944 PRCEj,FP,j,NGS OF1V(l) IJ. July

i3 nLot important, and it is desirable to have a frequencyrmultiplier requiring a minimum of adjustmenit duriingoperation, the buncher should be short (CN=-0.3, orless).

Operation of a short buncher at large signal levelscauses the output to be relatively insensitive to changesin both the buncher voltage and the input signal level.Thus a short buncher makes it possible to obtain nearlyoptimum output for a number of harmonics by simplychanging the voltage of the output helix. In the case of ashort buncher, the structure should have a high C, buteven moderately high values of QC would be per-missible.

CONCLUSION

The experimental studies show that the traveling-wave frequency multiplier can provide useful output atharmonics as high as the fortieth, and perhaps consider-

ably higher. '[he saturation power output, even for highharmonics, approximates the power output that can beobtained for the same beam current in a normaltraveling-wave amplifier. This indicates that the har-monic current content of the bunched beam at thebuncher exit can be very high. The low efficiency com-monly associated with a klystron frequency multiplieris not characteristic of the twfm.A detailed quantitative investigation of the behavior

of the traveling-wave frequency multiplier was notattempted.

ACKNOWLEDGMENT

The authors wish to thank Dr. L. A. Roberts ofHuggins Laboratories for help in providing parts forthe tube, and T. Wessel-Berg and Drs. Roberts,D. A. Dunn, H. Heffner, and M. Chodorow for helpfuldiscussions.

Very Narrow Base Diode*R. H. REDIKERt, ASSOCIATE MEMBER, IRE, AND D. E. SAWYERt, MEMBER IRE

Summary-Techniques have been developed to fabricate semi-conductor diodes with rectifying junction to ohmic contact distancesof the order of microns. The current-voltage relationship of such adiode is a function of the degree of imperfection of the ohmic contact.If it were possible to make ideal ohmic contacts, the diode wouldexhibit extremely poor rectification. The rectification ratio of ger-manium diodes for practical ohmic contacts, however, is of the orderof 105 to 106. The current-voltage relationship, the small-signal fre-quency response, and the switching characteristics of the very narrowbase diode are analyzed using the appropriate boundary condition atthe ohmic contact. The alloy junction current-voltage characteristicsfollow very closely the (esVIakhT-1) relationship with values of abetween 1.02 and the theoretical value 1.00. Because of the narrowbase width, the series bulk resistance for typical designs is between0.3 and 3 ohms. Thus the entire range of forward currents can beobtained at low forward voltages. The diode is a high-frequency de-vice both for small-signal applications and for switching applications,although the ultimate high-frequency capability is reduced becauseof the imperfection of the ohmic contact. In switching applications,the reverse recovery time may be limited as much by junctioncapacitance as by hole storage. A method of fabrication is describedand small-signal applications at uhf are discussed. A computer diodedesign that switches at speeds up to 5 mc is described. This diodehas the advantageous combination of low forward-voltage drop andhigh-frequency capability.

I. INTRODUCTIONHE very narrow base germanium diodes withwhich this paper is concerned have base widthsfrom 1 micron to 10 microns. The electrical char-

* Original manuscript received by the IRE, February 18, 1957.The research reported here was supported jointly by the U. S. Army,Navv, and Air Force under contract with Mass. Inst. Tech.

t Lincoln Lab., M.I.T., Lexington, Mass.

acteristics of these diodes, which cannot be duplicatedin any other presently available type of diode, are de-sirable in both computer and small-signal applications.A cross-sectional view of a typical narrow base diode isshown in Fig. 1. The diameter, d, of the active area of

N - TYPE-0GERGERMANIUM

RECTIFYINGJUNCTION- OHMIC

CONTACT

Fig. 1-Cross section of a very narrow base diode (not to scale).

the diodes may vary from 0.005 cm to more than 0.15cm. For diodes in which d is larger than 0.030 cm, therectifying junction is an indium alloy junction while

944, July

Redier and Sawyer: Very Narrow Base Diode

junctions of 0.005 cm diameter are made by bonding agallium-gold wire.

Successful operation of very narrow base diodes ispossible only because ohmic contacts are not ideal. Thetechnique of fabricating ohmic contacts that have agiven degree of imperfection and the technique ofselective controlled etching the depression opposite therectifying junction are described in Section V.The advantageous combination of low forward-

voltage drop and high-frequency capability makes thisdiode useful in many computer circuits. High-speedoperation (switching rates above 1 mc and possiblyabove 10 mc) is a result of the small spacing betweenthe rectifying junction and ohmic contact which mini-mizes hole-storage effects. Also, because of the narrowbase width, the series bulk resistance of the diode issmall. For the computer diode whose specifications aregiven in Section VI, the bulk resistance is less than 3ohms and for special applications resistances below 0.05ohm should be possible. Because of the low series bulkresistance, at forward currents up to several milli-amperes most of the voltage applied to the diode ap-pears across the rectifying junction. The diode currentis related to the junction voltage, Vj, by the equation1= fo(eqVil,kT-1) where for the very narrow base alloydiode the value of a has varied between 1.02 and thetheoretical value of unity. For conventional gold-bonded or point-contact junctions, the value of a is con-siderably larger than unity and for a given ratio of for-ward current to saturation current, the forward voltagefor the very narrow base diode is significantly smallerthan that for these conventional types of switchingdiodes. Thus for the very narrow base alloy diode, theentire range of forward currents can be obtained at lowforward voltages. In the subsequent analysis, thequantity a, which for the narrow base alloy diode isclose to unity, is omitted.

