avalanche injection

146 TEEE TRANSACTIONS O N ELECTRON DEVICES, VOL. ED-14, NO. 3, MARCH 1967 Properties of Avalanche Injection and Its A...

0 downloads 125 Views 1MB Size
146

TEEE TRANSACTIONS O N ELECTRON

DEVICES, VOL. ED-14, NO. 3, MARCH 1967

Properties of Avalanche Injection and Its Application to FastPulse Generation and Switching YOSHIHIKO MIZUSHIMA

AND

Abstract-The positive- and negative-resistance characteristics of the avalanche-injection diode are derived from a set of fundamental equations. The field dependence of the ionization rate-constant,the resistivity of the avalanching region, andtheinjected current are taken into account to compute the final voltage-current characteristics. From these characteristics, the transient electrical time constant for switching is estimated. The discussions of the injection-stimulatedavalanche are extended to a transistor for pulse generation a t a high repetition rate. Sharp pulses as fast as 500 MHz have been observed with this “injection-controlled avalanche thyristor.” The device is suitable for pulse amplification. Also realized are negative resistances in both emitterand collector characteristics, which also operate very rapidly. Discussions are speculatively extended to the possibility of a repetition rate ashigh as 1000 MHz.

INTRODUCTION

A

S THE T I M E CONSTANT of an ordinary semiconductor device is restricted by the driftvelocity of the carrier, v, an active element utilizing the avalanche effect is very promisingbecause of the improvement of the current rise-time constant into the form of l / a v [l] seconds). Thus the ionization rate constant a renders a device of very high speed. We intended to predict the whole range of voltagecurrentcharacteristics of theavalanche-injectiondiode [2]-[6], the L-H junction, from a set of fundamental equations, for which, as iswell known, it has been very difficult to find exact solutions. Gunn [3]treatedtheequationswith-reasonable As he simplifications to deduceanegativeresistance. took only an exponential function for a in its field dependence, the success of his work depended on the deduction of the negative resistance and not on turnover or sustaining voltage evaluation,which are required for any discussion of the switching properties and for proper extension to the avalanching transistor.T o compute the general curve one mustconsider the general behavior of the parameters, which have beendeniedin the usual analytical treatment. In PartI we shall show how the parameters determine the I/-J characteristics of theavalanche-injectiondiodes, which is an improvement of Gunn’s analysis. With V-J characteristics onecan determine ideally the electricalswitchingtime-constant, whichis very Manuscript received March 10, 1966; revised December 23, 1966. The authors are with the Electrical Communication Laboratory, Nippon Telegraphand Telephone Public Corporation,Musashino-shi, Tokyo, Japan.

YOSHIHARU OKAMOTO

much faster than that of hitherto known negative-resistance switches. In Part I1 the predicted property of the “injectionstimulated avalanche thyristor77 is extended to a thinbasetransistor, where aninjection from theemitter stimulates an avalanche in the collector region. In this way a high-repetition-rate pulse trainisfoundtobe generated when the avalance switches off each time by itself,or a bistablenegative-resistanceswitching is realized when the avalanche is in the stationarystateeither condition depending on the degree of limitation of the injection. Explanations of the above operation are given. Forhigh-repetition-rate pulse generation, theimportance of theemittertimeconstantis discussed.

PARTI : ANALYSISOF

THE

AVALANCHE INJECTION

Derivation of the StaticProperty

In the following theequations shallbe treatedin rationalized MKS units. Equations of continuity and Poisson’s equation are dP

-=

at

g

- Y - - div J p 4

I

dn

- _- g - r + - d i v J , 4

at

div E

4

=-

J

[F - 9% + (immobile charge density)],

(2)



where p and n are the hole and electron density, J p and J , thecorrespondingcurrentdensity,respectively; g and r arethegenerationandrecombinationrates; E the field intensity; E the dielectric constant;andthe other notations are as usual. Following Gunn, several assumptions will be made: 1) For static characteristics

ap---an _- 0. at

at

2) As the electric field is very high, the drift velocity reaches its saturation value v , ~ and , the diffusion current may safely be neglected. 3) Length of the space-charge-free drifting space is made sufficiently thin so that the voltage drop lies exclusively in the space-charge region.

