SWITCHING IN SEMICONDUCTOR

DIODES

MONOGRAPHS IN SEMICONDUCTOR PHYSICS

Volume 1: Heavily Doped Semiconductors

by Viktor I. Fistul'

Volume 2: Liquid Semiconductors

by V. M. Glazov, S. N. Chizhevskaya, and N. N. Glagoleva

Volume 3: Semiconducting II-VI, IV-VI, and V-VI Compounds by N. Kh. Abrikosov, V. F. Bankina, L. V. Poretskaya,

L. E. Shelimova, and E. V. Skudnova

Volume 4: Switching in Semiconductor Diodes

by Yu. R. Nosov

In preparation: Semiconducting Lead Cbalcogenides

by Yu. I. Ravich, B. A. Efimova, and I. A. Smirnov

Organic Semiconductors and Biopolymers by L. I. Boguslavskii and A. V. Vannikov

SWITCHING IN SEMICONDUCTOR

DIODES Yurii R. Nosov

A. F. Ioffe Physicotechnical Institute Leningrad, USSR

Translated from Russian by

Albin Tybulewicz Editor, Soviet Physics-Semiconductors

Springer Science+Business Media, LLC • 1969

Yurii Romanovich Nosov was born in 1931, in Moscow. He gradu­ated in 1954 from the Physics Department of the M. V. Lomonosov State University in Moscow. Since graduation, he has been engaged in research on, and the design of, fast-response semiconductor pulse diodes. In 1964, Nosov was awarded the degree of Candidate of Technical Sciences by the A. F. Ioffe Physicotechnical Institute in Leningrad. In 1965, he was promoted to the rank of senior scientist in the specialty of electronic technology and devices. He is a mem­ber of the All-Union Society "Znanie," the A. S. Popov Scientific and Technical Society for Radio Engineering and Electrical Communi-

cations, and of the ''Trud'' Sporting Association.

The original Russian text was published by Nauka Press, Moscow, in 1968 as part of a series on "Physics of Semiconductors and Semi­conducting Devices" and has been revised by the author for this

English edition.

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FIZICHESKIE OSNOVY RABOTY POLUPROVODNIKOVOGO DIODA V IMPUL'SNOM REZHIME

ISBN 978-1-4899-6172-3 ISBN 978-1-4899-6343-7 (eBook) DOI 10.1007/978-1-4899-6343-7

Library of Congress Catalog Card Number 69-12535

© 1969 Springer Science+Business Media New York Originally published by Plenum Press, New York in 1969.

Softcover reprint of the hardcover 1st edition 1969

All rights reserved

No part of this publication may be reproduced in any form without written permission from the publisher

Preface to the American Edition

It gives me great pleasure to learn that this book, whose ori­gin owes much to the work of American scientists and engineers on semiconductor technology. will reach American and other English­speaking readers.

I am grateful to Plenum Publishing Corporation for arranging the American edition of this book and to Mr. Albin Tybulewicz for his translation.

September 5, 1968 Yu. R. Nosov

v

Preface to the Russian Edition

One of the most important applications of semiconductor diodes is their use in electronic pulse circuits.

The response of these diodes under switching conditions is governed by the phenomena of accumulation and dispersal of non­equlibrium carriers, which are also observed in other p-n junction devices.

It was found in the late 1940's that when point-contact ger­manium diodes were used in circuits through which short (several tenths of a microsecond) electrical pulses were being passed, the effective reverse resistance of these diodes decreased considerably below the static value. Further studies showed that when a diode was switched rapidly from the forward to the reverse direction, an anomalously large reverse current flowed for some time.

In view of the importance of this phenomenon in the efforts to reduce the response time of pulse circuits, many investigations of the phenomenon were carried out and these investigations pro­vided the basis of a theory of transient processes in semiconductor diodes.

It was established that the rate of dispersal of nonequilibrium carriers, accumulated in the diode base, is governed by the proper­ties of the diode itself, as well as by the switching conditions. This made it possible to reduce the response time of the diodes and to develop methods for the determination of the optimal opera­ting conditions of these devices in pulse circuits. Later it was found that this theory of transient processes had other important applications, in addition to its usefulness in reducing the response time of diodes and of pulse diode circuits.

vii

viii PREFACE TO THE RUSSIAN EDITION

This theory has served as the corner-stone of the studies of the processes of the accumulation and dispersal of excess charges in transistors and thyristors and, through its application, the upper frequency limit of these devices has been increased. Secondly, the theory has stimulated the development of such new devices as charge-storage diodes and some special types of varactor for fre­quency multiplication.