Because of the very small value possible for the prod-uct of the series bulk resistance and junction transitionlayer capacitance, the very narrow base diode can beused at reverse biases as a variable capacitor with calcu-lated Q above 100 at 109 cps. The diffusion capacitance,which limits the frequency of operation in forward bias,is also small because of the very narrow base width.Very narrow base diodes, which have been fabricatedwith gold-bonded rectifying junctions to reduce capaci-tance, may have application as uhf mixers. Because thejunction diameter of these diodes is about 25 times thebase width, the planar junction theory developed inthis paper should still apply.When the reverse bias is increased so that the space-

charge region punches through to the ohmic contact, thediode exhibits a low dynamic impedance. Switchingtime between the low-impedance punch-through regionand the high-impedance reverse-bias region is capaci-tance limited and can be reduced below 10 millimicro-seconds. Operation of the very narrow base diode in thepunch-through region will not be described in this paper.

In this paper, the operation of the diode in the low-impedance forward and high-impedance reverse states

will be investigated. The current-voltage relationship,the small-signal frequency response, and the switchingcharacteristics will be analyzed. A method of fabricationwill be described, and several applications of the diodewill be discussed. In the analysis which follows, the baseregion has been assumed to be n-type, the minoritycarriers holes. The results can be applied to diodes withp-type base regions by a suitable change in notation.The analysis should be applicable to semiconductordiodes in general, in addition to the germanium diodesthat have been fabricated.

II. CURRENT-VOLTAGE RELATIONSHIPA. The Planar Junction Current- Voltage Relationship

The operation of narrow base diodes is very sensitiveto the properties of the ohmic contact. The ohmic con-tact may be characterized by the ratio, s, of the currentdensity to the change in the charge density of minoritycarriers at the contact,

Js =

q(p - pn)(1)

All symbols are defined at the end of this paper. Thequantity s is the contact generation velocity and isanalogous to the surface recombination velocity. Anohmic contact at which there is no change in carrierdensities irrespective of the current will be denoted asan ideal ohmic contact. An ideal ohmic contact has ans value of infinity.

If one neglects the leakage resistance that shunts thejunction, but includes the deviation from ideal behaviorof the ohmic contact, the current in a planar junctiondiode can be determined from the diffusion equation andis given by

I qDpnA L

w wD sinh + sL cosh-

L L(eqVilkT - 1).

w wD cosh- + sL sinh

L L

(2)

The minority carrier current in the heavily doped re-crystallized "emitter" region is justifiably neglected in(2). For narrow base diodes where w<<L, (2) reduces to

I qDpPn 1 (ezVIkT - 1)A w D 1

1 +-sw

or rearranging terms

I I- = qpns (eQVijkT - 1).A sw

1+-D

(3)

(3a)

Fbr L>>w>>D/s, the term

(1/+ D -

1 +-\SW/

in (3) is close to unity and the saturation current is aninverse function of the effective base width w. As the

1957 945

PROCEEDINGS OF THE IRE

diode reverse voltage is increased and the space-chargeregion becomes larger, the effective base width de-creases and the reverse current increases and does notsaturate. For this case, all the minority carriers gener-ated at the ohmic contact are not collected at the recti-fying junction at low reverse voltages, but as the voltageis increased and the effective base width becomes nar-rower, more and more of the carriers are collected.

If, on the other hand, w<<D/s, the fraction in (3a) isclose to unity, the reverse current is independent of wand does saturate. In this case, all the generated carriersat the ohmic contact are collected; there are no furthercarriers to collect irrespective of base width. If we takethe value of s to be 5 X 104 cm/second, the quantityD/s for an n-type germanium base layer is 8.8X10<cm. The computer diode described in Section VI has adesign base thickness of about 0.8XI0-s cm. For thisdiode, the fraction in (3a) varies from 0.52 to 1.00, asthe reverse voltage is increased from zero volts towardspunch through, and w decreases from 10-' cm towardszero. This increase in saturation current by 92 per centin 20 volts is perfectly consistent with back impedancesabout 1 megohm. If, on the other hand, the ohmiccontact were ideal (s= oc), the fraction in (3) would beunity, and the "saturation" current would vary as thereciprocal of the effective base width increasing from itslow voltage value to infinity as the reverse voltage wasincreased. For this case, the reverse impedance of thevery narrow base diode would be too low for it to haveany practical application. Thus, the very narrow basediode is feasible only because ohmic contacts are notideal. The value of s of 5 X 104 cm/second used abovewas determined by substituting the experimental valueof the saturation current for various computer-typediodes into (3a).

