IEEE TRANSACTIONS O X ELECTRON DEVICES VOL. ED-13, NO. 7 JULY 1965

Gate Turn-Off in p-pz-p-pz Devices

Abstract-A simple two-dimensional model for gated turn-off of a p-n-p-n device is used to derive an expression relating the storage time and the turn-off gain. The observed dependence of storage time on turn-off gain fits the derived expression well for devices specially fabricated consistant with the assumptions of the model. The fall time is discussed qualitatively.

INTRODUCTION HILE SEVERAL authors have discussed the gate turn-off of p-n-p-n switche~,l-~ there has been no attempt to give a physical description or

formalization of the transient effects during gate turn- off. We have measured the storage time of special gold- doped GCS (gate controlled switch) structures as a func- tion of turn-off gain and found a nonlinear relationship between these parameters. I n this paper we will propose a model which will relate the storage time and turn-off gain for these special gold-doped structures. From this model we shall derive expressions for the storage time t , (see Fig. l), and the amount of current which can be controlled. Results of measurements of storage time will be presented and compared with expressions derived from the model. Results of measurements of the fall time (see Fig. 1) will also be presented along with a qualitative discussion of the factors affecting fall time.

I n order to turn off a p-n-p-n device, the excess carriers (carriers in excess of the equilibrium values) must be removed from the bases of the device. Of course, the excess of both types of carriers must be removed, but since in most cases in semiconductors space charge neutrality must exist, removal of one type of carrier is always balanced by removal of a carrier of the opposite type. Thus, following a common practice in this type of prob- lem, we will concern ourselves only wit’h one type of excess carrier which we shall choose to be the minority carrier.

A detailed qualitative description of the minority carrier distribution a t various stages in the turn-off will precede the derivation of the storage time and the maximum cur- rent which can be controlled. Briefly, however, the min- ority carrier plasma in the iron" region of the GCS is

paper was presented In part at the 1964 IEEE Electron Devices Manuscript received August 25, 1965; revised April 4, 1966. This

Meeting, Washington, D. C. The author is with Westinghouse Research Laboratories,

Pittsburgh, Pa. 1 R. H. van Ligten and D. Navon, “Base turn-off of p-n-p-n

switches, 1960 IRE W E S C O N Conv. Rec., pt. 3, pp. 49-52. 2 J. M. Goldey, I. N. Mackintosh, and I. M. Ross, [‘Turn-off

gain in p-n-p-n triodes,” Solid-State Electronics, vol. 3, pp. 119-122, April 1961.

n-p-n-p silicon-controlled rectifier,” IEEE Trans. on Electron a D. R. Muss and C. Goldberg, “Switching mechanism in the

Devices, vol. ED-10, pp. 113-120, May 1963.

J1 J2 J3

“A

t ,--- Switch Closed

Fig. 1. GCS with gate biased for turn-off.

Fig. 2. Hole and electron flow in a partially turned-off GCS.

“squeezed” toward the center of the active area of the device (see Fig. 2) until the device finally turns off. The storage time t , can be divided into the time required to “squeeze” the plasma to a size such that the minority carriers in the center of the plasma can be reduced by the gate current, and the time to reduce the minority carrier concentration in this plasma to values such that the blocking junction comes out of saturation or forward bias. We will derive an expression for the former which for the turn-off conditions of interest is several times the latter. Thus, the latter time is neglected.

An expression for the velocity with which the edge of the ((on” region is “squeezed” will be derived for constant gate current. Minority carrier transport at the edge of the ((on” region will be considered only from the point of view of their removal by the gate current opposed

590

1966 WOLLEY: TUXN-OFF IN p-n-p-n DEVICES 691

by the diffusion of carriers in a direction opposite to the gate current. When these currents become equal, as happens for low gate currents, the velocity goes to zero and the storage time becomes infinite. The storage time t, will be obtained by integrating this velocity from the edge of the emitter to the dimension a t which the con- centration in the center of the plasma begins to be reduced. This dimension will be selected to be an arbitrary con- &ant L,, which is of the order of the diffusion length of minority carriers in the base to which the gate lead is attached. An expression for the maximum current which can be controlled will be derived in terms of the maximum turn-off gain, the reverse breakdown voltage of the emitter adjacent to the gate, and the resistance of the base under that emitter.