MIZUSHIMA AND OKAMOTO: PROPERTIES OF AVALANCHE INJECTION

4) Electronsand holes are considered to be of equal property, except for the sign of charge. 5) Recombination is neglectedmainlyforease of mathematical treatment. This is true when the medium is thin as compared with the path in lifetime, or when the current density is not too high. 6) Weassumemostly a one-dimensionalcasein the x-direction, ignoring the criterion for the transverse stability, although the turnover property was .~ explained in detail by Gibson [4] as due to the current-constriction effect.

147

n+

n

n

n+

b

(a) Flow of mobile chargein the sustained state in the avalancheinjection diode. Before triggering only the mobile charge N exists t o balance the ionized immobile impurities (not shown).

With these simplifications in a L-H ( n f - n )structure [Fig. l(a)], the above equations lead to the following:

so that

(b) Flow of mobile charge after the turnover in the collector region of a transistor (bistable operation). In a static configuration it is impossible to determine when the electron supply from the emitter is insufficient, so that the avalanche ceases automatically (pulse oscillation). Before the triggering charge no is injected, there exist only ionized immobile impurities (not shown). Fig. 1.

The electron current J , is divided into three partsJ n t ,JN, and J o ;n‘ and JnJare that partof the multiplied electron density, and the corresponding current, due to the “intrinsic avalanche” ( N = no = 0) treated by Gunn ; N and J N are the effective donor density and the corresponding current; gN is not included in thespacecharge contribution; no and J Oare the “injected” carrier density and the corresponding current. The term “injection” originates in the work of Gibson [4] and refers to the intentionally injected current (as from the third electrode) so that Jo can flow independent of avalanche. I t presumes the case of a transistor which will be discussed in Part 11. The ionization rate constanta ( E ) is given by McKay Fig. 2. Ionization rate constant asafunction of the electric field. andothers [7]-[12]. AlthoughsometheoreticalfuncCurves are combined to yield various V-J characteristics. Also taken from shown for comparison is an experimentalcurve tions are proposed 1131- [l5], they are neither easy in McKay [7]. Curves a , b, and c specify parameters for reference integrationnor inclose agreementwiththe experiin the following figures. mental value. Therefore, we tentatively choose the following functionalform, as given in Fig. 2, varying is depleted [Fig. 1(b) 1. We assume throughout that the than x. (cf. Fig. S), so that parameters as a , b, and c. The function is divided a t depletion layer is thicker thesituation is simplydescribed as n+n(depl).With point E , into two parts: relatively large current density the effect of the built-in a ( E ) = aOEmexp (alEm+l) for 0 5 E _< E, field due to the collector p - 9 2 junction becomes small 17). Therefore, = a2 E 2 E,. ( 5 ) enough to reachanavalanche(cf.Fig. the calculation for the avalanche-injection diode, n+-n Avalanche Injection in the Depletion Layer structure, is also tentatively applied. I and J, denote Consider an avalanche in the depletionlayer of a the ionized donordensityandthecorrespondinghypun+ junction, or rather in the collectorregion of an pothetical current defined by epitaxial-planar transistor, where the collector n-layer