B. Ohmic Bulk ResistanceThe voltage across the diode is the sum of the junction

voltage and the ohmic voltage drop across the bulkmaterial. For a narrow base diode in forward bias, thebulk resistance to minority carriers determines theohmic voltage drop. This bulk resistance can be ascer-tained from solution of the diffusion equations withappropriate boundary conditions and is given at lowlevel injection by',2

ratio of majority to minority carrier mobilities. Thebase width w which appears in (4) can be related by useof Poisson's equation to the resistivity and the punch-through voltage and is3

W = (2Yne) "' (VpPO) 1 (5)For n-type germanium, in the system of units volts,ohms, and centimeters, (2,ane)121= 1.01 XO1. Narrowbase computer diodes designed to meet the specificationsdiscussed in Section VI have had bulk resistances atlow-injection level below 3 ohms, while other diodesthat have been fabricated with lower resistivity ger-manium have had bulk resistances calculated -from (4)of less than 0.05 ohm.

Eq. (4) gives the series bulk resistance at low-injectionlevel. At large forward currents where the density ofinjected carriers is comparable to the net donor densityin the base region, conductivity modulation reducesthis bulk resistance even further. Because of its narrowbase width, however, the narrow base diode requires arelatively small amount of carrier injection to producethe concentration gradient necessary for forward currentflow. The ratio of the injected hole density in the baseregion to the current density is

sx1 +-

p-pn=

DJ qs

where x is the distance from the ohmic contact. Theother quantities are defined at the end of this paper. At1 ma forward current, the maximum injected holedensity for the computer diode of Section VI is less than5 the donor density. Thus for this diode, low level in-jection theory applies at forward currents of thismagnitude.

It should be kept in mind that (4) gives the series bulkresistance to minority carrier current. Although this isthe bulk resistance when the junction is forward biased,when the junction is reverse biased the series bulk re-sistance that becomes important at high frequency is theresistance to the majority carriers which cross the baseregion to charge the transition-region capacitance. Formajority carriers, the bulk resistance is given by

powR =--,

A (7)

(6)

R (W)b. (4)

This resistance is the resistance which would be ex-

pected for majority carrier flow multiplied by b, the

1 The derivation of (4) is included in Lincoln Lab. Tech. Rep. 137(unpublished). This technical report also includes more complete de-sign theory than reported here for narrow base diodes which meetdifferent electrical specifications and more detailed information ondiode manufacture.

2 In this paper the base region is considered sufficiently doped soonly the majority carriers need be taken into account in the calcula-tion of the resistivity; i.e., po=-ql.&ND.

the conventional resistance-resistivity relationship forplanar geometry.

III. SMALL-SIGNAL FREQUENCY RESPONSEA. Junction Transition-Region CapacitanceThe junction transition-region capacitance per unit

area for an abrupt alloy planar junction is given by

3 Eq. (5) is derived with the assumption that the width of thespace-charge region is much larger than the Debye length; i.e., thespace-charge region is completely depleted of mobile charge carriers.

946 July

Rediker and Sawyer: Very Narrow Base Diode

CT 1/2

A 2,UnPO(V + VO)_ (8)

Vi is the voltage applied to the junction and is consid-ered positive in reverse bias, i.e., Vj3 V,. Eq. (8) hasbeen derived with the assumption that the space-chargeregion is completely depleted of mobile charge carriers.If this assumption were valid, V0 would have been equalin value to the internal contact potential of the junction.Although this assumption is not strictly correct, (8) maystill be used if V0 is considered for any given diode a"constant" of the equation.48 In the derivation of (8)the resistivity of the recrystallized region has been as-sumed to be much smaller than that of the base region.The equivalent circuit of a diode in its high-impedance

state is shown in Fig. 2. This circuit is applicable fromvery low frequencies to ultra-high frequencies. Twoquantities which may establish the upper-frequencylimit of this circuit are the dielectric relaxation time EpOof the semiconductor and the diode lead inductance. Thedielectric relaxation time is 1.4 X 10-12 seconds for 1ohm-cm germanium and by proper packaging the diodelead inductance can be reduced so that it may be neg-lected at frequencies below 500 mc.The product of the series bulk resistance and the

junction capacitance is independent of the junction area.Combining (5), (7), and (8), this product is

RCTVP 12 - F7jl/2

° (V + 1V)1/2 (9)

where the reduction of the effective base width by thejunction transition layer has been included. The di-electric constant e for germanium is 1.41 X 10-12coulombs per volt-cm.

R

GFig. 2-Equivalent circuit of a diode in its high impedance state.

G is the junction conductance and R is the series bulk resistance.CT is the transition layer capacitance.

On the basis of (10), a diode that is fabricated from 0.5ohm-cm material with a punch-through voltage of 15volts and is operated about a reverse bias of 10 voltsshould have a Q larger than 4000 at 100 mc and largerthan 800 at 500 mc. If lower resistivity material wereused, even higher Q's should be obtainable. While fordiodes fabricated to date the series resistance to minoritycarriers has been explained by (4), the series resistanceto majority carriers at uhf has been higher than thatcalculated from (7). Hence, values of Q as high as pre-dicted by (10) have not been obtained.The additional series resistance has been attributed

to the "ohmic" contact and work is in progress to im-prove this contact.