The development of the theory of transient processes in diodes has made it possible condiderably to extend investigations of re­laxation processes in semiconductors under nonequilibrium condi­tions, in particular, the recombination of nonequilibrium carriers.

The main purpose of this book is to acquaint the reader with the physical basis of the operation of a semiconductor diode under pulse conditions, and to give, whenever possible, quantitative rela­tionships describing transients in diodes.

The variety of various possible switching conditions in cir­cuits is practically infinite and, therefore, it has not been possible to discuss all the conditions. Instead, a description is given of the most general mathematical methods for solving the equations des­cribing transient processes, and these methods are presented in such a way as to enable the reader to analyze those pulse conditions which are not discussed in this book.

A model of a planar diode with a semi-infinite base is dis­cussed in the greatest detail. This is done because the basic for­mulas for this model are the simplest and clearest; moreover, the most important relationships obtained for the planar diode are found to apply approximately to other diodes.

Problems associated with the application of the theory of transient processes in the practical design of fast-response diodes and of circuits incorporating such diodes are not discussed in this book; readers interested in the design aspects are directed to spe­cialist texts on this subject [62,103,166].

The list of references is reasonably complete but it does not cover fully all the numerous applications.

For convenience, the symbols used are explained in the text and are also collected together in a separate list.

PREFACE TO THE RUSSIAN EDITION ix

The author is grateful to Candidate of Technical Sciences L. S. Berman for reading the manuscript and for his valuable ad­vice; to Candidate of Technical Sciences O. K. Mokeev for discuss­ing some of the problems condidered in this book; and to L. V. Gu­byrin and L. A. Kuranova for their help in writing Chapter III and selecting the literature relevant to this chapter. The author is much indebted to 1. S. Egorova without whose help in the prepara­tion of the manuscript this book would not have been published.

Contents

Notation ........................... . xiii

CHAPTER 1. Basic Electronics of the Switching Processes in Semiconductor p-n Junctions. . . . . . . . . 1

§1. Introduction.. . . . . . . • . . . . . . . . . . . . . . . . . . 1 §2. Transformation of Basic Equations. . . . . . . . . . . 4 §3. Solution of the Diffusion Equation (at Low

Injection Levels) .. . . . . . . . . • • . . . . . . . . . . . 10

CHAPTER II. Switching in a Planar Diode. . . . . . . . . 25

§4. Transient Processes without a Limiting Resistance in the Diode Circuit ............. 25

§5. Switching of a Diode Circuit with a Limiting Resistance. . . . . . . . . . . . . . . . . . . . . 38

§6. Switching of a Diode Circuit with an Infinite Resistance . . . . . . . . . . . . . . . . . . . . .. 53

§7. Small-Signal Transient Characteristics of a Diode. . . . . . . . . . . . . . . . . . . . . . . . . . .. 66

§8. Methods for the Observation of Transient Processes in Diodes. . . . . . . . . . . . . . . . . . . . . 69

§9. Main Experimental Results . . . . . . . . . . . 82

CHAPTER III. Planar Diode with a Thin Base. . . . . 96

§10. Steady-State Distribution of Holes in the Base. . . . . . . . . . . . . . . . . . . . . . . . . 96

§11. Switching without a Resistance in the Diode Circuit. . . . . . . . . . . . . . . . . . . . . . . .. 107

§12. Switching in a Circuit with a Limiting Resistance .......................... 118

§13. General Estimate of the Response of a Thin-Base Diode. . . . . . . . . . . . . . . . . . .. 127

xi

xii CONTENTS

CHAPTER IV. Transient Processes in a Diode with a Small-Area Rectifying Contact ...... .

§14. Ideal Model of a Point-Contact Diode ... . §15. Transient Conditions. . . . . . . . .... . §16. Experimental Investigations ..... .

CHAPTER V. Effect of an Electric Field in a Diode Base on Transient Processes ...... .

§17. Built-in Internal Field in a Diode Base. §18. Forward-Biased Diode with a Built-in

Field ...................... .

130

131 141 153

160

160

165 §19. First (Recovery) Phase. ...... ... ... ... 171 §20. Reverse Current Decay. . . . . . . . . . . . . . . . .. 175

CHAPTER VI. Transient Processes in Diodes During the Passage of a Forward Current Pulse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

§21. Introduction. . . . . . . . . . . . . . . . . . . . . . . . .. 179 §22. Establishment of a Forward Resistance

in a Planar Diode . . ............. . §23. Establishment of a Forward Voltage

Across a Diode with a Hemispherical p-n Junction. . .......... .

