2 = (u, - u J 2 .


0.5

0.75

f

I 25

15

175

2

2.25

2 5

2 75

3

3 25

35

3 75

4

4 25

45

4.75

5

FIG. 32. Intensity distribution in the diffraction patterns from opaque strips of various widths. The zeros indexed by the values of (UI - u2)/2 indicate the levels of zero intensity of the respective curve. The dots on the curves indicate the geometrical shadow of the edge of the strip.

206

0

u,- u 2 -

I 1

2

3

4

5 0

JIfi f KOMRSKA

I 2 3 4 5 u,*u,6- 2

7

FIG. 33. The graph of the function Z(120) giving the intensity of the diffraction patterns from the opaque strip. The curves of the previous figure represent the sections through the surface I by the planes (ul - uJ2 = const. The geometrical shadow of the edge of the strip is given by the condition u2 = 0, i.e., in the graph (14% + 4 2 = (ul - u2)/2.


0

2

I 4

2

3

4

5 0 1 2 3 4 5 6 7

u,+u,- 2

FIG. 34. The graph of the function cP/27r (121) characterizing the phase of the diffraction from the opaque strip. The geometrical shadow of the edge of the strip is given by the condition u2 = 0, i.e., in the graph (ul + u2)/2 = (ul - u2)/2.

208 JIfif KOMRSKA

D

I I

0.5

0.2

0. I

0.05 . . -2 -1.5 - I -0.5 0 0.5 I /.5 2

xrpmi-

Fro. 35. Diffraction pattern from the opaque filament (47). The thickness of the filament t2 - 4 1 = (4.15 f 0.05) x lo-* nun, XO = (4.33 f 0.03) x lo-' mm, the distance from the source to the speciment ro = (143.16 f 0.57) mm, and the distance between the specimen and the plane of observation z = (33.77 f 0.50) mm. As the density D on the photographic plate (curve a) is approximately within the linear region of the calibration curve, the calculated intensity distribution Z (curve b) is plotted in logarithmic scale in order to stress the agreement between theoretical and experimental curves.

D. More Complicated Diffraction Phenomena

Among the great variety of diffraction phenomena produced by the diffraction screens with various complex transmission functions considerable attention has been devoted to the case of partially transparent half-planes (48-53). It is caused by the effort to employ the diffraction phenomena for checking the axial astigmatism of the objective lens of the electron microscope (48, 51): The axial astigmatism of the objective lens can be determined from the slightly defocused images of circular openings in partially transparent films. As the off-focus distance has to be small (51) the openings transmit a large number of Fresnel's zones (cf. Eq. 73a if z+O). Then it should be possible to approximate the diffraction pattern in the vicinity of the Cfeometrical shadow of the opening edge by the diffraction by a half-plane. In fact, the interpretation of diffraction phenomena in slightly defocused images is much more complicated. The troubles arise from the existence of the transition region. Rather than being rectangular the borders of the film are rimmed by a wedge-shaped region in which the transmissivity z and the phase shift e differ from the values belonging to the points far removed from the borders of the film. The numerical investigation by Fert and Laffite (549 has shown that if the width A& of this transition region is comparable with


the radius a, = [A02] ' /2 of the first Fresnel's zone (cf. Eq. 73b if ro + a), the transition region essentially influences the diffraction pattern. With the existence of the transition region they have also explained the experimental fact found by Haine and Mulvey (SI), namely, that the fringe spacing between the first intensity maxima on both sides of the projection of the opening edge increases in the overfocused image more steeply then predicted by calculations based on the assumption that the functions T and E change discontinuously at the edge of the film.

Another difficulty encountered in interpreting slightly defocused images is the fact that the specimen thickness t is comparable with the off-focus distance z. Even if the specimen border were ideally rectangular there occur diffraction phenomena of width A( w [ A O t ] * / z in the plane x rimming the projection of the specimen border onto the plane x . If the distance z is large, the influence of this rim is negligible. On the other hand if the off-focus distance z is comparable with the specimen thickness t the width [Ao t ] ' / z is comparable with the radius [Aoz]'/z of the Fresnel's zone. Then, the rim in the plane x essentially influences the diffraction phenomena in the defocused image.

In books on quantum mechanics the electron diffraction by a double slit or by a couple of circular openings is frequently discussed. Marton (ZI)

Fro. 36. The electron diffraction pattern from two circular openings (45) [see also (37, 44, 38)]. (By courtesy of Professor Ch. Fert.)

210 JIRf KOMRSKA

intended to carry out this experiment in about 1950, but was restrained from doing so because of experimental difficulties resulting from the short electron wavelength. Nevertheless, in 1956 (37) and 1961 (38, 44, 45) Faget and Fert published diffraction patterns from a couple of circular openings. One of their patterns (45) is reproduced in Fig. 36. The interference fringes in the shadow region between the two openings are clearly distinguishable. The detailed interpretation of these patterns, however, has not been made (38). In particular, the absence of the diffraction fringes in the projections of the openings is not explained. The authors only mention the dark fringe in the center of the diffraction pattern and explain it by the influence of the finite source size.

Disregarding these not fully explained facts mentioned in Section 1II.D we may conclude Section 111 as follows: The scalar diffraction theory adequately explains all the details of electron diffraction patterns from uncharged macroscopic obstacles, provided the conditions of optical diffraction (33), (34), (35) and the condition Ahl ; / [&~] ' /~ 6 1 are satisfied.

IV. SCATTERING OF ELECTRONS BY CHARGED OBSTACLES

If the electrons are incident onto the charged obstacles, the potential energy U of the electrons is a function of position and the scattering patterns depend both on the shape of the obstacles and on the field U (which itself depends, of course, on the geometry of the obstacles). If the scattering field satisfies the conditions (l), the interpretation of the scattering patterns may be based on the diffraction integral in the form of (29) and (49), respectively. The phase of the integrand of the diffraction integral then involves both the phase shift q ( M ) caused by the path differences (cf. Eq. 31), which was studied in detail in the preceding section, and the phase shift cpu(M) caused by the field U (cf. Eq. 32). If we succeed in expressing analytically the potential energy U, the integrals in (32) can be calculated without particular difficulties and so the analytical expression for the phase shift cprr is found. Nevertheless, it is probably always necessary to compute numerically the diffraction integral in order to find the values of the wavefunction at the points of observation.

In this Section two types of the scattering phenomena are discussed in detail. Section 1V.A deals with the scattering of electrons by the charged dielectric sphere situated on a transparent conductive film. In this case the rotational symmetry of the whole problem makes it possible to carry out analytically one integration in the diffraction integral, so that only a one- dimensional integral is to be computed. In Section 1V.B the electron interference phenomena obtained by the electrostatic biprism are interpreted. In this case the problem is two-dimensional and, moreover, it has mirror symmetry.

There is an essential difference in the character of the preceding section and this one. In Section I11 while discussing particular diffraction phenomena

SCALAR DIFFRACTION THEORY IN ELECTRON OPTICS 21 1

we have expressed the diffraction integral in terms of special functions; we have also presented as comprehensive graphs of the intensity and the phase distribution as possible, but we have not discussed the individual special features of the diffraction patterns. These particular points are widely discussed in books on light optics, especially in older ones (36). The particularities of the scattering patterns are now studied in detail in this section. The reason for this consists in the fact that up to now insufficient endeavor in the purely wave-mechanical interpretation of the scattering by charged macroscopic obstacles has been made in the literature. For example, the scattering phenomena by charged obstacles observed in shadow electron microscopy are usually interpreted only roughly with the use of the concept of the trajectory and of the relations of classical mechanics. Also, the interference produced by the electrostatic biprism is not currently treated as a scattering problem. Its interpretation is usually based on the model of the interference phenomenon from two coherent virtual sources. Here, we try to present a straightforward interpretation based on the purely wave-mechanical standpoint. It does not employ any model and is not more complicated than the traditional interpretation.

A . Scattering of Electrons by a Charged Dielectric Sphere Lying on a Conductive Supporting Film

When irradiating the dielectric specimen by the illuminating beam in the electron microscope, the specimen becomes charged. The origin of these charges can be explained by the secondary emission. If the yield of the secondary electrons is greater or smaller than unity, a positive or negative charge appears on the specimen. These charges do not appear in the focused electron image; in the course of the exposition they can, however, shift the image or a part of it, and thus deteriorate the pattern. The charges, however, become evident in shadow electron microscopy.

By means of shadow electron microscopy the fluctuating charges in insulating foils (formvar, collodion, A1,0,, SiO) have been observed by Mahl and Weitsch (24) and by Drahol and Delong (25). Mahl and Weitsch have explained the migration of charges by nonuniform internal charging in the foil, which gives rise to an electric field. The intensity of this field es$mated from the deflection of electron trajectories is of the order of lo6 V/cm. Such a high field gradient can provoke electron field emission which neutralizes the charges. L

If the dielectric particles lie on a conductive film, their charge increases up to a certain value and then a dynamical equilibrium of charging and discharging prevents further charge increase. It is interesting to note that the resulting charges are positive, as verified several times experimentally (55,

212 JIRf KOMRSKA

26, 27). The magnitude of these stationary charges depends on the material and the geometry of scattering objects and on the energy and current density of the incident electrons. Two examples described in the literature give general information about the magnitude of the charges : The interpretation of the scattering pattern of cube-shaped NaCl crystals with a 1 pm edge gave 2 V voltage between the supporting film and the upper face of the cube (26). In the case of latex particles of 0.56 pm diameter a voltage of 4 V between the supporting film and the point of the sphere furthest removed from the supporting film has been determined.

The electron scattering by a charged polystyrene latex particle situated on an earthed carbon film gives rise to pronounced scattering patterns (27) (see also Fig. 38). With the use of the diffraction integral (29) from Section 1I.B these scattering patterns can be interpreted in particular detail as will now be shown.

I . The Formulation of the Problem

A general treatment of the scattering of electrons by the charged dielectric sphere lying on a conductive supporting film will be illustrated by the interpretation of the pattern shown in Fig. 38. Therefore, the values of the experimental parameters of this particular scattering phenomenon are (see Fig. 37): ko = (1.45 f 0.01) x lo9 mm-'; the distance of the source Po from

'FIG. 37. Geometry of the experimental arrangement for observing the electron scattering by the charged dielectric sphere situated on a conductive supporting film.


the supporting film ro = (75.0 & 1.5) mm; the distance between the supporting film and the plane of observation n, z = (4.15 & 0.20) mm; the diameter of the latex sphere 2a = (5.57 5 0.1 1) x

Because the earthed conductive film screens off the field from the charges on the sphere it is advantageous to identify the plane x to which the diffraction integral is related and the plane of the film (Fig. 37). Then the scattering field outside the sphere may be approximated by the field which (i) above the film is the same as the field of the dipole formed by the charge in the center of the sphere and its electrostatic image with respect to the plane x , and (ii) beneath the film is equal to zero:

mm.

where 2 is the number of elementary particles on the sphere. Let the sign of 2 be specified such that 2 > 0 if the total charge on the sphere is positive and Z < 0 if the charge is negative.

The scattering pattern is observed at a large distance from the supporting film. Therefore, in specifying the transmission function in the plane x we can neglect the fluctuations of the transmission function of the carbon film itself: Within the area of one Fresnel’s zone there is such a large number of these fluctuations that the transmission function may be considered to be a constant corresponding to the respective mean value. The value of this constant is inconsequential, because it reduces the amplitude and shifts the phase of the scattered wave as a whole, which does not influence the distribution of the relative intensity in the pattern. Thus, the transmission functionf(A4) in the plane x may be chosen to be zero within the region of the geometrical shadow of the sphere and unity outside this region:

where

pi = a(1 - 2a/ro)-1/z = a/(l + a/ro) ( 1 24)

is the radius of the shadow region of the sphere in the plane x .

specified. In this way all the quantities appearing in the diffraction integral (29) are

214 JIfif KOMRSKA

2. The Diffraction Integral

First, we shall calculate the integrals giving the phase shift cp,(M) caused by the field U (cf. Eq. 32). From (122b) it follows that j: U(P + s,t)dt = 0 for all the sw , including so. In order to evaluate the integral j: U(Po + r, t )dt it is necessary to find the coordinates of the point Po + r,t. From Fig. 37 it is obvious that rM = ter + qe, + roec, where the e’s are the unit vectors in the directions of the coordinate axes, so that the point Po + r,t has the coordinates t t , qt, ro(t - 1). Then it follows from (122a) that if 0 6 t 4 1 and (t2 + q2)t2 + ro2(t - 1)2 + 2m0(t - 1 ) = 0 the potential energy U is given by

-{(t2 + q2 + ro2)t2 - 2r0(r0 + a)t + (ro + a)2>-1/2).

Using the relation

-- In {2[A(At2 + Bt + C)]’/’ + 2At + B} + const., dt

if A > 0,

and introducing the polar coordinates T 2 + q2 = p 2 we find

where

F(p) = 11 + ( a / ~ ) ~ J ” ~ [ l + ( ~ / r ~ ) ~ ] ’ / ~ + p/r0. (126)

Unfortunately, 1: U(Po + ro t ) dt is divergent. Therefore. in contradistinction to (32), it is not possible to relate the phase shift caused by the presence of the field U to the origin. We relate it to the boundary Ml of the geometrical shadow of the sphere (cf. Fig. 37). The radius of the shadow region is p = pi (cf. Eq. 124). From (125) it follows that

+ (127) Ze2 [ 1 - a/ro ~ ( p 1) - 4ns0

rl /:U(Po + r,t)dt = -In - 1 + a/ro F ( p , ) + 1 - a/ro


With respect to (125) and (127) the phase shift cp,(M) related to the point Ml is

ko ko Ze2 2E 4ns0

p,(M) = - 2 I0 [ry U(Po + rM t ) - rl U(Po + rlt)l d t = - - - R(p),

The phaseshift p(M) due to the path differences (cf. Eq. 31) is given by

The substitution of (60) and (128) into the diffraction integral (29) yields (60)-

1 0 +(P) = D , Srn 1” exp [ - iko p - cos(O - x) dO

P I 0 SO

where, in contradistinction to (30),

The integral representation (62) of the Bessel’s functions makes it possible to rewrite the diffraction integral (130) in the form

where the parameters cl, c 2 , and c3 are (cf. the experimental values given in Section IV.A.1 with so A z)

cl = ko/so = (3.50 & 0.18) x lo6 rnm-’,

ko 1 c2 = - (- + $) = (1.82 f 0.10) x lo6 mm-’,

4n ro (133)

ko - (2.22 0.01) x 10-3. e2 cj=---

l 6a2~ , E

216 JIkf KOMRSKA

The distribution of relative intensity is given by I = $$*/$o$o* (cf. Ao2/(ro + 2)’. With the use of (131), (132), Section ILB.8), where +o$o*

and (133) we then obtain the resulting expression for the relative intensity: 00 2

W = ( 4 7 1 ~ ~ ) ~ 1 Sp,J,(c~o~)exp{2ni[e~ p 2 - z c 3 W)]>P d p 1 . (134)

3. Determination of the Magnitude of the Charge

For computing the intensity distribution I(o) according to (134) it is necessary to know the number Z of elementary charges on the particle. This number depends on the parameters of the illuminating beam, being the result of a dynamical equilibrium between charging and discharging. Therefore, it is advantageous to determine it from the scattering pattern itself. Its determination can be based on the following consideration: The integrand of (134) is a rapidly oscillating function. The main contribution to the value of the integral comes from that part of the integration region where the phase of the integrand is stationary, i.e., from the surroundings of the value p = ppl given by

2c2Pst = zc3Q’(Pst)9 (135)

where the dash denotes the derivative with respect to p . It may be expected therefore, that the first minima in the intensity distribution are approximately at those points cli where the argument clripst of the Bessel function Jo is a zero pointjoi of Jo, i.e.,

c ~ ~ s t r i = j o i * (136)

Thus, having measured the radii oi of the dark rings in the scattering pattern in Fig. 38 we obtain from (135) and (136)

where

2c2 8 n ~ ,

c3 c4=-=-- e2 ($ + i ) E = (1.63 f 0.09) x lo9 mm-2. (138)

The second dark ring in Fig. 38 has the radius o2 = 2.28 x mm. mm. Taking With jO2 = 5.52 it follows from (136) that pst = 6.93 x

into account that

-- P - P 3 w - a z / p 2 W P ) 2a P W P ) + F(P) ’


FIG. 38. The electron scattering by a charged polystyrene latex sphere situated on a supporting carbon film (27). For the values of the experimental parameters see Section 1V.A. 1.

we obtain pSt/Q’(p,,) = 6.44 x lo-’ mm’. Hence, from (137) and (138)

Z = 1.05 x lo3, (139)

and the total charge on the latex sphere is Ze = 1.68 x C. The voltage between the supporting film and the point of the sphere most distant from the supporting film is 2Ze/(3a) = 4.02 V.

4 . Comparison of the Theory and the Experiment

Knowing the values of all the parameters of the integral in (134) it is possible to compute the intensity distribution corresponding to the scattering phenomenon in Fig. 38. The lower curve in Fig. 39 giving the intensity distribution Z(a) represents the results of the computation of (134) with the values given by (133) and (139). The upper curve is the photometric trace of the density distribution in the photographic plate showing the pattern reproduced in Fig. 38. The deviations in the values of intensity minima (especially the first minimum) and in the central maximum are believed to be caused by the finite size of the electron source and by the imperfections of the photographic registration and of the photometer recording. Otherwise the calculated intensity distribution is in good agreement with the experimental one. More- over, the interpretation of the scattering pattern enables us to determine the magnitude of the charge on the particle with a precision of about 10%.

21 8 JIRf KOMRSKA

0 0.005 ulrnrnl -- FIG. 39. Comparison of theory and experiment. The upper curve represents the photo-

metric trace of the density distribution D in the photographic plate of the scattering pattern given in Fig. 38. The lower curve shows the intensity distribution Z(o) calculated according to (134) with the values of the parameters given in (133) and (139).

B. Electron Interference Phenomena Produced by Electrostatic Biprism

In 1955 Mollenstedt and Duker (25,26) described their well-known electron interference experiment (Fig. 40). Using a metallized filament placed between two grounded plates they split the electron beam into two parts, and by

M, Mz Ml M2

FIG. 40. Analogy between the electrostatic biprism in electron optics and Fresnel biprism in light optics.


applying a positive potential to this filament they caused the two parts of the electron beam to interfere. The action of such an electrostatic biprism was then analogous to the action of the Fresnel biprism in light optics.

Since 1956 this experiment has been repeated in several laboratories (37, 56-6Za) and has become the basis of electron interference microscopy [see e.g. (62-65)] and interferometry (66, 67). Recently these interference phenomena have been used for measurements of quantized magnetic flux trapped in superconducting tubes (68, 69). Up to now about 110 papers have been published dealing with the interference phenomena produced by the electrostatic biprism.

Let us consider the scattering (or interference) patterns observed at different potentials of the biprism filament shown in Fig. 41. If the filament has the same potential as the outer electrodes of the biprism (zero potential), a diffraction pattern of the filament is observed in the plane of observation (Fig. 41c). At negative filament potentials the electrons are deflected from the axis plane of the optical system (cf. Fig. 42) and the intensity distributions in the plane of observation resemble the diffraction of a filament with a larger diameter (Figs. 41a, b). At positive filament potentials the paths of the

FIG. 41. Interference patterns at different filament potentials (47): (a) pf = -20 V; (b) 'pf = -10 V; (c) 'pf = 0 V; (d) 'pf = 10 V; (e) pr = 20V; (f) 'p, = 30 V.

220 JlRf KOMRSKA

electrons passing on both sides of the filament are deflected towards the plane of symmetry of the optical system, and in the plane of observation pronounced interference fringes are recorded (cf. Figs. 41d, e, f).

Following the classification of Faget (38) the electrostatic biprism with a positive filament potential is called a convergent interference device, and a biprism having a negative filament potential will thus be a divergent interference device. In light optics the divergent Fresnel biprism (see Fig. 42) was known in the last century (70).

FIG. 42. Analogy of the “divergent ” Fresnel biprism and electrostatic biprism at negative filament potential.

The individual properties of the electron interference phenomena produced by the electrostatic biprism (e.g., the spacing of the interference fringes, the width of the interference region, etc.) are usually discussed on the basis of a model which approximates the phenomenon by the interference of two electron beams coming out of two virtually separate and coherent sources [cf., e.g., (38, 47)]. Even though the conclusions derived from such a model are very useful we should avoid using models if possible. In this section the interference phenomena produced by electrostatic biprism are treated as the scattering of electrons by the electrostatic field of the biprism (71). We shall specify the scattering field (cf. Eq. 141) and then, without using any model, all the details of the interference pattern will be derived from the properties of the diffraction integral.

1. Formulation of the Problem

Our aim is to find the intensity distribution in the interference pattern by calculating the diffraction integral. To be able to judge the justification of the individual approximations which will be introduced we give in Table I the values of the experimental parameters.

SCALAR DIFFRACTION THEORY IN ELECTRON OPTICS 22 1

TABLE I

VALUES OF EXPERIMENTAL PARAMETERS

Wave number of electrons Energy of electrons Electron source to filament

Filament to plane of observation

Filament diameter Distance of the biprism plates Filament potential Investigated region of the

plane of observation Source width Monochromaticity of electron

distance

distance

beam

ko E

ro

Z

2a 2b Vf

A X O I X O

(1.45 f 0.01) x lo9 mm (74.8 & 1) keV

(143.16 & 0.57) mm

(33.77 & 0.50) mm (4.15 f 0.05) x mm (2.0 f 0.1) mm -35 v < Vf < 35 v

-3 x mm < x < 3 x mm 2 x mm

1 x 1 0 - 3

We shall describe the incident electrons by a cylindrical wave having an axis parallel to the biprism filament. Therefore, we may use the diffraction integral in the form of (49) derived in Section 1I.C for the case of two-dimensional waves. The straight line x to which the diffraction integral is related passes through the center of the filament 0 and is perpendicular to the plane specified by the filament and the source Po (cf. Fig. 43). (Such a choice of the

J * Pfx,z)

Fra. 43. Geometry for the calculation of the intensity distribution in the plane of observation rr.

222 lI#f KOMRSKA

straight line x contradicts the requirement that there should not be any scattering objects behind it. In our case, however, half of the filament protrudes behind it. Nevertheless, the Green's function in the form of (42) is applicable even in this case, because the filament is opaque (cf. Eq. 140) and very thin in comparison with its distance from the plane of observation n.) The choice of the reference frame 0, @, is evident from Fig. 43.

The biprism filament is opaque for electrons. Therefore, the transmission function along the straight line x has the form

f ( @ ) = O if [ ( / < a , f ( < ) = I if l@l>a . (140)

Troubles arise while expressing analytically the scattering field U. Some biprism designs-very useful and convenient from the experimental point of view-have the filament very short and the filament holders very massive (38, 72). The filament holders are at the same voltage as the filament, and therefore they strongly influence the field in the close proximity of the filament. Then it is usually impossible to express analytically the field inside the biprism. Fortunately, the first interference experiments by Mollenstedt and Duker (16) were performed with a biprism with a long filament and filament holders outside the biprism. The authors have shown numerically that the field in the proximity of the filament corresponds to the field in the cylindrical capacitor.

Therefore the scattering field is approximated by the field of the cylindrical capacitor, the inner electrode of which has the same diameter 2a as the biprism filament, and the outer electrode having the diameter 2b equal to the distance between the plates of the biprism. Outside the biprism the field is supposed to be screened off and, therefore, equal to zero. Then, the potential energy U of electrons is expressed by

U(<, 0 = 0 if t2 + c2 2 bZ, (141b)

In this way all the quantities appearing in the diffraction integral (49) are qf being the voltage applied to the biprism filament.

specified.

2. The Difraction Integral

by the field U (cf. Eq. 32). From (141b) it follows that First we shall calculate the integrals giving the phase shift q u ( M ) caused

- 1 "1

U(Po + rM t ) d t = J~ U(Po + rM t ) d t , (142) JO dr


where (see Fig. 43)

where (see Fig. 43)

1 1

f0 U(P + s;t) d t = j U(P + s o t ) d t . (147) l-b/(xl+z2)’/’

To calculate the integral (142) we must know the coordinates of the point Po + r,t. FromFig. 43 it follows that they are 5t and ro(t - 1). Then, it follows from (141a) that if 6, I t 5 1, and u2 5 (c2 + ro2)t2 + roZ(l - 2t) I bZ, the potential energy U is given by

Using the relation

J4AC - B2 A

Iln(At2 + Bt + C) dt = ln(AtZ + Bt + C) - 2t +

2At + + constant if 4AC - B2 > 0, (148) arctan J4AC - B2

and the expression (143) for 6, , we find after a lengthy manipulation

224 JIki KOMRSKA

Bearing in mind that 15 I / r o Q 1, and supposing that the integration region of the diffraction integral (49) may be chosen such that

151 4 b, (150)

(this condition is acceptable, because if the integration region were (- b, b), it would involve almost lo7 Fresnel zones. In our calculations (cf. Eq. 161 below) the integration region was restricted to l(Imax/b < lo-’), then it is possible to simplify (149) into the form

- b 1 + - - +- - . (151) [ ; (3’ :4 (:)“I) It is much easier to calculate the integral (144)

To calculate the integral (145) we specify the coordinates of the point P + s,t. From Fig. 43 it follows that they are x + (5 - x)t and z(1 - t). Then,

x)’ + z2 x(5 - x) - z z t Z + 2 b2

b’ U(P + s,t) = -lelcp, ln[c‘ -

2 In(a/b)

Hence, using the integral (148) and the expression (146) for 6 , , we obtain

- lelvr ze t - x l t l U ( P + s , t ) d t = - ln(a/b) [z’ + (t - x)’I1/’ (T (In b - I)

I/’ (5 - 4‘ 2 5 - x + arctan - Z - sgn t( [b (1 + 7) - 11

Again, bearing in mind that 15 - x I / z 4 1, and supposing that (b/C)’ B 1 (cf. Eq. 150), the expression (153) may be simplified to the form

- b[l + (:)’ + 4 (:)4]). (154)


It is easy to evaluate the integral (147):

With respect to (151), (152), (154), and (155) the phaseshift cpU(M) (32) is given by

The sum rM + sM is obtained from (93) by putting q = y = 0:

From (140), (152), (155), (156), and (157) it follows that the diffraction integral (49) has the form

- a

(158)

where

D, = ‘ )I , (159)

* t[($ + &) I n 7 I tl + n sgn 5 - (1 + ;$)I), (160) b

and t,,, denotes a value of coordinate 5 such that any enlargement of the integration region of the diffraction integral has a negligible influence on the value of the wavefunction.

The intensity of the unperturbed wave is proportional to $o(P)$o*(P) = ~ A o H o ( l ) ( k o R ) ~ ’. Using the asymptotic expression (44) for the Hankel’s function we obtain $o$o* = 2A02/(nk,R) = 2A02/[nko(ro + z)].

From Section II.B.8 it follows that the distribution of the relative intensity in the interference pattern is given by the expression

226 JIM KOMRSKA

Using this relation the intensity distribution has been computed. Before comparing the computed and experimentally found intensity distribution it will be shown that a good many of the individual properties of the interference pattern can be obtained even without computation, just by analysis of the properties of the stationary points.

3. Special Properties of the Interference Pattern

The main contributions to the value of the wavefunction come from the surroundings of those points in the plane x , where the phase of the integrand of the diffraction integral is stationary. From the positions of these stationary points it is possible to delineate the region in the observation plane ~t in which pronounced interference phenomena are observed, to determine the positions of the intensity maxima, the spacings of the fringes, etc.

a. The stationary points. The positions of the stationary points are determined by the condition that the derivative of the phase of the integrand in (158) with respect to the variable of integration is equal to zero. Then the differentiation of (160) leads to the equation

With respect to the numerical values of the experimental parameters in Table I and to the condition (150), this equation is approximately satisfied if

from which it follows that there are at most two stationary points M1(tl, 0), M 2 ( t 2 , 0) and that their coordinates are given by

roz l e l v , 1 +II---

ro x t2 = ro + z In(a/b) 2E *

(162a)

(162b)

It is obvious from (162) that the stationary points are in the plane x situated symmetrically with respect to the point Mp(rox/(ro + z), 0) (see Fig. 44).

b. The interference region. Evidently, the interference fringes become faint whenever one of the two stationary points is screened off by the biprism filament. Thus, the coordinates of the boundary points M l ( x l , , z) , Mz(xza , z)


FIG. 44. The stationary points M I , M2.

of the interference region of the plane of observation (cf. Fig. 40) re by the conditions g, = a, g, = -a, and it follows from (162) that

x1,2= - + [ n z - - iE + ; 0.0 + z)] '

Then the width W of the interference region is given by

l e t % 1 Q w = x2 - x, = -2 nz - - + - (ro + 4. [ In(a/b) 2E ro

zcified

(Note that ln(a/b) < 0.) The condition for the appearance of pronounced interference fringes is W > 0, i.e.,

(el% 1 a nz - - + - (ro + z ) < 0. In(a/b) 2E ro

From this relation two conclusions may be drawn: (i) For the appearance of interference fringes in the plane of observation

n(at a distance of z > 0 from the biprism filament) the voltage qf applied to the filament must satisfy the condition

228 JIEi KOMRSKA

(ii) At a certain filament voltage 'pf > 0 the interference fringes are observed only if the distance z of the plane of observation n from the biprism filament satisfies the condition

7r-- ln(a/b) 2E ro

z >

Even with the divergent biprism (see Fig. 42) the interference fringes can be obtained when an optical system is used for observing the virtual patterns in planes of observation in front of the biprism (70). Then z < 0.

c. The spacing of interference fringes. From the fact that the wavefunction at points P(x , z) of the plane of observation is given especially by the contributions coming from the stationary points M , and M 2 , the following condition for the intensity extremes is obtained :

1 1 exp [ iko [ rl + s1 - (? I jar,u(Po + rlt) d t + s1 ja,lU(P + sit) d t ) / 2 E ] )

= iexp(iko[r2 + s2 - ( r 2 [d:;(Po + r2t ) d t + s2 U ( P + s 2 t ) d t ) / 2 E ] ) , 1

52

-+ _j __+ + where rl = P o M l , s1 = PMl , r2 = P 0 M 2 , s2 = P M 2 . This condition is equivalent to the equation

1

- [rl jarlU(Po + r,t) dt + s1

1 1

- r2 ja U(Po + r2 t ) dt - s2 Id U(P + s2 t ) d t ] / 2 E ) = nn, r 2 * 2

n = 0, & 1, &2, . . . . (166)

The numerical values in Table I justify the following simplifications :

r1 + s1 - r2 - s2 = - " - " [(el + t2)($ + f) - 2 3 ; (167) 2

from (151) it follows that

1

r l /d,lU(Po+ r l t ) d t = -

rz J6 U(Po + r 2 t ) dt = - 1

r2


and from (1 54), 1

s1 j6 U(P + s , t ) d t = -

s2 ja V(P + s,t ) d t = - *I

1

32

If the points of observation lie inside the interference region the coordinates of stationary points are such that [ t1 [ = tl, [ t2 [ = -<,, and therefore

- 1

- sz s, V(P + s, t ) d t = - I e ' " n(tl + tZ). (168) 52 W / b )

With the use of (167) and (168) the equation (166) takes the form

nn n(T1 + tZ)=-. (169)

2 k0

Substituting the coordinates of the stationary points (162) for t1 and 5, and writing ko = (2mE)'/z/ii, we obtain the following condition for the positions of intensity extremes in the plane of observation:

It follows from (170) that inside the interference region the extremes of intensity are at equidistant positions and the spacing of the bright fringes is

Thus we have found that the spacing of the fringes is inversely proportional to the filament voltage and proportional to the square root of the accelerating voltage.

In a similar way further properties of the interference patterns can be explained. Only two of them will be mentioned here.

If the point of observation P lies outside the interference region and if the filament voltage cpf satisfies the condition (164), the filament edge is to be taken as one of the stationary points. For example, substituting the value t1 from (162a) and t2 = - a into (169), we can determine that outside the interference region the spacing of faint interference fringes decreases with increasing distance from the middle of the interference pattern.

230 JIfif KOMRSKA

At negative filament voltages the main contributions to the value of the wavefunction in the dark central region of the pattern (cf. Fig. 45) come from the filament edges. Putting = a and c2 = -a in (169) we can determine that the positions of the extremes of intensity in the central region of the pattern are independent of the filament voltage and correspond to the extremes of the interference pattern from two coherent sources situated at the edges of the filament as found experimentally (26, 38).

4. Comparison of Theory and Experiment

For the comparison of theory and experiment we use the experimental material from our laboratory. Unfortunately, for this purpose the filament holders of the biprism are too massive and the filament is short (72). Con- sequently, the gradient of the field in the proximity of the filament is smaller than the gradient calculated from (141a). It was found experimentally that the patterns produced by this attenuated gradient of the field are the same as the patterns from the biprism with the ideal field (141) but with a smaller filament voltage qfl. The ratio qfl/qf can be determined from the ratio of fringe spacing calculated from (171) and measured from patterns in Fig. 41. With a precision of 4% this ratio does not depend on the filament voltage, being qP;/qf = 0.55. With the use of these values of qf' and the parameters given in Table I the intensity distribution has been calculated from (161). Figures 45-47 illustrate the agreement of the theory and experiment. The curves (a) in these figures are experimental ones; they represent the photometric records of the density distribution in the negatives of the patterns. The curves (b) are the calculated intensity distributions.

(i) The scattering phenomena at negative filament potentials represent the pattern in Fig. 45 taken at qr = - 20 V, i.e., qf' = - 11 V.

(ii) At zero filament potential the interference pattern is in fact the diffraction pattern from an opaque filament (cf. Fig. 35).

(iii) Interference phenomena at low positive filament potentials, where the interference region is very narrow and contains only a few interference fringes, are represented in Fig. 46 by the pattern recorded with qf = 7.5 V, i.e., q; 2 4 V.

(iv) With increasing positive filament potential the spacing of interference fringes decreases (cf. Eq. 171). That is why the influence of the finite source width (cf. Table I) appears more enhanced in the experiment. From the interference pattern at the filament potential qf = 30 V, i.e., 'pf' = 16.5 V, given in Fig. 47, we can see that this gives rise to an increased background intensity and reduces the visibility of interference fringes. Nevertheless, with regard to positions of the interference maxima and minima, and even the relative intensities of individual interference maxima, the theory and the

SCALAR DIFFRACTION THEORY IN ELECTRON OPTICS 23 I

-3 -25 -2 -/.5 - I -05 0 05 / / 5 2 25 x&Jl-

FIG. 45. Scattering pattern produced by electrostatic biprism at negative filament potential vr = -20 V, i.e., vf’ = - 11 V (47). Densitometer trace of the density distribution D (in arbitrary units) on the photographic plate (curve a) compared with the calculated intensity distribution I (curve b). For the experimental parameters see Table I.

FIG. 46. Interference pattern at filament FIG. 47. Interference pattern at filament potential qf = 7.5 V, i.e., vr‘ 4 V (71). potential vr = 30 V, i.e., vr’= 16.5 V (47).

experiment are in very good agreement [provided the filament potentials do not reach the values at which the contrast of the interference is reversed (38,

We may conclude Section IV by stating that the scalar diffraction theory provides an adequate explanation of the scattering patterns from the charged obstacles if the conditions (l), (33), (34), and (35) are satisfied.

731-

232 JIfif KOMRSKA

v. SUMhlARY

In this article we have shown possible applications of the scalar diffraction theory in electron optics. The scattering patterns from both charged and uncharged macroscopic objects are discussed. These patterns are currently observed while using nonconventional techniques of electron microscopy. The potential energy of electrons in the scattering fields is small in comparison with their kinetic energy. Under this condition it was possible to express the wavefunction at points of observation in terms of the diffraction integral.

If the scattering objects are uncharged the diffraction integral may be simplified into the form currently used in optics. Because of the very small wavelength the conditions necessary for the simplification of the diffraction integral are well satisfied in electron microscopy. Therefore, a good agreement between the experimentally found and the calculated intensity distributions is achieved, as demonstrated in many examples in Section 111.

A more complicated situation arises when the electrons are scattered by charged obstacles. In this case the diffraction integral has a form suitable for the description of the scattering in slightly nonuniform media. The numerical calculations in Section IV have confirmed a good agreement with experiment. Moreover, even without numerical computations the scattering patterns can be discussed in remarkable detail by using the properties of the points in the integration region at which the phase of the integrand is stationary. This was illustrated in Section IV.B.3 on the electron interference produced by the electrostatic biprism.

ACKNOWLEDGMENTS This paper represents the substance of lectures which I had the opportunity to deliver

at the University of Aston, Birmingham, England in the autumn of 1968. I am pleased to have this opportunity of thanking Mr. T. Mulvey for kindly inviting me to take part with these lectures in the postgraduate course held under his supervision. I am deeply grateful to Professor S. E. Hunt and to all the members of the Department of Physics for their hospi- tality.

I thank Professor V. DrahoH from the Institute of Instrument Technology in Brno for enabling me to collect the material for this paper, for his continuous interest in my work, and for his comments. To Mr. W. James of Aston and Mr. M. Lenc and Mr. M. Novotnf of Brno I am indepted for great help and encouragement in the course of many discussions during the preparation of the text. Finally, I wish to express my gratitude to Mrs. Z. Kulier- OVA and Mrs. J. TAborskA for their long and patient assistance in the numerical calculations and the writing of the manuscript.