B. Junction Diffusion CapacitanceWhen a diode is operated in forward bias or at very

low reverse bias, the diffusion capacitance cannot beignored. If one neglects the transition-region capacitanceand the junction leakage resistance, the small signal re-sponse of a planar junction can be determined from thediffusion equation and is given by

i _ qj.ApPeQil*' (D(1 + j sr)"2Sinh - (1 + jwT)lI2 + sL cosh- (1 + jor)1/2A L (1 + jwr)1/2 vv1ei"'.A L I I-)1/ jo)1D(1 + jr)12 cosh - (1 + j.r)112 + sL sinh - (1 + jwr)112

L .L L

A diode operated in reverse bias can be used as avariable capacitor' (see Section VI). A figure of meritfor this circuit element is the ratio of series reactance toseries resistance. At high frequencies, where the shuntconductance (see Fig. 2) can be neglected, this ratio is

1 1 (ViT+ V0)1/227rfRCT 27rfEpo (V1p2 V.112)

'D. R. Muss, "Capacitance measurements on alloyed indium-germanium junction diodes," J. Appl. Phys., vol. 26, pp. 1514-1517;December, 1955.

6 R. F. Schwarz and J. F. Walsh, "The properties of metal tosemiconductor contacts," PROC. IRE, vol. 41, pp. 1715-1720; Decem-ber, 1953.

6 L. J. Giacoletto and J. O'Connell, "A variable-capacitance ger-manium junction diode for uhf," RCA Rev., vol. 17, pp. 68-85; March,1956.

The imaginary part of the quantity multiplying thesmall-signal voltage on the right-hand side of (11) is thesusceptance of the diffusion capacitance.

For narrow base diodes where w<<L and for frequen-cies where w<<(D/w2), (11) reduces to

- = qp.seqvi / kTA sw

1+D

s2w2

D2~~~~~~~~~~~~~~~~I

yw*1 1+ jw 13 SW

1 +-D

qv1 ei .

kT(12)

(11)

1957 94:7

PROCEEDINGS OF THE IRE

At forward voltages above several kT/q the small-signalcurrent can be expressed in terms of the direct current Iby combining (3) and (12)

s2w2

kT SW1+-

D

(12a)

In Fig. 3, the real and imaginary parts of the small-signal admittance Y=i/vj are plotted as a function offrequency for a diode with a 2-micron base width. Thetheoretical conductance and susceptance as determinedfrom (11) are compared with the values obtained fromthe low-frequency approximation (12). As indicated inFig. 3 for frequencies where the susceptance is less thanthe conductance, (12) can be used in place of (11).

If the ohmic contact were ideal (s = oo), the reactiveterm in the parentheses in the right-hand side of (12)would be jw(w2/3D). For the narrow base diodes where(sw/D)2<(1, this term is jw(wls). Because of the imper-fection of the ohmic contact, the diffusion capacitancedetermined by this reactive term is increased by thequantity 3D/sw. As shown in Fig. 3, the frequency wherethe susceptance of a diode with a 2-micron base widthis equal to its conductance is increased by a factor offour, when the s of the ohmic contact is increased by thissame factor from 50,000 cm/second to 200,000cm/second. Work is underway to further increase thevalue of s of the ohmic contact. However, if high reverseresistance is desirable, the value of s must not be in-creased to the point where (sw1D)>>1, because then asdescribed in Section II, the diode back current will nolonger saturate.The small-signal admittance of the junction diode

varies exponentially with the junction voltage Vj [see(11) or (12)]. At forward voltages where V1 is muchlarger than kT/q the capacitance associated with thisadmittance is much larger than the transition-layercapacitance discussed in Part A of this section. As Vj isreduced to zero, the diffusion capacitance decreases ex-

ponentially, and for reverse biases where VjI is againmuch larger in magnitude than kT/q, the diffusion ca-

pacitance is completely negligible. Because the diodeshave such narrow base regions, the diffusion capacitanceis usually small when compared to the transition-layercapacitance for all reverse biases down to kT/q.

IV. SWITCHING SPEED FOR COMPUTER DIODES

A. Effect of Hole Storage on Reverse Recovery Time

The switching speed of the narrow base diode is estab-lished by the time it takes to switch the diode from theforward low-impedance state to the reverse high-

FREQUENCY (Mcps)

Fig. 3-The theoretical real and imaginary parts of the small-sig-nal admittance of a narrow base diode with a 2-micron base widthfor two different values of ohmic contact generation velocity. Theimaginary part of the admittance as determined from the ap-proximation (12), is compared with that determined from theexact equation (11).

impedance state. Before the diode will exhibit the highimpedance normally associated with its reverse biasstate, the minority carriers (which we will assume areholes) stored in the diode when it is in the forward low-impedance state must be removed.

For a diode with an ideal ohmic contact, Lax andNeustadter7 and Kingston8 have shown that the hole-storage switching time is a decreasing function of theratio of the maximum reverse current to the forwardcurrent the diode was conducting. This maximum re-verse current is the applied reverse voltage divided bythe loop impedance. The loop impedance includes thediode ohmic bulk resistance. As is seein from Fig. 4,which is adapted from Kingston, the switching time dueto hole storage for the narrow base planar diode variesfrom 1.9 (w2/D) to 3X 10-3 (w2/D) asl /Iff varies from10-2 to 102.