CHAPTER VII. Transient Processes in Semiconductor Diodes and Fundamentals of Recombination Theory ............ .

§24. Introduction .................. .

§25. Lifetime of Holes under Various

183

191

197

197

Recombination Conditions ......... 201 §26. Influence of Trapping Levels on

Transient Processes in Diodes. . . . . . 209 §27. Recombination Properties of Gold-Doped

Germanium and Silicon . . . . . . . . . . . . . . . . 214

Literature Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 231

b =0 J.Ln/J.Lp Ce , Cp_n , Cd

Dn,Dp E

En =0 q~E/2kT Et Ev,Ec

Ea , E{3 hK hp- n hy i rec

i o• h

Notation

normalized radius of a hemispherical p-n junction

ratio of the current during the first phase of a reverse switching transient and the for­ward current

ratio of the electron and hole mobilities . capacitance of. respectively, the encapsulation,

the p-n junction, and the diode as a whole diffusion coefficients of electrons and holes electric field normalized electric field energy level of a trap energy levels of the upper edge of the valence

band and the lower edge of the conduction band

energy levels of a and {3 trapping centers transfer function of the bias ratio width of the space-charge region transfer function of the circuit admittance reverse current corresponding to the comple-

tion of the second phase of a reverse switch­ing transient (recovery current)

total diode current and diode current density forward diode current and forward current

density reverse diode current and reverse current

density during the first phase of a switching transient

xiii

xiv

k

Ln Lp Zn Zp = Lpv'2b/(b + 1)

Nd,Na Nt Na , Nf3 n,p

nno' npo

P1

Qrec Qst q

R = r/Lp Rb Ri RZ RR ro S

SR T J' = t/Tp J d = tdlTp

NOTATION

electron and hole current densities in a diode saturation current and saturation current den-

sity of a p-n junction Boltzmann's constant diffusion length of electrons in a p-type region diffusion length of holes in an n-type region nebye screening length effective diffusion length of holes at hi~h in­

jection levels effective densities of states in conduction and

valence bands donor and acceptor concentrations trap concentration densities of a and f3 trapping levels electron and hole densities densities of electrons in n- and p-type semi­

conductors under thermodynamic equili­brium conditions

densities of holes in n- and p-type semicon­ductors under thermodynamic equilibrium conditions

denSity of holes in the base at the edge of the base side of the space-charge region during passage of a steady-state forward current ("impressed denSity")

recovered charge stored charge magnitude of electron charge normalized radius vector base resistance differential forward resistance of a diode load resistance in a diode circuit "residual" base resistance radius of a hemispherical p-n junction p-n junction area surface recombination velocity absolute temperature normalized time normalized delay time between the end of a

forward current pulse and beginning of a reverse voltage pulse

Dr ub ud uD uf Uo up-n ur vd vn • vp W Wn = W/Lp x =x/Lp 'Y ~ = P/nno on. Op ~ #J.n.#J.p Pn Un. up

NOTATION xv

normalized duration of a forward current pulse normalized duration of the linear part of the

"tail" of the postinjection (open-circuit) emf across a p-n junction

normalized pulse front rise time normalized duration of the first phase of a

transient after switching from forward to reverse direction

normalized duration of the second phase of a transient after switching from forward to reverse direction (decay of the reverse cur­rent from io to 0.1 io)

time constant of charging the barrier capaci-tance

amplitude of a reverse voltage pulse (step) voltage drop across the base total voltage drop across a diode Dember voltage drop across the base forward voltage drop across a diode ohmic voltage drop across the base voltage drop across a p-n junction steady reverse voltage drift velocity of carriers thermal velocities of electrons and holes base thickness normalized base thickness normalized position coordinate injection efficiency of a p-n junction injection level excess electron and hole densities dielectric (Maxwellian) relaxation time electron and hole mobilities resistivity of an n-type semiconductor cross sections for the capture of an electron

and a hole by a recombination center

electron and hole lifetimes lifetimes of minority carriers. respectively,

at low. arbitrary. and high injection levels lifetime of electrons in a heavily-doped p-type

semiconductor

xvi NOTATION

lifetime of holes in a heavily-doped n-type semiconductor

steady-state and non-'steady-state hole life-times

radiative recombination lifetime average carrier trapping time equilibrium barrier height (built-in potential)

in a p-n junction