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Recent Advances in Biological Temperature Measurements*

HARDY W. TROLANDER

Yellow Springs Instrument Company, Inc., Yellow Springs, Ohio

AND

JAMES H. VEGHTE

Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, Ohio

I. Conductive Electric Thermometry ............................................................ A. Introduction .................................................................................... B. Current Practice in Biology C. Thermistors .................................................................................... D. Thermistor Thermometry .................................................................. E. Quartz Resonator Thermometry ......................................................... F. Conclusions ....................................................................................

11. Radiation Thermometry ........................................................................ A. Introduction .................................................................................... B. Infrared Electromagnetic Spectrum, Detectors, and Radiographs. ................. C. Biological Infrared Radiography.. ....................................................... D. Future Considerations ..................................................................... References ..........................................................................................

...............................................................

235 235 23 8 242 252 259 261 261 261 264 266 269 210

1. CONDUCTIVE ELECTRIC THERMOMETRY

A. Introduction

The evolution and growth of the life sciences over the past ten years has encouraged the development of a variety of instrumentation for experimental and routine purposes. Advances in medicine, oceanography, and, broadly, the study and control of man’s immediate environment have caused the measurement of many quantities to be made routinely at sites which until recently were regarded as obscure. Biological temperature measurements

* Section I of this chapter is the work of H. W. Trolander and Section 11 that of J. H. Veghte.

235

236 HARDY W. TROLANDER AND JAMES H. VEGHTE

have increased in variety and frequency and to an extent that has had a substantial influence upon the temperature measuring art. An examination of the circumstances within which these measurements are made is useful towards identifying the recent and perhaps durable advances in this art.

Biological measurements routinely occur within a spectrum extending somewhat beyond those limits of environment within which biological organisms survive. Presently the great bulk of biological temperature measurements fall between - 60°C and + 125°C with heavy emphasis upon the region between -5°C and +5O”C.

Certain organisms, man for example, are equipped lo maintain a fairly high order of temperature regulation. Other organisms adopt, with subtle differences, their immediate environmental temperatures.

Currently most thermometrical measurements depend upon conduction to communicate heat between the biological organism and the sensor of its temperature. This mechanical contact between body and sensor establishes a clear and direct channel of communication. However, the equally direct yet changing stresses within the biological environment often require that the sensor possess considerable mechanical strength. This requirement is costly in terms of thermal mass, and hence the sensor may tend to influence the temperature at the site being measured. Particularly when discrete measurements must be made at the interface of an organism with its environment, as for example skin or near surface temperatures of man, communication via radiation will probably be less perturbing to the site of information. Yet it is fundamental to present the communication theory that the interposition of any medium between source and receptor will, to some degree, degrade the quality of the information transfer.

Within the world of biological temperature measurements, the aforemen- tioned limitations on measurement by conduction and radiation are very real and restraining to present practice of the art. Developments within the last decade do not appear to substantially change the balance between the tradeoffs and compromises required to utilize either mechanism. Thus there has been considerable progress in practical thermometry based on both means of transferring thermal information. At the same time, there does not appear to have been any salient advance in devices utilizing convection as the means of communicating thermal state, and which are also useful in routine biological thermometry.

Looking toward the future, present thermometric means appear to fall most short of their users’ requirements in those instances where measurements must determine “ state ” at interfaces. Presently, continuous measurements of the core temperatures of unrestrained mammals, birds, etc., are practical through the use of implanted sensors and implanted or “piggy- backed ” telemetry. When data are needed to aid in unraveling energy transfer

ADVANCES IN TEMPERATURE MEASUREMENTS 237

phenomena between freely moving organisms and their environment, the present state of the art is very inadequate, and improved quantification of these relationships is a present pressing requirement within several of the subdisciplines of biology. Given that the interfaces in question are also irregular in shape and generally are not of uniform composition, it is likely that necessity will tend to require the invention of improved radiometrical systems as the means for obtaining more substantive data.

A favorite preoccupation within many of the experimental areas of the life sciences is the gathering of multiparametered data in massive quantities. This activity is abetted by the relatively high state of development of the electricity based communications art and the availability of large computers. In turn these tools of communication and computation have exercised an almost pervasive influence upon current developments in biological thermometry. For example, the classical mercury-in-glass thermometer has many desirable characteristics ; adequately high resolution, excellent linearity and stability with time, etc., which might be expected to spur the development of a variety of specialized new versions for biological applications. But its information format does not readily exist in combination with simple means for simultaneous remote communication and (or) direct entry into present-day computers. Admittedly, mercury-in-glass has other limitations, but this particular restriction currently appears to override any force toward overcoming the others, and the art remains essentially as it was many years ago.

On the other hand the present combination of circumstances offers a veritable mother lode for those of us who seek to prod the art of temperature sensing with electrical devices. Improved forms of older and well-characterized devices such as thermocouples and pure metal resistance thermometers have appeared in response to the growing metrological needs of biology. Certain forms of other devices, well known yet despised because of their sensitivity to temperature, are now highly regarded as thermometers. Advances in the semiconductor art have revealed a wide variety of devices with potentially excellent characteristics as biological temperature sensors. Additionally, the older semiconductor art has matured to the point where thermistors made from combinations of the oxides of certain of the transitional metals have become well characterized and reproducible.

A statement of task, involving basic biological measurements of almost any sort, implicitly recognizes that evolution has tended to favor the development of those life forms which had means for isolating their vital functions from the immediate effects of rapid and often harsh environmental changes. In the instance of a biological temperature measurement, more often than not it seems that the site of interest lies within a surround consisting of a material which includes among its characteristics that of being a first-rate thermal barrier. Penetration of this barrier even in those comparatively few


instances where a natural orifice accesses the site of interest is traumatic, often to the extent of influencing the data.

B. Current Practice in Biology

Ten years ago the routine practice of electric thermometry was limited to a minority of the subdisciplines of biology. The bulk of the applications were in research, and most of the instrumentation required that its users have some proficiency as metrologists in addition to their primary professional disciplines. Thus while resistance and thermoelectric thermometry were hardly new, biological problems as a class required apparatus capable of identifying small differences or changes of temperature which was beyond the state of the art as routinely practiced in other fields. Typically a resistance or thermocouple thermometer covered a span of hundreds of degrees and seldom needed to resolve to fractions of a degree. Introduction to widespread biological use required that spans be shortened and resolution increased, each by roughly an order of magnitude. Since many of the sites of measurement were mobile or semimobile as well, there was a general compounding of problems of lead resistance, variable thermal gradients between site of measurement and reading instrument, and structural strength of sensors. Additionally many systems required high-gain amplifiers which added uncertainty to deflection types of meter presentation.

The situation was such that while a user who was sophisticated in electric thermometry could usually collect data accurate to today’s best standards, the system under measurement had to be so constrained as to interfere with what to the biologist (or surgeon or biochemist, etc.) was the primary practice of his discipline.Thus in ordinary hands a mercury-in-glass fever thermometer was often a more accurate and useful tool than the best of the electrical systems.

Although other requirements may also be isolated as precedents, it appears that the practice of open-heart surgery initiated in the 1950’s and matured into relatively routine clinical procedure by the early 1960’s provided a significant impetus for newer forms of electric thermometry ( I ) which were then extrapolated into broader use throughout the various specialized areas falling under the biological umbrella.

Returning to the problem, open-heart surgery required that the patient be forced into a hypothermic state by the application of ice or other cooling means to the greater part of his total peripheral area. Simple instrumentation was needed to establish that the required reduction of the patient’s temperature had been achieved. Since the skin is an insulator, near-surface temperatures were inadequate as indicators of the desired thermal state.

The solution, now widely practiced, employs a thermistor suitably insulated


and of small enough size to be introduced deeply into the body. Sites in the esophagus or rectum are adequately distant from the surface. A wheatstone bridge operating off-null as a deflection instrument and powered by a flash- light battery is normally monitored by the anesthesiologist during the procedure. The thermistor has adequate structural strength for the application and the sensitivity necessary to drive a rugged moving-coil microammeter calibrated in fractions of a degree without amplification. Thermistors were readily available with electrical resistance values which matched common moving-coil meters while at the same time both their resistance level and sensitivity to temperature were such that the ordinary user could forget about the effects of lead resistance. The thermistor thermometer thus developed was a very simple instrument which the surgeon found generally unobtrusive and required very little attention from the anesthesiologist.

Further development resulted in the availability of thermistors whose characteristics were closely controlled (2) thus obviating the need for individually calibrating the sensor to the instrument. Multichanneled temperature measurement systems which were capable, for example, of determining " mean weighted skin temperature " of human subjects through the use of thermistor sensors appeared (3). Such systems required the development of passive networks whereby the nonlinear response of the thermistors was compensated for by the nonlinear transfer function of the network. The technique, however, is generally restricted to temperature excursions on the order of 50°C or less depending upon the degree of nonlinearity which is tolerable. This limitation was noticeably relaxed by the successive development of active networks whereby the nonlinearity of the thermistor was compensated for by one or more additional thermistors (4). As a consequence of these events, thermistor sensors are presently employed within a spectrum of instrumentation ranging from the simple surgical thermometer through large multiparametered automatic data gathering and processing systems, covering spans in excess of lOO"C, with sensor networks displaying less than 1 part in 1000 deviation from linearity with temperature.

Another development of considerable consequence to the life-environmental sciences has been the quartz crystal thermometer (5). Crystal orientation or "cuts" which result in quartz resonators linear in frequency with temperature thus result in a temperature transducer which is easily read in digital format. Crystal resonators are capable of high resolution, and may be read to 0.0001"C using conventional digital circuitry. Locating the oscillator circuitry at or near the site of measurement permits the crystal frequency to be transmitted over leads for a considerable distance. Transmission losses attenuate the signal, but for all practical purposes do not otherwise alter it; hence the accuracy of the system is largely independent of this effect. Since the quality of the information from the sensor is, over a considerable range,


independent of its amplitude, the system is naturally immune to most electrical noise. Although the quartz thermometer is also quite elegant in other ways, its freedom from the effects of noise and lead resistance is perhaps its prime virtue for biological measurements.

Present quartz thermometer sensors are bulky and expensive in comparison with thermocouples and thermistors. Hence for now and the immediate future their biological applications will probably be somewhat restricted.

Thermoelectric thermometers, which are perhaps the oldest common electrical sensors of biological temperatures, continue to evolve at a pace necessary to insure their continued use. For all practical purposes, progress over the past decade has been exclusive of the thermocouple sensor itself. Thus improved forms of stable high gain dc amplifiers, cold junction control or compensators, etc. allow thermocouples to be used more conveniently, but have not changed the fundamentals governing their use. Compared with resistance and quartz crystal thermometry, thermocouple sensors provide very small signals, and minute inhomogeneities in the material of the leads are likely to produce spurious components in their outputs in the presence of thermal gradients adjacent to their active junctions.

However in comparison to thermistors, quartz sensors, etc., thermocouples can be made very small. Present states of their respective arts indicate that thermocouples are producible to sizes an order of magnitude smaller than those of their nearest competitors, miniature thermistors. This is likely to remain the case, since the thermocouple may be regarded ideally as an interface which itself has no volume. Thus when it is necessary to determine the temperatures of points with electrical sensors, thermocouples of very fine wire most closely approximate the ideal sensor.

Copper-constantan couples form the basis for most of the thermoelectric measurements of biological temperatures. These relatively high output thermocouples (42 pV per "C at 37°C) are easily adapted to serve a variety of measuring circumstances, and hence in many instances continue to be preferred over other electrical sensors for advanced biological research (6).

Pure metal resistance thermometers, commonly nickel and platinum, although widely used industrially, play a relatively nominal role in the routine thermometry of biology and medicine. Developments within this area of resistance thermometry over the past decade, although considerable, have not usually been of obvious advantage to a biologist with a temperature measurement problem. Two considerations limit applications ; the principal one being the bulk of the sensor, followed by its lack of effective sensitivity.

During the early 1960's pure metal films deposited on substrates appeared to show considerable promise of at least partly overcoming the problems of bulk associated with wire wound elements. The films allow much higher levels of impedance to be obtained, and thus the size of the sensor may be to

ADVANCES IN TEMPERATURE MEASUREMENTS 24 1

a greater degree independent of the impedance level necessary to match the rest of the system and (or) swamp out the effects of long copper conductors acting as additional resistance thermometers. Unfortunately general application of this development appears to be at a hiatus, but hopefully this will be temporary. We speculate that at least for the applications under discussion, surface effects compromise bulk resistivity of the metal to the extent that readily reproducible elements require further development of the technology of depositing thin yet very uniform and homogeneous films. For example, the temperature coefficients of platinum film resistance thermometers differ substantially from that of the bulk metal, and change as a function of film thickness.

Higher impedance in the sensor would also overcome to a great degree the lack of effective sensitivity of the wire wound pure metal elements. As used here the term effective sensitivity relates to not only the temperature coefficient of the element but also its resistance level to that of the lead wires bearing its signal to the point of measurement, the purpose being to determine the extent to which the leads as additional resistance thermometers may degrade the information of the sensor. In other words, we must be concerned with the effective signal to noise ratio as seen at the measuring instrument rather than at the sensor.

We present as an example a comparison between two practical sensors, one being a platinum sensor of 100 ohms at 25"C, and the second being a thermistor of 5000 ohms at the same temperature, Changing the temperatures of the sensors by 1 "C changes the resistance of the platinum element by 0.38 ohms and that of the (nickel-manganese) thermistor by 220 ohms. The flexibility of resistance thermometry needed in biological applications is severely compromised when the introduction of 0.38 ohms of spurious resistance produces an error of 1°C in the measurement; experts in resistance thermometry would have no problem in dealing with the error, but particularly since they often must monitor four or five additional parameters at the same time, biologists generally do.

When the site of measurement (or control) is not mobile and consists of a relatively large thermal mass, platinum resistance thermometry has maintained its position as the preferred means for best accuracy and stability. Hence, although the effective sensitivity of the platinum resistance thermometer is low in comparison with that of thermistors or quartz resonators, because of its stability it is applied to those biological applications where its size may be accommodated and which require the best accuracy in measurement or control capable within the art.

Both nickel-manganese thermistors and quartz resonators appear to be of the necessary stability to function as secondary laboratory standards for many demanding biological applications. Thermistors are attractive for these


purposes since their sensitivity makes for easier readout by less sophisticated instrumentation to a given accuracy level. The information format presented by the quartz resonator is of great clarity, and with refinements in the means of supporting the crystals within their sensor housings, quartz crystal thermometers are likely to approach the stability of their platinum counterparts.

Presently practical standards for biological and medical thermometry are neither agreed upon nor widely used. The preceding comparison between thermistors, quartz resonators, and platinum resistance thermometers is perhaps relevant then to the question of whether there is a need for working standards for the biological-environmental temperature range not presently fulfilled by platinum resistance thermometry. The question needs asking, since within our experience it is often not feasible to refer an electrical temperature sensor to an established standard, the cost of use of which is within the normal scope of a biological or medical laboratory. Given the nature of biological measurements, some form of transfer standard which is referrable to fixed points or platinum standards, yet capable of measurements physically closer to the site of the biological data, would prove generally useful. We speculate that the growing social pressures upon the environmental and medical sciences may result in the development of a practical biological- environmental temperature scale less rigorously defined than the International Practical Temperature Scale, but based upon more flexible measurement systems than current strain-free platinum resistance thermometers and bridges. Thermistors, quartz resonators, and ruggedized platinum elements each appear to be capable of fulfilling the sensing function of an intermediate measurement system of this nature. At the present time thermistors offer an additional advantage in that their readout means may be simpler for a given accuracy level in comparison to those for platinum and quartz.

C. Thermistors

The word thermistor although widely used does not appear to have a generally accepted reasonably precise definition. As used herein, a thermistor is intended to mean a thermally sensitive resistor composed of solid semiconducting material whose primary function is to exhibit a change in electrical resistance with a change in resistor temperature.

In comparison with transistors (where the field is dominated principally by Si and Ge), the materials of thermistors are neither restricted nor orderly. Among commonly used materials are Mn, Ni, Cu, B, Co, Fe, U,Os, Sic, as well as Si and Ge. Presently a large percentage, if not all, of the thermistors for biological applications are based upon the nickel-manganese oxide system which characteristically displays a coefficient of resistance on the order Of 4 %/Co in the region 3540°C. Fe, Co, and Cu are common additives/


fillers to the basic system to raise or lower the bulk resistivity of the material. This is a flexible system; it permits the resistivity of the material to be tailored over a range on the order of 105/l.

A common method of preparation of the basic system involves the ball- milling of NiO and Mn,O, in a proportion of 1Ni : 2Mn by weight. Often a temporary binder (such as liquid lucite) is added, and the material is shaped through pressing or extruding. The “green” material is then fired to a sintered state at an elevated temperature, typically in the region of 1200°C. Finely divided silver in a frit of boron oxide-lead oxide glass is then applied to the appropriate surfaces of the thermistor and fired at a temperature in the vicinity of 700°C to become the contacting mechanism. An alternative for the production of bead thermistors involves the application of the semiconductor materials in slurry form to parallel wires, usually platinum- iridium. The material is formed into a drop which bridges and surrounds the wires and is then fired.

An examination of thermistors produced in this fashion may reveal the presence of several distinct crystal phases within each whole structure. The major constituent is the cubic spinel Nil -xMn2+X04 with minor phases of cubic NiO and tetragonal Nil -xMn2 +x04 spinel. Extending the cooling time of the material (following the firing temperature) appears to eliminate the tetragonal phase. This has been recognized in earlier work (7). It has been observed that when the thermistors are “ aged ’’ at about 1050°C following the firing cycle, the NiO phase disappears and only the single-phase NiMn,04 spinel remains.

It has been assumed that this process for producing stable nickel-manganese oxide thermistors is optimal when the reaction is exactly as follows :

NiO + Mnz03 - NiMnz04,

It is tempting to assume that the single phase material, being the equilibrium configuration of the Ni-Mn system below 11Oo”C, is a more stable manifestation than those which are multiphasic. However to the present time evidence apparently does not confirm this assumption experimentally with the degree of consistency that breeds confidence. There is evidence (8) which indicates that the spinel crystal structure has two different lattice sites available for the transition metal cations. One is tetrahedrally coordinated with oxygen and the other is octahedrally coordinated with oxygen. A change in the degree of inversion takes place as the sample temperature is lowered from 1050 to 300°C. The degree of inversion is a measure of the concentration of nickel ions on octahedral sites. Changes in inversion will control the charge carrier concentration and hence will appear as changes in resistivity. We are satisfied that aging in Ni-Mn oxide thermistors is caused mainly by


resistivity changes in the bulk material, and hence speculate that the mechanism of aging is probably an ion exchange process between neighboring lattice sites. Additional work is presently being undertaken to test this proposition, since at this time our empirical data arrived at through some ten years of process iteration is still in disharmony with this explanation of the aging phenomena.

Our particular preoccupation with the aging phenomena stems from long range objectives loosely identified and set forth some fifteen years ago. At that time we speculated that for biological applications the art of thermistor resistance thermometry might be advanced by some two orders of magnitude over its then existing state. Although they had long since been recognized as useful thermometrical devices and our speculations were consistent with earlier predictions (9) , users tended to regard thermistors as 1°C devices; that is, if calibrated at one temperature, then resistance at an only modestly offset temperature was predictable to 1"C, and for general purposes stability was regarded as on the order of 1°C. At best, unit to unit processed interchangeability was also on the order of 1°C. On this basis, we speculated that the thermistor could be evolved to 0.01"C status. That is, it would become routine state of the art, and economical to repeatedly prepare thermistors all of which would follow a nominal resistance versus temperature characteristic over a major portion of the biological temperature spectrum within an error band defined in temperature as kO.01 "C. Additionally the thermistors would remain within the above tolerance for a period defined arbitrarily as on the order of five to ten years when maintained within their useful temperature spectrum.

Thus defined, the objective was approached by approximately one order of magnitude within five years, and thermistors then appeared to warrant serious consideration as resistance thermometers of medium precision and accuracy. Through the efforts of Mr. James Swindells, a calibrating facility for thermistors was placed in service at the U. S. National Bureau of Standards and made available in a manner similar to the existing facilities for the calibration of mercury-in-glass and platinum resistance thermometers.

The data contained within Table I were collected from the initial group of thermistors which we submitted to NBS. These thermistors are representative of the state of the art at the time of their fabrication. The gathering of data from this group of thermistors has not yet been concluded.

In order to convey the sense of thermometrical stability, the data from NBS (which is in ohms) have been translated into the equivalent temperature deviation from the nominals of the thermistors. During the period covering this study the International Practical Temperature Scale (IPTS) was revised (IPTS 1948 to IPTS 1968), and hence the translation also includes rational- ization of the raw data which were collected according to the IPTS in effect


TABLE I

THERMISTOR REPRODUCIBILITY-STABILITY WITH TIME SHOWING INma DEVIATION FROM NOMINAL PLUS DRIFT WITH TIME

75,790 7355 1200 394.9 Nominal resistance: ohms ohms ohms ohms

Temperature : - 40°C 0°C + W C + 70°C

Thermistor 1 12/28/62 1/07/64

12/22/64 1/24/66 1/05/67

1212 1 167 3/30/70

Thermistor 2 12/28/62 1/07/64

12/22/64 1/24/66 1/05/67

12/21/67 3/30/70

Thermistor 3 12/28/62 1/07/64

12/22/64 1/24/66 1/05/67

12/21 167 3/30/70

Thermistor 4 12/28/62 1/07/64

12/22/64 1/24/66 1/05/67

12/21/67 3/30/70

Thermistor 5 12/28/62 1/07/64

12/22/64 1/24/66 1/05/67

12/21/67 3/30/70

+O.lO"C $0.09 +0.09 +0.08 + 0.09 +0.08 +0.08

f0.11 +O.ll + 0.09 $0.09 +0.09 +0.08 + 0.08

+ 0.03 +0.03 f0.01 +0.01 +0.01 -0.02 -0.03

+ 0.05 +0.04 + 0.04 +0.03 + 0.04 + 0.04 +0.04

+ 0.03 +0.05 + 0.05 +0.04 + 0.05 +0.04 + 0.04

+O.O6"C +0.05 +0.04 +0.04 + 0.04 + 0.04 + 0.04

+ 0.07 +0.06 + 0.05 +0.04 + 0.04 +0.04 + 0.03

+0.04 + 0.04 $0.01

0.00 -0.01 -0.02 -0.03

f0.04 + 0.03 + 0.03 +0.03 + 0.03 +0.03 10.02

+ 0.02 + 0.02 +0.02 +0.01 $0.01 +0.01 0.00

+O.O4"C $0.02 f0.01 f0.01

0.00 + 0.02 f0.01

+ 0.04 $0.02 +0.01

0.00 -0.03 +0.01 -0.01

+ 0.07 $0.05 + 0.03

0.00 -0.02 -0.02 -0.03

+ 0.05 + 0.03 +0.03 f0.03 + 0.02 +0.03 f0.02

+ 0.03 +0.02 t0.01 +0.01

0.00 0.00

-0.01

+O.O2"C -0.01 -0.01

0.00 +0.01 +0.01

0.00

+0.01 -0.01 -0.05 - 0.02 -0.03 -0.03 -0.03

+0.06 + 0.04 +0.01 -0.01 -0.01 -0.02 -0.04

+0.04 +0.01 +0.02 $0.03 +0.02 +0.04 t-0.02

$0.03 0.00

-0.01 $0.01 -0.01 f0.01 -0.01


at the time of measurement. Thus if the thermistors had been read by an ideal thermistor thermometer calibrated in degrees Celsius to the nominal resistance values of the table, the uncorrected readings of each of the thermistors would have been in error as shown. NBS indicates that the thermistors are measured by means yielding an uncertainty of 0.01"C. Aging is read as the difference between the initial and final errors for each thermistor. Since the coefficient of resistance with temperature is negative, temperature readings moving in the negative direction are an indication of increasing resistance with age.

The data, excepting thermistor # 3, indicate that within its uncertainty the resistance increases uniformly (in temperature), independent of temperature level. Thus the slope of each curve shifts upwards without skewing. This would be anticipated, since changes in contact resistance (normally milliohms) during the period are likely to reflect in the data only if catyclysmic.

The slight skewing of the slope of thermistor # 3 is apparently not a function of contact resistance, and a mechanism for its explanation is unknown to us. The early history of this thermistor is in keeping with the others of the group, but during the later period, when the others are apparently approach- ing a final stable level, the aging of # 3 continues at an approximately constant rate.

The thermistors were prepared in August of 1962 to conform to nominal temperature-resistance values which had been established and well characterized during a period of several years prior to 1962. The thermistors are disks of approximately 0.2 cm diameter and 0.025 cm thickness. They were randomly selected from a routinely prepared group of approximately one thousand thermistors, and measured for a period of three months prior to the first NBS measurement, to establish that their early history conformed to previous experience with thermistors of similar composition and preparation.

In our experience the phenomenon of aging as it occurs in the routine use of these thermistors as resistance thermometers is manifested by an increase in their resistance with time. Therefore we prepare the thermistors to resistance values lower than their nominal values in order to extend the period of time during which they will remain within their specified tolerances. This is readily accomplished by making the initial dimensions of the thermistor such that it issues from the process mentioned earlier at a resistance level lower than nominal, and thereafter removing material to raise its level nearly to the nominal value.

We take the data of Table I to be representative, and use it for corrobora- tive purposes within our internal program of measurements. To date this has involved the measurement of more than lo6 of these thermistors individually during their earlier history, over a period of time which we believe to be


sufficient to establish probability of general conformity to the behavior of the control thermistors. Sampling techniques are used to gather additional long- term history. Platinum resistance thermometers used as internal standards are recalibrated at NBS on alternate schedules of two years each, and inter- nally verified at appropriate fixed points each six months.

The thermistors of Table I and others which are being subjected to NBS calibration are also available as standards of a lower order, and occasionally are so used to aid in the resolution of the annoying discrepancies which seem to plague standards laboratories almost invariably during periods of critical measurements.

All thermistors on NBS calibration schedules are measured against our platinum resistance thermometers immediately prior to and following their NBS calibrations. As a consequence, close cross-referencing between types is maintained, and the platinum resistance thermometers are additionally corroborated. Another check is provided by measuring the platinum resistance thermometer at the triple point of water prior to its measurement of the thermistors.

The values of Table I support the following observations:

1. Thermistors may be produced to fall within a 0.1"C error band about a specified nominal resistance-temperature characteristic throughout the major portion of the biological temperature spectrum.

2. Given the normal thermal limits of the biological environment, present art permits preparation of thermistors the characteristics of which are closely predictable for periods in excess of five years, and aging during the period will be on the order of 0.1"C or less

It should be noted that the preceding observations apply to the art as it existed some years ago; presently thermistor resistance thermometers may be produced economically to an equivalent 0.03"C with respect to resistance level and slope over a substantial portion of the biological spectrum. Aging programs to accelerate changes of current production in thermistors by maintaining them at higher than rated temperature limits have produced data which imply improved stability compared with that of the thermistors of Table I.

It may be that a means of fixing an equilibrium distribution of Ni and Mn ions on a particular lattice site of the spinel, as suggested earlier, will be found, and will help to stabilize the system. It is also likely that further development of the mechanisms for establishing and maintaining electrical contact with the thermistor material will be needed. However, it is likely that only a modest improvement is required since contact aging phenomena appear to be of second importance to those of the bulk material.


The preceding discussion has emphasized the development of thermistors which display a high order of reproducibility and stability in combination. Either characteristic is available by itself, perhaps even to the 0.01 "C level, from among existing types. Certain bead types maintain a high order of stability but their resistance-temperature characteristics are not adequately reproducible. By comparison, the stability of disk types often suffers, but generally their resistance-temperature characteristics may be more con- sistently reproduced. Such statements must of necessity be vague, for this whole area of the semiconductor art is not yet well ordered.

At least several crystal structures and many material components, as noted earlier, are commonly found in the thermistor family. Since this area is still in disarray, its practice is heavily dependent upon slight empirical knowledge and intuition to an extent that is often discomforting. At the hardware level of development, progress has been achieved mainly through laborious iteration of materials and processes. Hence combining two characteristics which already exist, but separately, into an improved thermistor is a possibility, though through a process of development involving both large amounts of time and serendipity.

Lumping the characteristics of reproducibility and stability together allows interchangeability of sensors without respect to time. An accurate general purpose resistance thermometer for biological-environmental application must not only be small and sensitive, but also economically viable for usage which involves a high incidence of destruction of sensors, yet frequently requires exacting long term measurements within circumstances which make the sensor inaccessible for calibration or replacement. For example, many vertical temperature profiles of large bodies of water are measured with thermistor plummets which have a useful life measured in seconds; it is not economical to recover the sensor. Patient monitoring sensors in hospitals are rendered useless through the destruction of their outer surrounds by repeated heat or chemical sterilizations. During measurement of the rectal temperature of an elephant under stress, the elephant maintains the option to discontinue the gathering of data, and so on. On the other hand, similar sensors may be used to gather long-term data on soil temperatures, or are embedded in glaciers, etc., for periods of years. Thus the requirements of biological thermometry, aided by the recent degree of interest in biological data of all sorts, have materially altered the practice of resistance thermometry. By contrast, in the recent past, as a typical application of resistance thermometry, a nickel sensor in an industrial process control was usually semipermanently connected to its monitoring or controlling instrument. Adjusting the instrument to the particular resistance of a noninterchangeable sensor was not onerous since it needed doing infrequently. Platinum resistance thermometers were expected to have very long lives and were treated as expendable in only quite exceptional circumstances, etc.


Presently metallic oxide thermistors are the most commonly used resistance thermometers within the span of biological-environmental measurements, and their usage continues to grow. In addition, the transducers of biological data other than temperature are frequently temperature sensitive, and thermistors are often incorporated within them to precisely compensate for the temperature artifact.

Having considered progress in reproducibility and stability of thermistors, it is appropriate to consider what if any progress has been made in mathematically describing their behavior; that is, what are the applied mathematical equations which are operational over useful spans of temperature to determine thermistor resistance at temperature TI when the resistance is known at To. Since we have been developing the proposition that thermistors are useful for quite accurate measurements, are they characterized to a degree that is comparable to that of the Callendar equation and its recent extensions (10) for platinum?

An early reference (9) identified the following equation as characterizing the thermistor over a limited temperature range:

(1) R(T) = R, e ( B / T - W T o ) ,

where R(T) is the resistance at temperature T (degrees Kelvin), Ro is the resistance at temperature To , e is the Naperian base (2.718), and B is a constant with dimensions in degrees Kelvin.

For example, to test Eq. (1) the data from Table I may be applied to calculate the value of B (3819°K) over the interval 0-70°C. Then the equation is employed to calculate the resistance of the thermistor at midrange (35°C) and yields a value of 1442 ohms. However, measurement of the thermistor yields 1471 ohms, or a spread between calculated and actual equivalent to 0.5"C. Thus while inspection of Eq. (1) conveys the sense of what is happening to the resistance, accuracy requires that its use be confined to very narrow intervals.

A closer approximation is offered by

R(T) = AeBIT. (2)

For certain thermistors the accuracy of Eq. (2) is somewhat improved by an addition to the exponent

R(T) = AeB/(T+e), (3)

where 0 is on the order of tens of Kelvins (If).

expanded version of (1) However, for a number of years we have successfully employed an

R(T) = R , exp[B(l/T - l/To) + C(l/T - l/T0)2], (4)

which has proven to closely match nickel-manganese thermistors (we have not checked Eq. (3) against Eq. (4) with sufficient data to permit comparisons).


As a typical example, over the interval 0-100°C with measured values at O'C, 50°C (811.3 ohms), and 100°C (152.8 ohms) the values of B and C are calculated to be 3810 and -14,41O0K, respectively, and our data indicate that the resistance value calculated by Eq. (4) for any temperature within the interval matches the measured value to an equivalent +_ 0.02"C.

Within our experience Eq. (4) is also effective for purposes of extrapolation. With respect to the preceding interval, typical values at -25°C and 150°C match the data on the order of 0.03-0.05"C.

Through trial and error it has been established that for best results the data for R, should be taken at the lowest temperature of the interval, the second point being at or slightly below mid-interval temperature, with the third point necessary for simultaneous solution of B and C being at the upper temperature extremity.

For practical use, then, Eq. (4) fits the measured curve for the thermistors within limits of variation which are somewhat less than those of the reproducibility of the thermistors from unit to unit over year to year. Thus it appears to be as close an approximation of reality as is practically useful at this time.

Table I1 illustrates the characteristics of other thermistors within this

TABLE I1

CHARACTERISTICS OF PRESSED NICKEL-MANGANESE THERMISTORS

Resist- Resisti- ance Dia- Thick- vity B C

at 25°C meter ness at25"C Modifier 0-100°C 0-100"C (ohms) (cm) (cm) (ohm-cm) ( O K ) (OK)

100 0.2 0.08 24 Cu 2730 -62,900 1,Ooo 0.2 0.08 240 Cu 3180 -138,000 3,000 0.2 0.07 3,000 none 3810 -137,000

10,000 0.2 0.04 4,500 Fe 3460 -195,000 100,OOO 0.2 0.03 75,000 Fe 3850 -252,000

1,000,oOO 0.2 0.02 l,OOO,OOO Fe 4380 -362,000

family. The modifiers are added to alter resistivity and, in combination with process variables, are responsible for the differences in the slopes denoted by the respective B and C values of the thermistors.

Figure 1 illustrates several of the common sensor styles which house thermistors for biological applications. Figure l a details a rectal esophageal probe for humans and larger animals evolved from the type, as noted earlier, first used in open-heart surgery. The outer covering of the thermistor and


(a) Rectal esophageal

1/16 max + 4

(b) Surface temperature

(C)Tubular for pipes 6 closed vessels

Thermistor

24 Gauge needle

(d) Hypodermic needle

0.039

(e) Implantable probe

r 0.100

(f) Special oral probe

FIG. 1. Typical thermistor probes for biological applications.

lead wire is vinyl and quite flexible. Relatively soft, it is also inert to body fluids, and may be left at the site for considerable periods of time. The construction of the surface temperature probe, Fig. lb, is based upon a thin section of stainless steel to which the thermistor is mounted and then insulated with an epoxy material, thus achieving fairly high surface-to-mass and front- to-back thermal conduction ratios.

The tubular probe of Fig. lc illustrates a special type of an otherwise commonplace form. It was developed to monitor and control the temperature of the blood circulating within artificial heart-lung machines. The connector provides a hermetic seal, since the probe is frequently steam sterilized during its normal course of service. The hypodermic needle is also steam sterilizable and is employed for a variety of subcutaneous applications involving both animal and plant life. Often used for somewhat similar purposes, the probe of Fig. le may be semipermanently implanted in vital organs; it is characterized by its low thermal mass and delicacy of construction. The probe of Fig. 1 f was developed for intermittent measurement of oral temperatures during space flight, and collects other data during the interval between oral measurements.


With the exception of Figs. Id and le, the sensors employ thermistors similar to those whose stability was discussed earlier, with resistance-temperature values corresponding to the nominals of Table I.

Among the many forms of thermistors not discussed herein are several types which may in the future offer certain advantages, provided that their technologies are developed to overcome present shortcomings for biological applications. Single crystal silicon carbide thermistors, for example, appear to have inherent characteristics favoring long term stability. Although their sensitivities tend to be lower than those of the Ni-Mn system, greater temperature excursions may be tolerated. Methods of orienting and affixing contacts appear to be a present problem and within our experience these thermistors often show a noticeable rectifying as well as a resistance characteristic. Since their ability to operate over a wider temperature range is not a special virtue for biological applications, and their apparent polarizing to the extent of an equivalent 0.5"C or greater is a distinct disadvantage, silicon carbide thermistors have received limited acceptance within this application area. Likewise, the virtues of diamond thermistors are perhaps best exploited by application to greater temperature excursions than those normal to the biological spectrum.

For bolometric applications such as those found within biological infrared radiography, film thermistors, with or without substrates, are frequently used as detectors. Basic processing is similar to that of the disk and bead thermistors, and frequently their materials and their temperature characteristics following fabrication approximate those of disks and beads. Film thermistors are therefore principally differentiated from other types by very high surface to volume ratios ; that is, by geometric rather than compositional differences.

D . Thermistor Thermometry

Developments in thermistor thermometers over the past decade have tended to be focused on the process of adapting an older art-resistance thermometry-to the special characteristics of a newer transducer. As with other resistance thermometers, thermistors display a generally continuous resistance-temperature function. Thus at both boundaries marking the thermometrical interval of temperature for a chosen range of measurement, a resistance thermometer has a value of resistance other than zero. Hence a reference is required to establish one or both of the boundaries. This means that in one way or another some form of bridge connection is likely to be found within the measurement apparatus for those instances where fairly uniform resolution is required throughout the chosen temperature interval. Since linearity with temperature is virtually a general requirement of biological thermometry as it is now practiced, most thermistor thermometers are


designed to approximate this characteristic. But thermistors are very nonlinear in comparison with pure metal temperature sensors and hence much of the earlier art was not applicable or was not easily applied to their means of readout. Thermistors are relatively both small and highly sensitive. Taken together, these characteristics compound the possibility that noticeable self- heating of the sensor may occur under unexpected circumstances. For example, a thermistor operated in a constant current mode may display no noticeable self-heating at say 40°C but must dissipate twice the energy at 20°C since its resistance has doubled in the short span of 20°C. Now apply it to typical biological measurements, and in one instance it may sense the temperature of a liquid of high thermal capacity and conductivity while in the next it may be applied to measure the temperature of what is an excellent natural thermal insulator.