B. Figure of Merit for Hole Storage

Although the hole-storage switching time varies withthe circuit used, the ratio of the forward current to thecharge of the holes stored during forward conductiondepends only on the physical parameters of the diode.For a narrow base planar diode with an ideal ohmic con-

7 B. Lax and S. F. Neustadter, "Transient response of p-n junc-tion," J. Appl. Phys., vol. 25, pp. 1148-1154; September, 1954.

8 R. H. Kingston, "Switching time in junction diodes and junctiontransistors," PROC. IRE, vol. 42, pp. 829-834; May, 1954.

948 July

IV 1

1 +s 3

Rediker and Sawyer: Very Narrow 1Base Diode

'Dtw2

10-2 101i 1.0 10 100JrJf

Fig. 4-Hole-storage switching time for the narrow base diode. t1 isthe duration of constant current phase and t1+t2 is the totalswitching time required for the junction voltage to reach 90 percent of the applied reverse voltage.

tact, such as was considered by Kingston, the figure ofmerit is given by

I/Qh =2D/w2. (13)Thus, the figure of merit is related to the reciprocal ofthe switching time.

If one includes the deviation from ideal behavior ofthe ohmic contact, the figure of merit for a planar alloydiode is given by

If 1

Qh Tr

w sL wsinh- + - cosh -

L D L

w sL w\sinh-+ - cosh--1

L D\ L

(14)

For the narrow base diode, with w<<L, (14) reduces to

If 2D 1

Qh w2 2D1+-

SW

The computer dliode whose specifications are discussedin Section VI has been designed with a base width of10-3 cm. The figure of merit for the hole storage for thisdiode calculated from (15) is 3.2X 10-7 second. In thiscalculation, the s value of 50,000 cm/second which wasexperimentally determined from the current-voltage re-lationship was used.

C. Effect of Junction Capacitance onReverse Recovery Time

Very narrow base diodes have been fabricated forwhich in normal switching operation the reverse re-covery time is caused by junction transition-layer capac-itance rather than hole storage. This has been shownexperimentally by varying the forward current throughthe diode while the initial reverse current and the re-verse bias voltage were kept constant. The switchingtime was found to be insensitive to the forward currentexcept for unusually large values of the ratio of forwardcurrent to initial reverse current. As indicated by Fig. 4,if the switching time were due primarily to hole storage,it would have been a rapidly varying function of theforward current. The very narrow base diode is to ourknowledge the first alloy diode where junction capaci-tance rather than hole storage may limit the switchingspeed for diode currents which are normally encounteredin computer service.

For optimum design of the narrow base diode forfast-switching applications, the effects of both junctioncapacitance and hole storage must be minimized. As afirst step in the design of this diode, we have attemptedto minimize the sum of the charge of the holes storedduring forward conduction (hole storage) and the chargein the space-charge region during reverse bias (thechange in this charge with voltage is the junction capaci-tance).The charge in the space-charge layer of an alloy junc-

tion with reverse bias Vj can be determined fromPoisson's equation and is

(2eV ) 1/2

11nPo(17)

The charge of the stored holes which are necessary toproduce a forward current I.f for a narrow base diode isfrom (15)

(15) w2 /2D2D SW)

(1Sa)

which for an ideal ohmic contact (s = X ) reduces to (13).For limiting small base widths, w<<D/s, the figure ofmerit becomes

If s=. ~~~~~(16)Qh W

If we use (5) to express the base width in terms of thebase resistivity and the punch-through voltage, (lSa)becomes

Q = I [DV1pO + ( Vppo)]. (18)D s

1957 1149

O7CCP1I75 OF YYi, - Iv GJuly

lf the operating voltage V, and the puncli-thlough volt-age Vp (which can be considered the maximnum voltage)are kept constant, as the resistivity is increased, thebase width and Qh increase, but the junctioni capacitanceand Q,, decrease. There is an optimum resistivity forwhich the sum of Qh and Q,, is a minimum.

In a typical computer application the reverse voltageapplied to the diode may be 10 volts. If the punch-through voltage for a diode with an n-type base region is20 volts and s=5X104 cm/second, the resistivity forwhich the sum of Qh and Q,, is a minimum is the realroot of the equation

APo3/2 + 1.95po - 19.5 - = 0,

If(19)

where If/A is in amperes per cm2. For If/A = 1 amp/cm2,the optimum resistivity is 4.7 ohm-cm with a corre-

sponding base width of 9.7 X 10-4 cm, while for If/A 10amps/cm2 the optimum resistivity is 0.69 ohm-cm witha corresponding base width of 3.7X10-4 cm. For thesecases the charge stored in the space-charge region islarger than the charge of the holes stored during forwardconduction: for the first Qh/QC= 0.72 and for the secondQh QIC= 0.86.