THEORY

.&lode1 Figure 1 shows a GCS in a circuit biased for turn-off.

In this paper, Region I will be referred to as the cathode emitter, Region I1 as the gat’ed base, Region I11 as the ungated base, and Region IV as the anode emitter. Gate turn-off is accomplished by reverse biasing the cathode emitter. In order to reverse bias the cathode emit,ter, excess carriers must be removed from the gated base of the switch. The removal of carriers and turn-off s tark from the edge of the emitter adjacent to the gate contact. Figure 2 shows a GCS which is partially turned off. The portion of the cathode emitter junction J , ad- jacent to the gate contacts is reverse biased, and the portion of the blocking junction J , underneath the reversed biased part of J 1 is no longer forward biased or in saturation in transistor terminology. The excess car- riers in the gated base below the portion of the junction J , which is reversed biased have been removed. Thus, the gate current I , must flow laterally through a base resistance determined by the geometry of the cathode emitter and gate, the gat,ed base width, and the un- modulated conductivit’y of the base. I n this intermediate state, the central portion of the device is still “on”; i.e., the blocking junction J,, and the cathode emitter junc- tion J , , are forward biased. The anode current is relatively unchanged and is determined by the external circuit. Since the ‘(on” area has been reduced by the gate cur- rent, the current density in regions that remain (‘on” is higher than when the whole device was conducting. The concentration of current into a smaller region will be referred to as (Lsqueezingf’ of current or “on” area. This is analogous to “crowding” in transist,ors but op- posite in that in crowding” the current is concentrated or “pulled” toward the emitter periphery, while in this case the current is “pushed” away from the periphery. In addition, the “squeezing” is a dynamic situation while the term “crowding” in transitors usually describes a steady-state situation.

We will obtain the velocity with which the “on” region is “squeezed” by a constant current gate pulse by con-

lpKx I slope = - - 1

0 ’b ( b) ( cl

Fig. 3. n/Iodel for deriving the velocity of turn-off in a GCS.

sidering the net rate of removal of minority carriers from an elemental volume at the boundary between the “on” and “off” regions, as seen in Fig. 3(a).

An exact solution for the velocity depends on the ratio of the excess carrier density to the equilibrium density and cannot be obtained in closed form. An equation for the velocity considering both majority and minority car- riers is obtained in the Appendix. Using an extremely simplified model involving assumptions which are re- latively poor, we can obtain an expression for the velocity which has the same general form as the more exact solu- tion for high level injection, and using this model, an expression for the storage time can be obtained in closed form with a single arbitrary parameter, L,. The parameter L, is the effective diffusion length of elect’rons in the assumed solution at the edge of the (‘on” region and is a function of the electric field, the minority carrier life- time, and the ambipolar diffusion constant. In the sim- plified model the net rate of removal of electrons at the left-hand boundary in Fig. 3(a) will be assumed to be the gate current minus the diffusion current of electrons into the elemental volume. The widt’h will be assumed to be large enough such that at the right-hand boundary the current is entirely due to holes and thus the minority carrier current is zero. Part of the cathode emitter junc- tion J , is forward biased and part is reverse biased, and the blocking Junction J , may also be both forward and reversed biased in this region. I n fact, part of the reverse gate current may be in the x direction rather than in the x direction. We will combine any such current with the x-direction component which is independent of x and neglect any net gain or loss of carriers from the elemental volume in the x direction. The minority charge density in the elemental volume w7ill be approximated by the densit,y in the region. While t’he density is not equal to t’his value, it is proportional to it. Finally, in the simplified model we will neglect recombination in this transition region. All three of the latter assump- tions are poor but they will suffice to give the form of the dependence of velocity on gate current, if not an exact relationship.

502 IEEE TRBKSBCTIONS ON ELECTRON DEVICES JULY

The concentration of the minority carriers in the “on” region will be obtained in terms of the current density in the “on” portion of the cathode emitter. It will be assumed that, as the turn-off proceeds, the redistribution of minority carriers in the “on” region is sufficiently rapid that the density of carriers is a function only of the “on” a,rea and not of time. This is true if storage time or the sweep-out time is greater than the transit time across the gated base. For low gate currents the assump- tion is satisfactory, but for high gate turn-off currents or low turn-off gain the storage time approaches the gated base transit time and the assumption is not so good.