Each of the three factors in the above circumstances is simple to perceive and deal with. Operating together within a simple thermistor thermometrical system (using two or more styles of thermistor sensors) results in the possibility of self-heating as a function of three independent variables. That this is no longer simple to deal with is well illustrated by erroneous reports of thermistor instability in the early literature, and continuing instances of its occurrence while using apparatus of current design. Thus the essence of thermistor thermometer design is concentrated upon thermistor dissipation and nonlinearity, and to an extent rarely found in other forms of resistance thermometry.

The derivative of resistance with temperature of a nickel-manganese thermistor is not only a factor of ten larger than that of platinum, but the second derivative is also much larger. However, many of the techniques which are used to linearize other forms of resistance thermometers are also applicable to thermistors (22). Thus earlier efforts (23) made use of fixed resistors included in simple networks, shunting the thermistor to establish a region of linearity. Such techniques are effective for narrow intervals, but when extended tend to excessively load the thermistor and hence nullify its effective sensitivity.

Thermistor nonlinearity bears a close resemblance to the characteristic nonlinearity of certain common bridge connections. As it turns out, the two characteristics are often found together, and thus it is useful to treat both as components of a single problem open to systematic solution.

Figure 2a is a linear network provided with a source e,, a resistance thermometer R(X), and output terminals 3-4. The output terminals provide a deflection output in current or voltage which could be used to activate a meter calibrated in temperature, or be referenced to and read by a nulling means such as a Kelvin-Varley divider.

The resistance thermometer R(X) may be replaced with a source e ( X )


83-4 e,= eb R, /R (X) tR,

FIG. 2. Equivalent linear networks.

equivalent to the voltage across it, as in Fig. 2b, in accordance with the compensation theorem. Now there are two sources; e,, , being fixed, produces constant components of current and voltage throughout the network, while e ( X ) produces variable components as a function of X. Therefore the output 3-4 will be linear with temperature only if e (X) is linear with temperature.

The Thevenin equivalent, Fig. 2c, establishes that linearization where possible is dependent upon the value of R , in the network.

Also from Thevenin, Fig. 2c may be replaced by Fig. 2d provided that e, = e,, R , / R ( X ) + R1. Thus when the output of a voltage divider (half of a bridge) as in Fig. 2c is linear in voltage, the two sections of the divider, R, and R,, connected in parallel as in Fig. 2d will be linear in resistance.

Summarizing, a resistance thermometer must have a nonlinear response if, in the voltage divider connection, a linear output voltage is required, and similarly a nonlinear resistance thermometer may be linearized in resistance by paralleling it with a fixed resistance of value equal to that of the fixed resistance of the divider.

By inspection of Fig. 2c, when R(X) is an increasing function of X, then the first derivative of R ( X ) with respect to X must also be an increasing function of X as a condition for linearity. When R ( X ) is a decreasing function of X , its derivative must similarly decrease with respect to X.

Differentiating Eq. (1) or graphing the nominal data of Table I establishes that thermistors meet the general requirement for linearity in the voltage dividerconfiguration.Thisraises thequestionofhow closely thermistorsmeet the requirement; overwhat span oftemperature will e ( X ) remain linear and to what degree ? Answers have been provided in part (10, I]), but given the complexity


of Eq. (4), finding curve-fitting intervals is difficult and requires individual solutions for individual segments of the temperature range. Over intervals of 20"C, deviation from linearity is generally limited to within plus and minus 0.5%; for the interval 0-100°C the deviation is on the order of 2%. As a practical method, a particular range may be solved by looking upon the network as an analog for its own equation, and iterating from it the value of R , for best linearity in the region of interest (14). The process is not difficult; the value of R , approximates the mid-range resistance of R ( X ) . Additionally, the maximum power transfer to the thermistor is limited by R , and occurs when R ( X ) = R,. Thus for the thermistor P,,, = eb2/4R,.

The voltage divider circuit of Fig. 2c, regarded as half of a bridge, is the basic circuit for most simple thermistor thermometers. Addition of the second half of the bridge provides a reference which is adjustable for nulling thermometers or fixed for deflection types.

The circuit of Fig. 2d is often employed to compensate for the positive temperature coefficient of the copper meter coil found in deflection-type thermistor thermometers. The network, with its thermistor physically located nearby the coil, is placed in series with it and thus maintains a constant load on the bridge irrespective of changes in the ambient temperature of the instrument,

When deflection types are used, intervals on the order of 10°C are spread full-scale on meters requiring 25 pA for maximum deflection. Bridge supplies approximate one volt. Energy at the thermistor is on the order of

When a given instrument must cover several ranges, values of R , appropriate to the condition for linearity are selectively switched. However, to meet requirements for higher linearity, as, for example, a thermistor thermometer capable of reading over a span of 100°C or more in uniform increments, nonlinear potentiometers and various methods of signal conditioning may be used. Generally these solutions introduce additional uncertainty into the measurement.

Our work in this area has led to an alternative solution which appears to have certain advantages toward maintaining accuracy of measurement while improving linearity. We assume that the basic network of Fig. 2c is an appropriate means for energizing thermistors for several reasons :

W.

1. Thermistor nonlinearity and bridge nonlinearity are largely self-cancelling. By contrast should R, be variable to match R ( X ) no such cancelling occurs, and unless the supply voltage el is made variable, energy dissipation by the thermistor varies widely (by a factor of 50 to 1 over the range 0-100°C).

2. When the network provides a deflection output, its efficiency is high; typically for the range O-IOO"C, on the order of 75 % of the supply voltage e, is converted to the output signal e ( X ) .

3. Multiplexing of the thermistor sensors is readily accomplished.


_ _ _ _ - _

R3 R2

Figure 3 illustrates one means of adding additional thermistors to the network to improve linearity. The network readily fits Thevenin’s theorem ; that is, by changing only one connection, its characteristic of a constant incremental change of resistance with temperature is converted to that of a voltage divider with a constant incremental change of output voltage with temperature. The number of thermistors is a function of the temperature span to be covered and the degree of linearity desired. These two conditions independently establish the ratios between the various thermistor resistance values.

Bearing in mind that all of the thermistors must equilibrate to the temperature being measured, practical limits for the number of thermistors employed in the network are determined both by size of the sensor and its cost. Net- works of up to N = 3 thermistors are meeting current requirements for linearity versus temperature range versus cost.

A direct mathematical solution for the values of the components of the network is difficult if not impossible. In general, accuracy requires the substitution of Eq. (4) for each of the thermistors in the network. The resultant network equation is thus complex, and its direct solution appears to lie beyond the practical limits of current nonlinear mathematics.

Within our experience, networks require ratios of resistance for each of the thermistors with respect to the other thermistors which are large enough so that thermistor resistivity must be altered to maintain desirable geometry as a sensor. This results in the use of thermistors with somewhat different

I eb

i

FIG. 3. Multiple thermistor linear network. (a) N thermistor network, linear resistance with temperature. (b) N thermistor network, linear output e(x) with temperature.


slope characteristics for each of the legs of the network. These differences prevent the use of identical B and C values in solving the network equation and hence tend to close off possible means of simplification.

However, given the precondition that one is able to make reasonable first guesses about the ratios needed between the values of the thermistors for a desired temperature range, a computer search using iterative techniques readily produces solutions for the values of the fixed resistances for optimal linearity. The example given in Fig. 4 illustrates such a network for the range

Rlo= 1839 ohms at Oo C Rx= 1839 ohms-9.17ohms (0- 100 "C)

RT I

R,, RTZ

Linear resistance versus temperature

E,= 1.250 volts eo= 1.057voltsat 0 ° C eo= 1.057 volts-5.31 x 10-3 volts/'C JS?) RTI eo (0- IOOOC)

RT3 RTZ

Linear % versus temperature

A, ~2,175ohms R2=4,031 ohms R3=9,025 ohms

FIG. 4. Characteristic three thermistor linear network (O-lOO°C).

0-100°C. In the voltage divider configuration, the output of the network is 0.425 %/"C of the supply voltage; thus a substantial portion of the supply is converted into e, , the network output signal. Figure 5 illustrates network linearity, and the dependence of the network upon each of the thermistors over its temperature range. Deviation from linearity expressed independently is maintained within plus and minus 0.04 % through error-splitting at the lower temperature extremity.

The supply voltage applied to the divider may be chosen to establish the


I00 %

90

00

70

60

? 40 4 30

20

10

0

!- 50

0 10 20 30 40 50 60 70 00 90 100 Temp. O C

FIG. 5. Network sensitivity as a function of the individual thermistors (for the network of Fig. 4).

condition that the network yields its data as a voltage in direct numerical coincidence with temperature. Hence digital readout or conversion is simple. Generally a signal of 10 x V/"C from multiple thermistor sensors is available without undue heating of the sensor. Network resistance levels are on the order of one to twenty kilohms and hence are normally free from the artifacts of lead resistance and leakage. In applications involving a number of sequentially read interchangeable sensors the fixed resistances of the network are usually integral with the reading instrument. Otherwise the resistors may be located adjacent to the sensor when two-lead devices are advantageous. As with most applications of resistance thermometry to biological measurement, direct current is usually employed to power the thermistors. Since the temperature of the media is generally a relatively slowly changing variable, the effects of the capacitance and inductance associated with the sensor and its leads rarely intrude upon the measurement.

Multiple thermistor networks satisfy the requirement for a temperature sensor with high sensitivity and linear characteristic extending over the usual intervals of biological temperatures. Their practical limits of application are not yet well established. With appropriate thermistor material and geometry it is likely that any degree of linearity may be approximated while maintaining a useful output level.

Network sensitivity and linearity allows high resolution by unsophisticated instrumentation, and simple interfacing with digital equipment. Since network sensitivity is not a function of temperature level, temperature differences and temperature averages are readily measured.


A comparison of networks employing several active elements (not necessarily thermistors) with other techniques for achieving linearity suggests that the addition of the active elements results in greater sensitivity and hence a higher signal to noise ratio than is obtained otherwise. Also the transfer function (from nonlinearity to linearity) is activated only by the quantity being measured. Other methods of linearizing may depend upon one or more additional variables which, not being direct functions of the measured quantity, necessarily influence the quality of the measurement.

A disadvantage of such a network is that its verification is somewhat complicated. Each of the thermistors must be measured at several points to establish that the relationships within the group have not altered as a result of differing aging characteristics, etc. Alternatively, a number of measurements taken over narrow intervals would be required to verify the behavior of the network as a whole.

Multiple thermistor networks appear to be practical for a variety of applications, most likely because thermistors are both small and comparatively cheap. We thus tend to speculate that for biological-environmental uses at least, the crossover region where such networks are no longer usefully small and economical occurs when the number of active elements must exceed four or five thermistors.

We are not aware of many instances involving the use of a series of similar nonlinear transducers acting upon each other to produce a linear characteristic, and the concept appears to raise several questions in the consideration of its advantages and disadvantages. To be harmonious with communication-information theory, a sensor should not weight the information it collects. Yet most do, for most are nonlinear and this is likely to be the nature of things. However, any sensor which meets the Thevenin condition for linearization may be employed in multiple to extend the region within which linearity is achieved. This has the nature of a somewhat general solution, and thus may be applicable to sensors found in other areas of measurement as well as to resistance thermometers other than thermistors.

E. Quartz Resonator Thermometry

The announcement in late 1964 of the identification of a quartz crystal orientation which resulted in a quartz resonator with a linear temperature- frequency characteristic was immediately recognized as a salient event in electrical thermometry. It had long been known that quartz resonators provided a good basis for accurate temperature measurements. The stability of quartz was well established and hence the announcement of a linear coefficient cut only added an additional capability to a material which was already very trustworthy. General acceptance thus occurred more rapidly than is


usually the case with new thermometrical tools. The discovery was timely; it occurred within an era which is placing greater importance on the desir- ability of transducers whose information might be put into digital format without conversion. Over the biological-environmental temperature range the linearity of quartz resonators compares very favorably with any of the practical electrical sensors, and resolution is an order of magnitude higher than needed to meet most exacting requirements. Since temperature modulates frequency, rather than level of signal, many of the irksome aspects of resistance thermometry are avoided.

In order to minimize size and achieve resolution, current forms of resonators operate at fairly high frequencies, commonly on the order of 9.4 MHz. The temperature coefficient of the cut is on the order of 35 ppm*/"C; thus the third harmonic yields 1000 Hz/"C. The region of essentially linear operation more than encompasses biological requirements ; deviation from linearity, for example, remains within 0.05% from 0 to 100°C.

Although quartz is a stable material, 35 ppm/"C is yet a very nominal coefficient, two orders smaller than that of platinum and more than three orders smaller than thermistors. Another way of emphasizing this point is to note that, everything else being equal, the material stability of the quartz resonator must be three orders of magnitude greater than that of thermistors to achieve comparable stability as a thermometrical device. Although quartz resonators as frequency control devices embody a massive amount of art, this does not particularly apply to the problem posed by the mechanical mounting of the crystal in the instance of its repeated cycling over wide temperature excursions. Regarding this situation comparatively, the attachment of connections to quartz resonators (and semiconductor sensors as well) must establish temperature and time stable interfaces between very dissimilar materials ; for practical purposes platinum and the other common pure metallic resistance thermometers incIude no such problem. The contact resistance of many thermistors is on the order of milliohms. Thus this component may be made less than a factor of of the total resistance over the useful temperature range of the thermistor and rarely needs accounting for during measurement. On the other hand, any change in the mechanical loading of the crystal resonator will effect a change of its frequency. When such a change is a function of time and temperature (or any other phenomenon which permanently alters the relationship between crystal and mounting means) it results in aging drift, or error in measurement unless compensated for. The foregoing is well known, but is emphasized since with regard to present forms of quartz thermometers a very small change in frequency, on the order of 3 ppm, is equivalent to a change in temperature of

* Parts per million is abbreviated as ppm in this text.


0.1"C. Since at a minimum two dissimilar materials are joined at the interfaces between conductors/mechanical supporters and crystal, it is appreciated that in this instance a shock resistant stable mounting, strain free with time and temperature, must be quite elegant.

It appears that the ability to extrapolate the temperature of a quartz resonator from a single standardizing measurement is on the order of that of platinum resistance thermometers. Thus, given more frequent standardizing than is normal to the practice of resistance thermometry, the quartz resonator is capable of a high order of accuracy. In practice this disadvantage is presently somewhat offset by the relative ease in making an electrical correction of oscillator frequency to trim out drift.

Quartz resonators are likely to remain expensive in comparison to other electrical sensors of temperature and their bulk precludes wholesale use for biological applications. However, the characteristics of the quartz thermometer make it an attractive standard for the biological laboratory, provided that use of a reference, such as a triple point (of water) cell, is included within the routine disciplines of the facility.

F. Conclusions

Requirements for biological, medical, and environmental data from sites heretofore considered awkward or remote have resulted in the refinement of a variety of electrical temperature measuring means. Although a number of other sensors show considerable promise, it is likely that within the immediate future, thermistors, thermocouples, quartz resonators, and pure metal resistance thermometers will remain the principal electrical sensors of biological temperatures.

Dependence of the forward voltage characteristic of semiconductor diodes and transistors upon temperature has resulted in certain applications of these devices as sensors. However additional development toward optimizing their characteristics as temperature sensors is needed. Pyroelectric sensors may become particularly attractive as high output devices provided that their stability with time is improved.

Currently multiple thermistor networks offer a unique solution to requirements for high sensitivity and linearity in combination; the technique may also be applied to other nonlinear sensors.

11. RADIATION THERMOMETRY

A . Introduction

Infrared radiography offers exciting prospects for obtaining temperature information from biological organisms. The method is not new-early thermocouple infrared detectors were used in the 1920's to measure skin


temperatures of humans. But only recently has the full potential of sensing infrared radiant energy been realized by the biologist. This realization resulted from the declassification of military infrared detectors in the late 1940’s and their use in space exploration. The climate within the scientific community now appears favorable for the exploitation of infrared radiography, and exciting opportunities in utilizing this portion of the electromagnetic spectrum lie ahead for research investigators in the biological and medical sciences.

In biological sciences, thermometry has played a significant role. One reason is that the tools, thermometers, have been available since the early Galilean water thermometer in the 1600’s to assess quantitatively the thermal state of organisms, and their microenvironment. The measurement was simple, and differences were observed as the organism responded to changing physical environments. Later, thermocouples gradually replaced thermometers as they were more amenable to biological experimentation.

However, the problems of secondary references, spurious tertiary junctions, and discrete mass and contact led to a search for a more accurate temperature measuring method. A few investigators turned to the infrared portion of the electromagnetic spectrum in the late 1920’s and early 30’s as one possible technique (15, 16).

Then, as now, several problems existed with infrared radiography, such as emissivity and absolute temperature references, and during the early ~ O ’ S , little use was made of this temperature measuring technique. After this period, a small number of environmental physiologists began work once again in this field (17, 18). But, thermistors were now competing with infrared measuring techniques, and it was not until the latter part of the 1950’s that visualization of this portion of the spectrum became an area of intense interest for the medical researchers. The early work by Lawson provided the catalyst which stimulated the recent interest in infrared radiographic studies in biology and medicine (19-21). Until then, the military applications had been classified and only a small number of environmental physiologists were aware of the possibilities of this expression of infrared radiation. Lawson’s work in the detection of breast carcinomas coincided uniquely with the concern of the medical profession, and the public, in the study of cancerous growths. Monies became available and the scientific instrumentation manufacturers became interested in the market potentials of infrared visualization techniques. During the period from 1956 to 1964, there was a gradual increase in the number of medical studies which employed infrared radiographic methods. After this initial upsurge of interest in radiographc studies, a pause appears to have occurred. Apparently, this pause resulted from the realization that most of the possible clinical uses utilizing this portion of the spectrum have been “ roughed in.” Also, many became aware that this instrumentation was expen-


sive, required experience in its use (manipulating two to four variables), and had definite limitations. However, the development of the instrumentation has continued unabated with finer and finer resolution and essentially real time scans of targets.

Two fundamental concepts should be considered before we focus our attention specifically on radiography. Why do biologists want to measure temperature ? Two generalizations may be suggested. First, theenvironmental physiologist is particularly concerned with determining normality, or deviation from this normality, of the organism in response to any natural change in its external or internal environment. These measurements allow the investi- gator to interpret the natural energy flux that occurs at the interface between the organism and its ecological niche. Second, the medical physiologists, or doctors are interested in detecting aberrant temperature patterns resulting from pathological changes of the organism, or its parts, to determine etiologies and remedial treatment. This activity is essentially limited in zoology to higher animals (domestic or pets) and man. These two broad thoughts have directed the efforts of most research investigators in biological temperature mensuration.

One further question must be considered; are absolute temperature measurements or temperature deviations from a null more significant? Scientific training has traditionally been predicated on absolutes, facts and numerical values. Therefore, the undercurrent in thermometry has been directed toward measuring absolutes. The question of absolute versus temperature differences, however, is particularly meaningful in infrared radiography. The accuracy of most infrared radiographical instruments is a few tenths of a degree difference, whereas its absolute accuracy is one, two, or three degrees Celsius depending on the accuracy of a secondary absolute reference. So the question is equivocal and must be answered on the basis of experimental intent.

Today, infrared radiography opens an exciting avenue to the biologist and medical researcher in that it offers a unique opportunity to measure accurately temperature differences of entire targets, not just discrete parts, without the problems inherent with contact thermometry. The errors associated with radiography can be minimized, but limitations have to be recognized as it is a surface measurement, and therefore a secondary reflection of underlying temperature shifts such as result from vasomotor changes.

For simplicity, we will treat infrared radiography as a dichotomy, the traditionally defined biological endeavor and that pertaining to the more practical clinical problems. Before reviewing work in these two fields, a few facts pertaining to the infrared electromagnetic spectrum and infrared detectors will be considered.


B. Infrared Electromagnetic Spectrum, Detectors, and Radiographs

Theoretically, any material above absolute zero emits radiation over the entire electromagnetic spectrum. At biological temperatures, i.e., 35"C, the energy A max is 9.2 p. The source of infrared radiation is the oscillation of the electrically charged particles found in the atoms or molecules which increases as the temperature of the solid, gas, or liquid increases. A concep- tual problem arises with infrared energy as it cannot be perceived by the human optical sensor. Therefore, the visualization of this portion of the spectrum must be accomplished by instrumentation.

Four detectors have been used to visualize infrared radiation: thermal, photoconductive, phosphorescent, and photochemical. The thermal detector is the only type which is nonselective or generally independent of wavelength. Three kinds of thermal detectors are used: the bolometer which uses a resistance thermometer such as a thermistor, thermocouple, and the Golay pneumatic cell. The other types of infrared detectors are sensitive to relatively narrow wavebands and respond directly to quanta of energy. The photoconductive detectors such as lead sulfide (PbS), or indium antiomonide (InSb) have peak responsivity wavelengths of 2.4 p and 5.0 p, respectively. The photochemical reaction to infrared radiation requires dyes, such as the cyanine group, which has a limit of 1.3 p while the phosphors have a A limit

A wide variety of infrared radiographs is now available and may be grouped according to the type of infrared sensor. At present the photon and thermal detectors are the most common. The thermal detectors respond to impinging energy over a wide spectral range and the resultant temperature change is converted into an electric signal. The thermistor bolometers have the advantage of small size and thickness (10 p). Further responsivity can be achieved by focusing the radiant energy by optical means such as infrared transmitting hemispheres or hyperhemispheres-germanium and silicon. The thermopile, another thermal detector, has a relatively slow response period and is composed of a number of thermocouple junctions connected in series. The pyroelectric detector is a recent development and it offers fascinating possibilities for an infrared sensor. It consists of a thin piece of ferroelectric crystal, such as triglycine sulfate, which may be sandwiched between two electrodes so that any temperature change of the crystal results in a voltage across the electrodes.

The other common type of infrared sensor, the photon detector, utilizes the change in the energy level or state of electrons within the detector material in response to radiant energy. The resulting current is then handled by either the photoconductive or photovoltaic effect. The explicit differences in the electron behavior of these two techniques is complex and the reader is referred

of 2 p.


to the book by Vasko (22). Simply expressed, the photoconductive detector uses the resistance change resulting from hole-electron generation. The photovoltaic effect, on the other hand, separates the hole-electron pairs by a p-n junction within the semiconductor material and a photovoltage is generated.

A number of infrared radiographs exist and a few representative types will be mentioned. The AGA “ Thermovision ” and Bofors “ infrared camera ” represent the current state of the art for photon detectors. Both are essentially real time displays (16 and 4 frames per second, respectively) with complex isothermal and color temperature displays. The detectors require liquid nitrogen cooling and are responsive in the 1.0 to 5.5 p range. The more recent HgCdTe detector used by Texas Instruments in its “Thermoscope” has a spectral range of 6 to 14 p which avoids the COz , HOH absorption bands and the problem of emissivity of human skin that is present in the 1 to 5.0 p region. This liquid nitrogen cooled detector has a 4.5 sec frame time. A new photovoltaic detector-PbSnTe-has recently become available commercially with characteristics similar to the HgCdTe detector. It has an extremely fast response time, 20 nsec, and is responsive over a spectral range of 8 to 13 p.

Infrared radiographs employing thermal detectors have approached a highly sophisticated level in the Barnes instruments such as the T-4 model. Germanium immersed bolometers which are responsive from 1 to 20 p are available. The accuracy of measuring temperature differences and minimal emissivity problems is offset by the relatively long scan time-up to 6 min. However, Barnes has recently introduced a new pyroelectric thermal detector that has partially overcome this problem and entire scans may be made in only 30 sec. The detector is a crystalline triglycine sulfate and is sensitive over a spectral range of 1.8 to 15 p. Other nonselective methods of rendering infrared radiation visible, such as the “ Evaporograph,” are available but lie outside the scope of this discussion. So, a number of commercial infrared radiographs are currently available and specific selection is predicated on experimental requirements. The differences in geometric display and resolution of various radiographs have recently been reviewed with representative outputs (23).

The problem of data analysis is a complex one and has been handled by a variety of techniques. The simplest output is a scope image employed by the Bofors or AGA instruments. Permanent pictures may be made of these displays with oscilloscope camera attachments. The Barnes instrument has a Polaroid radiogram, “ thermogram,” as one possible output. Temperature values for an electronic gray scale may be calculated or a densitometer may be used. Also, the signal can be recorded on an appropriate recorder for most instruments. The Aerospace Medical Research Laboratory has developed absolute blackbody references which allow one to determine temperature


absolutes from - 50 to 50°C. Five thermoelectric reference blocks are aligned with a - 50°C liquid bath in contact with one side. In adhtion, the electrical signal has been placed on magnetic tape with an appropriate coder and saw- tooth signal. The analog data is digitized with an Adage Ambilog 200 Signal Processing System, and then by means of curve fitting the five absolute standards, a digital computer (IBM 7040-7094) prints out the absolute temperature values of the target. Not too surprisingly, the voluminous data collected in this manner presents one with the problem of too much data. A single average value for a 9 x 9 matrix is now being considered. The AGA “Thermovision ” also has an attachment which allows a tape output. Thus, analysis of radiographic outputs has become highly sophisticated but, for many applications, the simple visual integration of a picture by the human eye is adequate.

C. Biological Infrared Radiography

I . Biological Studies

The use of infrared radiographs in the biological fields has had a relatively short history. One of the earliest investigations was conducted in 1921 by Abbott using a “ Melikeron ” to study radiation from nude subjects (24). During the same year, Some studied the absorption of the “ heat rays ’’ by the skin (25). In another early study, Aldrich determined surface temperatures of man and clothing with the aid of a thermocouple and galvanometer (15). A short time later, in the thirties, other investigators became involved in using infrared radiographs (thermocouples) to measure skin surface temperatures and study the problem of emissivity (26-32).

In the late 1940’s, a few investigators continued to measure skin surface temperatures with Hardy’s “ radiometer or other modified thermocouple radiometers ” ( I 7). In a rather elaborate study, Pennes correlated skin surface temperatures with underlying tissues and blood temperatures (18). Not until the 1950’s, however, did investigators employ this method in studying other fauna. Wilson, for example, determined the feather and skin temperatures of chickens kept at constant environmental temperatures that varied from 23 to 30°C (33). He found feather temperatures rapidly approached ambient levels as air temperatures were increased to 32°C. These results were verified in another study, in which the surface feather temperatures of four species of Arctic birds were determined in environments of -7 to -40°C with a Barnes scanning I-8A instrument (34). In this study, the feather temperatures approached ambient temperatures as the weight and size of the bird increased. Various warm regions such as the eye-auricular region, the breast upper side, were readily identified (see Fig. 6). Hammel measured the emissivity of


F I ~ . 6. An infrared radiogram of a raven, Corous corax, shows the variations of feather- surface temperatures while in a -30°C environment. The feather temperatures vary from 10“ in the eye-auricular region to -13°C in the back area.

various Arctic birds and animals skins with a Hardy “ radiometer ” and found the values varied from 0.98 to 1 .OO (35). Recently, as more biologists became aware of the unique capability of infrared energy measuring devices, a number of diverse studies have been conducted in various biological fields. Two studies, both with a Barnes infrared radiograph, were conducted on horses to verify fractures and other equine problems (36, 37). Smith studied splints, bound tendons, and bruises, while Delahanty investigated fractures and sus- pected carcinomas. Delahanty reported that movement by the horses presented a major problem. With the rapid almost real scan times of more recent radiographs, this problem has been overcome. The hair covering the body surface presented a more serious problem in a short unpublished study by Veghte at the School of Veterinary Medicine, Ohio State University. Natur- ally, any body insulation (feathers or hair) does present a problem in determining the underlying skin surface temperatures. Osteopetrotic lesions (bone abnormality) in chickens were found to be 3°C warmer than normal bones (38). In another field, Gates has studied the energy flux in ecological niches and determined leaf surface temperatures and radiant exchange of animals such as sheep with both a Hardy “radiometer” and a portable Barnes “ camera ” (39, 40). Other studies have ranged from studying surface temperature changes of the cortex of cats in response to drug administration to the use of a Barnes infrared microscope to measure the temperature rise during wing vibration of moths (varied 8 to 20°C above ambient) (41, 42). Another unusual study has been the detection of submerged whales, por- poises, and schools of fish which produced luminescence by disturbance of


the water with infrared detectors in space satellites (43). This variety of studies indicates the potential use of infrared radiometers in detecting surface temperatures of living matter and, the authors feel, the beginning of a renewed intense research effort in the field of biological thermometry.

2. Human Studies

The clinical applications of infrared radiography have had a pronounced effect on the development of infrared imaging devices. Because of the potential market and early enthusiasm within the medical profession in the use of radiographs for detecting breast carcinomas, considerable research has been devoted to these instruments. The evapograph and later the Barnes Radio- graph was used in Lawson’s early work to detect breast carcinomas (Z9-2Z). He found that the skin overlying carcinomas tended to be a few degrees warmer than that of the surrounding surface. His studies stimulated tremen- dous clinical interest, and over fifty papers have been published since 1964 on the detection of breast cancers by various infrared radiographical methods (44-46). After this initial outburst of enthusiasm, serious shortcomings were found which have attenuated the usefulness of this technique. Advances in instrumentation, such as shorter scan time, ease of operation, and mobility have partially offset some of the problems. This initial interest and surge of research studies quickly spread to other medical areas, and it was found that a variety of pathologies disturb the temperature patterns of the overlying skin surface. For example, Birnbaum found that abnormal location of the foetus placenta could be discerned with a Barnes instrument and the physician could be alerted to potentially hazardous obstetrical complications (47). Orthopedics was another area of interest because both fractures or knee problems result in vascular blockage and concomitant cooler temperatures over the affected area. Also, rheumatoid arthritis results in inflammation that could be discerned by increased surface temperatures (48). The delineation of live and necrotic tissue in the case of burn and frostbite is clearly shown by temperature differences (49, 50). These studies and one unpublished frostbite study conducted at Fairbanks, Alaska, clearly illustrated the effectiveness of this approach in remedial treatment and early removal of detritus. It is rather surprising that further use of the equipment has not been pursued in these areas.

A rather large number of studies have been conducted in which various abnormalities may be detected because of vascular disturbances. Clinical problems such as dysbasia, cerebrovascular tumors, meningeomas, extra- cerebral haematomas, varicose veins, and thrombosis of internal carotids can all be discerned by cooler temperatures overlying the problem area (5Z-54). Other studies have dealt with the effect of smoking which causes


peripheral vasoconstriction, delineation of sweating areas in normal and paraplegic men, location of herniated disks (elevated skin temperatures), and the effectiveness and rapidity of sympathetic blocking agents (55-60).

Aside from the numerous clinical studies, a number of more fundamental studies have been conducted to determine the surface temperatures of human subjects under a variety of environmental circumstances. In these studies, investigators have used radiographs to determine surface temperatures over the entire body. For example, a Barnes scanning radiograph was used to assess skin temperatures of nude men after standing in a 4°C environment for two hours (60). The colder areas, such as the nose, abdomen, hands, patella, feet, gluteus maximus, and lower calf muscles were easily discernible. The surface temperatures of the subjects in a thermoneutral environment showed similar differences between identical body regions as seen in the cold, but the magnitude of these temperature gradients was less. In a sweating subject, the skin temperatures were uniform over the entire body. Also a radiograph has provided a feasible approach to assessing radiative heat loss from clothed individuals under Amtic field conditions (61). Obvious design faults such as zipper configurations, compression or insufficient insulative materials, and the effect of wrinkles are readily discernible. Thus, this technique can be used in a very practical manner to design functional clothing for personnel in cold environments.

The emissivity of the skin is particularly important for determining absolute temperatures-especially with quanta detectors. These detectors are normally limited to the near infrared spectrum where the amount of energy at 30°C is small ( N 5 % between 3 p and 6 p) and the slope of the energy curve is steep so that any error is large. Therefore, errors in assumed emissivity or curved isothermal surfaces may present problems (62-64). We have also found the depth of field decreases rapidly as the target is moved closer to the instrument, and large errors in absolute temperatures may occur at distances less than 3 ft.

This terse recapitulation will acquaint the reader with the wide variety of clinical problems that have been studied with the use of radiographic methods and possible future applications. More detailed information may be obtained from several sources (22, 23, 35, 42).

D . Future Considerations

The rapid development of infrared radiography in the past ten years has provided the biologist and clinician with an extremely useful device for measuring surface temperatures without physical contact. No longer do discrete temperature points provide a mental restraint in the visualization of surface energy fluxes. The temperature pattern over the entire target surface


may now be visualized and measured. Also, dynamic temperature changes can now be measured with the use of real time scanners. The development of new photon detectors such as the HgCdTe or PbSnTe detectors offers the advantages of high speed and resolution while avoiding the problems associated with the older detectors of emissivity, and COZY H(m absorption bands. But the pyroelectric detector offers even further advantages over either the quanta or thermal detectors. Therefore, the instrumentation exists, or will shortly, that will enable the person interested in biological measuration to determine the surface temperature of any target-microscopic or larger-that can be exposed to air. The potential of this equipment is just being realized, and agricultural mapping of the earth, determining water temperatures, locating possible earth fractures to forecast earthquakes, defining precursor temperature patterns which can be used to predict cancerous activity, and delineating live and necrotic tissue in burn or frostbitten patients, all offer exciting possibilities for the temperature measurers. When will it end-probably never. The authors look forward to the day when it will be possible to take real time scans of flying birds to study in-flight temperature fluxes or measure the entire energy flux between plants and animals in their natural ecological niches. Limitations are present but we feel this avenue of biological temperature measurement will at last free the researcher from contact thermometry and allow the study of unfettered subjects.

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24. Abbott (1921) [referred to in L. B. Aldrich, Smithson. Misc. Collect. 81 (1928)l. 25. C. Sonne, Acta Med. Scand. 54, 358 (1921). 26. K. Buttner, Strahlentherapie 58, 345 (1937). 27. J. D. Hardy, J. Clin. Invest. 13, 615 (1934). 28. J. D. Hardy and C. Muschenheim, J. Clin. Invest. 13, 817 (1934). 29. G. Hofmann, Strahlentherapie 65,477 (1939). 30. F. H. Humphris, Brit. J . Phys. Med. 1, 118 (1938). 31. J. Plotnikow and R. Mibayash, Strahlentherapie 40,546 (1931). 32. J. Saidman, C. R. Acad. Sci. 197, 1204 (1933). 33. W. 0. Wilson and T. H. Plaister, Amer. J. Physiol. 166, 572 (1951). 34. J. H. Veghte and C. F. Herreid, Physiol. 2001. 38,267 (1965). 35. H. T. Hammel, J. Mammal. 37, 375 (1956). 36. W. M. Smith, Ann. N. Y. Acad. Sci. 121, 248 (1964). 37. D. D. Delahanty and J. R. Georgi, J. Amer. Vet. Med. Ass. 147, 235 (1965). 38. V. L. Sanger, J. A. Holt, and W. A. Reynolds, Can. J. Comp. Med. Vet. Sci. 29, 259

39. D. M. Gates, “Energy Exchange in the Biosphere.” Harper, New York, 1962. 40. D. M. Gates, Appl. Opt. 7, 1803 (1968). 41. R. Melzack, J. Stewart, and R. Bambridge, Electroencephalog. Clin. Neurophysiol. 20,

42. P. S . Callahan, Appl. Opt. 7, 1811 (1968). 43. J. S. Butz, Air Force 51, 46 (1968). 44. J. Gershon-Cohen, Ann. N. Y. Acad. Sci. 121,4 (1964). 45. K. Lloyd Williams, F. J. Lloyd Williams, and R. S. Handley, Lancet 2, 1378 (1961). 46. R. B. Barnes, Science 140, 870 (1963). 47. S. J. Birnbaum, Ann. N. Y. Acad. Sci. 121, 209 (1964). 48. N. F. Boas, Ann. N . Y. Acad. Sci. 121, 223 (1964). 49. R. N. Lawson, G. D. Wlodek, and D. R. Webster, Can. Med. Ass. J . 84, 1129 (1961). 50. G. Buwalda, in ‘‘ Medical Thermography ” (S. Heerma van Voss and P. Thomas, eds.),

51. N. J. M. Aarts, J. Radiol. Electrol. Med. Nucl. 48, 76 (1967). 52. E. 0. Backlund, J. Radiol. Electrol. Med. Nucl. 48, 39 (1967). 53. P. I. Branemark, Deut. Med. Wochenschr. 91,961 (1966). 54. C. Gros, A. Wackenheim, and C. Vrousos, J. Radiol. Electrol. Med. Nucl. 48,45 (1967). 55. A. Smessaert, D. Befeler, R. G. Hicks, and J. Connell, Amer. J. Surg. 109, 594 (1965). 56. E. R. Heinz, H. I. Goldberg, and J. M. Taveras, Ann. N. Y. Acad. Sci. 121,177 (1964). 57. J. Edeiken, J. D. Wallace, R. F. Curley, and S . Lee, Amer. J. Roentgenol. Radium Ther.

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Systems Approach to Skeletal Control: Concept of the System

R. TOMOVIC

Department of Electrical Engineering, University of Belgrade, Belgrade, Yugoslavia

I. Introduction ....................................................................................... 273 11. Rehabilitation of Amputees and Paralyzed Persons .................................... 274

111. Systems Approach to Muscle Control ...................................................... 276 IV. Multifunctional Hand Prosthesis ............................................................ 278 V. Arm Control ....................................................................................... 279

VI. Robots for Physical Rehabilitation ......................................................... 280 References .......................................................................................... 281

I. INTRODUCTION

The word system may be used in many different ways. Here it refers to control systems with inputs and outputs, i.e., multivariable control systems. The number of controlled variables involved in body activities amounts to several hundreds.