D. Forward Switching Transient

When a diode is switched from reverse bias to forwardbias, the hole distribution in the base region associatedwith the equilibrium forward current must be re-

established. The effect on the switching transient ofthe storing of these holes depends on the forward cur-

rent to which the diode is being switched.If the forward current is small enough so that the

junction resistance is large compared with the ohmicbulk resistance, the transient will be determined by thejunction. In the approximation of (12) the junction isrepresented by a parallel RC network, the hole storagecharge being approximated by the charge on thecapacitor. The RC product for the computer diode de-scribed in Section VI is 2.4X 10-8 seconds. Although (12)is not valid for frequencies above 1/RC, the RC productis an indication of the transient response time. For verynarrow base diodes in normal computer service, theforward switching transient is due to the junction im-pedance. In most computer applications, the effects ofthis forward switching transient are much less importantthan the effects of the reverse transient.At large forward currents where the ohmic bulk re-

sistance is large compared with the junction resistance,a transient may occur because of changes in the bulkresistance. These changes will occur if the hole storageis large enough to modulate the bulk conductivity, inwhich case the bulk resistance of the diode is initiallyhigher than its steady state value. The figure of meritfor hole storage given in (15) can be used as a figure ofmerit for this forward switching transient. In this case,the reciprocal of this figure of merit is the time it takes

the forward current to establish the stored minoritycarrier charge and modulate the bulk conductivity. Forany switching source with internal resistance the diodevoltage decreases with time during the conductivitymodulation transient. On the other hand, for the samesource if the transient is determined by junction im-pedance, the diode voltage increases with time duringthe transient.

Because of its small base width, the narrow basediode has low ohmic base resistance and in addition cancarry currents of the order of milliamperes at low injec-tion levels. Hence, the conductivity modulation tran-sient, while common in many commercially availablediodes, is negligible for the narrow base diode.

V. A FABRICATION TECHNIQUEControlled selective bath etching has proved to be a

successful technique in the fabrication of very narrowbase diodes.9 The diodes are prepared by alloying anindium button into n-type germanium by conventionalmeans. Simultaneously with the alloying, an antimony-gold plated kovar ring is bonded to the germanium tobe used as an auxiliary ohmic contact during furtherfabrication. If smaller area rectifying contacts are de-sired, a gold-gallium bonded contact is used instead ofthe indium alloy contact. After the rectifying contactis "cleaned up" by conventional methods, the diode isinserted into the bath etcher as shown in Fig. 5. Aplastic washer, coated with a silicone compound, pro-trudes below the bottom of the bath, and makes awatertight seal to the top surface of the germanium die.This seal prevents the bath electrolyte from reachingthe kovar base tab, and is necessary for successful bathetching. When the diode is removed from the etcher, thesilicone compound is removed from the germanium die.An electrolyte that has been used successfully in bathetching is an aqueous solution of 7.4 grams per liter in-dium trichloride and 2.1 grams per liter hydrochloricacid. Bath agitation is provided by feeding electrolyteat low pressure through a jet above the germaniumsurface.When the switch of Fig. 5 is in position E, a depression

is etched into the germanium opposite the indium but-ton. The electrolyte is biased negative by a voltagesource with respect to the germanium while the alloyedbutton is forward biased by the current source composedof R, and Vf. During etching the terminal characteristicsof the bath assembly resemble those of a p-n-p transis-tor.10"'1 The alloyed button current may be designatedthe "emitter" current; the electrolyte current, the "col-

9 Another technique to fabricate very narrow base diodes has beendescribed by R. H. Rediker and J. Halpern, "Outdiffused junctiondiode," Second Annual Meeting of the PGED of the IRE; October,1956.

10 C. G. B. Garrett and W. H. Brattain, "Self-powered semicon-ductor amplifier," Phys. Rev., vol. 95, pp. 1091-1092; August, 1954.

11 W. H. Brattain and C. G. B. Garrett, "Experiments on theinterface between germanium and an electrolyte," Bell Sys. Tech. J.,vol. 34, pp. 129-176; January, 1955.

OCAv '@ July

Rediker and Sawyer: Very Narrow Base Diode

SW IA

VP'

Va

)METERRELAY

SW 1B

Fig. 5-Controlled selective bath etching. When switch is in positionE, a depression is being etched into the germanium opposite theforward biased indium button. When switch is in position S, theindium button is reverse biased, a plate is being deposited on ger-manium, and the width of base layer opposite the button is beingsensed. The switch alternately contacts the E and S positions.

lector" current; and the current through the kovar base,the base current. Collector current saturation slopes inthe megohm range are obtained. It is found, as reportedin the literature,"2 that the magnitude of the saturationcurrent is in good agreement with that calculated from thearea of germanium exposed to the bath electrolyte andthe thermal generation rate of holes from the n-typebase. The a of the bath assembly for collector voltagesabove that required for collector current saturation islarger than unity. Of course, a's smaller than unity can

be obtained by reducing the collector voltage. The col-lector resistance in the so-called voltage saturationrange is usually about 750 ohms.