IEEE TRAXSACTIOXS MARCH ON DEVICES, ELECTRON

148

1967

The term “injection” is the same as before but here i t Theturnovervoltageistwotothreetimeslarger acquires a practical meaning as the injection electroln than the value predicted by Gibson [4] when the corresponding x. is assumed tobeequalto Gibson’s dot through the base into the collector region. The equations withJI are analogous with those of J a - ; radius y o , although the critical current densities a t VT agree with each other. J = J, J, = Jpf i-J o In Fig. 5 the state of our computation on VT of n+-n junction is compared with the usual breakdown voltage aE ( B V ) of a p-n junction[7],[9],[16], [17]. Forthe ( p - ?$ - a0 I). ax E curve m = 3 , Jo is arbitrarily chosen as 1.6A/cm2or no= lo8 ~ m - ~For . the curve m = 6 an approximate Details of the calculation of the above set of equa- solution was tried to fit with the BV. This figure intions are described in Appendix I. dicates the similarity to the real p-n junction case and the importance of the space-charge field due to mobile Numerical Results carrier. Punch-through-voltage ( V ~ Tin) the usual sense The results of computation of V--7 characteristics are is also shown for convenience in a later section, where shown in Figs. 3-7, where the adopted functional form the parameter is the base width. of a(E) has been given in Fig. 2, McKay’s data being In Fig. 6 the numerical resultis alsoshownwith considered as the standard. Relative permittivity is 12, injectionas a parameter: m = 1 and N < 10l2 ~ r n - ~ and v, = 107 cm/s as for silicon. (nearly intrinsic). I t is seen that VT decreases with inT h e results are of the required magnitude, although jectionnearlyaswithimpuritydensity,as supposed the current density is not directly comparable to the by Gibson. reported value, as the effective area is not easily deIn Fig. 7 turnovervoltages of the n+-n (depl) and termined and is variable as a function of current. For n f - p (depl) junctions, whichis consideredanalogous instance, in the negative-resistance region the current to the collectorbreakdown voltage (BVcB)of a tranhas an inherent tendency to constrict of itself. sistor, are computed as a function of the injected elecIn Fig. 3 we see the case of m = 1/2 and 1 for the tron current from the emitter into the collector region. nearlyintrinsic,noninjecting case (no= N < cn1-3), Results of boththe nf-n(dep1) andthe n*-p(dep1) where the V-J characteristics are shown to depend on arenot far apart, so long astheinjectedcarrier is theshift of alphain Fig. 2 . Largeralpharesults in greater than the impurity density. The main result to lower turnovervoltage which is especiallysignificant be noted in Fig. 7 is that B VCBdecreases with injection. for low-field values. Figure 8 gives some examples of space-charge region T h e minimum sustaining voltage appears to be due thickness xg. For high current density x0 is relatively to, and exclusively determined by, the saturationof the ionization rate. The minimum voltage becomes smaller as alpha increases, as is expected. The reported minimum voltage, 10 to 20 volts for silicon, agrees with the known saturation value of alpha (-lo5 cm-l), and for lower voltageanabnormallylargealpha will berequired. In the negative-resistance part of the voltagecurrent characteristics the terminal voltage is proportional to the inverse root of the current density, and proportional t o ( E V J ~which / ~ , is consistent with Gunn’s result [ 3 ] .As we have neglected the contribution of the diffusion term and the potential drop outside thespacechargeregion,theaboveresultinthelow-current densi.ty region is less exact than elsewhere. Figure 4 shows the results of variation of m from 2 to 6, which are qualitatively indifferent to each other. In this case the resistivity of the medium is taken as a parameter.Otherwise, for intrinsicmaterialtheturnover point is not to be deduced except a t m J($)'+

sign is pre-

4 a z ~ . ~ ~ a d B . (11)

and

+y ($>'I -

MIZUSHIMA AND OKAMOTO: PROPERTIES OF AVALANCHE INJECTION

155

If we neglect J N and Jo (intrinsic semiconductor without injection), where

So in the purely intrinsic case the turnover voltage VT is not to be deduced if m 2 1. Avalanche-Injection in the Depletion Layer

so that

In the case of the depletion region of a transistor, (6) is solved in the same way as shown above. The result is 1

For J o = Q the integration is simply accomplished by using again an approximate function Y o ( E ) which should be graphically determined:

Y(E)

-

(21,

-J

+

JI)

aJ, I _

=

dE

EV,

and

+ Y o @ )= K I E ( ~ + exp ~ ) ’ (it2E(3-m)’2), ~ m &) and from % = x c to xa ( E S E , ) . A t x=x, the valueof J,/ J is connected continuously. The result is