The case where many variables are controlled simultaneously in real time is a very difficult one from the theoretical and practical point of view. A special branch of control science-the theory of large systems-is concerned with problems involving many variables. It is interesting to point out that the use of mere feedback principles is not sufficient to solve multivariable problems of high dimensions. The control of large systems requires such concepts as multilevel organization, hierarchy, decomposition, coordination, principles not used in small scale problems ( I ) .

Large systems are also unique from the point of view of implementation of control decisions. While in the case of systems with a reduced number of variables the implementation of the control may be completely mechanized, it is not so in large systems. The most efficient implementation of the control in large systems is the combined action of man and the machine (thecomputer). Thus, instead of automatic control, man-machine control is frequently applied to large systems. The design of man-machine control requires new approaches and optimization principles (2).

273

274 R. TOMOVIC

The above ideas are used as a starting point for the explanation of muscular control in man and animal. It is shown that important improvements in the design of robots and artificial limbs can be obtained by using the systems approach.

11. REHABILITATION OF AMPUTEES AND PARALYZED PERSONS

It is a sad fact that the state of the art of prosthetic and orthotic devices has changed very little compared to advances in other fields of engineering and medicine. Some reasons why inadequate progress in this field has been made will be given.

It must be clearly recognized that the rehabilitation aids for amputees and paralyzed persons belong to man-machine control problems. Therefore, all attempts to improve only engineering design are doomed to be a failure. Nevertheless this obvious fact was not always taken into consideration. As an example let us mention the time-sharing control for artificial limbs. When more than two channels are used the device is rejected by the patient since the nervous system is organized in a different way. Man is very inefficient at keeping track of long sequences of motions at a voluntary level.

Another weakness in the design of rehabilitation equipment was the lack of a unifying theoretical approach. Each device was designed rather as an isolated unit. Prosthetic and orthotic devices were considered as totally different design problems. The same holds true for the aids for the upper and for the lower extremities. Only recently was it emphasized that from the control engineering point of view all artificial limbs have many aspects in common (3).

Man-machine design of rehabilitation aids for skeletal activities must take into account the following aspects: (1) generation of control signals, (2) processing of control signals, (3) energy supply, and (4) compactness. Since a man-machine relation is involved, performance requirements of a special nature must be met by the designer.

So far two basic methods have been used to generate control signals for artificial limbs. Both depend on the activity of the remaining muscles since direct use of the nervous system for control is not feasible at present. In the first approach the mechanical contraction of the muscle is used to activate the transducer whose output is normally an electric signal.

The myoelectrical activity of the muscle during contraction is also used for control purposes. The output may be discrete or proportional.

The first working model of the hand prosthesis using myoelectrical control was an important event in the rehabilitation field (4). However, many discussions on advantages and disadvantages of myoelectrical control have ob- scured some of the more essential facts. In particular, improvements of rehabilitation aids with increased number of degrees of freedom in order to

SYSTEMS APPROACH TO SKELETAL CONTROL 275

better match the anatomy and flexibility of human extremities were neglected. These improvements do not depend so much on how the control signals are derived but rather on how many external control sites are needed.

As pointed out before, the hierarchical organization of the nervous system does not lend itself to time-sharing external control. Parallel or time-sharing external coordination of several muscle groups for control purposes is a very heavy burden on the patient. In this way only two, or a maximum of three independent external control sites may be used. Therefore new approaches must be found to control multivariable mechanical systems for rehabilitation purposes.

One-level control implies one-to-one correspondence between the body site and the degree of freedom of the mechanical device. Time-sharing control belongs essentially to the same class. Using this approach, the limitations of man’s capacity for external control of artificial limbs are reached very quickly. In our opinion this was the greatest obstacle to the radical improvement of rehabilitation aids.

Multilevel control of artificial limbs overcomes the above limitations. Using this approach many degrees of freedom can be controlled with few independent signal sources. Multilevel, hierarchical control of artificial limbs thus fits naturally into the organization of the nervous system. The patient uses a reduced number of control sites, ideally only one, and has at his dis- posal a rehabilitation aid which is much more similar in shape and functions to its human counterpart.

The idea of multilevel control in prosthetics was first introduced for the hand (5). Later it was extended to the lower extremities. This approach is helpful in studying the general problem of skeletal control in man and animal.

Myoelectrical signals are currently used for one-level control or time- sharing control of rehabilitation aids. A new way of using bioelectrieal activity of muscles is interesting. In certain cases, as in arm control, the activity of sinergetic muscles can be detected by simultaneously recording and processing myoelectrical signals. The ensemble of myoelectrical signals derived from coordinated muscle activity serves as an input to the pattern recognition controller. The electromyographic pattern thus obtained is used to coordinate the motion of the paralyzed or amputated arm. In this way efforts in external control are reduced to a minimum.

The feasibility of the above approach was studied with respect to the above-elbow arm control. Myoelectric signals were recorded from thefollow- ing muscles: anterior and posterior deltoids, both leads of the biceps, the lateral head of the triceps, and the thromboids. The experiments have shown that it is possible to classify different arm motions like elbow flexion orprona- tion and supination (6) with a high degree of probability under varying load conditions.

276 R. TOMOVIC

Application of the multilevel control and electromyographic patterns in prosthetics and orthotics solves in a completely new way man-machine communication. Such an approach requires minimum learning and coordination effort even if complex motions are involved.

Efficient man-machine communication and signal processing are vital for the acceptance of rehabilitation aids by the patient. However, energy supply and compact design are also essential for the overall success. While the miniaturization of electronic circuits does not represent a great problem today, other engineering tasks are still difficult. Very soon the engineer realizes that muscles are highly compact actuators. As a matter of fact, there are no engineering actuators which directly transform chemical energy into mechanical work.

In order to give an example let us mention that a hand prosthesis must weigh no more than 350400 gm. For the terminal device with one degree of freedom this is not difficult to achieve. But with articulated fingers, external power, and antropomorphic proportions the task is challenging.

111. SYSTEMS APPROACH TO MUSCLE CONTROL

Motor activity in man or animal represents a large control system. Almost 800 muscles are involved in the motor activity of the human body. The majority of these muscles are attached to the skeleton and control its many degrees of freedom. There is no equivalent of such a complex mechanical structure in engineering, with amazing control performance ranging from locomotion in all environmental conditions to ballet, crafts, sports, etc. It should be kept in mind that most complex skeletal motions, involving hundreds of muscles, are controlled within fractions of seconds. How is the control of the skeletal activity organized ?

The answer to the above question is lacking. In fact, the study of the motor activity of the body is greatly limited by the lack of knowledge about how the information in the nervous system is processed. The essential part of any control system is the processing of input information and the coding of messages sent to the actuators. In the absence of this knowledge, the problem of animal motor control has been tackled from different angles.

Individual joints, especially those with one degree of freedom, can be considered for certain purposes as servomechanisms. For instance, when dealing with position and tracking tasks the theory of servomechanisms provides a means of describing the dynamical behavior of individual joints in terms of mathematical control models. Thus transfer functions and nonlinear and sampled data models for human motor activity have been derived. These models are valid for specific tasks. The theory of servomechanisms is unable to cope with real time control of complex skeletal activities. Muscular control


in its full complexity must be studied by other means (neurophisiology, biology, physics, computer and control sciences).

Systems approach to muscle control is concerned with a specific problem. The amount of primary information describing full dynamic behavior of the human skeleton is so large that it cannot be processed at one level in order to derive the control in reasonable time. Systems theory explores the principles and methods of how control problems of large dimensions can be transformed into decisions involving fewer variables. Therefore, the systems approach is becoming very helpful in bioengineering. The results obtained in this way are not only of theoretical value but are of great practical significance for the design of rehabilitation aids, industrial manipulators, and robots in general.

The following general multilevel control scheme has been used in the design of multivariable rehabilitation aids and rehabilitation robots. The man- machine control of the assistive device is performed at three levels: decision level, coordination level, and dynamic (adaptive) level.

The formal description of the first level is the set of decisions available to the human operator in order to perform a specific skeletal activity. For instance, such an activity may be the grasping and the manipulation of objects or locomotion in known environmental conditions. The design problem is to find the minimum set of decisions for the given skeletal activity. In the case of locomotion with fixed speed in a building, it is sufficient to consider the following choices: stand, sit, walk on leveI ground, climb the stairs, and change the direction of motion. The implementation of these decisions can then be handed over to the machine.

In order to reduce further the dimensionality of the multivariable control problem it should be kept in mind that many skeletal activities are of a repetitive nature (manipulation, locomotion, sports, dance). The idea is to separate the fixed, unchangeable part of the repetitive skeletal activity from the dynamic control of the motion.

Using the systems approach the given repetitive skeletal activity, for instance, walking on the level ground, is described by two distinct mathematical models. Algorithmic or coordination models describe the skeletal activity in terms of finite joint states. The following joint states may be used to derive the coordination model of the given skeletal activity : loose, locked, rotation, reverse rotation. This model does not take into consideration continuous body trajectories but emphasizes, rather, repetitive features of certain skeletal activities. Although full dynamic information is not contained in this model some essential features of the repetitive body motions can be thus described in coded form with relatively few variables.

Full dynamic description of the skeletal activity is given at the third, so- called dynamic or adaptive level. Here, conventional continuous type mathematical models are used. The great advantage of multilevel control of pros-

278 R. TOMOVIC

thetic and orthotic devices lies in the fact that the amount of information processed is essentially reduced. In this way complex body movements can be reproduced artificially using simple, small size computers. On the other hand, the task between the man and the machine is divided in an optimal way. The man remains the decision maker while the machine takes care of information processing.

Several examples are given in order to point out the advantages of multilevel organization of the control of human extremities.

IV. MULTIFUNCTIONAL HAND PROSTHESIS

The hand can be considered as the terminal device of the arm which takes it to the desired point in space. The distinction is not formal since two tasks are associated with the control of the upper extremities: grasping of the object and positioning of the arm. In the man these two tasks are solved simultaneously, It is true that there is strong interaction between the terminal device and the arm supporting it but to a certain extent the control models of the two functions can be separated.

Until recently most of the artificial hands were produced with rigid fingers and just one type of grasping action (pinch). Speaking practically, the control of the hand was reduced to one degree of freedom. Evidently, such a design limited the rehabilitation capabilities of the hand prosthesis and increased the positioning effort of the arm for the amputee.

The artificial hand with articulated fingers and several types of grasping actions is a relatively new concept (5). Before such a terminal device having several degrees of freedom could be used for rehabilitation purposes a feasible control system had to be designed. Feasible in this application means a reduced number of control signals provided by the amputee. The multifunctional terminal device, so-called Belgrade hand, needs for its control just one control site generating an electrical signal proportional to muscle contraction.

When the multifunctional terminal device was first proposed for rehabilitation purposes many new questions arose. It was asked if there is a need for multifunctional hands for below or above-elbow amputees. This doubt could be dispersed only by elaborate clinical experiences. The evaluation results published recently have shown that sophisticated terminal devices with multilevel control are accepted by the patients (7). As a matter of fact, this trend has been widely accepted today so that several new types of multifunctional hand prostheses are currently being developed. The future certainly belongs to articulated, multifunctional terminal devices.

The availability of a sophisticated terminal device initiated interesting clinical studies. It was soon discovered that it is quite a difficult task to develop evaluation methods and criteria for comparison of different kinds of externally


powered electronic terminal devices. This is understandable since performance of this man-machine system must be evaluated by disabled persons. Further work is now under way in order to obtain generally accepted evaluation procedures for externally controlled hand prostheses.

V. ARM CONTROL

The combined task of controlling the hand function and its displacement in space is extremely difficult. In fact, a good artificial arm does not exist today. The reasons are several. To start with, it is hardly possible to build an externally powered device with the weight, power, and compactness of the human arm. With advances in technology it is more and more likely that this difficulty will be overcome but the control task remains unsolved.

The positioning of the arm in space requires adequate input data. Using vision the man is able to evaluate continuously the vector distance to the target. Note that the vector distance to the target is the minimal information needed to locate the object in the space. In the case of the artificial arm the visual input must be transformed into electrical form and applied to the external control system. The artificial arm, excluding the hand, should be built with seven degrees of freedom in order to preserve the flexibility of the natural extremity. This poses a difficult control problem, to see that the minimum input information in the form of the vector distance is used in order to guide the multivariable mechanical device to the desired target. The problem can be formulated in another way. The arm, being a multivariable mechanical system has, in free space, an infinite number of different ways to reach the target. What is the criterion by which man selects just one trajectory leading to the target? The same question holds for motion with indirect access to the target.

It is easy to recognize that the target approach by the arm represents an optimal control problem. Unfortunately, we do not know the criterion function by which the actual trajectories are selected. On the other hand, the mathematical model of the arm is so complex that even with all necessary information available it would be impossible to solve the optimal control task in real time with a small size computer.

The simplest engineering solution for the artificial arm control is either to reduce the degrees of freedom of the mechanical system and/or to use sequ- ential (time-sharing) control. However, none of these solutions leads to the full restoration of the lost capacities of the disabled person. The available assistive devices are very poor approximations to the patient’s needs.

The above situation requires a new solution for the control of the upper extremities. First of all, new control philosophies for the target approach by the arm must be formulated. Next, the implementation of the assumed control principles must be studied in terms of computer time and size. The computer

280 R. TOMOVIC

output in this case is either the visual display of the target approach by the arm or (what is much better) the artificial arm is directly coupled to the computer so that actual trajectories in three dimensions are observed. This computer-arm system is coupled to the human operator and the different control philosophies are checked by the man-machine interactions.

Several experimental research stations of this kind are now installed in different countries. An interesting control philosophy for the arm has been proposed based on the phenomenon of sinergy in muscle control. The idea is to describe formally the type of skeletal activity when several muscle groups are organized to contribute to the same motion. This is in contrast to the one- degree of freedom joint control with alternate activation of agonist-antagonist muscles. The concept of sinergy has been implemented on the computer and is quite promising for external control of the upper extremity (8).

VI. ROBOTS FOR PHYSICAL REHABILITATION

The systems approach to muscle control leads to a completely new type of assistive device for the rehabilitation of paralyzed persons. Two kinds of applications are considered. The physical rehabilitation of paralyzed persons requires extended periods of exercises. Since the patient’s control of skeletal activity is reduced or lost completely, he needs special environment (water) or human assistance to move the body.

A new method of assisting the partly or completely paralyzed persons to restore skeletal activity is currently under investigation. It is based on multilevel, man-computer control of robots. The feasibility of this method for the rehabilitation of paralyzed persons depends on the following facts. First, it is necessary to have an active exoskeleton. Parts of this active exoskeleton can be attached to the patient in order to assist his remaining capabilities of motion. However, in the case of completely immobilized persons they can be carried around imbedded in the walking machine. In the first application the new device assists the patient during the physical exercise, while in the second application the mobility of the patients is restored by artificial locomotion instead of using the wheelchair.

Medical application of robots depends again not only on the engineering skill but on the control system. In this application a fully automatic robot is of very little use. An essential requirement when using robots for hospitals and artificial locomotion is the semiautomatic, man-machine control. The control task must be organized so that the patient remains the decision maker while the decision implementation is turned over to the machine (computer).

The design of man-machine control systems for locomotion has been made possible by applying finite automata theory in a new way (9).

When biped locomotion is involved, the gait stability must be explicitly

SYSTEMS APPROACH TO SKELETAL CONTROL 28 1

taken into consideration. An important requirement for rehabilitation use is the reduced size of the computer controlling both the locomotion and the gait stability. The biped gait stability has been treated as an inverted pendulum problem. It can be proved that a multivariable structure of inverted pendulums can be automatically restored to equilibrium position.

However, this approach does not lend itself to man-machine control. For rehabilitation purposes it is essential to reduce the number of controlled variables. An adequate solution of the gait stability problem needs a bioengineering approach instead of the purely mechanical one.

In the course of walking the leg joints are coordinated in a unique way. This by itself reduces the number of free variables (10). A second important reduction is due to the gait stability. Gait stability means essentially that after each step the end position of the whole body should be the same as at the beginning. If this repeatability can be assured the biped locomotion is maintained. Thus, by combining the multilevel approach with the repeatability conditions, feasible solutions for artificial locomotion of completely paralyzed patients are obtained.

A computer controlled exoskeleton to assist physical rehabilitation has been designed (IZ). The system will be used first for artificial locomotion of paraplegics. It is assumed that the patient can maintain gait stability by using the cane. In a later stage, man-computer controlled robots will be used for artificial locomotion of quadruplegics. In this case the gait stability will also be under external control. Experiments with this new kind of assistive device have been carried out in Belgrade with a team of medical specialists. There is no reason to exclude the possibility of having in the future hospitals for physical rehabilitation equipped with robots to assist patients in their exercises, as well as imagining paralyzed persons walking with an externally controlled exoskeleton instead of using wheelchairs.

REFERENCES 1. M. MesaroviC, D. Macko and Y. Jakahara, Multilevel Systems.” Academic Press

2. R. TomoviC, On man-machine control, Aufomarica 5, No. 4, 4 0 1 4 0 3 (1969). 3. R. TomoviC and R. Bellman, Systems approach to muscle control, Mafh. Biosci. 8,

4. A. E. Kobrinski et al., Problems of bioelectric control, Proc. Isf IFAC Congr., Moscow 1960, Butterworths, London, 1960.

5. R. TomoviC and G. Boni, An adaptive artificial hand, Trans. IRE AC-7, No. 3, 3-10 (1 962).

6. W. R. Wirta and F. R. Finley, Engineering principles in the control of external power by myoelectric signals, Arch. Phys. Med. Rehabil. 49,294-296 (1968).

7. H. Kay, M. KajganiC and N. Ivanzevif, Medical Evaluation of the Belgrade Electronic Hand, Proc. 3rd Symp. Exfernal Confrol Human Exfremities, 1969, pp. 129- 137. Yugoslav Committee ETAN, Belgrade, Post Office Box 356 (1969).

New York, 1970.

NO. 3/4,265-277 (1970).

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8. M. GavriloviC and M. Marie, An approach to the organization of the artificial arm control, Proc. 3rd Symp. External Control Human Extremities, pp. 307-322, Yugoslav Committee ETAN, Belgrade, P.O.B. 356, 1969.

9. R. TomoviC and R. McGhee, A finite state approach to the synthesis of bioengineering control systems, ZEEE Trans. Human Factors Electron. HFE-7, No. 2, 65-69 (1966).

10. M. VukobratoviC, and D. JuriEiC, Contribution to the synthesis of biped gait, IEEE Trans. Bio-Med. Eng. BME-16, No. 1 (1969).

11. M. VukobratoviC, D. JuriEiC, D. Hristif, 2. StojiljkoviC and V. &rid, “An Investigation to Restore Locomotion and Stability Functions of the Severaly Disabled,” Progress Rep., Part I, Project SRS-YUGO-29-69, Social Rehabilitation Service, Washington, D.C.

Functional Electrical Stimulation of Extremities

L. VODOVNIK

Faculty for Electrical Engineering, University of Ljubljana, LjubGana, Yugoslavia

I. Introduction ....................................................................................... 283 11. Classification of FESE ........................................................................ 284

111. Motoric FESE .................................................................................... 285 IV. Implanted Systems .............................................................................. 288 V. Examples of New Systems ..................................................................... 289

References .......................................................................................... 2%

I. INTRODUCTION

Electrical stimulation of neuromuscular preparations has been known from the time of Galvani. Since then, the development of electrophysiology has depended on progress in electrical engineering and this is true even today.

An example of this parallel evolution is a new field in rehabilitation- functional electrical stimulation of extremities (FESE).

Patients were for decades stimulated with large, clumsy stimulators built with tubes or electromechanical devices, which were located in departments of physical medicine. Mostly peripheral lesions were treated, since nobody saw much sense in stimulating stroke patients, quadruplegics, paraplegics, or patients with cerebral palsy.

In the early sixties when the transistor came into general use, the time was ready for a new approach in electrical stimulation. Since transistors enabled the construction of small portable stimulators, Liberson ( I ) proposed in 1962 that drop-foot in hemiplegic patients be compensated by electrical stimulation of the peroneal nerve. The stimulator was worn on the belt of the patient and triggered from a heel switch. Such a stimulator markedly improved the walking gait of stroke patients with peroneal palsy.

This electronic peroneal brace-a simple device per se-created new concepts in the rehabilitation of patients with deficiencies of the locomotor system and triggered the development of FESE.

283

284 L. VODOVNIK

11. CLASSIFICATION OF FESE

Originally, functional electrical stimulation was intended only to provoke functional movements during activities of daily living in patients with paralyzed extremities (2, 24. Recent work and current developments seem to require a larger scope of FESE and thus a classification of functional stimulation is proposed.

Quite generally, if electrical stimuli are applied to skeletal neuromuscular systems, the following useful effects or applications are known :

a. Functional muscle contraction (motoric stimulation). b. Facilitation of voluntary functional muscle contraction (facilitating sti-

c. Inhibition of involuntary muscle contraction (inhibitory stimulation). d. Pain reduction. e. Electrodiagnosis.

The first three effects are comprised in a generalized definition of FESE. In the first experiments of Liberson, it had already been observed that

stimulation at some time t had effects also a few hours or days later. Thus, regardless of the neurophysiological mechanisms producing these effects there exists in principle the possibility that stimulation in the past (at t ) may have some effect much later, e.g., at time t + z.

If the musculoskeletal dynamics is neglected (i.e., realistic time units for t and T are days and weeks) and if E(t + z) denotes any specific effect at t + T due to electrical stimulation S at t , the relation between E and S can be described as

Thus, in general, stimulation at t can cause an effect at t + z, and if the relation described by Eq. (1) exists at least for some z > 0, the stimulation has some therapeutic effect. If E exists only as long as S is present (i,e,, z = 0), there is no therapeutic effect due to electrical stimulation, and the system works only as an orthotic device.

The above stated problem of long-term effects of stimulation adds a new dimension to our classification of FESE and will certainly be one of the most exciting research areas in the coming years. Another dimension to the classification of FESE can be added if the location of the stimulating electrodes in the neuromuscular system is included. Figure 1 shows a vector matrix presentation of the system where different topological possibilities for stimulation are indicated. Of course, not all of these possibilities have been explored yet, but we believe that a classification should always be sufficiently general to include also investigations which might be expected in the future.

mulation).

E(t + 7 ) =f[S( t ) ] . (1)

FUNCTIONAL ELECTRICAL STIMULATION OF EXTREMITIES 285

I

FIG. 1 . Vector matrix presentation of neuromuscular system. r = input vector from higher centers; e = efferent signal vector; c = output vector; a = afferent signal vector. [k(s)], [L(s)] = matrices representing the neuronal pool in the spinal cord. [M(s)] = matrix representing the musculoskeletal system. [R(s)] = matrix representing the receptors. Possible “Points of attack” with electrical stimulation: A, brain stimulation; B, stimulation of the motoneurone pool; C, efferent stimulation; D, muscle stimulation; E, receptor stimulation; F, afferent stimulation.

111. MOTORIC FESE

According to our classification let us first discuss motoric functional stimulation. The aim of this type of stimulation is to produce functional contractions of the paralyzed muscle. The intensity of contraction or at least the possibility of starting and stopping the contraction has to be under the voluntary control of the patient. Schematically the problem is shown in Fig. 2. Normally, man controls the output vector c (position, force, velocity, etc.) of an extremity through combinations of nerve pulse frequencies which can be represented by the input vector r.

Pathological situations exist when the output vector c is independent of the input vector r, if r does not exist or if r does not represent the volitional desires of the patient. In order that the patient might regain voluntary control over his paralyzed limb, usually another-normally innervated-auxilliary signal source r, must be found on his body, and after signal processing a control signal n is available. This signal can be applied to different parts of the damaged neuromuscular loop in order to produce an output c which will be well correlated with r, and thus with the desires of the patient.

This, in short, is a control-theoretical statement of our problem. In medical terms, Fig. 2 represents an orthotic system using electrical stimulation. To be

286 L. VODOVNIK

. FIG. 2. Block diagram of orthotic system using functional electrical stimulation. Block

E combines blocks L and K from Fig. 1.

even more general, it should be mentioned that instead of electrical stimulation other types of stimulation could be used as well. For example, mechanical stimulation (3) seems to be quite promising, but we will be concerned here only with electrical stimulation. Furthermore, the existence of an adequate control signal n will be assumed and problems concerning r, , S, and P will not be discussed except for some specific examples described at the end of the chapter.

Many of the basic properties of stimulated normal neuromuscular systems have been described elsewhere (4-9). Therefore, only some of the most important results will be reviewed here.

For isotonic contractions it was found (4) that the simplest transfer function between the output angle 4 and the stimulation current I is

where K,, K2 are constants, J is the moment of inertia of the rotating extremity, and z is a delay time.

For isometric contractions Crochetiere (5) found an empirical equation between maximum torque T and stimulation current of the form

T = K log(Z/Z,), (3)


where K is a constant and 1, is the threshold current. (For I = I t , the torque is zero). For small sinusoidal perturbations the frequency response was determined to be of the form

T(s) kle-rs G(s) = - =

I($) (s + kJZ * (4)

Using these type of data a continuous control system was designed. A simplified form of the system is shown in Fig. 3. The output/input transfer function of the uncompensated system was found to be (9)

where A , is an amplification constant.

n

FIG. 3. Simplified control system using stimulated muscles as actuators.

Nonlinearities (dead zone and saturation) were analyzed using the describing function technique. Without compensation the system was unstable and a twin-T filter had to be inserted for stabilization.

In Vodovnik et al. (8), two types of switched control systems were described and an analogue computer model for a stimulated antagonistic musculoskeletal system was proposed.

One of the most important problems in FESE is the reduction of torque due to fatigue. Some recent work can be found in Peckham (10) but much more work has to be done before any final conclusion regarding the mechanism of fatigue and optimum stimulation current could be made. Crochetiere proposed to " bypass " the fatigue problem by an electromagnetic lock (7), but a clinically acceptable control of the lock is still under development.

288 L. VODOVNIK

Recent work shows that variable delays, elasticities, and viscosities as well as some hysteresis might be important nonlinearities in FESE and are probably responsible for some of the stability problems which were encountered during experiments with control systems using stimulated muscles as actuators. These nonlinearities, as well as facilitatory and inhibitory stimulation (IZ), are in the early stages of research and will have to be discussed at a later time.

For musculoskeletal systems which are unable to produce the required forces for a given dynamic performance with stimulation, a new approach is proposed. It is suggested that an externally powered control loop be added in parallel to the stimulation control loop. Both loops would be working simultaneously, one “helping” the other. Such a system is called a hybrid control system.

IV. IMPLANTED SYSTEMS

In almost all clinically applied systems of functional stimulation and in the majority of experiments on normal humans, cutaneous electrical stimulation is used. This method, adapted from conventional physical therapy, has only one advantage: under normal conditions of application it has no traumatic effects. This, however, is a very important advantage and it may still take a while before other methods of stimulation will be widely used on patients. But we are interested in new approaches; therefore let us discuss alternatives. First let us enumerate the obvious disadvantages of cutaneous stimulation :

1. The electrodes have to be applied every time stimulation is required (e.g., daily). If patients have to do that by themselves, it represents an additional physical and psychological burden which has to be overcome if an orthotic system is to be successfully used.

2. The location of electrodes is sometimes very critical with the resulting inconsistency and irreproducibility of movements.

3. Practically the whole voltage drop is consumed across the skin and only approximately 10% of the stimulation voltage reaches the motor point or nerve area.

4. As the skin has a rather high density of pain receptors, cutaneous stimulation can be unpleasant or even painful. This disadvantage turns however to an advantage if use is made of afferent stimulation, and sensory signals are exploited to facilitate motor neurons in the neuronal pool of the spinal cord.

There are two alternatives which alleviate or eliminate the above mentioned


drawbacks : (a) percutaneous stimulation, and (b) application of completely implanted stimulators.

In percutaneous stimulation the electrode wire is inserted through the skin with a hypodermic needle. A special spiral electrode was developed at Case Western Reserve University (12) for percutaneous pickup of myoelectric signals but only limited experience exists on the use of these electrodes for stimulation.

The major disadvantages of percutaneous electrodes are the possibility of infection at the point of insertion and the danger of wire breakage. These drawbacks are usually eliminated with an implanted stimulator only to be replaced with another major problem-trauma due to surgery. Even in healthy animals or humans this is an important factor. On patients with paralyzed extremities where pathological metabolic changes might prohibitively prolong the healing process, any surgery should be performed with caution.

Thus, none of the two alternatives to cutaneous stimulation seem to be without problems and much more work has to be done before more patients will be able to benefit from these advanced techniques.

If surgery can be minimized, the implanted stimulators could certainly be preferred to percutaneous stimulators. We feel that-in addition to technologi- cal advantages-implanted systems will be psychologically better accepted as an integral part of the human body than surface electrodes or connectors for percutaneous electrodes. In general, there are four major problem areas which have to be dealt with when implantable stimulators are designed.

1. Electronics (miniaturization, energy transfer, etc.). 2. Encapsulation and tissue reaction. 3. Electrode properties (mechanical breakage, corrosion, electrical im-

4. Electrophysiology of stimulated neuromuscular systems. pedance, etc.)

These problems have been dealt with to some extent by Lale, Peckham, JegliE, Lorig (10,13-15) and many other workers in the heart-pacemaker and bladder-stimulation fields, but there are still no definite solutions in sight.

v. EXAMPLES OF NEW SYSTEMS

The most widely used device applying FESE is the electronic peroneal brace which was mentioned in the Introduction.

Figure 4a shows a schematic diagram of this brace which is now commercially available from at least two manufacturers. There are however some drawbacks to this system :

290 L. VODOVNIK

1. The duration of the pulse train of the stimulation current is constant

2. The microswitch is mounted in the heel of the shoe and thus all shoes

3. Wires leading from the shoe to the stimulator are unpractical and

4. The attachment of electrodes is critical and some patients dislike the

and optimized for a given average walking rate.

worn by the patient need some adaptation.

unaesthaetic, which is very important especially for female patients.

sensation accompanying electrical stimulation.

Heal-

Recewer and

( 0 ) ( b) (C)

Fro. 4. Various versions of the electronic functional peroneal brace.

To eliminate some of these difficulties advanced versions of the brace were developed.

In order to change the pulse train duration with the speed of walking a rate meter was added to the system, and a brace with walking rate dependent tetanization has now been evaluated. For fast walking the stimulation times are shorter, for slow walking the times become longer. Some preliminary results of this system were reported in GraCanin et al. (16).

To eliminate the problems of shoe adaptation and wires from the switch to the stimulator a system shown in Fig. 4b was designed. A miniature radio- transmitter and switch were inserted in an insole which is adjusted to the shoe of the patient. The triggering signal-generated every time the patient lifts his heel-is sent to the receiver which activates the stimulator. If the patient now wants to change shoes, he has simply to put the insole in the new shoe and the system is operational again.

For the patient where elimination of sensation and simplified handling is desired, the system shown in Fig. 4c was developed. The link from the heel to the receiver remains the same as in Fig. 4b, but another radiofrequency link is added from a coil around the leg below the knee to a miniature receiver implanted behind the knee, close to the peroneal nerve. This system was

FUNCTIONAL ELECTRICAL STIMULATION OF EXTREMITIES 29 1

FJG. S(a). Electronic peroneal brace with radiofrequency control and implantable stimulator. J, insole with switch and transmitter; S, receiver and transmitter; F, transmitting oscillator coil; G, implantable stimulator; P, charger.

292 L. VODOVNIK

FIG. 5 6 ) . Subject with surgically implanted stimulator wearing the system of Fig. 5(a).


described in JegliE et al. (17) and a similar one but with more extensive surgery was published by McNeal and Wilemon (18). Figure 5 shows the apparatus and a subject with the surgically implanted stimulator.

For patients with more than one paralyzed muscle group a three-channel stimulator was developed (Fig. 6). The stimulator is triggered by a radio switch in a way similar to the peroneal brace. Each channel has a variable delay time zi l ( i = 1,2,3) which can be independently adjusted for each channel. After this delay a stimulation train starts with a duration of ~ ~ ~ ( j = 1,

- Receiver and three- channel stimulator

Radio - t ransmi tt er T and switch in insole of shoe

FIG. 6 . Block diagram of three-channel stimulator. Sw, T, switch and transmitter in insole of shoe; R, receiver; T ~ ~ , T ~ ~ , 731, delay times; T ~ ~ , T ~ ~ , 732, stimulation times; S1, S2, S3, stimulators; El, El, E3, electrodes.

2,3). The delays can be varied between 50 ms and 1.2 sec. Instead of triggering with the heel switch manual triggering with a switch and transmitter in the handle of a crutch could be provided as well.

Figure 7 shows the system on a patient, and Fig. 8 is a typical stimulation sequence on a patient with paralysis of the M. Tibialis anterior and M. Peroneus, the M. Quadriceps and the Hamstrings (knee flexors). A detailed account on this work is found in Kralj et al. (19). Recent work towards multichannel stimulation was also initiated by Milner et al. (20) who tested their system on the leg of a frog and on humans.

294 L. VODOVNIK

FIG. 7. Hemiplegic patient walking with three-channel stimulator,


For upper extremities, GraEanin and MarinEek (21) described a Functional Electronic Radial Brace for patients who lost voluntary control of extension of the wrist and fingers.

I n spite of the work described, which shows definite sound trends of progress, there are still major problem areas where much more research has to be done before more sophisticated orthotic systems will be available for patients.

FIG. 8. A typical stimulation sequence during the swing phase of walking. A, stimulation of N. Peroneus; B, stimulation of M. Quadriceps; C, stimulation of knee flexors. Time scale: 100 msec per division; voltage scale: 10 V per division; frequency: 50 Hz; pulse width: 0.3 msec.

These areas are:

1. Information sources with continuous control signals. They are especially important for upper extremity orthotics.

2. Neurophysiology with emphasis on investigations of “learning ” capabilities at different levels of the central nervous system and eludication of release phenomena and other pathological conditions in the locomotor system.

3. Biomechanical and control theoretical investigation of musculoskeletal systems.

4. Materials technology which should provide us with optimum electrodes, biologically stable materials, and subminiature electronic circuitry for im- plants.

296 L. VODOVNIK

Until more is known in the above mentioned fields only very simple, open loop devices will be used by the patients, and the task of the engineer remains to help bridge the present gap between theoretical possibilities shown for example in Vodovnik et al. (22) and clinical application.

REFERENCES

1. W. T. Liberson, H. J. Holmquest, D. Scott, and M. Dow, Functional electrotherapy: Stimulation of the peroneal nerve synchronized with the swing phase of the gait of hemiplegic patients, Proc. 3rd Int. Congr. Phys. Med., Washington, D.C., 1960, pp. 705- 710. Westlake Press, Chicago, Illinois, 1962.

2. L. Vodovnik, C. Long, J. B. Reswick, A. Lippay, and D. Starbuck, Myo-electric control of paralyzed muscle, ZEEE Trans. Bio-Med. Eng. BME-12, No. 3, 4 169-172 ( 1 965).

Za. L. Vodovnik, M. DimitrijeviC, T. Prevec, and M. Logar, Electronic walking aids for patients with peroneal palsy, World Med. Electron. 4, 58-61 (1966).

3. L. A. Hedberg, B. Oldberg, and P. A. Tove, EMG controlled muscle vibrators to aid mobility in spastic paresis, 7th Int. Conj: Med. Biol. Eng., Stockholm, 1967, p. 197.

4. L. Vodovnik, The dynamic response of a musculoskeletal system due to electrical stimulation, Case Institute of Technology, Report EDC 4-64-10, Cleveland, Ohio, 1964.

5. W. J. Crochetiere, L. Vodovnik, and J. B. Reswick, Electrical stimulation of skeletal muscle-a study of muscle as an actuator, Med. Biol. Eng., 5 , 111-125 (1967).

6 . L. Vodovnik, W. J. Crochetiere, and J. B. Reswick, Control of a skeletal joint by electrical stimulation of antagonists, Med. Biol. Eng. 5, 97-109 (1967).

7. W. J. Crochetiere, On the use of electrically stimulated muscle as a controlled actuator of limb, Ph.D. Thesis, EDC 4-67-17, Case Institute of Technology, Cleveland, Ohio, 1967.

8. L. Vodovnik, A. Kralj, D. KelSin, and M. BorovSak, Simulation of purposeful movements by electrical stimulation of muscle, Proc. Int. Symp. External Control Human Extremities, Dubrovnik, 1966, pp. 14-53 (1967).

9. L. Vodovnik and J. B. Reswick, Control theory concepts in functional electrical stimulation of extremities, Theoretical supplement to Automatika, 1, 33-38 (1965).

10. H. Peckham, Design considerations in electrical stimulation of skeletal m u d e , M.Sc. Thesis, Case Western Reserve Univ., June 1968.

11. M. DimitrijeviC, F. GraEanin, T. Prevec, and J. Trontelj, Electronic control of paralyzed extremities, Biu-Med. Eng., 3, 8-19 (1968).

12. C. Caldwell, A new transcutaneous electrode, Report No. EDC 4-67-17. Case Western Reserve Univ., Cleveland, Ohio, August 1967.

13, P. G. Lale, Muscular contraction by implanted stimulators, Med. Biol. Eng. 4, 319 (1966).