Etching of the n-type germanium is limited by theflow of holes which are injected at the alloy rectifyingcontact. These holes diffuse across the n-type base andparticipate in the etching process at the germanium-electrolyte interface opposite the alloy junction. In addi-tion to localizing the etched depression opposite thealloy junction, it is possible in bath etching to vary thedistribution of the injected holes and hence the radius ofcurvature of the etched depression. For collector volt-ages which are large enough so that a is larger thanunity, the direction of base-current flow is into the basecontact. For this case a voltage drop occurs laterally inthe base beneath the fusion area. The polarity of thisvoltage is such as to produce greater hole injection near

the center of the emitter area than at the emitterperiphery. As etching continues, the base becomes pro-

gressively thinner, and for a given constant emitter cur-

rent the etching localizes even more at the center of thefusion. On the other hand, for collector voltages forwhich a is smaller than unity, the base-current flow isout of the base contact. The lateral base voltage now

tends to bias off the central region of the emitter so thatetching should occur at a faster rate at the periphery

12 A. Uhlir, Jr., 'Electrolytic shapin of germanium and silicon,"Bell Sys. Tech. J., vol. 35, pp. 333-347; March, 1956.

than at the center. The curvature of the etched depres-sion expected from the above considerations is (le-creased somewhat because while the hole injection is re-duced where the base region is more positive, the electro-lyte-germanium voltage is increased. The etching ratehowever, is much more sensitive to hole injection thanito the electrolyte-germanium voltage. Controlled selec-tive bath etching, which incorporates hole injection inton-type germanium, not only yields well delineate(detched surfaces of controlled curvature but also mini-mizes surface pitting. Unless a source of holes is pro-

vided by such means as injection or optical generationelectrolytic methods of etching n-type germanium atany practical rate of germanium removal usually lea(dto excessive surface pitting.

In order to produce very narrow base diodes, theetching must be stopped when a predetermined basethickness remains opposite the alloy junction. Whenthe switch in Fig. 5 is in position S, the thickness of then-type germanium region remaining between the p-typerecrystallized region under the alloy button and thesurface of the depression is being sensed. The electrolyteis biased positive with respect to the germanium so thatindium is plated onto the germanium surface. Also, a

reverse voltage V. is applied across the indium alloyjunction. This voltage creates a space-charge regionthat penetrates from the alloy junction a distance winto the base. Using Poisson's equation, the equationwhich relates w to the base resistivity po in ohm-cm andV. in volts can be derived.3

w = 1.01 X 10-4V\Vapo cm. (5a)

When etching has proceeded so that the space-chargeregion of the reverse biased diode reaches the p-typeinversion layer under the plate being deposited, the re-

verse current of the diode increases. This increase incurrent operates a relay and stops further etching. Byadjust'ng the sensing voltage Va and the germanium re-

sistivity, widths as low as a micron can be sensed.Figs. 6 and 7 are metallographic sections of two bath-

etched devices made with 5 ohm-cm n-type german-

ium. In Fig. 6, the alloy junction diameter is 0.030 inchand the n-type base thickness is approximately 5 mi-crons and is quite flat. The rectifying junction of thediode whose section is shown in Fig. 7 was made by goldbonding a 0.002-inch-diameter gold-gallium wire to a

germanium blank. The minimum base thickness of thisdiode is approximately 2 microns.

After the diode is bath etched, ohmic contact mustbe made to the thin base region. In order to maintainthe base-width control inherent in bath etching, thepenetration of the ohmic contact into the base regionmust be kept to a minimum. Ohmic contacts have beenmade by plating, by evaporation, by alloying, and bysoldering. One successful method of making the ohmiccontact to computer-type narrow base diodes is to platea gold-antimony contact on the germanium surface

1957 t;, ".

PROCEEDINGS OF THE IRE

Fig. 6-Photomicrograph of the cross section of a bath-etched device.The alloy junction diameter is 0.030 inch and the n-type basethickness is approximately 5 microns and quite flat. The junctionbetween the p-type recrystallized germanium and the n-type baseis not shown.

Fig. 7-Photomicrograph of the cross section of a bath-etched devicewith a gold bond as rectifying contact. The diameter of the goldwire is 0.002 inch and the minimum base thickness is 2 microns.The line in the germanium above the etched depression shows thejunction of the p-type recrystallized region and the n-type baseregion.

which has first been abraded with a spray of an aqueoussolution of either No. 1, No. 2, or No. 3 Alumina'" froman artist's air brush. While this ohmic contact is verysatisfactory for computer diodes, as mentioned in Sec-tion III, the seemingly large contact resistance (-5ohms) to the flow of majority carriers at uhf has par-tially vitiated the advantages of the diode at uhf. Tech-niques are now being developed to make ohmic contactswhich it is believed will not suffer this problem of con-tact resistance to majority carriers. In the laboratorymodels, the ohmic contact to the thin base region hasbeen connected to the kovar ring contact with conduct-ing paint.

Is Distributed by Buehler Ltd., Evanston, Ill.