Since GCS devices generally have gate contacts on both sides of the cathode emitter stripe, it will be assumed that the “on” region is “squeezed” uniformly from both sides. Derivations will be made considering one-half of the emitter of width S / 2 , and the gate current for this part of the emitter will be assumed to be I G / 2 , as seen in Fig. 3 (a).

The minority carrier distribution in the ((on” region of the gated base will be assumed to be as shown in Fig. 3(b) ; i.e., only diffusion current in the x direction is assumed. This is a reasonable approximation for an n-p-n-p structure in which the gated base is relatively narrow and the ungated base is wide compared with the minority carrier diffusion length in t,hat base. Both of these requirements are met in the gold-doped device to which comparison of the model and experiment will be made. Further, the minority carrier concentration at the center junction cannot be zero if the device is to be and this junction forward biased. Just as there is some penetration of the minority carrier distribution into the collector region of a transistor in saturation, there will be a penetration of the minority carrier dis- tribution of the gated base into the ungated base region of the GCS. In this case the gated width could be replaced by wei, which would be greater than the physical base width w,. We will make the derivation using the physical base width. We will assume no variation of carrier con- centration along t’he length of the emitter, the y direction in Fig. 3.

Velocity of Tum-O,f f Using this model, we now derive an expression for the

velocity of “squeezing” of the ‘lon” region from which the storage time will be derived. The concentration of minority carriers in the gated base is a function of both x and E (see Fig. 3), and can be written as

4 x 9 4 = n(x)f(.>. (1)

The x component of the current is given by

J.(E, z) = eD, an(x, x ) / & ,

or

J,(z, z) = eD,f(z) an(z)/az. (1)

The gradient in the x direction has been assumed to be constant.

an(x ) /dx = -n,/w, ( 3

and

n(4 = 4 - 4 ~ 3 , (4) where n, is the concentration at the cathode emitter.

The x dependence of minority carrier concentration as shown in Fig. 3(c) is

f ( x ) = 1, 0 < x 5 Et,) (5) and

f ( X ) exp { -(X - X b ) / L , } $6 5 X < (6)

where L, is an arbitrary constant which is a function of the electric field, lifetime, and ambipolar diffusion con- stant.

The cathode current is

1K/2 = I , = /- J E ( x , %)T dx 0

= - Ten, D, dx lw, X b

- I, Ten, D, exp { - ( x - xb)/Ln) dx/wp

= -Ten, Dn(xt, + L n ) / W p , (7)

where I , = the total cathode emitter current, T = the length of the emitter stripe, and (7) can be written as

In,\ = W , I K / ~ T ~ D , ( % f Ld - (8)

The lateral diffusion current which flows into the elemental volume Tw,Axb from the (‘On” region iS

Iz(X*) = jWP TJm(S*, 2) dz. (9)

Jr (xb , x> = eD, W X , 4/dxIr=zb

= eDnn(z)f‘(Eb>

= -eD,n(z)/L,. (10)

Substituting (4) and (10) into (9) and integrating,

Iz(x,) = -Ten. D,w,/2Ln. (1 1)

The minority charge in the elemental volume which is negative because it is electronic is given by

W D

A& = -AXb / Ten ( x , x) dz. (12)

Using the approximation that f ( x ) ‘V f ( x 6 ) = 1 through- out t,he Axb region, n ( z ) is given by (4), and (12) becomes

AQ = -Te In, 1 w,Ax,/2. (13)

1966 WOLLEY : TURN-OFF IN p-n-p-n DEVICES 593

boundary:

dx,/dt = - ( IQ/ I~ (2Dn/w3 (x, + Ln) + Dn/Ln* The cathode current during turn-off is given by

I K = I , - I C . Let us define

it, = ~ : / 2 D n , the diffusion transit time for the gated base.

If we define the turn-off gain as

P = IdIr7, then (16) can be written as

dxb/dt = -t;:(/3 - 1 ) - ’ ( z b + L,) + D,/L,.