14. A JegliE, E. Vavken, M. Strbenk, and M. Benedik, Electrical stimulation of skeletal muscle by directly powered implanted R F receivers, Pruc. Symp. External Control Human Extremities, Dubrovnik, 1966, p. 42 (1967).

15. R. J. Lorig, Myo-electric RF stimulation of skeletal muscle using implant methods, MSc. Thesis, Case Western Reserve Univ., Cleveland, Ohio, June 1968.

16. F. GraEanin, A. Kralj, and S. ReberSek, Advanced version of the “Ljubljana functional electronic peroneal brace ” with walking-rate controlled tetanisation, 3rd Int. Symp. External Control Human Extremities, Dubrovnik, 1969, pp, 487-493 (1 970).


17. A. JegliE, E. Vavken, and M. Eknedik, Implantable muscle or nerve stimulator as part of an electronic brace, 3rd lnt. Symp. External Control Human Extremities, Dubrovnik,

18. D. R. McNeal and W. Wilemon, Treatment of spasticity through functional electrical stimulation, Neuroelec. Conf. San Francisco, 1969, pp. 46-50.

19. A. Kralj, A. Trnkoczy, and R. ACimovid, Correction of the gait cycle of hemiplegic patients by means of a three-channel functional electrical stimulator, Elektrotehn. Vesfn. (1971). In press.

20. M. Milner, A. 0. Quanbury, and E. P. Edwards, Human locomotion by ordered electrostimulation of the available musculature, National Research Council, Div. Mech. Eng. Report LTR-CS-11, Ottawa, Canada, September, 1969.

21. F. GraEanin and I. MarinEek, Development of new systems for functional electrical stimulation, 3rd Znt. Symp. External Control Human Extremities, Dubrovnik, 1969, pp.

22. L. Vodovnik, Some topics on myo-electric control of orthotic/prosthetic systems, general problems, Report No. EDC 4-67-17, pp. 1-30. Case Western Reserve Univ., Cleveland, Ohio, August 1967.

1969, pp. 593-603 (1970).

495-501 (1970).


Author Index

Numbers in parentheses are reference numbers and indicate that an author's work is referred to, although his name is not cited in the text. Numbers in italics show the page on which the complete reference is listed.

A

Aarts, N. J. M., 268(51), 271 Abbott, 266, 271 Abdurazakov, A., 48(19), 75 Abdurazakova, F., 48(19), 75 Abrams, R. H., 16, 39 ACimoviC, R., 293(19), 297 Adlam, J. H., 26(67), 40 Adolphsen, J. W., 91(47), 135 Agarwala, B. N., 87(32), 134 Ahrons, R. W., 85(8), 134 Ainsworth, W. W., 132 (169), 138 Albright, F. J., 123(153), 138 Aldrich, L. B., 262(15), 266, 270 Aldridge, R. V., 18, 19, 20, 39 Alexeff, I., 26, 40 Aliev, Yu. A., 52(52), 74, 76 Anashin, A. M., 30(78), 40 Anaskin, I. F., 219(61), 234 Anderko, K., 91(48), 135 Anderson, E. E., 120(135), 137 Anderson, 0. A., 24, 40 Anstead, R. J., 91(46,47), 92(46,47,52), 135 Antman, S., 73, 77 Arbman, E., 49(33), 75 Argout, P., 59(99), 61(99), 77 Ardni , A. J., 57(85), 77 Arnott, R. G., 243(7), 270 Artsimovich, L. A., 9, 10, 30, 39, 40 Ashner, 3. D., 97(81), 136 Atalla, M. M., 102(94), 136 Attardo, M. J., 87(32), I34 Aufderheide, A. R., 97(77), 120(77), I35 Averin, V. G., 25, 26(65), 40

B

Babykin, M. V., 27,40 Backlund, E. O., 268(52), 271 Bainbridge, K. T., 49(31), 75

Baker, D. R., 22, 34, 40, 41 Baker, W. R., 24(57), 40 Balakhanov, V. Ya., 32, 41 Balodis, M., 48(15, 21), 75 Balzer, R., 59, 61(102), 74, 77 Bambridge, R., 267(41), 271 Baranov, S. A., 52, 74, 76 Barber, N. F., 53(54), 76 Barnes, R. B., 268(46), 271 Bart, J. J., 94(57), 96(57), 135 Bartlett, A. A., 49, 73, 75 Bartolomew, G. A., 44, 75 Bastard, C., 59(96), 77 Baudry, A., 50(46), 76 Beakley, W. R., 253(13), 270 Becker, J. A., 244(9), 249(9), 270 Befeler, D., 269(55), 271 Bekefi, G., 36,41 Belenkii, S. N., 52(52), 74, 76 Bellicard, J.-B., 49, 76 Bellman, R., 274(3), 281 Beds, C. E., Jr., 50(47), 76 Benedik, M., 289(14), 293(17), 296, 297 Benjaminson, A., 239(5), 270 Benzinger, T. H., 240(6), 270 Berenyi, D., 48(20), 73, 75 Berger, N. K., 27, 40 Berger, W. M., 94(55), 95(55), 120(132),

124(159), 126(159), 127(159), 135, 137, 138

Bergkvist, K. E., 67, 69, 70,72, 77 Berglund, C. N., 102(93), 136 Bergmark, T., 44(6), 75 Berlovitch, Ye. E., 54, 76 Bernstein, E. M., 57(82), 77 Berstein, M. J . , 24(58), 40 Bester, M. H., 120(138), 137 Beuzit, P., 59(100), 61(100), 77 Bezmel'nitsyn, V. N., 25, 26(65), 40 Bharucha, D., 59, 61(102), 74(102), 77

299

300 AUTHOR INDEX

Bird, R. P., 49, 73(35), 75 Birdsall, C. K., 20, 39 Birnbaum, S. J., 268,271 Bisggrd, K. M., 56, 57(84), 74, 76, 77 Black, J . R., 87(28, 30), 95(64), 119(30),

Blair, J. C., 88(39), 94(39), I34 Blech, I. A., 87(29), 88(36), 119(129), 134,

Bludman, S. A., 54(66), 76 Boas, N. F., 268(48), 271 Bobrovskii, G. A., 30, 40 Boersch, H., 140, 193, 196, 197, 201(43),

219(56, 69), 233, 234 Bogolyubov, N . N., 21,40 Bohm, D., 5 , 7 ,38 Bond, R., 121(145), 137 Bondarenko, V., 48(21), 75 Boni, G., 275(5), 278(5), 281 Booth, N., 22, 40 Booth, W., 81(4), 134 Born, M., 157(29), 168(29), 175(29), 233 BorovSak. M., 286(8), 287(8), 296 Bosson, G., 249(1 l), 254(11), 270 Bouasse, H., 174(36), 211(36), 233 Boucher, B., 243(8), 270 Bowman, R., 121(145), 137 Branemark, P. I., 268(53), 271 Brauer, J. B., 86(22), 122(22, 148), 123(22),

130(22), 134, 137 Bray, A. R., 102(94), I36 Brinton, J., 122(151), 123(151), 129(165),

Brown, R. W., 132(169), 138 Browning, G. V., 82(6), 119(123), 134, I37 Bruinsma, P. J . T., 56, 76 Bryant, R., 120(138), I37 Buchel'nikova, N. S., 13(33), 16, 17, 39 Buhl, R., 219(64), 234, 243(8), 270 Burgess, R. R., 89(41), I34 Burhop, E. H . S., 5(8), 7(8), 38 Buritz, R. S., 91(44), 135 Buttner, K., 266(26), 271 Butz, J. S., 268(43), 271 Buwalda, G., 268(50), 271

134, 135

137

138

C

Caldwell, C., 289(12), 296 Callahan, P. S., 267(42), 269(42), 271 Camac, M., 54(62), 76

Campbell, D. S., 109(118), 137 Campbell, J. F., Jr., 91(42), I35 Carrikre, Z., 174(36), 211(36), 233 Cartan, L., 53(57), 76 Castman, B., 44(7a), 75 Chaikin, S. W., 104(104), 136 Chambers, R. G., 219(57), 234 Chen, F. F., 13, 19, 22, 23, 39, 40 Cherstov, L. A., 66(107), 68(107), 74(107), 77 Chou, N. J., 95(65), 99(65), 135 Chu, T. K., 12, 18, 19, 20(44), 22(45), 39 &it, V., 281(11), 282 Clark, L. C., 238(1), 270 Clarke, J. F., 13, 39 Cole, K. S., 255(14), 270 Coleman, M. G., 89(41), 134 Colgate, S. A., 24(57), 40 Collins, D. R., 120(140), 137 Colteryan, L. E., 119(123), I37 Combs, C., 97(79), 136 Connell, J., 269(55), 271 Coppi, B., 31, 40 Coroniti, F. V., 33(91), 34(91), 41 Cox, C. D., 49(24), 75 Cox, R. H., 94(56), 107(110), 108(110),

Cox, W. P., 120(135), I37 Crochetiere, W. J. , 286, 287, 296 Crook, G. W., 33(90), 41 Crosthwart, D. L., Jr., 94(56), 119(56), I35 Cummings, D. G., 119(123), 137 Cunningham, J. A., 85(10), 89(40), 94(10),

Curley, R. F., 269(57), 271 Currie, E. H., 14, 39 Cziapas, A. F., 219(61), 234

115(110), 119(56), 135, 136

I34

D

DAngelo, N., 12, 39 Daniel, H., 47, 51, 53, 68(50), 72, 74, 75,

Daughney, C. C., 35, 37(94), 41 Davidsohn, U. S., 97(76), I35 Davis, D. O., 118(122), 120(122, 133, 136!,

Davisson, C. J., 140, 232 Dawson, J . M., 24, 27(60), 40 Day, P. P., 56, 74(78), 76 Deal, B. E., 102(96), 136

76, 77

I37

AUTHOR INDEX 301

DeDionigi, R., 13,39 Deev, V. M., 25, 40 de Haan, E. F., 49(32), 75 de Jager, C. W., 56, 76 Dekanosidze, E. N., 181(42), 234 Delahanty, D. D., 267, 271 Delong, A., 146(25), 201(47), 208(47), 211,

219(47, 60, 65), 220(47), 222(72), 230(72), 231(47, 73), 233, 234

Demidov, A. M., 44, 75 Demidov, 8. A., 32(84, 86), 41 Dempsey, D. F., 54(59), 76 Denison, D. M., 49(23), 75 DeSilva, A. W., 35(96), 37(96), 41 Devaney, J. R., 88(38), 94(38), 106(107),

de Vries, C., 49(38), 56, 76 D’Heurle, F. M., 87(31), 134 Diamond, J. M., 249(10), 253(12), 254(10),

Diehl, D. A., 109(119), 137 Dimitrijevid, M., 284(2a), 288(1 I), 296 Dimock, D., 37, 41 Dionisio, J. S., 77 Dobratt, R. D., 94(56), 119(56), 135 Dolmatova, K. A., 69(110), 77 Douma, F. Th., 56, 76 Dow, M., 283(1), 296 Downes, G. H., 104(102). 136 DrahoS, V., 146(25, 27), I77(39), I8U(39),

181(39), 201(47), 208(47), 211, 212(27), 217(27), 219(47, 60, 65), 220(47), 222(72), 230(72), 231(47, 73), 233, 234

107(107), 109(107), 115(107), 134, 136

270

Drummond, W. E., 33,41 Dudley, R. H., 120(141), 137 Duffek, E. F., 118(122), 120(122), 137 Diiker, H., 141, 159(16), 218(15, 16), 222,

DuMond, J. W. M., 57(91), 74, 77 Dunbar, R. C., 106(106), 107(106),

109(106), lll(lO6), 115(106), I35 Durn, D. A., 24,40 Dupree, T. H., 2, 7, 11, 25, 38, 39, 40 Dzhelepov, B. S., 48(19), 50(49), 69(111),

230061, 233

75, 76, 77

E Eastlund, B., 13(33), 39 Edeiken, J., 269(57), 271 Edwards, E. P., 293(20), 297

Edwards, R., 86(16), 134 Egorov, Yu. S., 49(25), 75 Eidel’man, Yu. I., 13(33), 39 Eisenberg, P. H., 86(25), 97(78), 130(25),

Elagin, N. I., 32(84, 86), 41 Eldridge, J. M., 95(65), 99(65), 135 Etievant, C., 22, 40 Ewan, G. T., 50, 73(43), 76

134, I35

F

Fadley, C. S., 50, 76 Fafarman, A., 91(44), I35 Faget, J., 174, 198, 200(38, 44), 208(52),

209(37, 38, 44), 210, 219(37, 63), 220, 222(38), 230(38), 231(38), 233,234

Faggin, F., 106(105), 136 Fahlman, A., 48(17), 75 Fanchenko, S. D., 32,41 Farley, 5. L., 124(158), 138 Feokistov, A. I., 49(30), 75 Fert, Ch., 174, 198, 200(44, 45), 208,

Fewer, D. R., 94(59), 95(59), 135 Finley, F. R., 275(6), 281 Fitzgerald, D. J., 95(69), 97(82), 135, I36 Fletcher, W. H. W., 15, 21, 22, 39, 40 Fontanesi, M., 13, 39 Forsythe, D. D., 104(100), 106(105), 136 Fowler, H. A,, 219(58), 234 Fowler, P. W., 269(64), 271 Fowler, T. K., 6, 38 Frana, J., 49(28), 75 Fredricks, R. W., 33, 34, 41 Freedman, M. S., 56, 74, 76 Friedman, M., 26(67), 37, 40, 41 Frohman-Bentchkowsky, D., 106(109), 136 Fuller, C. R., 88(37), 91(37), 107(37),

Furth, H. P., 24(57), 31(80), 40

209(37, 44,45), 210,219(37,63),233,234

108(37), 134

G

Gaffney, J., 120(139), I37 Galeev, A. A., 31, 40 Gardner, M. E., 57(93), 74(93), 77 Gardner, P. D., 85(8), 134 Gardner, W. R., 89(40), 134 Garosi, G. A,, 36,41 Gasior, M., 57, 77

302 AUTHOR INDEX

Gates, D. M., 267,271 Gavrilovif, M., 280(8), 282 Gavriluk, V. I., 49(30), 75 Gavrin, P. P., 27(70), 40 Geiger, J. S . , 50, 73(43), 76 Geissler, K. H., 5, 38 Gelsing, R. J., 107(112), 108(112), 136 Geoffrion, C., 73, 77 Georgi, J. R., 267(37), 271 Germer, L. H., 140,232 Gershon-Cohen, J., 268(44), 271 Gill, W. L., 94(59), 95(59), 132(170), I35,

Giroux, G., 73, 77 Givens, M. P., 166(32), 233 Glang, R., 97(85), 136 Glaser, W., 143, 144(22), 233 Glass, R. A., 121(143), 137 Glinski, V. J., 86(14), 134 Goetzberger, A., 96(74), I35 Goldberg, H. I., 269(56), 272 Goldenbaum, G. C. , 35(96), 37(96), 41 Gorbunov, E. B., 30(78), 31, 40 Gott, P., 86(20), 123(54), 130(20), 134, 138 GraEanin, F., 288(11), 290, 295,296,297 Grad, H., 31, 40 Graetzer, R., 57(82), 77 Graham, R. L., 50, 73, 76 Granatstein, V. L., 36, 41 Granberg, G. L.,66(107),68(107), 74(107), 77 Gray, A,, 177(40), 233 Graybill, S . E., 26, 40 Green, C. B., 244(9), 249(9), 270 Green, I. M., 33(90), 41 Gnem, H. R., 35(96), 37(96), 41 Grigoriev, E. P., 49(25), 75 Grohmann, G., 219(56), 234 Gromov, K., 48(19), 75 Gros, C., 268(54), 269(58), 271 Gross, W. G., 54(61), 76 Groth, T., 44(7a, b, c), 75 Grove, A. S. , 85(7), 95(69), 96(71), 102(96),

129(7), 134, 135, I36 Grunditz, Y., 73(119), 77 Grundy, P. J., 142(19), 233 Guest, G. E. , 26(66), 40 Gumenyuk, B. A,, 66(107), 68(107), 74, 77 Guterman, C., 77 Guthart, H., 36, 41 Gutmann, F., 249(11), 254(11), 270

138

H

Hai, F., 16, 39 Haine, M. E., 208(51), 209, 234 Halseth, M. W., 9, 10, 39 Hamberger, S . M., 26, 37,40, 41 Hamilton, A. E., 132(169), 138 Hamisch, H., 219(56), 234 Hamiter, L. C. , Jr., 98(87, 88), 123(87, 88),

Hammel, H. T., 266, 269(35), 271 Hammond, D. L., 239(5), 270 Hamrin, K., 44(6), 75 Handley, R. S. , 268(45), 271 Hanley, L. D., 132(171), I38 Hansen, M., 91(48), 135 Hardy, J. D., 262(16), 266(27, 28), 270, 271 Harper, J. G., 85(10), 94(10), 134 Harries, W. L., 23, 40 Harris, J. S. , 166(32), 233 Harruff, R. W., 239(4), 270 Hartman, T. E., 88(37, 39), 91(37), 94(39),

136

107(37, 1 lo), 108(37, 1 lo), 115(1 lo), 134,136

Hasegawa, A., 14, 39 Hastings, J. A., 97(77), 120(77), I35 Hauser, V . E. , 85(12), 118(12), 120(12), 134 Hausrath, D. A., 128(162), I38 Hayward, R. W., 43, 75 Hebermehl, G., 181(41), 233 Hedberg, L. A., 286(3), 296 Heden, P. F., 49(41), 76 Hedgran, A., 43,49(2), 75 Hedman, J., 44(6), 49(41), 75, 76 Heerma van Voss, S. F. C., 265(23),

Heinrich, F., 59, 61(102), 74(102), 77 Heinz, E. R., 269(56), 271 Helmer, R. G., 50(48), 73, 76 Hendel, H. W., 12, 18, 19, 20(44), 22, 39 Hendler, E., 239(3), 270 Hentzchel, H., 107(110), 108(110),

115(110), 136 Hercog, R., 53(56), 76 Hermance, H. W., 104(102), 136 Herreid, C. F., 266(34), 271 Herrmann, D. B., 104(103), I36 Hibi, Y. , 219(59), 234 Hicks, R. G., 269(55), 271

269(23), 271

AUTHOR INDEX 303

Hillier, J., 140, 208(48), 233, 234 Hintenberger, H., 54(60), 76 Hochman, H. T., 109(113), I37 Hodgson, T., 269(63), 271 Hoffmann, H., 211(55), 234 Hofman, A., 59, 61,74(102), 77 Hofmann, G., 266(29), 271 Hofstein, S . R., 103(97), 136 Hogan, J., 31, 40 Hoh, F. C., 7, 8, 9, 39 Hok, 0. P., 49(32), 75 Holladay, A. M., 132(166), 138 Hollander, J. M., 50, 76 Holmes, L. S . , 35, 37(94), 41 Holmquest, H. J., 283(1), 296 Holt, J. A., 267(38), 271 Holter, 0., 10, 39 Homes-Siedle, A. G. , 97(80), 136 Hooper, E. B., Jr., 3, 38 Horsley, A. W., 110(120), 137 HristiC, D., 281(11), 282 Huber, O., 49(34), 75 Hubert, P., 57, 77 Hufford, M. E., 174(35), 233 Humphris, F. H . , 266(30), 271 Hyman, C., 269(59), 271

I

Ikeganii, H., 54, 74(73), 76 Ikezi, H., 34, 41 IllCs, F., 48, 73, 75 Ingraham, A. P., 87(32), 134 Irvin, J. C., 95(68), 135 Ise, J., Jr., 24(57), 40 IvanEeviC, N., 278(7), 281 Ivanov, D. P., 30(78), 40 Ivanova, G. D., 66(107), 68(107), 74(107),

77

J

Jacobi, G. T., 86(17), 134 Jahn, P., 51, 68, 74(50), 76 Jakahara, Y. , 273(1), 281 JegliE, A., 289, 293, 296, 297 Jen, N. C., 13, 19,39 Jenkins, R. T., 97(82), 136 Jensen, T. H., 27, 28, 38, 40, 41 Jonsson, C., 21 I(%), 234

Johansson, A., 73(119), 77 Johansson, G., 44(6), 75 Johnson, R. R., 10,39 Jones, M. W., 49(24), 75 Josephy, K., 13(33), 39 Judd, D. L., 54(65, 66), 76 Jukes, J. D., 2, 38 Jungerman, J. A., 57(93), 74, 77 JuriEid, D., 281(10, I l l , 282

K

Kadomtsev, B. B., 2, 9, 10, 11, 15, 35

Kaganskii, M. G., 54, 76 Kajganif, M., 278(7), 281 Kalinin, Yu. G., 28, 40 Kaminskii, D. L., 54, 64(105, 106), 76, 77 Kang, K. D., 89(41), 134 Kankeleit, E., 57(80), 77 Kapfer, V. C., 122(148), 137 Karchevskii, A. I., 25, 26, 40 Karlson, S.-E., 44(6), 75 Kastler, A., 198, 234 Katoh, T., 49(26), 75 Kaw, P. K . , 24, 27(60), 40 Kay, H., 278(7), 281 Keen, B. E., 15, 18, 19, 20, 21, 22, 39, 40 Keen, R. S. , 81(3), 86(21), 87(3), 88(21),

91(49), 94(55), 95(55), 98(86), 99(91), laO(91), I04(101), 106(49, 91, 106), 107(3, 86, 91, 106, 113), 108(3, 86, 113), 109(3, 86, 91, 106, 113), 110(49), 111(106), 115(91, 106), 116(3), 118(21), 119(21, 49, 86), 123(86), 124(86, 91, 101, 113), 127(113), 128(86, 91), 130(21), 132(91), 133, 134, 135, 136

37(16), 38, 39

Keil, J. G., 89(41), I34 Keilhacker, M., 34,41 Keller, M., 219(62, 66), 234 Kelman, V. M., 64, 69(110), 74, 77 KelHin, D., 286(8), 287(8), 296 Kennel, C. F., 33(90,91), 34(91), 41 Kent, G. I., 13, 19, 39 Kerwin, L., 53(58), 76 Kerwin, R. E., 86(16), I34 Keys, L. K., 121(142), 137 Khambata, A. J., 81(2), 133

304 AUTHOR INDEX

Kharchenko, I. F., 25,40 Khidr, M. S . , 128(160), 138 Kinder, E., 208(49), 234 King, W. J., 50(45), 76 Kino, G. S . , 6, 38 Kirkendall, E. O., 119(125), 137 Klein, D. L., 86(16), 134 Klein, N., 98(89, 90), 136 Klein, T., 106(105), 136 Knowless, J. W., 44, 75 KO, W. H., 102(95), 136 Kobrinski, A. E., 274(4), 281 Koh, Y., 49(26), 75 Kohman, G. T., 104(102), 136 Koidan, V. S . , 26, 27(72), 40 Kolb, A. C., 33, 41 Kolesnikov, N. V., 49, 75 Komrska, J., 146(27), 177(39), 180(39),

181(39), 201(47), 208(47, 53), 212(27), 217(27), 219(47), 220(47, 71), 222(72), 230(72), 231(47, 71), 233, 234

Kons, J. B., 106(106), 107(106), 109(106), 111(106), 115(106), I36

Koopman, E. W., 57(83), 77 Kormicki, J., 48(16), 75 Kornherr, M., 34(92), 41 Kovrigin, C . D., 49, 75 Kralj, A., 286(8), 287(8), 290(16), 293,

Krall, N. A,, 12, 39 Krimmel, E., 142(18), 219(67), 233, 234 Kruer, W. L., 24, 27, 40 Kudryavtsev, A. M., 13(33), 39 Kuklik, J., 49(28), 75 KukoC, A., 57(86), 77 Kuntze, M., 51, 68(50), 74(50), 76 Kunze, H. J., 35, 37(96), 41 Kuper, A. B., 102(95), I36 Kupryashkin, V. T., 49(30), 75 Kurie, F., 49(22), 75 Kumetsov, E. I., 29, 30(77), 40

296,297

Landgren, J., 44(6), 75 Larson, E. G., 243(7), 270 Lashinsky, H., 14, 15, 16, 39 Lathlaen, R., 107(113), 108(113), 109(113,

119), 124(113), 127(113), 136,137 Latishev, G. D., 49, 75 Lauffenberger, H. A., 124(157), 128(157),

Lawler, H. C., 118(122), 120(122,133), 137 Lawrence, J. E., 95(62), 128(160), 135, 138 Lawson, R. N., 262, 268, 271 Lee, F., 97(76), 135 Lee, S., 269(57), 271 Lee-Whiting, G. E., 44, 45, 50, 52, 59, 60,

61, 69, 70, 75, 76, 77 Leheny, R. F., 13(33), 39 Lehnert, B., 2, 7, 8, 38,39 Lenc, M., 146(27), 212(27), 217(27),

220(71), 231(71), 233,234 Lepselter, M. P., 85(1 l), 107(11 l),

108(111), 118(11), I20(11), 134, I36 Lesk, I., 95(63), 135 Liberson, W. T., 283, 296 Lidsky, L. M., 25, 40 Lifshitz, E. M., 141(17), 233 Lin, D. N., 28, 40 Lindberg, B., 44(6), 75 Lindgren, I., 57, 77 Lindgren, N. E. , 20, 39 Lindner, K., 102(94), 136 Lippay, A., 284(2), 296 Lischke, B., 219(69), 234 Lisitano, G., 13, 39 Lloyd Williams, F. J., 268(45), 271 Lloyd Williams, K., 268(45), 271 Logar, M., 284(2a), 296 Lommel, E., 169(34), 177, 233 Long, C. , 284(2), 296 Lorig, R. J., 289, 296 Lucenet, G., 59(97), 77 Lytle, W. J., 92(53), 135 Lyutii, I. N., 49(30), 75

138

L M

Labuda, E. F., 120(141), 137 LaEte, A., 208, 234 Lafoucriere, J., 59, 61(98-LOO), 77 Lale, P. G., 289, 296 Landau, L. D., 141(17), 233

McAskill, D., 49(24), 75 McAteer, 0. J., 92(53), 135 McCarthy, J., 93(54), 135 McCormick, J. E., 120(137, 138), 137

AUTHOR INDEX 305

McGhee, R., 280(9), 282 McGowan, R. F., 91(44), 135 McKelvey, A., 97(83), 104(83), 136 Macko, D., 273(1), 281 McNally, J. R., Jr,. 26(66), 40 McNeal, D. R., 293,297 Mahl, H., 146(24), 21 1, 233 Makoveckii, Yu. V., 49(30), 75 Maksimov, G. P., 37, 41 Malein, A., 26(67), 40 Malmberg, J. H., 38, 41 Maly, L., 49(36), 76 Mansberg, H. P., 239(3), 270 Marchand, N., 208(52), 234 Marib, M., 280(8), 282 Marinkk, I., 295, 297 Marinkov, L., 57(86), 77 Marshall, T. C., 13(33), 39 Marton, L., 140,209,219(58), 233,234 Mascart, M. E., 220(70), 228(70), 234 Mase, A., 31, 41 Massey, H. S. W., 5(8), 7(8), 38 Mathews, G. B., 177(40), 233 Mazzucato, E., 37, 41 Meade, D. M., 33,41 Meieran, E. S., 88(36), 134 Melzack, R., 267(41), 271 Mesarovib, M., 273(1), 281 Mesessa, A. J., 97(84), 104(84), 136 Metz, E. D., 122(149), 137 Metzger, A., 132(171), 138 Meyers, T. R., 124(157), 128(157), 138 Mibayash, R., 266(31), 271 Milek, J. T., 86(24), 130(24), 134 Miller, L. F., 1 1 8( 121), 120( 121), 121 (1 44), 137 Miller, W. C., 57(81), 77 Milner, M., 293, 297 Miner, C. E., 50, 76 Minkowitz, G., 181(41), 233 Mirnov, S. V., 31(79), 40 Mitchell, D., 269(63), 271 Mitchell, G. T., 106(106), 107(106),

Mitchdl, J. P., 97(81), 136 Mitropolskii, Y. A., 21(50), 40 Mitsuishi, T., 140, 233 Mladjenovib, M., 44, 45, 48(13), 49(39),

75, 76 Mollenstedt, G., 141, 159(16), 218(15, 16),

219(62, 67), 222, 230(16), 233, 234

109(106), 111(106), 115(106), 136

Moll, E., 51, 77 Molvik, A. W., 33(88), 41 Moore, G. E., 85(7), 129(7, 163), 134, 138 Morita, T., 36, 41 Mosher, D., 23, 40 Moussa, A., 49, 50(46), 76 Mugnier, D., 59(98-loo), 61, 77 Mulvey, T., 208(51), 209, 234 Muncheryan, H. M., 128(161), 138 Murakami, M., 25,40 Murphy, B. T., 86(14), 134 Muschenheim, C., 266(28), 271 Myers, D. K., 118(122), 120(122), 137 Myl'nikov, G. D., 32(85), 41

N

Nagasaki, H., 140, 233 Nedoseev, S. L., 27, 28(73), 40 Nedospasov, A. V., 8, 9, 10, 37(16), 39 Neidigh, R. V., 26(66), 40 Nicollian, E. H., 102(93), 136 Niewodniczanski, N., 48(16), 75 Nigh, H. E., 103(98), 136 Nordberg, R., 44(6), 49(41), 75, 76 Nordling, C., 44(6), 49(40, 41), 75, 76 Nozawa, N., 49(26), 75 Nyman, B., 73(119), 77

0

Oberman, C., 24,27(60), 37,40,41 Ohkawa, T., 3 2 , 4 l Oldberg, B., 286(3), 296 Oliver, C. B., 88(35), 134 Oliver, R., 269(62), 271 Olsen, B., 44(7a), 57(89), 75, 77 O'Neil, T. M., 38, 41 Orr, W. H., 97(84), 104(84), 136 Osaba, J. S. O., 49(22), 75 Osis, N. L., 48(15), 75 Overmeyer, J. C., 97(85), 136

P

Palmes, E. D., 262(17), 266(17), 270 Pankratz, J. M., 120(140), 137 Papyrin, A. N., 26(69), 27(72), 40 Paris, P., 54, 76

306 AUTHOR INDEX

Park, C. R., 262(17), 266(17), 270 Park, J. J., 45(50), 76 Parker, R. R., 17, 18, 19,39 Partridge, J., 132(171), 138 Patrick, R. M., 34, 41 Patten, C. G., 57(93), 74(93), 77 Paul, J. W. M., 35, 37(94), 41 Pearson, G. L., 244(9), 249(9), 270 Peck, D. S., 94(58), 121(58), 135 Peckham, H., 287, 289, 796 Peek, N. F., 57(93), 74(93), 77 Penner, S., 54, 76 Pennes, H. H., 262(18), 266, 270 Peregud, B. P., 64(104), 66, 74(104, 107),

Perepelkin, N. F., 32(86), 41 Perkins, F. W., 19, 22(45), 39 Perlman, M. L., 49, 76 Perrin, M., 243(8), 270 Person, K.-B., 4, 38 Petritz, R. L., 81(1), I33 Petrov, M. P., 30(78), 40 Petterson, G., 44(7a), 57(88, 89), 75, 77 Petterson, H., 73(119), 77 Philofsky, E., 119(127), 137 Plaister, T. H., 266(33), 271 Plantinga, G. H., 95(61), 135 Playner, Z., 49(36), 76 Pliskin, W. A., 108(116), 137 Plotnikow, J., 266(31), 271 Plough, C. T., 118(122), 120(122, 133), 137 Pogutse, 0. P., 2,38 Polevoi, R. M., 52(52), 74, 76 Polichar, R. M., 57(85), 77 Politzer, P. A., 12, 39 Ponomarenko, A. G., 26(69), 27(72), 40 Popovich, V. P., 25, 40 Porkolab, M., 6,38 Porter, F. T., 56, 74(78), 76 Prevec, T., 284(2a), 288(11), 296 Prokofiev, P. T., 48(15), 75 Pugh, E. R., 34,41 Puri, S., 24, 40 Pyle, R. V., 9, 10, 24(57), 39, 40

77

Q

Quanbury, A. O., 293(20), 297

R

Ramberg, E. G., 208(48, SO), 234 Rand, M. F., 97(81), 136 Rang, O., 141, 233 Razumova, K. A., 30(77), 40 Read, J. C., 132(169), 138 ReberHek, S., 290(16), 296 Recknagel, A., 208(49), 234 Reid, A., 140, 232 Reimer, L., 146(26), 212(26), 233 Reswick, J. B., 284(2), 286(5, 6, 9), 287(9),

Reynolds, W. A., 267(38), 271 Rezanka, I., '49(28), 75 Richardson, D., 118(122), 120(122), 137 Ristinen, R. A., 49, 73(35), 75 Robertson, H. S., 14, 39 Rodrigues de Miranda, W. R., 132(168),

Romanov, V. A., 64(106), 77 Rosenblum, E. S., 54(64), 76 Rosenblum, S . , 48(14), 75 Rosenbluth, M. N., 31(80), 40 Rossiter, T. J., 119(128), 137 Rothemund, W., 219(67), 234 Rothman, H. S., 36, 41 Rowberg, R. E., 13(31, 32), 39 Rowe, T. A., 85(7), 129(7), 134 Rudakov, L. I., 27, 28(73), 40 Rudmin, J. W., 33(88), 41 Rupp, E., 140, 233 Rusanov, V. D., 32(85), 41 Ryerson, C. M., 123(153), 138 Rynne, D. M., 91(45), 135 Ryutov, D. D., 32(84), 41 Ryutov, V. D., 28,40

296

138

S

Sagdeev, R. Z., 31(80), 40 Sah, C. T., 102(96), 136 Saidman, J., 266(32), 271 Sakai, M., 54(70-72), 76 Salirnov, R. A., 13(33), 16, 17, 39 Samoilov, P. S., 49, 75 Sanger, V. L., 267(38), 271 Sant'ana, J., 48(14), 75 Santoro, C. J., 106(107, 108), 107(107),

Sarace, J. C., 86(16), I34 I09(107, 1081, 115(107, 108), 136

AUTHOR INDEX 307

Scarf, F. L., 33(90, 91), 34(91), 41 Schaible, P. M., 97(85), 136 Schellenberg, L., 49(34), 75 Schiske, P., 143,233 Schlacter, M. M., 99(91), 106(91),

107(113), 108(113), 109(91, 113), 124(91, 113), 127(113), 128(91), 132(91), 136

103(99), 104(101), 107(113), 108(67, 113), 109(67, 113), 124(101, 113), 127(113), 133(101), 135, 136

Schlegel, E. S., 95(67), 96(70), 102(67),

Schlesinger, S . P., 13(33), 39 Schmidt, F. H., 57(92), 77 Schmidt, G. L., 22,40 Schmidt, J. A,, 22, 33(88), 40, 41 Schmidt, P. F., 85(12), 95(81), 118(12), 120

Schmutzler, F., 52(53), 72, 76, 77 Schnable, G . L., 81(3), 86(21), 87(3), 88(21),

(12), 134, 136

91(49), 94(55), 95(55, 67), 97(75, 83), 98(86), 99(91), 100(91), 102(67), 104(83, IOl), 106(49, 91), 107(3,86, 91, 113), 108(3,67, 86, 113), 109(3,67,86,91,113), 110(49),115(91), 116(3), 118(21, 75), 119(21, 49, 86), 123(86), 124(86,91, 101, 113), 127(1!3), 128(3,86,91),130(21), 132(91),133(101), 133,134, 135, 136

Schneer, G.H., 85(12), 118(12), 120(12), 134 Schneider, W., 57(87, 88, 89), 77 Schultz, G., 181(41), 233 Schulz, M., 36, 41 Schuyten, P., 121(146), 137 Schwartz, S., 87(33, 34), 134 Schwuttke, G. H., 95(60), 135 Scott, C. W., 86(25), 97(78), 130(25), 134,

Scott, D., 283(1), 296 Scott, F. R., 26(66), 27, 28, 40 Seeds, R. B., 129(164), 138 Seely, J. L., 86(15), 103(15), 134 Selikson, B., 119(124, 130, 131), 137 Sello, H., 87(29), 91(50), 92(50), 119(129),

134,135, 137 Sergeev, V. O., 49(2S), 75 Sermons, G., 48(21), 75 Sessler, A. M., 71, 72(116), 77 Sharp, M., 97(83), 104(83), 136 Shea, M. F., 57(81), 77

135

Sheffield, J., 9, 11, 39 Shepherd, W. H., 91(42), 135 Shestopalova, Y. , 50, 76 Shiba, H., 108(115), 137 Shibata, T., 69, 71, 77 Shpalek, 69, 71, 77 Shull, F. B., 49(23), 75 Shurtleff, W. O., 86(26), 130(26), 134 Shustin, E. G., 25, 40 Siegbahn, K., 43, 44, 45, 48(17), 49, 57(94),

59, 67(8), 73(119), 75, 76, 77 Silverman, R., 95(66), 135 Simmons, L. M., 249(11), 254(11), 270 Simon, A,, 5 , 7, 38 Simon, R., 123(156), 138 Simonen, T. C., 18, 19 ,20(44), 22(45), 39 Simpson, J. A., 140, 219(58), 233, 234 Sizoo, G . J., 49(32), 75 Skopina, V. I., 64(104), 74(104), 77 Skoryupin, V. A,, 27(70), 28, 40 Slabovik, R. L., 25, 40 Slack, L. S . , 49(22), 75 Slatis, H., 48(12, 18), 57(94), 77 Slaughter, R., 123(154), 138 Smessaert, A., 269(55), 271 Smigelskas, A. D., 119(125), 137 Smirnov, V. P., 37, 41 Smith, W. M., 267,271 Snow, E. H., 102(96), 136 Sokolnikoff, I. S . , 148(28), 233 Solli, G., 269(61), 271 Soltau, R. H., 86(20), 120(132), 130(20),