1 = 4~n,[az(Eo - E,) -!- { YII(E,))~]

APPENDIXI I CONSIDERATION FOR IMPROVEMENT THE REPETITION FREQUENCY (ROLEOF EMITTER TIMECONSTANT)

SPECULATIVE

OF

In Fig. 14 the emitter fall time is represented by

-

CERE‘In

(l+

1

-

V E Bv p

vi1

1,

(23)

where C, is the emitter capacitance,V, the peak height (see Fig. IS), and Vi theinjection level. In this case RE’ is the total effective emitter resistance. Thus the limit of pulse fall time is determined by the emitter time constant. Low- Field Approximation Under high injection the maximum attainable repetiIn the low-field range a ( E ) takes the form of acEm tion is limited by the pulse width itself (almost by the emitter fall time),andtosomeextentrelatestothe and we get emitter cutoR frequency but not to the collector cutoff frequency. The insensitiveness to the collector capacitance allows us to use the grounded-collector connection which is advantageous over the P T M case with respect to the heat-dissipation problem. The characteristic frequencyfr has the form of an inverted sum of cutoff frequencies of the emitter, base, and collector, as I n general,theanalyticaltreatment of thebinomial integration is possible when m - 1 or 3. For m = 3 , 1lfT = l/fE 1 l f B -!- l l f c . (24)

+

Other things being statistically averaged out, f~ or the maximumrepetitionfrequencyshould be in superlinear relation with fp. This is proved very roughly, as shown in Fig. 19 where various transistors (of epitaxialplanar or -mesa type, germanium or silicon) have been

156

I E E E TRAKSACTIONS ON ELECTRONDEVICES,MARCH

..

1967

.. ;

1

VEB

;\

i\

ii

. i .. .. .;. L - - L

mitt& supp$; X - - ,

*;+

-0.6 V \

, \

-

i

&e. time .

.$-+ .

fa//time Fig. 18. Emitter potential to explain the sawtooth behavior of Fig. 14. The emitter potential follows the heavy line when the avalanche occurs and ceases, until at the injection level it is fixed.

5-N Fig. 20. Schematicdiagram of the breakdownvoltage ( B V ) dependence on theimpurityandthe injectedcarrierdensity. Punch-through-voltageplaneintersectswith the B V plane as indicated. Upper region belongs to P T M transistor. The no-axis relates to the repetition frequency (Fig. 13), and at the right end there exists another limit duetotheemittertimeconstant, where the pulse width becomes comparable or equal to thelength of one cycle.

301 100

I

300

I

I

. .., *

1000

fr (MC)

Fig. 19. Relation between maximum attainable frequency (solid circle) of various transistors (silicon or germanium) versus their characteristicfrequency f ~ Arrows . indicate alpha-cutoff frequency. Open circles represent another mode of oscillation shown forcomparison, which relatesdirectly t o ST. I t is observed in the same circuitry but with heavy injection. I t is different from ’ our mode in the following respects: the collector bias islower than the avalanche-multiplication region, the waveform is sinusoidal and of invariable frequency, and there is a delay time for the buildup of oscillation (-10 ns).

tested for themaximumrepetition of our mode. (In Fig. 19 the open circles represent another mode of oscillation shown for comparison. With the collector voltage lower than the avalanche region and with larger injection, a sinusoidal oscillation of invariable frequency is observed in the same circuitry. The frequency of this mode is in linear relation with f T ; it may be attributed to thephaseshift of theusualcurrent-amplification factor aceat high frequency.) In Fig. 20 the breakdown-voltage characteristics described in Part I are represented schematically, where the collectorbreakdownvoltage is a function of impurity density and injection density (cf. Figs. 5 and 7). VpT diminishes slightly with injection [25]. When the V& plane is lower than the avalanche breakdown plane, the mode of the P T M transistor operates; our mode’s operation is shown in the hatched area.