Storage Time

The net rate of change of positive charge in the elemental volume is the sum of the convent’ional currents and is given by 11

AQ/At = 1 Q / 2 + I,. (14) Substituting (1 1) and (13) into (14) one gets

-Te [ne\ wpAxb/2At = IQ/2 - Ten, Dnw,/2L,,

Axb/At = - (I&)(Te In, I Wp/2)-’ + D,/L,.

Combining (8) and (15) and taking the limit as Ax 3 0, I w

we get an expression for the velocity of the (‘on” state $j 1( 0

w

I - -4

I - -6

1

W ’ s =

P

Dn -

I I I O I mlJ -

27 l~

20crn2sec-1 L, = 65 -

Ln = 50 II b -

Ln = 35 IJ

-Theoretical

Expt. ( 1 amp1 Unit TO-1801

10 40 Turn-Off Gain, i3

(20) Fig, 4. Measured and theoretical values of storage time vs. turn-off gain for a GCS conducting 1 amp of anode current.

The storage time can be divided into the time required to “squeeze” t’he ‘(on” region until a one-dimensional 1 I 1 1 1 I

device is obtained and the time required to remove the excess carriers from the one-dimensional device. We will

- S = 6 0 0 ~

neglect the latter time and obtain the former by integrat- Dn = 20 c m 2 s e i 1 L,, = 50 1.1 ing (20) in x from X/2 to L,. We select L, as the lower limit of the integration because it will be a small dimen- sion of the order of the diffusion length minority of - -

for the storage time to one arbitrary parameter. Thus, Q 10-5- -

one-dimensional device and it confines the expression carriers which is a reasonable value for the size of the

the storage time is given by - - -

- w =311.1 - P -

- -

I

v) 0

-*

t , = (P - l ) t t , In SLJW; + 2LyW: - p + 1 4L3W: - p $- 1 (22)

0 Expt I1 amp1

Expt ( 2 amp) Unit TO-0704 i

I n (22) the storage time becomes infinite as the de- / - A 0 -

nominator of the logarithmic term approaches zero (see

turn-off gain Turn-Off Gain, p Fig. 4 and Fig. 5 ) . This condition specifies a maximum 1 10 40

I 0 I I I / 1

Fig. 5 . Measured and theoretical values of storage time VS. turn-off P(Max) = 1 + 4Li/w:. (23) gain for a GCS for one and two amps of anode current.

594 IEEE TRANSACTIONS ON ELECTRON DEVICES JULY

On the other hand, several authors,’-3 using st one- dimensional model, have derived a maximum turn-off gain, @*(Max), which is given by

@*(Max) = ~ n p n / ( ~ n p , -I- or,,, - 1). (24) The smaller of (23) and (24) will be the maximum gain

which can be attained with any device. One can consider that the gain given by (23) is the maximum gain that can be used to reduce the ‘(on” region to essentially a orie-dimensional device and the gain given by (24) is the maximum gain which can be used to turn off the one- dimensional device. Thus, the smaller of the two is the limiting gain.

E$ect of Base Resistance on Turn-Off Navon and van Ligten’ observed that one of the factors

limiting turn-off of p-n-p-n devices was the lateral drop of the gate current causing the cathode emitter to break down. With the proposed model, the resistance is largest when the ‘(on” region is reduced to its minimum dimen- sion L,. The resistance under the half-width of the emitter in Fig. 3(a) is

R = np(X/2 - Ln)/w,T (25) where p , is the average resistivity of the unmodulated, gated base. The product of the resistance given by (25) and the gate current cannot exceed the reverse breakdown voltage of the cathode emitter, V c B E ) K G . Thus,

V ( B R ) K G 2 I G A ( S / ~ LJ/2wpT. (26) When 111, << S / 2 , (26) and (19) can be combined to give

1, 2 ~ P ~ , B E , K G / & (27) where

R, = p,X/w,T (28)

and is the total resistance under the cathode emitter. This resistance is nearly equal to the resistance between the two gate contacts. Thus, the maximum anode cur- rent which can be turned off is given by (27) with P as given by the smaller of (23) or (24).

The cathode emitter breakdown will also put a lower limit on the turn-off time. As can be seen from (22), the storage time can be reduced by increasing the gate turn-off current, i.e., decreasing the turn-off gain. In the next section it will be seen that the fall time also decreases with increasing gate current. However, the turn-off times are not decreased much for increases in gate current beyond the value determined by (27). Excess gate current above that determined by (27) is not effective in removing minority carriers from the “on” region, since the excess will be avalanche current through the reverse biased cathode emitter.