134,137 Sommerfeld, A., 142, 143, 144(20), 149,

152, 159(30), 162(30), 176(20), 233 Sonne, C., 266, 271 Sopher, R. P., 92(51), 94(51), 135 Sovtsov, M. S . , 49(25), 75 Spalding, I. J., 35(96), 37(96), 41 Spalek, A., 49(28), 75 Spannagel, G., 51, 68(50), 74(50), 76 Spitzer, L., Jr., 6, 17, 38 Spitzer, S . M., 87(33, 34), 134 Spratt, J. P., 97(75), 118(75), 135 Stahura, Z., 48(16), 75 Standeven, J. D., 97(75), 118(75), 135 Starbuck, D., 284(2), 296 Stephens, W. E., 53(55), 76 Sterling, J. J., 239(2), 270 Steuer, K. H., 34(92), 41

308 AUTHOR INDEX

Stewart, J., 267(41), 271 Stibunov, V. N. , 27(72), 40 Stix, T. H., 19, 39 StojiljkoviC, Z., 281(11), 282 Stoker, P. H., 49(32), 75 Stoyanova, I. G., 219(61), 234 Strbenk, M., 289(14), 296

Tryphonas, W. M., 121(143), 137 Tsukishima, T., 37, 41 Tsunemitsu, H., 108(115), 137

U

Strelkov, V. S., 30(78), 31(79), 40 Su, C. H., 37,41 Suddeth, J. A., 140, 219(58), 233, 234 Sunier, J . W., 57(85), 77 Suran, J. J., 85(9), 121(9), 134 Svartholm, N., 43, 49(2, 33), 54(63), 75, 76 Swahn, B., 73(119), 77 Sze, S. M., 96(72, 74), 135

T

Takahashi, S., 219(59), 234 Takeda, S., 37, 41 Takehoshi, I., 91(43), 135 Takuni, K., 54, 74(73), 76 Tamburrino, A. L., 122(148), 137 Tausher, L., 53(53), 76 Taveras, J. M., 269(56), 271 Taya, S., 69(113), 71(113), 77 Taylor, E. A., 50, 76 Taylor, G., 97(79), 136 Taylor, J. B., 6, 38 Taylor, R. J. , 34, 41 Tchan, N. S., 69(11 l), 77 Tebble, R. S., 142(19), 233 Terandy, J., 56, 74(78), 76 Thornassen, K. I., 17, 18, 19, 24, 39, 40 Thomson, G. P., 140,232 Thornton, C. G., 121(147), 126(147), 137 Tishkin, A., 69(11 I), 77 Titov, A. V., 32(85), 41 Toader, E. I., 8, 39 Tolliver, D. L., 106(107, IOS), 107(107),

109(107, 108), 115(107, 108), I36 TomoviC, R., 273(2), 274(3), 275(5),

278(5), 280(9), 281,282 Totta, P. A., 92(51), 94(51), 135 Tove, P. A,, 286(3), 296 Trnkoczy, A., 293(19), 297 Trolander, H. W., 238(1), 239(2, 4), 270 Trontelj, J., 288(11), 296

Uglam, J. R., 26, 40 Umarov, G. Ye., 48(19), 75 Unwin, P. N . T., 219(61a), 234 Uthe, P. M., 120(134), 137 Utyugov, E. G., 37, 41 Uyeda, R., 140,233

V

Vaccaro, J., 132(172), 138 Vadasz, L. L., 85(7), 129(7), 134 Valadares, M., 48(14), 75 Van Gelder, W., 85(12), 118(12), 120(12),

Van Krugten, H., 57(83), 77 Van Steensel, K., 107(112), 108(112), I36 Vasko, A,, 265, 269(22), 271 Vavken, E., 289(14), 293(17), 296, 297 Veghte, J . H. , 266(34), 269(60, 61), 271 Vinogradova, N. D., 30(77), 40 Vodovnik, L., 284(2, 2a), 286(4, 5, 6, 8, 9),

287,296,297 Vogel, P., 132(167), 138 von Laue, M., 140, 141,233 Voorhies, H . G., 32, 41 Vrousos, C., 268(54), 271 VukobratoviC, M., 281(10, 11). 282

134

W

Wackenheim, A., 268(54), 269(58), 271 Wagner, F., Jr., 56, 74(78), 76 Wahl, H., 219(68), 234 Walker, M., 97(83), 104(83), 136 Wallace, J. D., 269(57), 271 Walsh, J., 13(33), 39 Walter, R. L., 57(81), 77 Wang, C. C., 96(73), 135 Wapstra, A. H., 49(38), 76 Watmough, D. J., 269(62, 64), 271

AUTHOR INDEX 309

Watson, G. N., 162(31,) 169(31), 177(31),

Wattermann, H., 49(24), 75 Webster, D. R., 268(49), 271 Webster, S . L., 91(44), 123(153), 135, 138 Weinstock, J., 27, 40 Weissman, D. E., 36, 41 Weitsch, W., 146(24), 211, 233 White, M. L., 122(150), 138 Wickham, D. C., 243(7), 270 Wild, H., 49(34), 75 Wilemon, W., 293, 297 Wilkinson, R. G., 77 Williams, J. C., 104(103), 136 Wilson, W. O., 266, 271 Winsor, T., 269(59), 271 Wirta. W. R., 275(6), 281 Wlodek, G . D., 268(49), 271 Woehler, K. E., 9, 10, 39 Wohlleben, D., 219(56), 234 Wohn, F. K., 77 Wolf, E., 157(29), 166(33), 175(29), 233 Wolfson, J. L., 50(45), 76 Wong, A. Y., 13(31, 32), 16, 22, 39, 40 Wood, S . J., 89(40), 134

233 Workman, W., 86(19), 132(170), 134, 138 Wright, R. E., 24(57), 40 Wyndham, C. H., 269(63), 271

Y

Yablochnikov, B. A,, 26(69), 27(72), 40 Yada, K.,-219(59), 234 Yadlowski, E. J., 16,39 Yamamoto, H., 54, 74, 76 Yamazaki, T., 54(70), 76 Yanagawa, T., 91(43), 135 Yaremenko, Yu, G., 25, 40 Yon, E., 102(95), I36 Yoshikawa, S . , 31, 40 Yoshizawa, Y., 49(26), 69(113), 71(113),

Yu, A. Y. C., 85(13), 134 75, 77

Z

Zaininger, K. H., 96(73), 97(80), 135, 136 Zavoiskii, E. K. , 27, 28, 40 Zhivotov, V. K., 32(85), 41 Zinov'ev, 0. A., 32(85), 41 Zolotavin, A. V.. 49(25), 75

Subject Index

A

Aluminum penetration, 92-94 Aluminum wire bonds, failure mechanisms

Ambipolar diffusion, of plasma, 4-5 Amputees, rehabilitation of, 274-276 Arm control, systems approach to,

Axial symmetry, diffraction at screens

and, 120

279-280

with. 167-185

electromigration in, 86-89 metallization systems based on gold in, 94 open metal a t oxide strips and, 89-92 oxide shorts in, 95 in radiation-hardened integrated

reliability of other circuit elements

surface effects in, 95-96

circuits, 97

and, 97

Bipolar integrated circuits, types of, 85-86 Bulk failure mechanisms, 94-95

B C

Babinet’s theorem, 166-167 Beta-ray spectrometers, 43-74

azimuthally varying fields in, 71-72 comparison table for, 73-74 correctors for, 67-71 flat, with cylindrical field, 46-53 lenses for, 57-58, 66-67 multiple-loop ,61-64 optical analogy type, 64-67 performance parameters for, 45-46 ~ J d z type, 48-50 ~/%6 type, 52-53 ( ~ / 2 ) 6 type, 51-52 sector type, 53-56 semicircular, 47-48 toroidal (“ orange ”), 56-57 trochoidal, 58-64 “ winding field ” type, 53

Biological temperature measurements,

electric thermometry in, 238-242 infrared radiography in, 266-270

235-281

Cartesian coordinates, and diffraction

Charged obstacles, electron scattering

Charged sphere, electron scattering by,

Chip complexity, of integrated circuits,

Collisionless shocks, in plasma turbulence,

Conductive electric thermometry, 235-252 Conductive particles, in MOS failure

Contact resistance, between metallization

Convection cells, in plasma turbulence,

Cylindrical coordinates, diffraction in-

integral, 186-188

by, 210-231

211-218

128-1 29

33-35

mechanisms, 106

layers, 110-1 11

22-23

tegral at, 167-168

D quartz resonator thermometry in,

thermistors in, 242-259 Bipolar failure mechanisms, 86-97

aluminum penetration and, 92-94 aluminum-silicon contacts in, 97 bulk effects in, 94-95

259-261 Diffraction integral applicability conditions for, 156-158 in Cartesian coordinates, 186-188 charged sphere and, 214-216 in cylindrical coordinates, 167-168 in electron optics, 142-164

310

SUBJECT INDEX 311

electrostatic biprism and, 222-226 Fresnel’s integrals and, 188-190 Green’s function and, 148-149, 152-155 Lommel’s functions and, 177-185 modifications of, 155-1 56 for space waves, 147-159 for two-dimensional waves, 159-164 and wavefunction in specimen plane,

143-147 Diffraction patterns, 191-208

intensity distribution in, 158-159 at screens with axial symmetry, 167-185 by screens separated by mutually

perpendicular straight lines, 186-208 Diffraction phenomena, complicated,

Diffraction screen, 167-208 special case of, 191-208

Diffraction theory, 165-210 Discretionary wiring, in multilevel metal-

lization, 115-117 Drift waves, and transition to turbulence,

208-210

11-17

E

Electrical stimulation of extremities,

Electromigration, 87-89 Electron diffraction, by uncharged

283-296

obstacles, 165-210 see aZsu Diffraction; Diffraction integral

Electronic peroneal brace, 289-294 Electron interference phenomena, 21 8-231 Electron optics

diffraction integral in, 142-164 scalar diffraction theory and, 139-232

by charged obstacles, 210-231 by charged sphere on supporting film,

Electron scattering

211-218 Electrostatic biprism, interference

phenomena by, 218-231 Extremities, functional electrical stimula-

tion of, 283-296

F

Failure mechanisms bipolar, 86-97 categories of, 85

failure modes and, 82-83 in integrated circuit assembly, 118-122 integrated circuit reliability and, 122-133 in large-scale integrated circuits, 79-1 33 MOS (metal oxide semiconductor),

multilevel metallization and, 107-1 17 Failure modes, mechanisms and, 82-83 FESE, see FunctionaI Electrical

Stimulation of Extremities Field inversion voltage, as MOS failure

mechanism, 103 Fresnel diffraction, 169 Fresnel’s integrals, diffraction integral in

terms of, 188-190 Functional Electrical Radial Brace, 295 Functional Electrical Stimulation of

Extremities (FESE), 283-296 electronic peroneal brace and, 289-294 implanted systems of, 288-289 motoric, 285-288

98-1 06

G

Gate oxide breakdown, as MOS failure

Gate threshold voltage drift, 102-103 Gold wire bonds, failure mechanisms and,

Green’s function, 148-149, 152-154 Green’s theorem, 148

mechanism, 98-101

119

H

Hand prosthesis, multifunctional, 278-279

I

Implanted stimulation systems, 288-289 Infrared electromagnetic spectrum and

Infrared radiography biological, 266-270 in temperature measurements, 261-270

Integral theorem, diffraction integral and,

Integrated circuit assembly

detectors, 264-266

149-1 52

aluminum wire bonds in, 120 chip-to-package bonds in, 118-119 failure mechanisms in, 118-122 gold wire bonds in, 119 other than wire bonding in, 120-121

~

312 SUBJECT INDEX

packages in, 121-122 testing in, 121, 131

accelerated stress testing of, 131 assembly of, 118-122 complexity vs reliability in, 133 effect of LSI trends on reliability of,

failure analysis in, 127-128 failure mechanisms in, 79-133 large-scale, defined, 80-82 LSI reliability in, 131-133 metallization over topography of,

quality assurance in, 124 radiation-hardened, 97 rate of failure in, 122 reliability of, 122-123 reliability vs chip complexity in,

reliability vs LSI trends in, 128 reiiability tradeoffs and limitations in,

test structures in, 124-127

Integrated circuits

128

111-1 15

128-129

129-1 30

Interference pattern, electrostatic biprism and, 226-230

L

Large-scale integrated circuits (LSI) defined, 80-82 integrated circuit reliability and,

types of, 83-85 128-129

Lommel’s functions, 177-185

M

Magnetic beta-ray spectrometers, 43-74

Medium-scale integration (MSI), 80-82 Metallization layers

contact resistance between, 110-1 11 oxide shorts between, 109-111

see also Beta-ray spectrometers

MNOS transistors, 106 MOS (metal oxide semiconductor) failure

mechanisms, 98-1 06 conductive particles and, 106 field inversion voltage and, 103 gate oxide breakdown in, 98-101

gate threshold voltage drift and,

LSI circuits and, 80-85 oxide shorts and, 98 room temperature threshold shift in, 106 static electricity effects in, 101-102 surface-ion migration and, 103-106 surface potential and fast states in, 102

MOS integrated circuits, types of, 86 Motoric FESE, 285-288 MSI arrays, 83-85 Multilevel metallization

102-1 03

discretionary wiring or routing in,

failure mechanisms and, 107-1 17 over integrated circuit topography,

surface effects in, 108-109

115-1 17

111-115

Multiple-loop spectrometer, 61-64 Muscle control, system approaches to,

276-278

0

Opaque circular disk, diffraction at, 175 Opaque screen

circular aperture in, 169 right-angle boundary of, 191

Optical analogy spectrometer, 64-67 Oxide shorts

as bipolar failure mechanism, 95 between metallization layers, 109-1 10 as MOS failure mechanism, 98 open metal at, 89-92

P

Parallel-strip screens, 196-208 Paralyzed persons, rehabilitation of,

Peroneal brace, electronic, 290-294 Physical rehabilitation, 274-281 Plasma, diffusion of, 3-7 Plasma instabilities, feedback suppression

Plasma turbulence

274-276

of, 17-22

collisionless shocks and, 33-35 convection cells and, 22-23 drift waves and transition to, 11-17 experimental, 1-38

SUBJECT INDEX 313

feedback suppression of low-frequency

linear turbulence heating experiments

positive column instability and, 7-1 1 toroidal experiments in, 29-33 wind driven, 35-36

Positive column instability, 7-1 1

plasma instabilities in, 17-22

and, 23-29

Q

Static electricity effects, as MOS failure

Surface effects, in multilevel metallization,

Surface-ion migration, as MOS failure

Surface potential, as MOS failure

Systems approach

mechanisms, 101 -1 02

108-109

mechanism, 103-106

mechanism, 102

to muscle control, 276-278 to skeletal control, 273-281

Quartz resonator thermometry, 259-261

T R

Radiation hardening, in integrated

Radiation thermometry, 261-270 Rectangular screen, diffraction patterns

Robots, for physical rehabilitation,

circuits, 97

and, 193-196

280-281

S

Scalar diffraction theory, in electron

Sector magnet spectrometer, 53-56 Simon diffusion, of plasma, 5 Skeletal control, systems approach to,

Small-scale integration, 80-82 Space waves, diffraction integral for,

Spectrometers

optics, 139-232

273-281

147-1 59

see also Beta-ray spectrometers magnetic beta-ray, 43-47

SSI, see Small-scale integration

Temperature measurements, 235-252 infrared radiography in, 261-270 quartz resonator in, 259-261 thermistors in, 242-259

Test structures, in integrated circuits,

Thermistor thermometry, 242-259 Toroidal(" orange ") spectrometer, 56-57 Trochoidal spectrometer, 58-64 Two-dimensional waves, diffraction

integral for, 159-164

124-127

U

Uncharged obstacles, electron diffraction by, 165-210

W

Wavefunction in specimen plane, 143-147 transmission function and, 146147


Cumulative Author Index, Volumes 1-30

A

Ables, H. D.: see Kron, G. E. Abraham, J. M., Wolfgang, L. T., and

Inskeep, C. N. : Application of solid- state elements to photoemissive devices, XXII B, 671

Abraham, E.: Relaxation processes in ferromagnetism, VI, 47

Adams, J.: X-ray detection by channel electron multipliers, XXII A, 139

Ahmad, N., Gale, B. C., and Key, M. H.: Time resolution limitations in single-

stage image converter photography, XXVIII B, 999

Aikens, R.: see Hynek, J. A. Airey, R. W.: see McGee, J. D. Alexander, J. W. F., and Burtt, R. B.:

Bombardment-induced conductivity targets for image orthicons, XVI, 247

The study of photocathode composition by microbalance methods, XVI, 329

Allan, F. V., and Garfield, B. R. C.:

Allen, J. Denton: see Malling, L. R. Allen, J. Denton: The Mariner IV space-

craft television system, XXII B, 849 Alpern, M., Bijaoui, A,, and Duchesne,

M.: Sur le gain en sensibilit6, dans l’infra-rouge Proche, de la camkra tlectronique par rapport ii la photographie classique, XXII A, 5

Amboss, K.: The analysis of dense electron beams, XXVI, 1

Anderson, A. E.: see Wachtel, M. M. Anderson, A. E., and Schneeberger, R. J.:

Limitations to resolving power in electronic imaging, XVI, 299

Anderson, D. G.: see Flanagan, T. P. Anderton, H. : An x-ray image intensifica-

tion system for use with a point projection x-ray microscope, XXII B, 919

Anderton, H., and Beyer, R. R.: Dynamic

imaging with television cameras, XXVIII A, 229

Asano, M.: see Hirashima, M. Ashworth, F. : Field emission microscopy,

Aslam, M.: see McGee, J, D. 111, 1

B

Bacik, H.: see McGee, J. D. Bakken, G. S.: see Jordan, J. A., Jr. Bakos, G.: see Hynek, J. A. Baldinger, E., and Franzen, W.: Ampli-

tude and time measurement in nuclear physics, VIII, 255

Paul J., and Ter-Pogossian, M. : Image intensifying chains for medical scintillation cameras, XXII B, 927

Thonemann, F. F. : Automatic data processing in the physical sciences, XI, 185

Barnett, M. E., Bates, C. W., Jr., and England, L.: Electron optics of a photoconductive image converter, XXVIII A, 545

Ball, Jack, Niklas, Wilfrid F., Dolon,

Barlow, G. E., Ovenstone, J. A., and

Barton, G.: see Hynek, J. A. Baskett, J. R.: see Liu, J. D. Bates, C. W., Jr.: see Barnett, M. E. Bates, C. W., Jr.: Scintillation processes

in thin films of CsI(Na) and CsI(T1) due to low energy x-rays, electrons and protons, XXVIII A, 451

Batey, P. H., and Slark, N. A.: Perfor- mance of the transmission secondary- electron image intensifier, XXII A, 63

Baum, W. A.: see Frederick, L. W. Baum, W. A.: see Hall, J. S. Baum, W. A,: see McGee, J. D. Baum, W. A.: see Wilcock, W. L. Baum, W. A.: A critical comparison of

image intensifiers for astronomy, XXVIII B, 753

315

316 CUMULATIVE AUTHOR INDEX, VOLUMES 1-30

Baum, W. A.: Laboratory evaluation of image tubes for astronomical purposes, XVI, 391

Baum, W. A.: Magnetic focusing of image tubes, XXII A, 617

Baum, W. A.: The potentialities of photoelectronic imaging devices for astronomical observations, XU, 1

Baumgartner, W.: A light amplifier with high light output, XXVIII A, 151

Beckman, J. E.: Application of information theory to the evaluation of two image intensifier tubes, X W A, 369

search for molecular hydrogen in the interstellar medium, XXVIII B, 801

resolution phosphor screens, XXII A, 551

Beckman, J. E., and Egan, D. W.: A

Beesley, J., and Norman, D. J . : High-

Bellier, Mlle M.: see Wlkrick, G. Mnt , G. J.: see Geneux, E. Berg, A. D., Smith, R. W., and Prosser,

R. D. : An electron image store and analyser, XXII B, 969

Berger, Harold: see Niklas, Wilfrid F. Beurle, R. L., and Jenkinson, G. W.: A

charge image storage tube for character recognition, XXVIII B, 1043

experimental image storage tube for the detection of weak optical images of low contrast, XII, 247

Aberration in magnetic focus systems, XVI, 333

B. L. : Image intensifier design and visual performance at low light-levels, XXVIII B, 635

Beurle, R. L., and Slark, N. A.: An

Beurle, R. L., and Wreathall, W. M.:

Beurle, R. L., Daniels, M. V., and Hills,

Beyer, R. R.: see Anderton, H. Beyer, R. R.: see Boerio, A. H. Beyer, R. R.: see Collings, P. R. Beyer, R. R., and Goetze, G. W.: An

optically scanned SEC camera tube, XXII A, 241

Beyer, R. R., Green, M., and Goetze, G. W. : Point-source imaging with the SEC target, XXII A, 251

M., and Le Contel, J. M.: Sur Bied-Charreton, P., Bijaoui, A., Duchesne,

quelques progrb r k n t s apportds ii la camdra Blectronique ii focalisation klectrostatique et sur son application en physique et en &ionomie, XXVIII A, 27

Bijaoui, A. : see Alpern, M. Bijaoui, A.: see Bied-Charreton, P. Billig, E., and Holmes, P. J. : Defects in

diamond-type semiconductor crystals, X, 71

Binnie, D. M., Jane, M. R., Newth, J. A. Potter, D. C., and Walters, J.: Work, at Imperial College, London, on the use of image intensifiers in nuclear physics, XVI, 501

Biondi, Manfred A.: Atomic collisions involving low energy electrons and ions, XVIII, 67

orthicons with magnesium oxide targets, XVI, 213

Blamoutier, M.: Un tube de prise de vues sensible aux rayons X, XXVIII A, 273

Blewett, John P.: Recent advances in particle accelerators, XXIX, 223

Bloch, F. : see Brillouin, L. Boerio, A. H.: see Goetze, G. W. Boerio, A. H., Beyer, R. R., and Goetze,

Bogdanov, E. V. : see Kislov, V. Ya. Boischot, A., and Denisse, J. F.: Solar

radio astronomy, XX, 147 Boksenberg, A., and Newton, A. C.: An

electromechanical picture signal generating device, XXVIII A, 297

Boussuge, C.: see Rosch, J. Bouwers, A. : Low brightness photography

by image intensification, XVI, 85 Bowen, J. S.: see Dennison, E. W. Bowhill, S. A., and Schmerling, E. R.:

Blake, J., and Burtt, R. B.: Image

G. W.: The SEC target, XXII A, 229

The distribution of electrons in the ionosphere, XV, 265

Bowles, K. L.: Radio wave scattering in the ionosphere, XIX, 55

Boyer, L. A,: see Flory, L. E. Bradley, D. J., and Majumdar, S.:

Application of electron-optical deflexion and storage techniques to time-resolved interference spectroscopy, XXII B, 985

CUMULATIVE. AUTHOR INDEX, VOLUMES 1-30 317

Brand, P. W. J. L.: see Smyth, M. J. Brand, P. W. J. L., and Smyth, M. J.:

Use of a Lenard-window image tube for astronon ,1 spectrophotometry, XXII B, 741

Brand, P. W. J. L., and Wolstencroft, R. D.: Recent astronomical applications of a Spectracon, XXVIII B, 783

Branscomb, L. M.: Negative ions, IX, 43 Brauer, W. : see Hachenberg, 0. Brillouin, L. : Electronic theory of the

plane magnetron, 111, 85 Brillouin, L., and Bloch, F.: Electronic

theory of the cylindrical magnetron, 111, 15

Broerse, P. H. : Electron bombardment induced conductivity in lead monoxide, XXII A, 305

Brooks, F. P., Jr.: Recent developments in computer organization, XVIII, 45

Brooks, H.: Theory of the electrical properties of germanium and silicon, VII, 85

antennae, XIX, 255 Broussaud, G., and Simon, J. C. : Endfue

Brown, J.: Microwave optics, X, 107 Bruin, Frans: The autodyne as applied to

paramagnetic resonance, XV, 327 Burns, J., and Neumann, M. J.: The

channeled image intensifier, XII, 97 Burstein, E., and Egli, P. H.: The physics

of semiconductor materials, VII, 1 Burtt, R. B.: see Alexander, J. W. F. Burtt, R. B.: see Blake, J. Byatt, D.: Bright displays for radar ap-

plications, XVI, 265

c

Calderwood, J. H.: see Smith, C. W. Caldwell, D. 0.: see Hill, D. 0. Caldwell, D. 0.: Scintillation chamber

comparisons: fibers u. NaI and image intensifiers u. orthicons, XVI, 469

microanalysis, XIII, 317 Castaing, Raymond: Electron probe

Catchpole, C. E.: see McGee, J. D. Catchpole, C. E. : Measurement of the

spatial frequency response of image devices, XXLI A, 425

Catchpole, C. E.: X-ray image intensification using multistage image intensifiers, XVI, 567

Charles, D. R.: see Guillard, C. Charles, D. R., and Duchet, M.: Visible

and x-ray image devices working on the induced conductivity principle, XXII A, 323

Charman, W. N.: Cosmic rays and image intensifier dark current, XXIII B, 705

Charman, W. N., and Hewitt, A. V.: The infiuence of temperature on the performance of a cascade image intensifier, XXII A, 101

Charrier, Mlle, S., and Wltrick, G.: Proprietes des Photocathodes Liberees dans un Vide Eleve, XVI, 5

Chatterton, P. A,: see Smith, W. A. Chenettr, Eugene R. : Noise in semi-

conductor devices, XXIII, 303 Chernov, Z. S.: see Kislov, V. Ya. Chodorow, M.: see Warnecke, R. R. Churchill, J. L. W., and Curran, S. C.:

Pulse amplitude analysis, VIII, 317 Clayton, R. H., and Gumnick, J. L.: Use

of the image dissector in photocathode research, XXII A, 507

Cohen, M.: see Kahan, E. Coles, D. K. : Microwave spectroscopy,

Collings, P. R., Beyer, R. R., Kalafut, J. S., 11, 300

and Gwtze, G. W.: A family of multi-stage direct-view image intensifiers with fiber-optic coupling, XXVIII A, 105

Combes, M., Felenbok, P., Guerin, J., and Picat, J. P. : Electronic cameras for space research, XXVIII A, 39

Condon, P. E.: Image tubes in nuclear physics, XII, 123

Conrad, A. C., Jr.: see Jordan, J. A., Jr, Cooper, A. W.: see Oleson, N. L. Cooper, R., and Elliott, C. T.: Pre-

breakdown light emission from alkali halide crystals, XXII B, 995

The development of camera tubes for recording astronometric images, XXII A, 175

Cope, A. Danforth, and Luedicke, Eduard:

Corney, A.: The measurement of lifetimes


of free atoms, molecules, and ions, XXIX, 11 5

Corps, R. J.: see Groves, P. R. Cozens, J. R.: see von Engle, A. Cranstoun, G . K. L.: The application of

high-gain image intensification and closed-circuit television to field-ion microscopy, XXVIII B, 875

Crompton, R. W.: The contribution of swarm techniques to the solution of some problems in low energy electron physics, XXVII, 1

Culshaw, W.: Millimeter wave techniques, XV, 197

Curran, S. C.: see Churchill, J. L. W. Curzon, A. E., and Lisgarten, N. D.: The

electron-beam shadow method of investigating magnetic properties of crystals, XXIV, 109

Czekalowski, G. W. A., and Hay, G. A,: A quadrature spatial-frequency Fourier analyser, XXVIII B, 653

D

Danforth, W. E.: Thorium oxide and

Daniels, M. V.: see Beurle, R. L. Davies, J. G . : Radio observation of

meteors, IX. 95 Davis, G . P.: Experiences with magneti-

cally focused cascade image intensifiers, XVI, 119

Davis, Robert J. : The use of the Uricon- Celescope television system for ultra- violet astronomical photometry, XXTI B, 875

Dawson, P. H., and Whetten, N. R.: Mass spectroscopy using rf quadrupole fields, XXVII, 59

Day, J. E.: Recent developments in the cathode-ray oscilloscope, X, 239

Dean, R. J.: see Jennings, A. E. Decker, R. W.: Decay of S.20 photo-

electronics, V, 169

cathode sensitivity due to ambient gases, XXVIII A, 357

Large-image electronographic camera, XXVIII A, 19

Decker, R. W., and Mestwerdt, H.:

de Haan, E. F. : Signal-to-noise ratio of image devices, XII, 291

Deltrap, J. H. M., and Hanna, A. H.: Image intensifier system using reflective photocathode, XXVIII A, 443

Denisse, J. F.: see Boischot, A. Dennison, Edwin W. : A microphotometer

for use with photographic and electronographic recording image tubes, XXII A, 435

Dennison, Edwin W. : An isophote converter for use with signal-generating image tubes, XII, 307

Dennison, E. W.: The image orthicon applied to solar photometry, XVI, 447

Bowen, J. S.: An image-tube spectrograph for the Hale 200-in. telescope, XXVIII B, 767

Dennison, E. W., Schmidt, M., and

Deutscher, K.: see Kossel, D. De Witt, John H., Jr.: A report on the

image orthicon using slow readout, XVI, 419

Doe, L. A.: see Livingston, W. C. Dolan, W. W.: see Dyke, W. P. Dolizy, P., and Legoux, R. : A new

technology for transferring photocathodes, XXVIII A, 367

Dolon, Paul J. : see Ball, Jack Dolon, Paul J. : see Niklas, Wilfrid F. Donal, J. S.: Modulation of continuous-

wave magnetrons, IV, 188 Donati, S., Gatti, E., and Svelto, V.: The

statistical behavior of the scintillation detector : theories and experiments, XXVI, 251

Further developments in the application of scintillation chambers to space research, XXII B, 823

Doolittle, R. F., 11, and Graves, C. D.: The application of scintillation chambers to space research, XVI, 535

Doughty, D. D.: see Schneeberger, R. J. Doughty, D. D:. see Wachtel, M. M. Doughty, D. D.: Ultra-violet sensitive

Doolittle, R. F., and Graves, C. D.:

camera tubes incorporating the SEC principle, XXII A, 261

Dow, W. G.: Nonuniform D-C electron

CUMULATIVE AUTHOR INDEX, VOLUMES 1-30 319

flow in magnetically focused cylindrical beams, X, 1

Dow, W. G.: The general perturbational theory of space-harmonic traveling- wave electron interaction, XVII, 1

Dracass, J. : see Flanagan, T. P. Driard, B.: see Guyot, L. F. Driard, B.: ContriBle des monocristeaux

par tube intensificateur de luminance, XXVIII B, 931

Duchesne, M.: see Alpern, M. Duchesne, M.: see Bied-Charreton, P. Duchesne, M.: see Lallemand, A. Duchesne, M.: Sur la Realisation d’une

Camera Electronique de Grandisse- ment 1/7, XVI, 27

Duchesne, M. : Sur une Nouvelle Tech- nique d’Utilisation de la Camkra Electronique, XVI, 19

Duchesne, M., and HCzard, C . : Sur la realisation d’un objectif B immersion a lentilles cylindriques croiskes en vue de son utilisation comme systeme focalisateur de la camera Clectronique: rksultats prkliniinaires, XXII A, 609

Duchet, M. : see Charles, D. R. Duchet, M.: Time-response of photo-

cathodes, XXII A, 499 Dunham, Theodore, Jr. : Performance of

image tubes in the coude spectrograph at Mount Stromlo observatory, XXII B, 729

Dunlap, J.: see Hynek, J. A. Dupre, Mlle M.: see WIBrick, G. Dvofak, M.: Some properties of the tri-

alkali Sb -K -Rb -Cs photocathode, XXVIII A, 347

emission, VIII, 89 Dyke, W. P., and Dolan, W. W.: Field

E

Edgecumbe, J.: see Garwin, E. L. Egan, D. W.: see Beckman, J. E. Egli, P. H.: see Burstein, E. Eichmeier, J.: see Knoll, M. Einstein, P. A,: see Haine, M. E. Eisenstein, A. S.: Oxide coated cathodes,

I, 1

Elliott, C . T. : see Cooper, R. Elliott, C. T.: see Smith, W. A. Elvey, C. T.: Aurora borealis, IX, 1 Emberson, C. J . : see Wheeler, B. E. Emberson, D. L.: A comparison of some

properties of image intensifiers of the transmitted secondary emission multiplication type and of the cascade type, XXII A, 129

Emberson, D. L., and Long, €3. E.: Some aspects of the design and manufacture of a fiber-optic coupled cascade image intensifier, XXVIII A, 119

Wilcock, W. L.: Further work on image intensifiers with transmitted secondary electron multiplication, XVI, 127

Emeleus, K. G.: Plasma oscillations, XX, 59

England, L. : see Barnett, M. E. Ennos, A. E.: see Haine, M. E. Eschard, G., and Graf, J. : Quelques

Emberson, D. I-., Todkill, A., and

problhes concernant les multiplica- teurs canalises pour intensificateur d’image, XXVIII A, 499

obturateurs pour photographie ultra- rapide au temps de pose d’une nanoseconde, XXVIII B, 989

image tubes, XII, 73

Eschard, G., and Polaert, R.: Tubes

Essig, Sanford, E.: Field emission in

Evans, H. D.: see McGee, J. D.

F

Farago, P. S. : The polarization of electron beams and the measurement of the g-factor anomaly of free electrons, XXI, 1

Lawrence W. Fay, Theodore D.: see Frederick,

Fawcett, J. M.: see Jensen, A. S. Feibelman, W. A.: see Schneeberger, R. J. Felenbok, P.: see Combes, M. Ferguson, Etdon E. : Thermal energy

ion-molecule reactions, XXIV, 1 Filby, R. S., Mende, S. B., and Twiddy,

N. D. : A television camera-tube using a low density potassium chloride target, XXII A, 273


Flanagan, T. P., Anderson, D. G., Noe, E. H., and Dracass, J.: Properties and applications of glass scintillators, XVI, 547

Flinn, E. A.: see McGee, J. D. Flinn, E. A,: Progress report on a

Flory, L. E., Pike, W. S., Morgan, J. M., channelled image intensifier, XVI, 155

and Boyer, L. A. : A programmable integrating television system for use with the Stratoscope, XXII B, 885

Folkes, J. R. : see Garfield, B. R. C. Folkes, J. R. : Introduction of pre-formed

photocathodes into vacuum systems, XVI, 325

Foote, D. P.: see Kazan, B. Ford, W. K., Jr.: see Frederick, L. W. Ford, W. K., Jr.: see Hall, J. S . Ford, W. Kent, Jr.: Astronomical uses of

cascade intensifiers, XXII B, 697 Foreman, P. H., and Thumwood, R. F.:

An image intensifier tube using the multipactor principle, XVI, 163

Fowler, Richard G.: Electrons as a hydrodynamical fluid, XX, 1

Fowweather, F., and Harbour, J.: The application of image storage tubes to the observation of optical diffraction patterns, XII, 31 1

Franzen, W.: see Baldinger, E. Frederick, Lawrence W., Fay, Theodore

D., and Johnson, Hollis R.: Infra-red stellar spectroscopy with a mica- window tube, XXII B, 723

Frederick, L. W., Hall, J. S., Baum, W. A., and Ford, W. K., Jr.: Some astronomical uses of image intensifying tubes, XVI, 403

Freeman, K. G.: see Taylor, D. G. Frohlich, H., and Simpson, J. H.:

Intrinsic dielectric breakdown in solids, 11, 185

detector, IV, 258 Fromm, W. E.: The magnetic airborne

G

Gale, B. C.: see Ahmad, N. Ganson, A.: see McGee, J. D. Garfield, B. R. C.: see Allan, F. V

Garfield, B. R. C., and Thumwood, R. F.: A microbalance study of the Cs -Sb and Na -K -Sb photocathodes, XXII A, 459

Garfield, B. R. C., Folkes, J. R., and Liddy, B. T. : Improvements to photocathodes for pulse operation, XXVIII A, 375

Garlick, G. F. J. : Cathodoluminescence, 11, 152

Garlick, G. F. J.: Recent developments in solid state image amplifiers, XVI, 607

Garrett, C. G. B.: The electron as a chemical entity, XIV, 1

Garthwaite, E. : X-ray image intensifier using image orthicon tubes, XU, 379

Garwin, E. L., and Edgecumbe, J.: Response of low-density KCI foils to multi-meV electrons, XXII A, 635

Gatti, E.: see Donati, S. Gebel, R. K. H. : Low-energy quanta

image transducers using a controlled recombination mode, XXII A, 189

Gebel, R. K.H.: The fundamental infrared threshold in thermal image detection as affected by detector cooling and related problems, XXVIII B, 685

electronically scanned photoconductive image detectors for astronomical uses, XVI, 451

Gebel, R. K. H., and Deval, Lee: Some early trials of astronomical photography by television methods, XII, 195

Gebel, R. K. H. : The potentialities of

Geise, R.: see Gildemeister, 0. Geneux, E., BBn6, G. J., and Perrenoud,

J.: Magnetic coherence resonances and transitions at zero frequency, XXVII, 19

Geurts, A.: see Kiihl, W. Gibbons, D. J.: The tri-alkali stabilized

C. P. S . Emitron: A new television camera tube of high sensitivity, XII, 203

Giese, R., Gildemeister, O., and Schuster, G : Test of a high-resolution brenkov chamber with a four-stage image intensifier, XXVIII B, 919

Gildemeister, 0.: see Giese, R.