In Fig. 20 high repetition frequency is realized with large injection and low breakdown voltage. Low collector voltage is advantageous in low collector power dissipation or large current. High emittercutoff frequency is verydesirable in tworespects: 1) thelargecharge density for triggering is efficiently injected in a short period of time, and 2) the external RE can be made correspondingly small and therefore the emitter fall time is minimized. By considering the above effects,a repetition as high as 1000 MHz is estimated to be possible by using the epitaxial-planar structure and the relatively small. lead inductance.

ACKNOWLEDGMENT The authors are very grateful to Dr.T. Niimi, Dr. Y . Shigei, and Dr. N. Kuroyanagi for their encouragement and discussion of this material.

REFERENCES [l] A. von Engel, “Ionization in gases in electric field,” Handbuch d. Phys. Berlin: Springer-Verlag, vol. 21, 1956, pp. 504-573. [2] J. B. Gunn, “Avalancheinjection in semiconductors,” Proc. Phys. Soc. (London),vol. 69B, pp. 781-790,1956. -, “Highelectric field effects in semiconductors,” Prog. in Semiconductors. vol. 2. London: Wevwood and Co. Ltd., 1957, pp. 213-247. A. F. Gibson and J. R. Morgan, “Avalanche injection diodes,” Solid-State Electron., vol. 1, pp. 54-69, 1960. C . A. Hogarth, “A method of making negative-resistance twostate switching diodes,” Solid-State Electron., vol. 1, pp. 70-74, 1960. W. Rindner and A. P. Schmid, “The BNR diode, a currentcontrolled negative-resistance device,” I E E E Trans. on Electron Devices, vol. ED-11, pp. 136-147, April !964. K: G. McKay, “Avalanche breakdown in s11Icon,” Phys. Rev., VOI. 94, pp. 877-884,111954. A. G. Chynoweth,Iomzation rates for electrons and holes in silicon,” Phys. Reo., vol. 109, pp. 1537-1540, 1958. S. L. Miller, “Ionization rates for holes and electrons in silicon,” Phys. Rev., V O ~ . 105, pp. 1246-1249,1957.

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL.

ED-14,NO. 3, MARCH 157 1967

1101 A. G. Chynoweth, “Uniform silicon p-n junctions: II-Ionization rates for electrons,” J . Appl. Phys., vol. 31, pp. 1161-1165, 1960. I l l ] C. A. Lee, R. A. Logan, R.L. Batdorf, J. J. Kleimack, and W. Wiegmann, “Ionization rates of holes and electrons in silicon,” Phys. Rev., vol. 134, pp. A761-A773, 1964. [I21 J. 2.Moll and R. van Overstraeten, “Charge multiplication in silicon p-n junctions,” Solid-StateElectron., vol. 6, pp. 147157, 1963. [13] W. Schockley, “Problemsrelated to p-n junctions in silicon,” Sold-SLate Electron., vol. 2, pp. 35-57, 1961. [14] P. A. Wolff, “Theory of electron multiplication in silicon and germanlum,” PAY!. R e d . , vol. 95, pp. 1415-1420, 1954. [15] G. A. Baraff, “Dlstribution functions and ionizatlon rates for hot electrons in semiconductors,” Phys. Rev., vol. 128, pp. 25072517,1962. [16] J. Maserjian, “Determination of avalanche breakdown in pn ]unctions,” J . Appl. Pkys.i(Letters), vol. 30, pp. 1613-1614, 1959. [17] C. D. Root, D. P. Lieb, and B . Jackson, “Avalanche breakdown voltages of diffused silicon and geranium diodes,” IRE Trans. on Electron Devices, vol. ED-’7, pp. 257-262, October 1960.