Fall Time in Gate Turn-Off At the end of the storage time in a GCS, the bias on

the center junction is changed from forward to reverse. The fall time is determined by the time required to

remove the charge remaining in the two bases of the device, neglecting the charging of any junction ca- pacitances. The gate turn-off current aids in removal. of the carriers from the gated base; the minority charge, however, in the ungated base must either diffuse or drift to the center blocking junction J,, and be collected or recombine with majority carriers.

The fall time is then determined by considering the fall time of the two transistors, one of which has reverse base drive and one of which does not. The fall time of t.ransistors has been treated extensively in the literature. Hence, no attempt will be made to derive explicit rela- tions for the fall time of any particular structure. Instead, a few of the special considerations relevant to GCX’s will be discussed qualitatively.

The ungated base width Wn of a GCS is usually made relatively large in order that the device can block relatively high voltages and so that the turn-off gain can be made large by having a low a,,, [see (24)]. If the lifetime is large, the minority charge stored in this base is large and the characteristic time constant is

6, = w W 9 , , (29)

the diffusion transit time for minority carriers. The time constant associated with the ungated base can be made smaller by reducing the lifetime in this region, e.g., gold diffusion. The device will still switch when fabricated in this manner if the lifetime is not made too low. The Q! of the p-n-p portion may be maintained at the level required for switching by field-aided transport.“ Thus, the “on” forward drop would be higher by the product of the average electric field and base width. The transit time in a device in which the current is pre- dominately a drift current rather than a diffusion current is given by

&,(drift) NN wn/vd = w~/,uPVn (30)

where

vd = the drift velocity V , = the voltage drop across the ungated base p, = mobility of holes in the ungated base.

When the lifetime in the ungated base is small and t,, (drift) 5 t,,, then the removal of carriers in the un- gated base will take place at about the same rate as for the gated base. That is, the “squeezing” of the plasma of minority carriers in the ungated base will “follow” that in the gated base. If, however, the lifetime in the ungated base is large and t , , >> t,,, then the “squeezing” of the plasma of minority carriers in the ungated base will “lag” the “squeezing” in the gated base. In the latter case the plasma in the ungated base can be made to “follow” that in the gated base by using small gate turn-off currents (high turn-off gain), thus making t t , < t,.

The turn-off in a GCS with high lifetime in the ungated base is shown in Fig. 6. The trace to the left for the largest

4 R. W e Aldrich and N. Holonyak, Jr., “Multiterminal p-n-p-n switches, Proc. IRE, vol. 46, pp. 1236-1239, June 1958.

1966 WOLLEY: TURN-OFF IN P-n-p-n DEVICES 595

t u rn !Of/ Start of

- t Horizontal: 10 pseddiv Vertical: 0.5 amp/div From left to right:

IG = 1.0, 0.6, 0.4 amp p = 1.0, 1.7, 2.5

Fig. 6. Turn-off of a non-gold diffused GCS showing fall time characterized by two time constants.

gate current shows a small delay, a fall to 50 percent char- acterized by a small time constant (about one micro- second), and the remainder of the fall characterized by a longer time constant (about eight microseconds). Thus, the removal of carriers from the ungated base which is wider and has the longer time constant [‘lags” the removal in the gated base, and at the end of the storage time an appreciable number of carriers remains in this base as evidenced by the fact t’hat 50 percent of the fall is char- acterized by the longer time const’ant.

The traces to the right for smaller gate currents show longer storage times, a fall of 80 percent and 85 percent, respectively, characterized by the small time constant (again about one microsecond), and the rest of the fall characterized by a longer time constant (again about eight microseconds). With these turn-off conditions the reduction in the minority charge plasma in the ungated base “follows” that in the gated base better. The “squeez- ing” of the plasma in the ungated base results in a re- latively smaller number of stored carriers in this base because of a fall off in emitter efficiency in the lightly doped anode emitter with increased current density. Thus, the portion of the fall characterized by a longer time constant is less than for the large gate currents in which there is less “squeezing)) of the plasma in the ungated base.