Gildemeister, O., and Giese, R.: An image intensifier for track recording, XVI, 113

Ginzton, E. L.: see Warnecke, R. R. Gorlich, P.: Problems of photo-

conductivity, XIV, 37 Gorlich, P.: Recent advances in photo-

emission, XI, 1 Goetze, G. W.: see Beyer, R. R. Goetze, G. W.: see Boerio, A. H. Goetze, G. W. : see Collings, P. R. Goetze, G. W.: Secondary electron con-

duction (SEC) and its application to photoelectronic image devices, XXII A, 219

Goetze, G. W. : Transmission secondary emission from low density deposits of insulators, XVI, 145

Goetze, G. W., and Boerio, A. H.: SEC camera-tube performance characteristics and applications, XXVII A, 159

Goetze, G. W., and Taylor, A,: Recent applications of transmission secondary emission amplification, XVI, 557

Jerome: Hydrogen thyratrons, XIV, 207

Goldstein, L. : Electrical discharge in gases and modern electronics, VII, 399

Gordon, A. W.: see Raffan, W. P. Goto, S.: see Sasaki, T. Graf, J. : see Eschard, G. Graves, C. D.: see Doolittle, R. F. Greatorex, C. A.: Image intensification

using a flying-spot x-ray tube, XII, 327

techniques applied to diagnostic radiology, XVI, 593

Green, M.: see Beyer, R. R. Green, M., and Hansen, J. R.: The appli-

cation of SEC camera tubes and electrostatic image intensifiers to astronomy, XXVIII B, 807

Goldberg, Seymour, and Rothstein,

Greatorex, C. A.: Image storage

Grivet, P. : Electron lenses, 11, 48 Grivet, P. A., and Malnar, L.: Measure-

ment of weak magnetic fields by magnetic resonance, XXIII, 39

Grosch, G. A., and Krieser, J. K.:

Leistungsgrenze eines Sichtsystems mit Bildverstarker, XXVIII B, 603

Grosse, Achilles: see Wlerick, GCrard Groves, P. R., and Corps, R. J.: Applica-

tions of the image isocon tube, XXVIII B, 827

Guenard, P. R.: see Warnecke, R. R. Guerin, J.: see Combes, M. Guest, A.: see Manley, B. W. Guillard, C., and Charles, D. R.: On

some properties of electron bombardment induced conductivity, XXII A, 315

Guillemin, E. A.: A summary of modern methods of network synthesis, 111, 261

Gumnick, J. L.: see Clayton, R. H. Guyot, L. F. : Derniers Developpements

stir les Intensificateurs d’Image Rayons X A Grand Gain et les Tubes Convertisseurs #Image, XVI, 91

Guyot, L. F., Driard, B., and Sirou, F. : Tubes intensificateurs d’image pour observation des phenomhes lumineux rapidement kvolutifs, XXII B, 949

H

Hachenberg, O., and Brauer, W. : Secon- dary electron emission from solids, XI, 413

Haine, M. E. : The electron microscope- a review, VJ, 295

Haine, M. E., Ennos, A. E., and Einstein, P. A. : An image intensifier for the electron microscope, XII, 317

Hall, J. S.: see Frederick, L. W. Hall, J. S., Ford, W. K., Jr., and Baum,

W. A.: Astronomical tests of barrier- membrane image converters, XII, 21

Hanna, A. H.: see Deltrap, J. H. M. Hansen, J. R.: see Green, M. Harbour, J.: see Fowweather, F. Harth, W. : see Schaff, F. Hartmann, P. : see Vernier, P. Hasegawa, S.: Resolving power of image

tubes, XXVIII B, 553 Hasted, John B.: Inelastic collisions be-

tween atomic systems, XIII, 1 Hay, G. A.: see Ozekalowski, G. W. A.


Hay, G. A.: The image orthicon in diagnostic radiology, XVI, 581

Hay, G. A.: X-ray image intensification using optical television methods, XII, 363

Hayward, R. W. : Beta-ray spectrometers, v, 97

Heimann, W. : Experiments with a simple photo-electronic storage tube, XII, 235

Heimann, W.: Possibilities of reducing image defects in electron-optical imaging devices using electrostatic lenses, XXII A, 601

Heimann, W., and Hoene, E. L.: Im- provement of signal-to-noise ratio of image converters with S.1 photocathodes, XXVIII B, 677

ment of an infra-red vidicon-type pick-up tube with a lead sulphide target, XVI, 217

Heimann, W., and Kunze, C.: Develop-

Heinrich, Hans: see Stahnke, Ingeborg Herbstreit, J. W.: see Rice, P. L. Herbstreit, J. W.: Cosmic radio noise, I,

Herrmann, M., and Kunze, C.: A new 347

multiplier system with forty separate channels, XXVIII B, 955

graphy, IX, 239

ray image intensifiers and television channels, XVI, 610

quality in medical fluoroscopy, XXII A, 363

Herstel, W.: The observation of moving structures with x-ray image intensifiers, XXVIII B, 647

Hewitt, A. V. : see Charman, W. N. Hewitt, A. V. : see Kron, G. E. Hbzard, C. : see Duchesne, M. Hill, D. A., and Porter, N. A.: Photo-

graphy of extensive air showers in the atmosphere, XVI, 531

Hill, D. A., Caldwell, D. O., and Schluter, R. A. : Performance of an image intensifier system, XVI, 475

Hills, B. L.: see Beurle, R. L.

Hersey, J. B. : Electronics in oceano-

Herstel, W. : Some experiences with x-

Herstel, W. : The assessment of image

Hiltner, W. A., and Niklas, W. F.: A low background image tube for electronography, XVI, 37

Hiltner, W. A., and Pesch, Peter: Image tube research at Yerkes Observatory, XII, 17

Hinder, G. W. : see Iredale, P. Hirashima, M.: Optimum conditions for

activating silver-magnesium alloy dynodes in water vapour, XXII A, 661

Hirashima, M., and Asano, M.: Effects of caesium vapour upon target glass of image orthicon, XXII A, 651 ; XXVIII A, 309

of caesium vapour with gold, XXII A, 643

Hirashima, M., and Asano, M.: Some better materials for caesium vapour, XXVIII A, 381

Hirashima, M., and Asano, M. : Reaction

Hirayama, T. : see Kajiyama, Y. Hirsch, C. J. : A review of recent work in

color television, V, 291 Hirschberg, K. : see Kossel, D. Hobson, J. P. : see Redhead, P. A. Hoene, E. L.: see Heimann, W. Hok, G. : The microwave magnetron, 11,

Holmes, P. J. : see Billig, E. Holmshaw, R. T. : see Manley, B. W. Hooper, E. B., Jr.: A review of reflex and

Penning discharges, XXVII, 295 Hopmann, W. : The image orthicon in

high-speed photography, XXII B, 1011

Hopmann, W.: The influence of photocathode resistance and space charge on the resolution of magnetic focus systems, XXII A, 591

Hori, H., Tsuji, S., and Kiuchi, Y.: An infra-red sensitive vidicon with a new type of target, XXVIII A, 253

Thermionic energy conversion, XVII, 125

accelerators, XXV, 1

cameras, XXII B, 957

220

Houston, J. M., and Webster, H. F.:

Hubbard, Edward L. : Linear ion

Huston, A. E.: Image tube high-speed

CUMULATIVE AUTHOR INDEX. VOLUMES 1-30 323

Huston, A. E., and Walters, F. W.: Electron tubes for high-speed photography, XVI, 249

Hutter, E. C.: see Vance, A. W. Hutter, R. G. E.: The deflection of beams

of charged particles, I, 167 Hutter, R. G. E.: Traveling-wave tubes,

Hynek, J. A., Bakos, G., Dunlap, J., and vr, 371

Powers, W. : Advances in the application of the image orthicon to astronomy, XXII B, 713

Hynek, J. A., Barton, G., Aikens, R., and Powers, W.: Potentialities and limitations of image scanning techniques in astronomy, XVI, 409

I

Inghram, M. G.: Modern mass

Inskeep, C. N.: see Abraham, J. M. Iredale, P., and Ryden, D. J.: On the

spectroscopy, I . , 219

quality of photographic images recorded with the use of image intensifiers, XXVIII B, 589

D. W. S. : Position-sensitive photon counters, XXVIII B, 965

Iredale, P., Hinder, G . W., Parham, A. G . , and Ryden, D. J.: The observation of brenkov ring images with an image intensifier system of high gain, XXII B, 801

VI, 137

Iredale, P., Hinder, G. W., and Smout,

hey, H. F.: Space charge limited currents,

J

Jackson, F. W.: see Wardley, J. Jane, M. R.: see Binnie, D. M. JareS, V., and Novotn);, B.: Two methods

for the determination of the imaging properties of electron-optical systems with a photocathode, XXVIII A, 523

Jaumot, Frank E., Jr.: Thermoelectricity, XVII, 207

JedliEka, M.: Research on photocathodes in Czechoslovakia, XXVIII A, 323

JedliEka, M., and Vilim, P.: Some properties of the Sb -Rb -Cs photocathode, XXII A, 449

transmission of medium energy electrons through mica, XXII A, 41

Jenkinson, G . W.: see Beurle, R. L. Jennings, A. E., and Dean, R. J.:

Sensitization of electrostatically focused image converters, XXII A, 441

Measurement of TV camera noise, XXVIII A, 289

Jensen, Arthur S., Reininger, Walter G., and Limansky, Igor: The grating storage target, XXII A, 155

Lawrence W.

Jeffers, S., and McGee, J. D.: On the

Jensen, A. S., and Fawcett, J. M. :

Johnson, Hollis R.: see Frederick,

Johnson, J. M.: see Sackinger, W. M. Jones, Lawrence W.: see Perl, Martin L. Jones, Lawrence W., and Loo, Billy W. :

The use of image intensifiers with streamer chambers, XXII B, 813

Jones, L. W., and Perl, Martin L.: Two high-energy physics experiments using the luminescent chamber, XVI, 513

Jones, R. Clark: Performance of detectors for visible and infrared radiation, V, 1

Jones, R. Clark: Quantum efficiency of detectors for visible and infrared radiation, XI, 87

Jordan, J. A., Jr., Bakken, G . S . , and Conrad, A. C., Jr.: A cascade image intensifier camera for beam-foil spectroscopy, XXVIII B, 907

K

Kahan, E., and Cohen, M.: Comparison of the efficiency of image recording with a Spectracon and with Kodak IIa-0 emulsion, XXVIII B, 725

Hirayama, T.: Newly developed image orthicon tube with a MgO target, XXVIII A, 189

Kajiyama, Y., Kawahara, T., and

Kalafut, J. S . : see Collings, P. R. Kao, K. C . : see Smith, C. W.


Kaw, Predhiman Krishan: see Sodha,

Kawahara, T. : see Kajiyama, Y. Kawakami, H.: see Uno, Y. Kay, Eric: Impact evaporation and thin

film growth in a glow discharge, XVII, 245

Mahendra Singh

Kazan, B.: see Knoll, J. Kazan, B., and Foote, D. P. : Recent

developments in field-effect image storage panels, XXVIII B, 1059

Keen, Ralph S.: see Schnable, George L. Kennedy, David P. : Semi-conductor

Kennedy, S. W.: see Weingartner, H. C. Kerwin, L. : Mass spectroscopy, VIII, 187 Key, M. H.: see Ahmad, N. Khogali, A. : see McGee, J. D. Kidger, M. J.: see Wynne, C. G. King, J. G., and Zacharias, J. R.: Some

new applications and techniques of molecular beams, VIII, 1

Chernov, Z. S.: Physical foundations of plasma applications for generation and amplification of microwaves, XXI, 287

device evaluation, XVIII, 167

Kislov, V. Ya., Bogdanov, E. V., and

Kisteniaker, J. : see Snoek, C. Kiuchi, Y.: see Hori, H. Klein, N. : Electrical breakdown in solids,

Knoll, M., and Kazan, B.: Viewing stor-

Knoll, M., Eichmeier, J., and Schon,

XXVI, 309

age tubes, VIII, 447

R. W.: Properties, measurement, and bioclimatic action of ‘‘ small ” multimolecular atmospheric ions, XIX, 178

Kohashi, T., Nakamura, T., Maeda, H., and Miyaji, K.: A fast-response solid-state image converter, XXII B, 683

Kohashi, T., Nakamura, T., Nakamura, S., and Miyaji, K.: Recent developments in solid-state infra-red image converters, XXVIII B, 1073

Komrska, Jifi: Scalar diffraction theory in electron optics, XXX, 139

Konigsberg, R. L.: Operational amplifiers, XI, 225

Konrad, G. T., and Rowe, J. E.: Har- monic generation and multisignal

effects in nonlinear beam plasma systems, XXIX, 1

Kornelsen, E. V.: see Redhead, P. A. Kossel, D., Deutscher, K., and Hirschberg,

K. : Interference photocathodes, XXVIII A, 419

Krieser, J. K.: see Grosch, G. A. Kron, Gerald E., and Papiashvili, I. I. :

Progress in the development of the Lick-Stromlo electronic camera, XXII A, 59

Kron, G. E.: Advantages of a bakeable electronographic plate, XVI, 35

Kron, G. E. : A modified Lallemand image tube, XVI, 25

Kron, G. E., Ables, H. D., and Hewitt, A. V. : A technical description of the construction, function, and application of the U.S. Navy electronic camera, XXVIII A, 1

Kiihl, W., Geurts, A., and v. Overhagen, J. : Information transfer with high-gain image intensifiers, XXVIII B, 615

Kunze, C.: see Heimann, W. Kunze, C.: see Herrmann, M. Kunze, W., Meyerhoff, K., and Retzlaff,

G. : The useful luminance gain of image intensifier systems with respect to noise limitations, XXVIII B, 629

L

Labeyrie, A. : An image-tube Fourier spectrograph, XXVIII B, 899

Lallemand, A. : Perfectionnement de la camtra klectronique- application zi I’infra-rouge, XXII A, 1

camera electronique, XVl, 1

Wltrick, G.: La photographie electronique, XII, 5

Lallemand, A. : Quelques reflexions sur la

Lellemand, A,, Duchesne, M., and

Lamport, D. L.: see Stark, A. M. Lansiart, A., and Roux, G.: Spark

chambers and image intensifiers used in the scanning of radioactive objects, XXII B, 941

Laques, P. : Photographie des Ctoiles doubles au moyen de la camtra Clectronique Lallemand, XXII B, 755


Lashinsky, Herbert: Cerenkov radiation at microwave frequencies, XIV, 265

Lawless, W. L.: Developments in computer logical organization, X, 153

Le Carvennec, F. : Recherche d'un dispositif nouveau de tklevision thermique, XXVIII A, 265

Le Contel, J. M.: see Bied-Charreton, P. Leder, L. B.: see Marton, L. Legoux, R.: see Dolizy, P. Lechmann, J. : see Vance, A. W. Leifer, M., and Schreiber, W. F.: Com-

munication theory, 111, 306 Lenz, F.: See Mollenstedt, G. Liddy, B. T.: see Garfield, B. R. C. Liebmann, G.: Field plotting and ray

tracing in electron optics: A review of numerical methods, 11, 102

Limansky, Igor: see Jensen, Arthur S. Linden, B. R.: A survey of work at CBS

laboratories on photoelectronic image devices, XVI, 31 1

Lindsay, P. A,: Velocity distribution in electron streams, XIII, 181

Lisgarten, N. D.: see Curzon, A. E. Liu, I. D., and Baskett, J. R.: A high-

gain time-resolving spectrograph for diagnostics of laboratory simulated re-entry objects, XXVIII B, 1021

Livingston, M. S.: Particle accelerators, I, 269

Livingston, W. C.: Properties and limitations of image intensifiers used in astronomy, XXIII, 347

Livingston, W. C.: Stellar photometry with an image orthicon, XVI, 431

Livingston, W. C., Lynds, C. R., and Doe, L. A.: Recent astronomical research utilizing a high gain image intensifier tube, XXII B, 705

Long, B. E.: see Emberson, D. L. Loo, Billy W.: see Jones, Lawrence W. Low, W.: Electron spin resonance-a tool

in mineralogy and geology, XXIV, 51 Lowrance, J. L., and Zucchino, P. M.:

Integrating television sensors for space astronomy, XXVIII B, 851

Luedicke, Eduard, see Cope, A. Danforth Lynds, C. R.: see Livingston, W. C. Lynds, R.: see Powell, J. R.

Lynton, E. A., and McLean, W. L.: Type I1 superconductors, XXIII, 1

M

McGee, J. D.: see Jeffers, S. McGee, J. D.: see Smith, C. W. McGee, J. D., and Wheeler, B. E.: An

image tube with Lenard window, XVI, 47

McGee, J. D., Airey, R. W., and Aslam, M. : High quality phosphor screens for cascade image intensifiers, XXII A, 571

McGee, J. D., Airey, R. W., and Varma, B. P. : Cascade image intensifier developments, XXVIII A, 89

B. E.: Thin-window image intensifier with phosphor output, XVI, 61

McGee, J. D., Airey, R. W., Aslam, M., Powell, J. R., and Catchpole, C. E.: A cascade image intensifier, XXII A, 113

McGee, J. D., Aslam, M., and Airey, R. W. : The evaluation of cascade phosphor-photocathode screens, XXII A, 407

McGee, J. D., Flinn, E. A., and Evans, H. D.: An electron image multiplier,

McGee, J. D., Khogali, A,, and Ganson, A,: Electron transmission through mica and the recording efficiency of the spectracon, XXII A, 31

McGee, J. D., Khogali, A., Ganson, A., and Baum, W. A.: The spectracon- an electronographic image recording tube, XXII A, 11

McGee, J. D., McMullan, D., Bacik, H., and Oliver, M.: Further developments of the spectracon, XXVIII A, 61

McKay, K. G. : Secondary electron emission, I, 66

McLane, C. K.: Experimental plasma turbulence, XXX, 1

McLean, W. L.: see Lynton, E. A. McMullan, D.: see McGee, J. D.

McGee, J. D., Airey, R. W., and Wheeler,

XII, a i


McMullan, D., and Towler, G. 0.: Some properties of SEC targets, XXVIII A, 173

I, 317 McNish, A. G.: Ionospheric research,

Maeda, H.: see Kohashi, T. Maeda, H.: see Miyazaki, E. Maeda, H.: see Uno, Y. Majumdar, S.: see Bradley, D. J. Malherbe, A., Tessier, M., and Veron, S.:

Spectral response of S-l photocathodes in the near infra-red, XXII A, 493

Malling, L. R., and Allen, J. Denton: The slow-scan vidicon as an interplanetary imaging device, XXII B, 835

Malnar, L.: see Grivet, P. A. Manley, B. W., and Schagen, P.: The

tenicon: A high resolution information storage tube, XVI, 287

Manley, B. W., Guest, A., and Holmshaw, R. T. : Channel multiplier plates for imaging applications, XXVIII A, 471

Performance comparison of the SEC camera tube and the image orthicon, XXII A, 291

Marshall, F. B., and Roane, G . D.:

Martin, R.: see Wise, H. S. Marton, L., Leder, L. B., and

Mendlowitz, H. : Characteristic energy losses of electrons in solids, VII, 183

Massey, H. S. W. : Electron scattering in solids, IV, 2

Mayer, H. F. : Principles of pulse code modulation, 111, 221

Medved, David B., and Strausser, Y . E.: Kinetic ejection of electrons from solids, XXI, 101

Melton, B. S.: Contributions of electronics to seismology and geomagnetism, IX, 297

Mende, S. B.: see Filby, R. S. Mendlowitz, H.: see Marton, L. Mestwerdt, H.: see Decker, R. W. Metson, G. H.: On the electrical life of

an oxide-cathode receiving tube, VIII, 403

Meyerhoff, K.: see Kunze, W. Miller, D. E.: see Wilcock, W. L.

Miyaji, K. : see Kohashi, T. Miyaji, K. : see Miyazaki, E. Miyashiro, S., and Nakayama, Y. :

Electronic zooming with the image orthicon television pick-up tube, XVI, 195

Miyashiro, S., and Nakayama, Y . : Some methods of minimizing the black- border effect in the image orthicon television pick-up tube, XVI, 171

Miyashiro, S., and Shirouzo, S.: Electro- statically scanned image orthicon, XXVIII A, 191

Miyazaki, E.: see Uno, Y. Miyazaki, E., Maeda, H., and Miyaji, K.:

The evoscope-a fixed-pattern generator using a Au-Si diode, XXII A, 331

in design of magnetic beta-ray spectrometers, XXX, 43

Mockler, Richard C.: Atomic beam frequency standards, XV, 1

Mollenstedt, G., and Lenz, F.: Electron emission microscopy, XVIII, 251

Moreno, T. : High-power axial-beam tubes, XIV, 299

Morgan, B. L., Smith, R. W., and Wilson, G . A.: A storage image tube for optoelectronic computing, XXVIII B, 1051

MladjenoviC, Milorad S. : Recent advances

Morgan, J. M.: see Flory, L. E. Morton, G . A,: The scintillation counter,

IV, 69 Morton, G . A., and Ruedy, J. E.: The

low light level performance of the intensifier orthicon, XII, 183

Moss, H.: Cathode ray tube progress in the past decade with special reference to manufacture and design, 11, 2

Motz, H., and Watson, C. J.: The radiofrequency confinement and acceleration of plasmas, XXIII, 153

Miiller, Erwin W.: Field ionization and field ion microscopy, XIII, 83

N

Nakamura, S.: see Kohashi, T. Nakamura, T. : see Kohashi, T.


Nakamura, T. : see Sasaki, T. Nakayama, Y . : see Miyashiro, S . Narcisi, Rocco S . , and Roth, Walter:

The formation of cluster ions in laboratory sources and in the ionosphere, XXIX, 79

Nassenstein, H.: The boundary layer image converter, XVI, 633

Needham, M. J., and Thumwood, R. F.: A proximity-focused image tube, XXVIII A, 129

Nelson, P. D.: The development of image isocons for low-light applications, XXVIII A, 209

Neumann, M. J . : see Burns, J. Newth, J. A,: see Binnie, D. M. Newton, A. C. : see Boksenberg, A. Niklas, Wilfrid F.: see Ball, Jack Niklas, Wilfrid F., Dolon, Paul J., and

Berger, Harold: A thermal-neutron image intensifier, XXII B, 781

Niklas, W. F.: see Hiltner, W. A. Ninomiya, T., Taketoshi, K., and Tachiya,

H.: Crystal structure of niultialkali photocathodes, XXVIII A, 337

Niquet, G. : see Vernier, P. Nixon, W. C.: see Oatley, C. W. Noe, E. H.: see Flanagan, T. P. Norman, D. J.: see Beesley, J. Norton, K. A.: Propagation in the FM

broadcast band, I, 381 Novice, M. : see Szepesi, Z. Novotn)i, B. : see JareS, V. Nozawa, Y . : A digital television system

for a satellite-borne ultra-violet photometer, XXII B, 865

Nozawa, Y. : Characteristics of a television photometer, XXVIII B, 891

Nudelman, S . : Intensifiers: detective quantum efficiency, efficiency contrast transfer function and the signal-to- noise ratio, XXVIII B, 577

0

Oatley, C. W., Nixon, W. C., and Pease, R. F. W. : Scanning electron microscopy, XXI, 18 1

O’Keefe, T. W., and Vine, J . : A high- resolution image tube for integrated circuit fabrication, XXVIII A, 47

Okress, E. C.: Magnetron mode transitions, VIII, 503

Oleson, N. L., and Cooper, A. W.: Moving striations, XXIV, 155

Oliver, M.: see McGee, J. D. Oman, R. M.: Electron mirror

Ovenstone, J . A,: see Barlow, G . E. microscopy, XXVI, 21 7

P

Papiashvili, I. I . : see Kron, Gerald E. Parham, A. G.: see Iredale, P. Pawley, M. G., and Triest, W. E.: Multi-

Pease, R. F. W.: see Oatley, C. W. Perl, Martin L.: see Jones, L. W. Perl, Martin L., and Jones, Lawrence W.:

The regenerative image intensifier and its application to the luminescent chamber, XII, 153

channel radio telemetering, IV, 301

Perrenoud, J . : see Geneux, E. Pesch, Peter: see Hiltner, W. A. Petley, C. H.: see Taylor, D. G . Picat, J. P.: see Combes, M. Pierce, J. A.: Electronic aids to navigation

Pike, W. S.: see Flory, L. E. Pinsker, Z . G.: Electron diffraction

I, 425

structure analysis and the investigation of semiconducting materials, XI, 355

Pippard, A. B.: Metallic conduction at high frequencies and low temperatures, VI, 1

Polaert, R.: see Eschard, G. Porter, N. A.: see Hill, D. A. Potter, D. C.: see Binnie, D. M. Powell, J. R.: see McGee, J. D. Powell, J. R., and Lynds, R.: Methods

of increasing the storage capacity of high-gain image intensifier systems, XXVIII B, 745

Powers, W.: see Hynek, J. A. Prosser, R. D. : see Berg, A. D. Pulfrey, D. L.: see Smith, W. A.


R

Rado, G. T.: Ferromagnetic phenomena at microwave frequencies, 11, 251

Raffan, W. P., and Gordon, A. W.: The development and application of interference photocathodes for image tubes, XXVIII A, 433

Randall, R. P.: Charge integration experiments with a C.P.S. Emitron, XII, 219

Randall, R. P.: Dark current scintillations of cascade image intensifiers, XXVIII B, 713

Randall, R. P. : Operating characteristics of a four-stage cascade image intensifier, XXII A, 87

Kornelson, E. V. : Ultra-high vacuum, XVII, 323

Reininger, Walter G.: see Jensen, Arthur S. Retzlaff, G.: see Kunze, W. Reynolds, Geo. T. : Sensitivity of image

intensifier-film systems for observing weak light sources, XXII A, 381

single electron pulse sizes from multidynode electron multipliers, and single electron detection, XXII A, 71

Reynolds, G. T.: Photon interference experiments utilizing photoelectronic devices, XXVIII B, 939

R. A., Waters, J. R., and Zdanis, R. A. : Filament scintillation chamber experiments at Princeton University, XVI, 487

Riblet, Henry B.: Radio telemetering, XI, 287

Rice, P. L., and Herbstreit, J. W.: Tropospheric propagation, XX, 199

Richards, E. A.: Contrast-enhancement in imaging devices by selection of input photosurface spectral response, XXVIII B, 661

Redhead, P. A., Hobson, J. P., and

Reynolds, Geo. T.: The distribution of

Reynolds, T. T., Scarl, D. B., Swanson,

Richards, E. W. T.: see Wise, H. S. Rindfleisch, T., and Willingham, D.: A

figure of merit measuring picture resolution, XXII A, 341

Roach, F. E.: The nightglow, XVIII, 1 Roane, G. D.: see Marshall, F. B.

Roberts, Arthur: Amplification of transient images in high-gain photocathode-phosphor image intensifier systems, XII, 135

infrared radiation, XXVI, 171 Robinson, L. C.: Generation of far-

Rosch, J . : see Wltrick, G. Rosch, J. : Le gain possible de rCsolution

dans l’observation astronomique par l’emploi de la camera electronique de Lallemand, XII, 113

Rosch, J. , Wlkrick, G., and Boussuge, C.: Photographie des etoiles doubles au Moyen de la camCra electronique, XVI, 357

Rose, A.: Television pick-up tubes and the problem of vision, I, 131

Rose, D. C.: Intensity variations in cosmic rays, IX, 129

Roth, Walter: see Narcisi, Rocco S. Rothstein, Jerome: see Goldberg, Seymour. Roux, G.: see Lansiart, A. Rowe, E. G.: On some aspects of tube

reliability, X, 185 Rowe, J. E.: see Konrad, G. T. Ruedy, J. E.: see Morton, G. A. Russell, L. A.: High-speed magnetic-core

Ryden, D. J.: see Iredale, P. memory technology, XXI, 249

S

Sackinger, W. M., and Johnson, J. M.: An analysis of the low-level performance of channel multiplier arrays, XXVIII A, 487

Sackinger, W. M., and Johnson, J. M.: Effects of vacuum space charge in channel multipliers, XXVIII A, 507

Sasaki, T., Nakamura, T., and Goto, S.: Experiments on a wire-electrode type image intensifier using electroluminescence, XVI, 621

Scarl, D. B.: see Reynolds, G. T. Schaff, F., and Harth, W.: Computation

of imaging properties of image tubes from an analytic potential representation, XXVIII A, 535


Schaffner, J.: Junction transistor applica-

Schagen, P.: see Manley, B. W. Schagen, P.: see Woodhead, A. W. Schagen, P.: An image intensifier system

tions, V, 367

for direct observation at very low light levels, XVI, 75

approaches to photoemission at long wavelengths, XXVIII A, 393

Schluter, R. A.: see Hill, D. A. Schmerling, E. R.: see Bowhill, S. A. Schmidt, M.: see Dennison, E. W. Schnable, George L., and Keen, Ralph S.:

Schagen, P., and Turnbull, A. A.: New

On failure mechanisms in large-scale integrated circuits, XXX, 79

Schneeberger, R. J. : see Anderson, A, E. Schneeberger, R. J., Skorinko, G.,

Doughty, D. D., and Feibelman, W. A.: Electron bombardment induced conductivity including its application to ultra-violet imaging in the Schuman region, XVI, 235

Schon, R. W.: see Knoll, M. Schooley, Allen H. : Electronic instrumen-

tation for oceanography, XIX, 1 Schuster, G.: see Giese, R. Septier, Albert: Strong-focusing lenses,

Shapiro, G. : Subminiaturization

Shirouzo, S.: see Miyashiro, S. Shrager, Peter G., and Susskind, Charles:

Simon, J. C.: see Broussaud, G. Simpson, J. H.: see Frohlich, H. Singer, J. R.: Masers and other quantum

mechanical amplifiers, XV, 73 Sirou, F.: see Guyot, L. F. Skorinko, G.: see Schneeberger, R. J. Slark, N. A.: see Batey, P. H. Slark, N. A.: see Beurle, R. L. Slark, N. A,, and Woolgar, A. J.: A

transmission secondary emission image intensifier, XVI, 141

Smit, J., and Wijn, H. P. J.: Physical properties of ferrites, VI, 69

Smith, C. V. L.: Electronic digital computers, IV, 157

Smith, C. W.: An x-ray sensitive photo-

XIV, 85

techniques, 111, 195

Electronics and the blind, XX, 261

conductive pick-up tube, XII, 345

J. H., and McGee, J. D.: A study of pre-breakdown phenomena in n- hexane using an image intensifier tube, XXII B, 1003

Smith, C. W., Kao, K. C., Calderwood,

Smith, R. W. : see Berg, A. D. Smith, R. W.: see Morgan, B. L. Smith, R. W. : The application of the

electron image store and analyser to high-speed photography, XXVIII B, 101 1

Smith, W. A., Chatterton, P. A,, Elliott, C. T., and Pulfrey, D. L.: A high speed photographic study of the electrical breakdown of small gaps in vacuum, XXVIII B, 1041

Smith-Rose, R. L.: Radiowave propagation: A review, IX, 187

Smout, D. W. S.: see Iredale, P. Smyth, M. J.: see Brand, P. W. J. L. Smyth, M. J., and Brand, P. W. J. L.:

Linearity of electronographic emulsions, XXVIII B, 737

Snoek, C., and Kistemaker, J.: Fast ion scattering against metal surfaces, XXI, 67

Predhiman Krishan: Theory of the generation of harmonics and combination frequencies in a plasma, XXVII, 187

Sodha, Mahendra Singh, and Kaw,

Southon, M. J.: see Whitmell, D. S. Stahnke, Ingeborg, and Heinrich, Hans:

Special problems in measuring the modulation transfer function of x-ray image intensifiers, XXII A, 355

Stark, A. M., Lamport, D. L., and Woodhead, A. W.: Calculation of the modulation transfer function of an image tube, XXVIII B, 567

Sternheimer, R. M.: Parity nonconservation in weak interactions, XI, 31

Stone, H. D. : Preparation of high-resolution phosphor screens, XXII A, 565

Stoudenheimer, R. G.: Image intensifier developments in the RCA electron tube division, XII, 41

Strausser, Y. E.: see Medved, David B.


Stricker, S.: The Hall effect and its

Sturimer, W.: Some applications of solid applications, XXV, 97

state image converters (SIC), XVI, 613

Siisskind, Charles, see Shrager, Peter G. Siisskind, C.: Electron guns and focusing

for high-density electron beams, VIII, 363

Svelto, V. : see Donati, S. Swanson, R. A.: see Reynolds, G . T. Syms, C. H. A,: Gallium arsenide thin-

film photocathodes, XXVIII A, 399 Szepesi, Z., and Novice, M.: Solid-state

radiographic amplifiers and infra-red converters, XXVIII B, 1087

T

Tachiya, H.: see Ninomiya, T. Taketoshi, K.: see Ninomiya, T. Taylor, A.: see Goetze, G. W. Taylor, D. G.: see Schagen, P. Taylor, D. G.: see Woodhead, A. W. Taylor, D. G.: The measurement of the

modulation transfer functions of fluorescent screens, XXII A, 395

man, K. G.: Television at low light- levels by coupling an image intensifier to a Plumbicon, XXVIII B, 837

Taylor, S.: An infra-red-sensitive television camera tube, XII, 263

Tepinier, M.: see Vernier, P. Ter-Pogossian, M.: see Ball, Jack Tessier, M.: see Malherbe, A. Theile, R.: On the signal-to-noise ratio in

television storage tubes, XII, 277 Theodorou, D. G.: Research on photo-

cathode surfaces at the Bendix Corporation Research Laboratories Division, XXIIA, 477

Taylor, D. G., Petley, C. H., and Free-

Thonemann, F. F.: see Barlow, G. E. Thumwood, R. F. : see Foreman, P. H. Thumwood, R. F.: see Garfield, B. R. C. Thumwood, R. F. : see Needham, M. J. Todkill, A.: see Emberson, D. L. TomoviC, R.: Systems approach to

skeletal control: concept of the system, XXX, 273

Towler, G. 0.: see McMullan, D. Triest, W. E.: see Pawley, M. G. Trolander, Hardy W.,andVeghte,JamesH.:

Recent advances in biological temperature measurements, XXX, 235

Tsuji, S.: see Hori, H. Turnbull, A. A.: see Schagen, P. Twiddy, N. D.: see Filby, R. S. Twiss, R. Q.: On the steady state theory

of the magnetron, V, 247

U

Uno, Y., Kawakami, H., Maeda, H., and Miyazaki, E.: Cathode-ray tube with thin electron-permeable window, XXVIII A, 81

V

Vance, A. W., Hutter, E. C., Lehmann, J., and Wadlin, M. L.: Analog computers, VII, 363

Van den Handel, J.: Paramagnetism, VI, 463

Van der Ziel, A. : Fluctuation phenomena, IV, 110

van Roosmalen, J. H. T. : Adjustable saturation in a pick-up tube with linear light transfer characteristic, XXVIII A, 281

v. d. Polder, L. J. : Beam-discharge lag in a television pick-up tube, XXVIII A, 23 7

v. Overhagen, J. : see Kiihl, W. Varma, B. P.: see McGee, J. D. Veghte, James H.: see Trolander,

Hardy W. Vernier, P., and Hartmann, P. : RCsultats

obtenus a I’aide de la camCra Clectronique Lallemand dans I’ttude de l’kmission photoelectrique, XXII A, 519

Vernier, P., Hartmann, P., Niquet, G., and Tepinier, M. : etude de l’emission photodectrique des structures mCtal- isolant-metal, XXVIII A, 409

Veron, S. : see Malherbe, A.


Veron, S.: Quelques aspects der essais de depBt de photocathodes S a20 et d’ecrans fluorescents sur fibres optiques, XXVIII A, 461

Vilim, P.: see JedliEka, M. Vine, J . : see O’Keefe, T. W. Vine, J. : The design of electrostatic zoom

image intensifiers, XXVIII A, 537 Vodovnik, L.: Functional electrical

stimulation of extremities, XXX, 283 von Engel, A., and Cozens, J. R.: Flame

plasmas, XX, 99

W

Wachtel, M. M., Doughty, D. D., and Anderson, A. E. : The transmission secondary emission image intensifier, XII, 59

Wadlin, M. L.: see Vance, A. W. Wagner, K. H.: Application of image

intensifiers and shutter tubes to the study of gas discharges, XXVIII B, 1033

Wait, James R.: Recent theoretical advances in the terrestrial propagation of ULF electromagnetic waves, XXV, 145

Walker, M. F.: Performance of the Spectracon in astronomical spectroscopy, XXVIIL B, 773

observations obtained with the Lallemand electronic camera, XVI, 341

Walker, M. F.: Recent progress in the use of the Lallemand electronic camera in astronomical spectroscopy, XXII B, 761

Walker, M. F.: Recent astrononiical

Walters, F. W.: see Huston, A. E. Walters, J. : see Binnie, D. M. Wardley, J. : A high-resolution ruggedized

half-inch vidicon, XXII A, 21 1 Wardley, J. : An improved ultra-violet

sensitive vidicon, XVI, 227 Wardley, J., and Jackson, F. W.: A

13-mm all-electrostatic vidicon, XXVIII A, 247

Warnecke, R. R., Chodorow, M., Guenard, P. R., and Ginzton, E. L.: Velocity modulated tubes, 111, 43

Waters, J. R.: see Reynolds, G . T. Watson, C. J.: see Motz, H. Webster, H. F.: see Houston, J. M. Webster, W. M. : A comparison of analog-

ous semiconductor and gaseous electronic devices, VI, 257

Wehner, G . K.: Sputtering by ion bombardment, VII, 239

Weimer, Paul K. : Television camera tubes: A research review, XIII, 387

Weingartner, H. C., and Kennedy, S. W.: Modern vacuum pumps in electronics manufacturing, V, 21 3

Wendt, G.: INTIC, an image intensifying, integrating and contrast-enhancing storage tube, XXVIII A, 137

Wheeler, B. E.: see McGee, J. D. Wheeler, B. E., and Emberson, C. J. :

Some measurements on the direct recording of electron images using thin windows, XXII A, 51

Whetten, N. R. : see Dawson, P. H. White, J. E.: Tube miniaturization, 111,

183 Whitmell, D. S., and Southon, M. J.:

Image intensification in field-ion microscopy, XXII B, 903

Wijn, H. P. J.: see Smit, J. Wilcock, W. L.: see Emberson, D. L. Wilcock, W. L.: Routine measurement of

the responsive quantum efficiency of photoemissive cathodes, XXII A, 535

Wilcock, W. L.: Statistics of transmitted secondary electron multiplication, XXII A, 629

Wilcock, W. L., and Baum, W. A.: Astro- nomical tests of an imaging photomultiplier, XVI, 383

Statistics of transmitted secondary electron emission, XXVIII A, 513

astronomy, VII, 299

V, 137

Wilcock, W. L., and Miller, D. E.:

Wild, J. P.: Observational radio

Williams, F. E. : Solid-state luminescence,

Willingham, D.: see Rindfleisch, T. Wilson, G . A.: see Morgan, B. L.