[18] H. Fukuiand T. Matsushima, “Switchingcharacteristics of Esakl-diodes,” J . Inst. Elec. Commun. Engrs. (Japan), vol. 44, pp. 479-484, 1961. 1191 D. J.. Hamilton, J. F. Gibbons, and W. Schockl;y, “Physical princlples of avalanche transistor pulse circuits, Proc. IRE, vol. 47, pp. 1102-1108, June 1959. [20] W. Shockley and J . Gibbons, “Theory of transient build-up in avalanche transistors,” Trans. AIEE, no. 40, pp. 993-998, 1959. [21] J. R: A. Beale, W. L. Stephenson, and E. Wolfendale, “A study of hlgh-speed avalanche transistors,” Proc. IEE (London), vol. 104B, pp. 394-402, 1957. [22] T . Misawa, “Negative resistancein p-n junctionsunderavalanchebreakdown conditions: I and 11,” IEEE Trans. on Electron Devices, vol. ED-13, pp. 137-151, January 1966. [23] B. K. Ridley, “Specific negative resistance in solids,” Proc. Pkys. SOC.(London),vol. 82,pp. 954-966, 1963. [24] H. Schenkel and H. Statz, “Junctiontransistorswith alpha greater than unity,” Proc. IRE, vol. 44, p p . 360-371, March 1956. [25] M. Watanabe, private communication.

Effect of Surface Fields on the Breakdown Voltage of Planar Silicon P-TZJunctions ANDREW

s. GROVE, MEMBER, AND

IEEE, OTTO LEISTIKO, JR., WILLIAM W. HOOPER

MEMBER, IEEE,

Absfracf-The effect of surface fields on the breakdown voltage the field distribution within the depletion region near of planar silicon diodes is studied experimentally and theoretically. the surface would be altered, bringing about a change I t is shown that thebreakdown voltage can be modulatedover a very wide range by the application of an external surfacefield and that it in the breakdown voltage of the device. The effect of variousambients on the breakdown tends to saturation at a maximumand ata minimum valueas the gate voltage is varied in such a way as to deplete the lowly doped and voltage of germanium transistors was demonstrated by highly doped sides of t h e junction, respectively. Both the high- and Wahl and Kleimack [2]. Forster and Veloric [3] found the low-voltage saturation of the breakdown voltage appear to be due that the breakdown voltage of germanium diodes could to the formation of field-induced junctions which prevent further also be modulated with potential applied to a field plate variation in the shape of the depletion region, and hence the break(or gate) placed over the p-n junction. More recently, down voltage. Between these two extremes, the breakdownvoltage i s found to be approximately given by BV=mVc+constant, where Shockley and coworkers [4] showed that ions migrating V Ois the gate-+substrate potential. The slope m approaches unity on the surface of a silicon dioxide layer overlying a silifor low substrate impurity concentrations and for smalloxide thickcon p-n junction influence the breakdown voltage of the nesses. Numerical solutions of the two-dimensional potential disas predicted byGarrettand tribution problem give results which are in general agreement with junctionqualitatively Brattain [l]. In addition, Shockley and coworkers [4] the above experimental observations.

as well as others [5]-[7] notedthatthebreakdown voltage of planar silicon diodes can be modulated with potentialappliedtoa field plateoverthejunction. H E E F F E C T of surfacecharges on thebreakShockley and Hooper [8] proposed to put this phenomdownvoltage of p-n junctionshas longbeen recognized. GarrettandBrattain 111 suggested enon-the modulation of junctionbreakdownvoltage that in the presence of surface charges field lines in the by externally applied surface fields-to practical use in named the “surface controlled avalanche junction depletion region can terminate on these charges a device transistor. ” rather than on the impurity ions within the depletion The purpose of the present work is to consider the region. As a result, the shapeof the depletion region and effect of surfacefields on the breakdownvoltage of planar silicon diodes in greater detail. First, experiments Manuscript received August 31, 1966; revised October 3, 1966. A. S. Grove and W. N. Hooper are with Fairchild Semiconductor on gate-controlled $+n and n+p diodes having various Research and Development Lab., Palo Alto, Calif. 0. Leistiko, Jr., is with the Technical University of Denmark, oxide thicknesses and substrate impurity concentrations Lundtofte, Lyngby,Denmark. aredescribed. Then, the manner inwhich the break-

I. INTRODUCTION

T