EXPERIMENTAL All-diffused GCS’s were fabricated with a ring cathode

emitter which was about 600 microns wide. Gate contacts were placed on both sides of the ring structure in order to have a low base resistance R, and a large current turn-off capability. The inside diameter of the cathode emitter was large enough (0.135 inch) that the emitter could be considered as a linear strip and the measured storage time compared to the theory given by .(22). Gold was diffused into the ungated base through the anode emitter, The gold diffusion reduced the fall time of the device in accordance with the previous discussion. The

p-type base widths were made relatively small (20 to 30 microns). The relatively narrow gated base together with the gold = diffused ungated base makes the assump- tion of the charge distribution in Fig. 3(b) a reasonable one.

The measurements of the storage time and fall time were made using a low duty cycle tester which supplied constant-current, gate turn-on, and turn-off pulses with rise times of approximately 0.05 microsecond. The turn- off pulse was delayed 75 microseconds after the termina- tion of the turn-on pulse in order to insure uniform .two- terminal conduction at the beginning of the turn-off pulse. The maximum width of the turn-off pulse was 50 microseconds and the repetition rate was 60 seconds-’. The anode volt’age and the gate current were observed on an oscilloscope. The storage time and fall time (rise time of the voltage) were measured as a function of anode current, anode voltage, and turn-off gate current. The anode or supply voltage for all measurements reported here was 100 volts. The anode current being turned off was determined by dividing the anode voltage by the load resistance. The voltage wave form and current wave form as checked with current probe were nearly identical. The storage time was taken to be the time for the anode voltage to rise to 10 percent of the applied voltage after initiation of the gate turn-off pulse. Because of some ringing in the GCS’s with small fall times, the fall time of the current was taken to be the time for .the voltage to rise from 10 percent to 100 percent of the applied voltage for these devices.

COMPARISON OF THEORY AND EXPERIMENT The measured values of storage times a t various turn-

off gains are plotted in Fig. 4 for one of the gold-diffused GCS’s, TO-1801. This device had an emitter stripe width of about 600 microns and a gated base width of 27 microns. For the gated base doping profile obtained, the dlfFusion constant should range from about 10 cm2 s-l under the cathode emitter to about 35 cm2 s-l at the center junction. A value of 20 cm2 s-l fits the data best and is the value which was used. Curves computed from (22) using the above values of X, w,, and D, are plotted in Fig. 4 for L, with the values of 35,50, and 65 microns. The experimental data fit the theoretical curve fairly well for L, equal to 50 microns.

The storage times a t various turn-off gains of another device, TO-0704, of construction similar to TO-1801, but with a base width of 31 microns, were determined for both one ampere and two amperes of anode current. These data are plotted in Fig. 5. Again the supply voltage was 100 volts for both current’s. The theoretical curve for a base width of 31 microns with other parameters the same as for the TO-1801 device is also shown. Although the fit to the data is not as good as for TO-1801, the figure shows that the shape of the turn-off gain vs. storage time curves have the same relative shape independent of anode current. This result is expected from (22) where the storage time is a function only of the turn-off gain

596 IEEE TRANSACTIONS ON ELECTROK DEVICES JULY

’”%/ 1 i i I I 1 10 40

Turn-Off Gain, p

Fig. 7 . Fall time vs. turn-off gain for gold diffused GCS’s typical of three types of observed dependence.

as long as the gate currents are small enough to avoid the limitation of cathode emitter breakdown.

While the turn-off gain vs. storage time for all the gold diffused GCS’s fabricated had relatively the same shape, the turn-off gain vs. fall time curves differed considerably. Figure 7 shows three typical types of curves for devices turning off 2 amperes a t 100 volts supply voltage. No satisfactory correlation of the curve shapes to t’he device parameters such as base widths or base resistance could be made. If most of the carriers are st’ored in the gated base, the fall time should decrease with decreasing turn- off gains. The curves in Fig. 7 show that, in general, the fall time decreases with decreasing gain, but there are regions in which the fall time is relatively independent of gain for some devices. At low turn-off gains this could be explained by the same argument used before, that not all of the gate current is effective in removing carriers from the gated base because of breakdown in the cathode emitter; however, a t high turn-off gains, no explanation for the behavior is evident,

The maximum current which could be turned off with a gat,e drive of 50 microseconds, I A (max),,, was deter- mined for a number of different runs of the gold diffused GCS’s. These values of I , (max),, together with the resistance measured between the two gate contacts which is approximat’ely equal to R, in (28) are listed in Table I. From Table I it is evident that the lower the base re- sistance, the larger the current which could be controlled. The devices in Table I were all of the same basic geometry with slightly different base widths and base dopings giving rise to the differences in the base resistance. The cathode

emitter breakdown, V ( B R ) K C ) was relatively constant for all these devices. Ignoring any change in transport factor resulting from t’he change in the gated base doping profile, Table I generally confirms the relation between the maximum current and the base resistance given by (27).