VI. SOME APPLICATIONS OF THE VERYNARROW BASE DIODE

A. Computer Diode

A very narrow base diode has been designed for high-speed switching service and especially for computer ap-plications where it is desirable to minimize the forward-voltage drop at currents of the order of one milliampere.Table I gives the important electrical specifications forthe diode which has been called the Model II diode.This set of diode specifications is one of many to whichvery narrow base computer diodes can be designed. Be-cause of its low forward drop, the Model II diode shouldbe as useful in transistor computer circuits where volt-age swings may be less than 5 volts, as conventionalswitching diodes are in vacuum-tube computer circuitswhere voltage swings are at least 20 volts. As a resultof the relatively low-impedance level of most transistorcomputer circuitry, the reverse current of the Model IIdiode which is of the order of tens of microamperes isnot deleterious. In addition to having characteristics de-sirable in transistorized computers, the Model II diodeshould be superior to conventional diodes in applicationssuch as ladder networks in which many diodes are inseries, and in applications where it is desired to clampto within 0.1 volt of a given voltage.

TABLE IELECTRICAL SPECIFICATIONS FOR THE MODEL II VERY

NARROW BASE DIODEALL PARAMETERS DEFINED AT (25 ± 1.5)°C

Forward fV=O.llv I>1 macharacteristics -V=0.5 v I>100 ma

1-tt<25 uampV_> 15 volts

Reverse (Voltage at which I> 100 uamp)characteristics r1>750 Ku (3' v)

C<15 Auuf (31 v)

Reverse recovery time Reverse recovery time is the time for the<0.15 usec back resistance to recover to 100 K

(I<85 pamp) when the test diode isswitched from 2 ma forward current to6 volts reverse bias (initial reverse current6 ma).

Table II gives the physical design specifications forthe Model II diode. The punch-through voltage is de-termined by the specified maximum reverse voltage. Theresistivity was chosen so that for the anticipated for-ward current density the sum of the charge of the holesstored in forward bias and the space charge in reversebias is a minimum (See Section IV-C). The base thick-ness is defined once both the punch-through voltage andresistivity are determined (5). The diameter of the alloybutton is determined from the desired current-voltagecharacteristic. The maximum allowable saturation cur-rent determines the maximum diameter and the mini-mum allowable current at 0.11 volt forward determinesthe minimum diameter. Diodes made on a laboratoryscale to the physical specifications in Table II haveeasily met the electrical specifications of Table I.

July952

5Rediker and Sawyer: Very Narrow Base Di,cdzde

TABLE II*PHYSICAL DESIGN SPECIFICATIONS FOR THE MODEL II

VERY NARROW BASE DIODEResistivity of germanium 3.5 ohm-cm-4.5 ohm-cmDiameter of alloy button 0.027-0.030 inchPunch-through voltage 18-22 voltsFinal base thickness 8-10 microns

These physical specifications are based on an ohmic contact which has a gen-eration velocity, s, of 50,000 cm/second.

B. Applications at UHFA reverse biased alloy junction is a capacitarnce which

can be varied through variation of the bias voltage.Giacoletto and O'Connell6 have described the applica-tion of a narrow base alloy diode as a variable capacitorat uhf. As indicated following (10) above, it should inprinciple be easy to design a very narrow base diodewith a Q above 800 at 500 mcps. This value of Q, how-ever, has not been achieved in diodes fabricated to date.These diodes have had a series resistance to majoritycarriers at uhf an order of magnitude larger than thatexpected from the calculation of the ohmic bulk re-sistance. We believe this increase in resistance is due tothe ohmic contact and a program is under way to bothfurther understand and improve this contact.At frequencies at which the diode susceptance is less

than its conductance the very narrow base diode shouldprove useful as a mixer.14 The fabrication of successfulmixer diodes also awaits further improvement of theohmic contact.

14 A. Uhlir. Jr., "Two terminal p-n junction devices for frequencconversion and computation," PROC. IRE, vol. 44, pp. 1183-1191;September, 1956.

A.CKNOWLEDGMENT

The authors wisli to thank C. R. Grant, L. Krohn,W. H. Laswell, and Mrs. M. L. Barney for their help infabricating the dio(les. We are indebted to J. Lowen forhis help in solving the chemical problems associatedwith the bath etching process.

LIST OF SYMBOLSA =junction area.b =ratio of majority to minority carrier mobilities in base region.

CT=junction transition-region capacitance.D =diffusion constant for minority carriers in the base region.f= frequency.G =junction conduct.ance.I=diode current.If=forward current.',=maximum reverse current.s= small-signal current amplitude.J =diode current density.J=V-1.k =Boltzmann's constant.L = diffusion length for minority carriers in base region.ND= net donor density in base region.p =minority carrier density -in base region.

p, =equilibrium minority carrier density in base region.Q=ratio of series reactance to series resistance.

Qsc=charge in the space-charge layer when diode reverse biased.Qh=charge of the holes stored when diode forward biased.q =electronic charge.R= series bulk resistance.s =generation velocity of the ohmic contact.T=degrees Kelvin.V.= voltage applied in fabrication technique.= junction voltage.

V, = junction voltage considered positive in reverse bias.V0=a constant of (8).V= punch-through voltage.w =effective base width.x =distance from the ohmic contact.v;=small signal amplitude of junction voltage.e=dielectric constant in rationalized units.

g =mobility of majority carriers in base region.i,u= mobility of minority carriers in base region.Po= resistivity of base region at low injection level.=lifetime of minority cart-iers in the base region.

co=angular frequency.

1957