Wise, H. S., Richards, E. W. T., and Martin, R.: Digital read-out of an image intensifier using a vidicon or a scanning spiral slit plus a digital memory oscilloscope, XXVIII B, 981

WICrick, Gerard, and Grosse, Achilles: La camha electronique: un recepteur d'images sans lumikre diffusee, XXII A, 465

WICrick, G.: see Charier, Mlle S. Wlerick, G. : see Lallemand, A. Wlkrick, G. : see Rosch, J. Wlerick, G . : Etudes d'astres faibles en

lumiere totale avec la camera ilectronique, XXVIII B, 787

and Bellier, Mlle M.: La photographie electronique des planetes et ses applications photometriques, XVI, 371

Wlkick, G., Rosch, J., Dupre, Mlle M.,

Wolfgang, L. G.: see Abraham, J. M. Wolstencroft, R. D.: see Brand, P. W. J. L. Woodhead, A. W.: see Schagen, P. Woodhead, A. W.: see Stark, A. M. Woodhead, A. W., Taylor, D. G., and

Schagen, P. : A two-stage electrostatic image intensifier with a large photocathode area, XVI, 105

Woolgar, A. J. : see Slark, N. A. Woonton, G. A.: Relaxation in diluted

paramagnetic salts a t very low temperatures, XV, 163

Wreathall, W. M.: see Beurle, R. L. Wreathall, W. M.; Aberrations of diode

image tubes, M I 1 A, 583 Wynne, C. G., and Kidger, M. J . : The

design of optical systems for use with image tubes, XXVIII B, 759

Z

Zacharias, J. R.: see King, J. G . Zacharov, B. : Image resolution in thin-

window intensifiers using homogeneous fields, XVI, 67

Zacharov, B.: A demagnifying image tube for nuclear physics applications, XVI, 99

Zacharov, B., and Dowden, S . : An image intensifier with a thin end-window, XII, 31

Zalm, P. : Thermionic cathodes, XXV, 211 Zdanis, R. A.: see Reynolds, G . T. Zeitler, E.: Resolution in electron micro-

scopy, XXV, 271 Zimmermann, Bodo: Broadened energy

distributions in electron beams, XXIX, 257

Zucchino, P. M.: see Lowrance, J. L.

A

Cumulative Subject Index, Volumes 1-30

B

Accelerators linear ion, XXV, 1 particle, I, 269

Aids to navigation, electronic, I, 425 Airborne detector, magnetic, IV, 258 Alkali halide crystals, pre-breakdown

Amplification light emission from, XXII B, 995

of transient images, XII, 135 transmission secondary emission,

XVI, 557 Amplifiers

operational, XI, 225 quantum mechanical, XV, 73

Amplitude, pulse, analysis, VIII, 317 Amplitude measurement in nuclear

Analog computers, VII, 353 Antennae, endfire, XIX, 255 Astronometric images, camera tubes for

Astronomical

physics, VIII, 256

recording, XXII A, 175

observations, recent, obtained with Lallemand electronic camera, XVI, 341

converters, XII, 21

XVI, 383

XVI, 403

tests of barrier-membrane image

tests of imaging photomultiplier,

uses of image intensifying tubes,

Astronomy comparison of image intensifiers for,

image scanning techniques in, XVI, 409 observational radio, VII, 299 solar radio, XX, 147

Atomic collisions, XVIII, 67 Aurora borealis, IX, 1 Automatic data processing, XI, 185 Axial-beam tubes, XIV, 299

XXVIII B, 753

Barrier-membrane image converters, astronomical tests of, XII, 21

Beams deflection of, I, 167 high density electron, VIII, 363 magnetically focused cylindrical, X, 1 molecular, new applications and

techniques, VIII, 1 Beta-ray spectrometers, V, 97 Biological temperature measurements,

XXX, 235

C

Caesium vapor effects upon target glass, XXII A, 651 ;

getter materials for, XXVIII A, 381 reaction with gold, XXII A, 643

Cascade image intensifier, XXII A, 113 ;

XXVlII A, 309

XXVIII A, 89 astronomical uses, XXII B, 697 comparison with transmission secondary

emission type, XXII A, 129 dark current scintillations of, XXVIII B,

713 fibre-optic coupled, XXVIII A, 119 four-stage, characteristics of, XXII A, 87 influence of temperature on, XXII A, 101 magnetically focused, XVI, 113

Cascade image intensifier camera, for beam-foil spectroscopy, XXVIII B, 907

evaluation, XXII A, 407

ments, X, 239

Cascade phosphor-photocathode screens,

Cathode ray oscilloscopes, recent develop-

Cathode ray tube manufacture and design, 11, 2 progress, 11, 2 with electron-permeable window,

XXVIII A, 81

333

334 CUMULATIVE SUBJECT INDEX, VOLUMES 1-30

Cathodes oxide coated, I, 1 thermionic, XXV, 21 I

Cathodoluminescence, 11, 152 Cerenkov chamber, with four-stage image

intensifier, XXVIII B, 919 Cerenkov radiation, at microwave

frequencies, XIV, 265 Channel multiplier

for imaging applications, XXVIII A, 471 low-level performance of, XXVIII A,

problems concerning, XXVIII A, 499 vacuum space charge in, XXVIII A, 507 x-ray detection by, XXII A, 139

Channelled image intensifier, XII, 97 progress report on, XVI, 155

Characteristic energy losses, of electrons

Charge integration experiments, XII, 21 9 Charge particle beams, deflection of, I, 167 Cluster ions, in laboratory and iono-

Collisions, inelastic, between atomic

Color television, recent work in, V, 291 Combination frequencies, in plasma, 187 Communication theory, 111, 306 Computer logical organization, X, 153 Computer organization, recent develop-

Computers,

487

in solids, VII, 183

sphere, XXIX, 79

systems, XIII, 1

ments in, XVIII, 45

analog, VII, 363 electronic digital, IV, 157

Conduction, metallic, at high frequencies and low temperatures, VI, 1

Conductivity, electron bombardment induced, XVI, 235

Continuous-wave magnetrons, modulation of, IV, 188

Contrast-enhancement, in imaging devices XXVIII B, 661

Cosmic radio noise, I, 347 Cosmic rays

and image intensifier dark current,

intensity variations in, IX, 129 XXVIII B, 705

Coude spectrograph, performance of

Counter, scintillation, IV, 69 image tubes in, XXII B, 729

Crystals electron-beam investigating of, XXIV,

magnetic properties of, XXIV, 109 Currents, space-charge-limited, VI, 138 Cylindrical beams, nonuniform D-C

electron flow in, X, 1 Cylindrical magnetron, electronic theory

of, 11, 15

109

D

Data processing, automatic, in physical sciences, XI, 185

D-C electron flow, nonuniform, in magnetically focused beams, X, 1

Defects in diamond-type semiconductor crystals, X, 71

Deflection of beams of charge particles, I , 167

Design of cathode ray tubes, 11, 26 Detective quantum efficiency, of intensi-

fiers, XXVIII B, 577 Detector, magnetic airborne, IV, 258 Detectors

for visible and infrared radiation, V, 1 quantum efficiency of, XI, 87

Developments, image intensifier, XII, 41 Dielectric breakdown in solids, intrinsic,

Digital computers, electronic, IV, 157 Digital memory oscilloscope, XXVIII B,

Diode image tubes, aberrations of,

Discharges, electrical, in gases, VII, 401 Distribution of electrons, XV, 265

11, 185

981

XXII A, 583

E

Efficiency contrast transfer function, of intensifiers, XXVIII B, 577

Ejection, kinetic, of electrons from solids, XXI, 101

Electroluminescence, XVI, 621 Electromechanical picture signal generating

device, XXVIII A, 297 Electron as a chemical entity, XIV, 1

CUMULATIVE SUBJECT INDEX, VOLUMES 1-30 335

Electron beams broadened energy distributions,

dense, analysis of, XXVI, 1 high density, VIII, 363 polarization of, XXI, 1

XXIX, 257

Electron bombardment induced conductivity

image devices working on, XXII A, 323 properties of, XXIIA, 315

Electron diffraction structure analysis,

Electron emission microscopy, XVIII, 251 Electron emission, secondary, I, 66;

XI, 413 Electron flow, in magnetically focused

beams, X, 1 Electron guns, for high density electron

beams, VIII, 363 Electron image, direct recording, using

thin windows, XXII A, 51 Electron image multiplier, XII, 87 Electron image store and analyser,

XXII B, 969 Electron interaction, space-harmonic

traveling-wave, XVII, 1 Electron lenses, 11, 48 Electron microscope, VI, 269; XII, 317 Electron microscopy, resolution in,

Electron mirror microscopy, XXVI, 217 Electron multiplication, secondary image

Electron optics

XI, 355

XXV, 277

intensifiers, XVI, 127

field plotting and ray tracing in, 11, 102 scalar diffraction in, XXX, 139

Electron probe microanalysis, XIII, 3 17 Electron scattering, in solids, IV, 2; VII,

183 Electron spin resonance, in mineralogy and

geology, XXIV, 51 Electron streams, velocity distribution in,

XIII, 181 Electron tubes, for high-speed photo-

graphy, XVI, 249 Electronic aids to navigation, I, 425 Electronic camera, XVT, I , 19

diffused light in, XXII A, 465 electrostatically focused, in physics and

astronomy, XXVIII A, 27

focusing with cylindrical lens,

for enlargement 1/7, XVI, 27 for space research, XXVlII A, 39 in astronomical spectroscopy, XXII B, 761 in double-star photography, XXII B, 755 infra-red application of, XXII A, 1 in study of photoelectric emission,

new technique for utilization of,

photography of double stars by means

relation to standard photography,

study of weak stars, XXVIIl B, 787 Electronic devices, gaseous, comparison

with semiconductors, VI, 257 Electronic imaging, limitations to resolv-

ing power in, XVI, 299 Electronic photography, of planets,

Electronic theory

XXII A, 609

XXII A, 519

XVI, 19

of, XVI, 357

XXII A, 5

XVI, 371

of cylindrical magnetron, 111, 15 of plane magnetron, 111, 185

Electronic zooming, XVI, 195 Electronics

and the blind, XX, 261 contributions to seismology and

geomagnetism, IX, 297 in oceanography, IX, 239 modern, and electrical discharges

in gases, VII, 401 modern vacuum pumps in, V, 21 3 thorium oxide and, V, 169

Electronographic camera, large-image, XXVIII A, 19

Electronographic emulsions, linearity of, XXVIII B, 731

Electronographic plate, bakeable, advantages of, XVI, 35

Electron-optical deflexion and storage techniques, XXII B, 985

Electron-optical systems, imaging properties of, XXVIII A, 523

Electrons and ions, low energy, atomic collisions

involving, XVIII, 67 as hydrodynamical fluid, XX, 1 distribution of, in ionosphere, XV, 265


Electrostatic image intensifiers, application to astronomy, XXVIII B, 807

Electrostatic lenses, reducing defects in imaging devices using, XXII A, 601

Emission field, 111, 1 ; VIII, 90; XII, 73 transmission secondary, XIT, 59

Emitron, C. P. S., charge integration experiments with, XII, 219

Endlire antennae, XIX, 255 Energy conversion, thermionic, XVII, 125 Energy losses, of electrons in solids, VII,

Evaluation, semiconductor device, XVIII,

Evaporation, impact, in glow discharge,

Evoscope, fixed pattern generator,

183

167

XVII, 245

XXII A, 331

F

Ferrites, physical properties of, VI, 70 Ferromagnetic phenomena at microwave

frequencies, 11, 251 Ferromagnetism, relaxation processes in,

VI, 47 Field-effect image storage panels,

XXVIII B, 1059 Field emission, VIII, 90

in image tubes, XII, 73 microscopy, 111, 1

Field ionization, XIII, 83 Field ion microscopy, XIII, 83

image intensification in, XXII B, 903 Field plotting, in electron optics, 11, 102 Filament scintillation chamber, XVI, 487 Flame plasmas, XX, 99 Fluctuation phenomena, IV, 110 Fluoroscopy, medical, image quality in,

FM broadcast band, propagation in,

Focused cylindrical electron beams,

Focusing for high density electron beams,

Free atoms, lifetimes of, XXIX, I15 Frequency standards, atomic beam, XV, 1

XXII A, 363

I, 381

magnetically, X, 1

VIII, 363

Frequencies high metallic conduction at, VI, 1 microwave, XIV, 265

Functional electrical stimulation of extremities, XXX, 283

G

Gallium arsenide, thin-film photocathodes,

Gases, electrical discharges in, VII, 401 Gaseous electronic devices, VI, 257 Geomagnetism, contributions of elec-

Germanium, electrical properties of,

g-factor anomaly, of free electrons, XXI, 1 Glass scintillators

XXVIII, 399

tronics to, IX, 297

VII, 87

applications of, XVI, 547 properties of, XVI, 547

Glow discharge, impact evaporation and

Grating storage target, XXII A, 155 Guns, electron, high density, VIII, 363

thin film growth in, XVII, 245

H

Hale 200-in. telescope, image-tube

Hall effect, and applications, XXV, 97 Harmonic generation

in nonlinear beam plasma systems, XXIX, 1

in plasma, XXVII, 187

spectrograph for, XXVIII B, 767

n-Hexane, pre-breakdown using image intensifier, XXII B, 1003

High density electron beams, VIII, 363 High frequencies, metallic conduction

High-gain image intensifier, XII, 135 at, VI, 1

and field-ion microscopy, XXVIII B, 875 increasing storage capacity, XXVIII B,

745 High-power tubes, XIV, 299 High-speed photography

electron store and analyser application

image orthicon in, XXII B, 101 1 to, XXVIII B, 101 1

Hydrodynamical fluid, XX, 1 Hydrogen thyratrons, XIV, 207


I

Image amplifiers, solid state, recent

Image converter(s) developments in, XVI, 607

barrier-membrane, astronomical tests

boundary layer, XVI, 633 electrostatically focused, XXII A, 441 solid state, applications of, XVI, 613 solid state fast response, XXII B, 683

astronomical uses, XVI, 451

signal-to-noise ratio of, XII, 291 spatial frequency response of, XXII A,

of, XII, 21

Image detectors, photoconductive, for

Image devices

425 Image intensification, XII, 327

Image intensifier(s) low brightness photography by, XVI, 85

application to gas discharges,

application to luminescent chamber,

channeled, XII, 97; XVI, 155 developments of, XII, 41 digital read-out of, XXVIII B, 981 electrostatic, two-stage, XVI, 105 electrostatic zoom, XXVIII A, 537 for electron microscope, XII, 317 high gain, astronomical research utili-

zing, XXII B, 705 information transfer with,

XXVIII B, 615 in astronomy, XXIII, 347 magnetically focused cascade, ex-

periences with, XVI, 119 multi-stage, XVI, 567 observation of Cerenkov Ring with,

XXII B, 801 for observation of rapid luminescence

phenomena, XXII B, 949 for track recording, XVI, 11 3 in scanning radioactive objects, XXII B,

secondary emission, XII, 59 sensitivity of, XXII A, 381 thermal-neutron, XXII B, 781 transmission, XVI, 141 use of, in nuclear physics, XVI, 501

XXVIII B, 1033

XII, 153

941

visual performance at low light,

wire-electrode type, experiments on,

with fiber-optic coupling, XXVIII A, 105 with streamer chambers, XXII B, 813 with thin end-window, XII, 31 with transmitted secondary electron

x-ray, XII, 379

XXVIII B, 635

XVI, 621

multiplication, XVI, 127

some experiences with, XVI, 601 Image intensifier system, XVI, 75, 475 Image intensifying tubes, astronomical

Image isocon tube, XXVIII B, 827 Image multiplier, electron, XII, 87 Image orthicon@), XVI, 447, 581

uses of, XVI, 403

applications to astronomy, XXII B, 713 bombardment-induced conductivity

comparison of SEC camera tube and,

stellar photometry with, XVI, 431 using slow readout, XVI, 419 with magnesium oxide targets, XVI, 213

Image recording, comparison of efficiency,

Image scanning in astronomy, potenti-

Image storage techniques, XVI, 593 Image transducers, low energy quanta,

Image tube(s)

targets for, XVI, 247

XXII A, 291

XXVIII B, 725

alities and limitations of, XVI, 409

XXII A, 189

analysis of, XXVIII B, 603 computation of imaging properties,

demagnifying, for nuclear physics

field emission in, X I , 73 for high-speed photography, XXVIII B,

989 high-resolution, for integrated circuit

fabrication, XXVIII A, 47 intensifier, evaluation, XXII A, 369 laboratory evaluation, for astronomical

purposes, XVI, 391 Lallemand, modified, XVI, 25 Lenard window, XVI, 47

XXVIII A, 535

applications, XVI, 99

for astronomical spectrophotometry, XXII B, 741


low background, for electronography,

magnetic focusing of, XXII A, 617 modulation transfer function of,

orthicon, XII, 379 proximity-focused, XXVIII A, 129 research, XII, 17 resolving power of, XXVIII B, 553 signal generating, XII, 307 storage

application of, XII, 31 1 experimental, XII, 247 for character recognition, XXVIII B,

for optoelectronic computing,

Image-tube Fourier spectrograph,

Image tube high-speed cameras, XXII B,

Images, transient, in high-gain photo-

XVI, 37

XXVIII B, 567

1043

XXVIII B, 1051

XXVIII B, 899

957

cathode-phosphor intensifier systems, XII, 135

Inelastic collisions, XIII, 1 Infra-red converters, XXVIII B, 1087 Infrared radiation

detectors, V, 1 quantum efficiency of, XI, 87

Infra-red stellar spectroscopy, with mica- window tube, XXII B, 723

Infra-red television camera tube, XII, 263 Instrumentation, electronic, for

oceanography, XIX, 1 Insulators, low density deposits of, XVI,

145 Intensifier orthicon, performance of,

XII, 183 Intensifier tube, single-crystal,

XXVIII B, 931 Intensifiers, thin window image

resolution in, XVI, 67 with phosphor output, XVI, 61

Intensity variations, in cosmic rays, IX,

Interactions, weak, parity nonconservation

INTIC, image storage tube, XXVIII A, 137 Intrinsic dielectric breakdown in solids,

129

in, XI, 31

11, 185

Ion bombardment, sputtering by,

Ion microscopy, field, XIII, 83 Ion scattering, against metal surfaces,

Ionization, field, XIII, 83 Ionosphere, radio wave scattering in,

Ionospheric research, I, 317 Ions

lifetimes of, XXIX, 11 5 negative, IX, 43 “small ” multimolecular atmospheric,

VII, 239

XXI, 67

XIX, 55

XIX, 177 Isophate converter, XII, 307

K

Kodak Ha-0 emulsion, comparison of image recording with, XXVIlI B, 725

L

Lallemand electronic camera in astronomical observation, XII, 113;

Lellemand image tube, modified, XVI, 25 Large-scale integrated circuits, failure in,

Lead monoxide, electron bombardment induced conductivity in, XXII A, 305

XVI, 341

xxx, 79

Lenses electron, 11, 48 strong-focusing, XIV, 85

ment of, XXII A, 59

XXVIII A, 151

Lick-Stromlo electronic camera, develop-

Light amplifier, with high light output,

Linear ion accelerators, XXV, I Low background image tube, XVI, 37 Low density deposits, transmission secon-

dary emission from, XVI, 145 Low energy electron physics, swarm

techniques in, XXVII, 1 Low light levels, direct observation, image

intensifier for, XVI, 75


Low temperatures, metallic conduction at, VI, 1

Luminance gain, of image intensifier systems, XXVlIl B, 629

Luminescence, solid-state, V, 137 Luminescent chamber, X11, 153

high energy physics experiments, XVI, 513

M

Magnetic airborne detector, IV, 258 Magnetic beta-ray spectrometers, XXX, 43 Magnetic coherence resonances, at zero

Magnetic-core memory technology, high-

Magnetic fields, measurement of by

Magnetic focus systems

frequency, XXVII, 19

speed, XXI, 249

magnetic resonance, XXIII, 39

aberrations in, XVI, 333 photocathode resistance on resolution

of, XXII A, 591 Magnetically focused electron beams, X, 1 Magnetron

continuous-wave, modulation of, IV, 188 cylindrical, electronic theory of, 111, 15 microwave, 11, 220 mode transitions, VIII, 503 plane, electronic theory of, 111, 85 steady state theory of, V, 247

Manufacture of cathode ray tubes, 11, 2 Mariner IV spacecraft television system,

Masers, XV, 73 Mass spectroscopy, I, 219; VIIJ, 188

using RF quadrupole fields, XXVII, 59 Medical scintillation cameras, image

intensifying for, XXII B, 927 Memory technology, high-speed magnetic-

core, XXI, 249 Metal-insulator-metal structure, photo-

emission from, XXVIIl A, 409 Metallic conduction, at high frequencies

and low temperatures, VI, 1 Metal surfaces, ion scattering against,

XXI, 67

XXII B, 849

Meteors, radio observation of, IX, 95 Mica, electron transmission through,

XXII A, 31 ; XXII A, 41 Microanalysis, electron probe, XIII, 317 Microphotometer, for photographic and

electronographic image tubes, XXII A, 435

Microscope, electron, VI, 296; XII, 317 Microscopy

electron emission, XVIII, 251 field emission, 111, 1 field ion, XIII, 83 scanning electron, XXI, 181

Microwaves, plasma generation and

Microwave frequencies, amplification of, XXI, 287

Cerenkov radiation at, XIV, 265 ferromagnetic phenomena at, 11, 251

Microwave magnetron, 11, 220 Microwave optics, X, 107 Microwave spectroscopy, 11, 300 Millimeter wave techniques, XV, 197 Miniaturization, tube, 11, 183 Modulation

of continuous-wave magnetrons, IV, 188 pulse code, 111, 221

of fluorescent screens, XXII A, 395 of image tube, XXVIII B, 567 of x-ray image intensifiers, XXII A, 355

Modulation transfer function

Molecular beams, new applications and

Molecular hydrogen, in interstellar

Molecules, lifetimes of, XXIX, 115 Multialkali photocathodes, crystal

structure of, XXVIlI A, 337 Multichannel radio telemetering, IV, 301 Multidynode electron multipliers, single

electron pulse sizes from, XXII A, 71

foils to, XXII A, 635

electron, XXlI A, 629

techniques, VIII, 2

medium, XXVIII R, 801

Multi-MeV electrons, response of KCI

Multiplication, transmitted secondary

Multiplier electron image, XII, 87 with forty channels, XXVIII B, 955

Multisignal effects, in nonlinear beam plasma systems, XXIX, I


N

Navigation, electronic aids to, I, 425 Negative ions, IX, 43 Network synthesis, methods of, 111, 261 Nightglow, XVIII, 1 Noise, cosmic radio, I, 347 Nonconservation, parity, in weak inter-

actions, XI, 31 Nuclear physics

VIII, 256 amplitude and time measurements in,

demagnifying image tube for, XVI, 99 image intensifiers in, XVI, 501

Numerical field plotting, and ray tracing, in electron optics, 11, 102

0

Observation(s) astronomical, photo-electronic imaging

of meteors, radio, IX, 95 devices for, XII, I

Observational radio astronomy, VII, 299 Oceanography

electronic instrumentation for, XIX, 1 electronics in, IX, 239

Operational amplifiers, XI, 225 Optical diffraction patterns, XII, 311 Optical images, low contrast, detection of,

Optical systems, for image tubes,

Optical television methods, XII, 363 Optics

XII, 247

XXVIII B, 759

electron, 11, 102 microwave, X, 107

Oscillations, plasma, XX, 59 Oscilloscope, cathode ray, X, 239 Oxide-cathode receiving tubes, electrical

Oxide coated cathodes, I, 1 life of, VII, 404

P

Paramagnetic resonance, XV, 327 Paramagnetic salts, diluted, relaxation in,

Paramagnetism, VI, 463 XV, 163

Parity nonconservation, in weak inter-

Particle accelerators, I, 269; XXIX, 223 Penning discharges, XXVII, 295 Phosphor output, thin window image

intensifier, XVI, 61 Phosphor screens, high resolution,

XXII A, 551

571

actions, XI, 31

for cascade image intensifiers, XXII A,

preparation of, XXII A, 565 Photocathode composition, study of,

Photocathode sensitivity, decay of,

Photocathode surfaces, research on,

Photocathode(s)

by microbalance methods, XVI, 329

XXVIII A, 357

XXII A, 477

Sb-Rb-Cs, XXII A, 449 Cs-Sb and Na-K-Sb, micro-

balance study, XXII A, 459 image dissector in, XXII A, 507 improvements for pulse operation,

interference, XXVIII A, 419

near infra-red spectral response,

new technology for transferring,

per-formed introduction into vacuum

properties of, liberated in high vacuum,

reflective, image intensifier system using,

research in Czechoslovakia, XXVlII A,

responsive quantum efficiency of,

S -20, and fibre optic plates, XXVIII A,

time response of, XXII A, 499 Photoconductive image converter, electron

optics of, XXVIII A, 545 Photoconductive image detectors, elec-

tronically scanned, potentialities of, XVI, 451

MI, 345

XXVIII A, 375

for image tubes, XXVIII A, 433

XXII A, 493

XXVIII A, 367

systems, XVI, 325

XVI, 5

XXVIII A, 443

323

XXII A, 535

461

Photoconductive tube, x ray sensitive,


Photoconductivity, problems of, XIV, 37 Photoelectric image devices, survey of

Photo-electronic imaging devices, poten-

Photo-electronic storage tube, experiments

Photoemission

work on, XVI, 311

tialities of, XII, 1

with, XII, 235

at long wavelengths, XXVIII A, 393 recent advances in, XI, 1

Photoemissive devices, solid-state applica-

Photographic images, recorded with image

Photography

tion, XXII B, 671

intensifiers, XXVIII B, 589

astronomical, television methods, XII, 195

electronic, XII, 5 high-speed, electron tubes for, XVI, 249 low brightness, by image intensification,

of double stars, by electronic camera,

of extensive air showers, in atmosphere,

XVI, 85

XVI, 357

XVI, 531 Photometric applications, and electronic

photography of planets, XVI, 371 Photomultiplier, imaging, astronomical

tests of, XVI, 383 Photon counters, position-sensitive,

XXVIII B, 965 Photon interference, XXVIII B, 939 Physical properties, of ferrites, VI, 70 Pick-up tube@)

XVI, 217 infra-red vidicon-type, development of

television, I, 131 with linear light transfer, XXVIII A, 281

Picture resolution, figure of merit measuring, XXII A, 341

Plane magnetron, electronic theory of, 111, 85

Plasma flame, XX, 9 for generation and amplification of

harmonics and combination frequencies microwaves, XXI, 287

in, XXVII, 187 Plasma oscillations, XX, 59 Plasma turbulence, experimental, XXX, I

Plasmas, radio-frequency confinement and acceleration of, XXIII, 153

Propagation in the FM broadcast band, I, 318 tropospheric, XX, 199

Pulse amplitude analysis, VII, 317 Pulse code modulation, 111, 221

Q

Quadrature spatial-frequency Fourier analyser, XXVIII B, 653

Quantum efficiency of detectors, XI, 87 Quantum mechanical amplifiers, XV, 73

R

Radar applications, bright displays for,

Radiation XVI, 265

detectors for, V, 1 far-infrared, generation of, XXVI, 171

Radio astronomy, observational, VIl, 299 Radiology

diagnostic, image orthicon in, XVI, 581 image storage techniques applied to,

XVI, 593 Radio noise, cosmic, I, 347 Radio observation, of meteors, IX, 95 Radio telemetering, XI, 287

Radio-wave propagation, IX, 187 Ray tracing, in electron optics, 11, 127 Receiving tubes, oxide-cathode, electrical

life of, VIII, 404 Reflex discharges, XXVII, 295 Relaxation, in diluted paramagnetic salts,

R F quadrupole fields, mass spectroscopy

multichannel, IV, 301

XV, 163

using, XXVII, 59

S

Scalar diffraction, in electron optics,

Scattering XXX, 139

electron, in solids, IV, 2; VIII, 183


radio wave, in ionosphere, XIX, 55

to low energy, XXVIII A, 451

application to space research, XVI, 535 fibers versus NaI, XVI, 469 image intensifiers versus orthicons,

in space research, XXIIB, 823 Scintillation counter, IV, 69 Scintillation detector, statistical

SEC camera tube

Scintillation, in CsI(Na) and CsI(Tl), due

Scintillation chambers

XVI, 469

behavior of, XXVI, 251

and image orthicon, comparison, XXII A, 291

application to astronomy, XXVIII B, 807

optically scanned, XXII A, 241 Secondary electron conduction, and

photoelectronic image devices, XXII A, 219

Secondary electron emission, I, 66; XI, 413 SEC target, XXII A, 229

point-source imaging with, XXII A, 251 Seismology, contributions of electronics,

Semiconducting materials, investigation

Semiconductor crystals, diamond-type,

Semiconductor device@)

JX, 297

of, XI, 355

defects in, X, 71

comparison with gaseous electronic devices, VI, 257

evaluation, XVJII, 167 noise in, XXIII, 303

Semiconductor materials, physics of, VII, 1 Semiconductors, Type 11, XXIII, 1 Shutter tubes, gas discharge application,

Signal-to-noise ratio, XU, 277, 291 ; XXVIII B, 1033

XXVIII B, 577 with S -1 photocathodes, XXVIII B, 677

Silicon, theory of electrical properties,

Silver-magnesium alloy dynodes, in water

Single electron pulse sizes, distribution of,

Single-stage image converter,

VII, 87

vapour, XXII A, 661

XXII A, 71

photography, XXVIII B, 999

Skeletal control systems, XXX, 273 " Small " multimolecular atmospheric ions

bioclimatic action of, XIX, 177 measurement of, XIX, 177 properties of, XIX, 177

to, XVI, 447 Solar photometry, image orthicon applied

Solar radio astronomy, XX, 147 Solid state image amplifiers, XVI, 607 Solid state image converters, XVI, 613

infra-red, XXVIII B, 1073 Solid-state luminescence, V, 137 Solid state radiographic amplifiers,

Solids XXVIII B, 1087

characteristic energy losses of electrons

electrical breakdown in, XXVI, 309 electron scattering in, IV, 2 intrinsic dielectric breakdown in, 11, 185 kinetic ejection of electrons from, XXI,

secondary electron emission from,

Space-charge-limited currents, VI, 138 Space harmonic traveling wave electron

in, VIII, 183

101

XI, 413

interaction, general perturbational theory of, XVII, 1

chambers, XVI, 535 Space research, application of scintillation

Spectracon comparison of image recording with,

electronographic image recording tube,

electron transmission through mica and,

further developments of, XXVIII A, 61 in astronomical spectroscopy,

XXVIII B, 773 recent astronomical applications,

XXVIII B, 783 Spectrograph, high-gain, for simulated

re-entry, XXVIII B, 1021 Spectrometers, beta-rap, V, 97 Spectroscopy

XXVIII B, 725

XXII A, 1 1

XXII A, 31

mass, I, 129; VIII, 188 microwave, 11, 300 time resolved interference, XXII B, 985

Sputtering, by ion bombardment, VII, 239


Steady-state theory of magnetron, V, 247 Stellar photometry, XVI, 431 Storage tube(s)

photo-electronic, XII, 235 viewing, VIII, 448

Striations, moving, XXIV, 155 Strong-focusing lenses, XIV, 85 Structure analysis, electron diffraction,

Subminiaturization techniques, 111, 195 XI, 355

T

Target glass, effects of caesium vapour on,

Target@) XXVlIl A, 309

conductivity, bombardment-induced,

lead sulphide, XVI, 217 magnesium oxide, XVI, 213

multichannel, IV, 301 radio, XI, 287

at low light-levels, XXVIII B, 837 closed-circuit, and field-ion microscopy,

Television camera noise, measurement of,

Television camera tube, XII, 203;

for image orthicons, XVI, 247

Telemetering

Television

XXVIII B, 875

XXVIII A, 289

XXVIII A, 265 a review, XIII, 387 infrared, XII, 263 using potassium chloride target,

XXII A, 273 x-ray sensitive, XXVIII A, 273

Television channels, experiences with, XVI, 601

Television color, V, 291 Television methods, optical, XII, 363 Television photometer, XXVIII B, 891 Television pickup tube(s), I, 131

electronic zooming with, XVI, 195 image orthicon effect in, XVI, 171 minimizing black-border effect in, XVI,

171

XXVIII B, 851 Television sensors, for space astronomy,

Television storage tubes, signal-to-noise

Television system ratio in, XII, 277

for satellite-borne ultra-violet photo-

for stratoscope use, XXII B, 885 for ultra-violet astronomical photo-

meter, XXII B, 865

metry, XXII B, 875 Tenicon, high resolution information

storage tube, XVI, 287 Thermal energy ion-molecuIe reactions,

XXIV, 1 Thermal image detection, infra-red

threshold in, XXVIII B, 685 Thermionic cathodes, XXV, 211 Thermionic energy conversion, XVII, 125 Thermoelectricity, XVII, 207 Thin film growth, in glow discharge,

Thorium oxide, and electronics, V, 169 Thyratrons, hydrogen, XIV, 207 Time measurements, in nuclear physics,

Track recording, image intensifier for,

Transmission secondary emission, XVI,

XVII, 245

VIII, 256

XVI, 113

145 amplification, recent, XVI, 557 image intensifier, XII, 59; XVI, 141 statistics, XXVIII A, 513

Transmission secondary image intensifiers, comparison with cascade type, XXII A,

performance of, XXIIA, 63 129

Transistor applications, junction, V, 367 Transitions, at zero frequency, XXVII, 19 Traveling wave tubes, VI, 372 Trialkali Sb-K-Rb-Cs photocathode,

properties of, XXVIII A, 347 Tropospheric propagation, XX, 199 Tube miniaturization, 111, 183 Tube reliability, X, 185 Tube@)

axial-beam, high-power, XIV, 299 image, XII, 73 image converting, XVI, 91 image intensifier, multipactor principle,

image orthicon, XII, 379 infra-red television camera, XII, 263

XVI, 163


photoconductive pickup, XII, 345 television camera, XIII, 387

television pickup, I, 131; XVI, 171 television storage, XII, 277 traveling wave, VI, 372 velocity modulated, 111, 43 x-ray, XII, 327

C. P. S. Emitron, XII, 203

U

Ultrahigh vacuum, XVII, 323 Ultra-violet camera tubes, incorporating

Ultra-violet imaging, electron bombard- SEC, XXII A, 261

ment conductivity application, XVI, 235

Ultra-violet sensitive vidicon, XVI, 227 U.S. Navy electronic camera, XXVIII A, 1

v

Vacuum breakdown, high speed photographic study of, XXVIII B, 1041

Vacuum pumps, in electronics manufacturing, V, 213

Vacuum systems, preformed photocathode introduction into, XVI, 325

Velocity distribution, XIII, 181 Velocity modulated tubes, 111, 43 Vidicon

digital read-out of image intensifier

high-resolution ruggedized half-inch,

interplanetary imaging device,

using, XXVIII B, 981

x x I r A, 21 I

XXII B, 835

ultra-violet sensitive, improved, XVI, 221

Viewing storage tubes, VIII, 448 Visible radiation

detectors, V, 1 quantum efficiency of, XI, 87

Vision, problem of, I, 121 VLF electromagnetic waves, terrestrial

propagation of, XXV, 145

W

Wave techniques, millimeter, XV, 197

X

X-ray image intensification, XII, 363; XVI, 567

developments on, XVI, 91 X-ray image intensification system, for

X-ray image intensifier, X I , 379 X-ray image intensifiers, moving

X-ray sensitive photoconductive pick-up

X-ray tube, flying-spot, XII, 327

x-ray microscope, XXII B, 919

structures with, XXVIII B, 647

tube, XII, 345

Z

Zero frequency magnetic coherence resonances at,

transitions at, XXVII, 19 XXVII, 19

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