TABLE I COMPARISON OF BASE RESISTAIZCE ASD

TURN-OFF CAPABILITY

Run ohms , amps

TO-07 To-08 I 18 6 7

TO-09 23 i TO-14 2

CONCLUSIONS Gate controlled switches were fabricated with relatively

small gated base widths and were gold diffused in t’he ungated base regions. The storage time of these devices increased rapidly with increasing turn-off gain. The fall times were small and not obviously characterized by two different times as were those devices which were not gold diffused. The dependence of the current value between the two time constants of the fall time (see Fig. 6) of a non-gold diffused device was attributed to the change in current density in the anode emitter with storage time. Long storage times allow for a redistribution or “squeezing” of carriers in the ungated base. The fall off of emitter efficiency at the higher current densities gives fewer stored carriers in the ungated base than in the case of short storage times associated with larger turn-off currents.

A model for gate turn-off of a GCS was devised and expressions for the velocity of turn-off, the storage time, and the amount of current which can be controlled was derived. The fit of the theory ot the experimental data as evidenced in Fig. 4 and Fig. 5 and Table I indicate that the assumptions and approximations are good for the gold-doped devices studied.

APPENDIX The equations for lateral current densities of the holes

and electrons at the edge of the “on” region in the gated base of the GCSs are:

and

where n and p are the excess concentrations and no and p , are the equilibrium concentrations. The total current density in the half-width of the emitter is a constant in x and is the sum of (31) and (32). Thus,

1986 WOLLEY: TURN-OFF IN p-n-p-n DEVICES 597

Jg/2 = Jne + Jw* (33)

Making the usual assumption of space charge neutrality €or semiconductor n = p and dn/dx = dp/dx, substituting (31) and (32) into (33), and solving for qE,

qE = J , / 2 - e (34) PAD, - DJ 2 n(pn + p p ) + popI, n b n + P A + POP, 8%

where no has been neglected compared to p o in the p-type base.

Subst’ituting (34) into (31),

where

f = 1 + ( 1 + po/n) /b . (3 6)

Assuming no generation and neglecting any net loss of gain of carriers in the x direction, the divergence of the electron flux is given by

1’ an - O*J, , = - + R e at (37)

where R is the recombination rate. Substituting (35) into (37),

D, - - - + R. (38) d‘n dn ax2 - d t

For n constant

or

(39)

Substit’uting (39) into (38) and solving for u,

where

F = po/bf2nZ. (41)

Equation (40) gives us the velocity with which some specified value of n moves through the base region. It is not a valid equation for all x and t because we have not accounted for the net influx of carriers in the “on” region which keeps n from decreasing with time in the (‘on” region. This can be done as was done in the simplified model by requiring the integral of n over all x and x to be a constant, i.e., ( 7 ) . In order to compare (40) to the velocity obtained in the simplified model, consider the case where D, = D, and b = 1. A solution of the form given by (6) will then satisfy the differential equation and (40) is given by

vn=const = - (J,/2e)F + DJL, - R/Ln. (42)

Equations (42) and (15) are of the same form except that in (42) F replaces 2/n. and (D, - R) replaces D,. Note that I,/w,T = J,. The factor F depends on the ratio of po to n or the injection level. F is a constant equal to p;‘ for po/n >> 1 and is po/4n2 for p , << 1. For p o / n SY 1, F is roughly proportional to l /n, the dependence obtained from the simplified model.

ACKNOWLEDGMENT The author wishes to thank Y. C. Kao, L. Saxon, and

R. Adams for assistance in fabrication of the devices, and R. Ravas and M. Sirchis for design of the turn- off test equipment.