Solid-State Electronics Vol. 35, No. 7, pp. 891-895, 1992 0038-1101/92 $5.00 + 0.00 Printed in Great Britain. All rights reserved Copyright © 1992 Pergamon Press Ltd

PARASITIC CONDUCTION CURRENT IN THE PASSIVATION LEDGE OF AIGaAs/GaAs

HETEROJUNCTION BIPOLAR TRANSISTORS

WILLIAM LIUt and JAMES S. HARRIS JR

Solid State Laboratory, McCullough Building No. 226, Stanford University, CA 94305, U.S.A.

(Received 28 October 1991; in revised form 9 January 1992)

Abstract--Passivating the extrinsic base surfaces of A1GaAs/GaAs heterojunction bipolar transistors with a thin A1GaAs emitter ledge is widely utilized to reduce the extrinsic base surface recombination current. The effect on current gain of this ledge being only partially depleted is analyzed. This analysis examines the ledge parasitic conduction current as a function of device geometry. Results indicate that even with an undepleted portion of the ledge as thin as 50/~, the elimination of base contact recombination current requires a passivation ledge length 6 times longer than from devices with a fully-depleted passivation ledge. The effect of a base quasi-electric field on the current gain as a function of passivation ledge distance is also discussed. This theoretical analysis is compared with published experimental work.

I. INTRODUCTION

Typical emitter-up AIGaAs/GaAs heterojunction bipolar transistors (HBTs) are fabricated with mesa etching techniques which create an exposed extrinsic base surface. Because of free GaAs surface is charac- terized by a high surface recombination velocity[l], the extrinsic base surface recombination current can be a major component of the overall base current[2]. To increase the current gain, passivation to this extrinsic base surface by having a thin depleted AIGaAs layer on top of this surface is often used[3-6]. However, if the passivation ledge distance (between the base and emitter contacts) is very short, then a significant number of minority carriers, which diffuse sideways without getting recombined at the passivated extrinsic base surface, would finally reach the base contacts. Since an ohmic contact surface can be considered as one with infinite surface recombina- tion velocity, the recombination current at the base contacts would still limit device current gain to low values even though the extrinsic base surface recom- bination current has been eliminated by the passiva- tion ledge[3,7]. Theoretical solution to the 2-D current continuity equation in the base region indi- cates that the minimum passivation ledge distance needed to suppress the base contact recombination is roughly 3000 A[8].

This theoretically calculated minimum distance, however, is significantly shorter than the experimen- tally observed value of 2 + 0.5 lam[3]. One possible explanation for this discrepancy is that the passiva- tion ledge in the devices described in Ref. [3] might not be fully depleted by the combined free surface

tCurrently with Central Research Laboratories, Texas Instruments.

and base-emitter junction depletion regions. When the base-emitter junction is forward biased, the junc- tion depletion region decreases and parasitic emitter current will first flow through the undepleted portion of the passivation ledge and then, upon reaching the end of the ledge (nearby the base contacts), be injected into the base. Because this parasitic current conduction is injected closer to the base contact, it increases base contact recombination, thus decreas- ing the effective passivation ledge distance. That is, the current gain decreases in a similar fashion to the current gain decrease in structures with a fully depleted, but much smaller passivation ledge.

In this paper, a theoretical analysis is carried out, taking into account the parasitic emitter current conduction through a partially depleted passivation ledge. Calculated results from this analysis indicate that with an undepleted portion of the ledge as thin as 50A, complete elimination of the base contact recombination current requires a longer passivation ledge ( ~ 10 times longer) than expected from a fully-depleted passivation ledge. These calcu- lated results are compared with the previously mentioned experimental result[3]. The current gain as a function of passivation ledge distance is also calculated for devices with built-in base quasi-electric fields.

2. THEORETICAL ANALYSIS

The emitter region of an HBT passivated with a thin A1GaAs ledge is shown schematically in Fig. 1. This A1GaAs passivation ledge formed by the fabri- cation process described in Ref. [3] is ~ 800 A thick (The thickness of the AIGaAs emitter.) A simple calculation shows that the top 400 A of the passiva- tion ledge is depleted due to surface Fermi level

891

892 WILLIAM LIU and JAMES S. HARRIS JR

~ Depleted Portion of the Emitter Ledge

Intrinsic

Emitter Emitter Ledge

n+ GaAs )

~ n - A I G ~ J ( 0 ) i X ~ a l ' X , '1~ I Base Contact ,,

Fig. 1. The geometry of the surface passivated HBT structures under consideration. The AIGaAs ledge is adjacent to the extrinsic base and passivates the surface.

pinning. An additional portion of the ledge is depleted by the base-emitter junction; however, the thickness of this depletion region depends on the potential drop across the forward biased junction. At low base-emitter bias levels, such as at Vbc = 0.4 V, the junction depletion thickness is ~ 5 4 0 A . Therefore, the 800 A is fully depleted by the combination of the free surface and the junction depletion regions. However, at relatively high Vb,'S, such as 1.2 V, the junction depletion thickness decreases to ~ 2 4 0 A , and a portion of the 800A ledge is thus undepleted. This unde- pleted port ion can be much thicker than expected when the 800 A AIGaAs grown by various epitaxy growth techniques turns out to be even

slightly thicker, due to a miscalibration in the growth rate.

In the following, it is assumed that, after consider- ing the effects of both the exposed base surface and base-emitter junction depletion regions, the remaining undepleted ledge thickness is A (Fig. 1). The ledge current density, which flows in the undepleted portion of the ledge, and thus flows parallel to the base-emitter junction interface, is denoted as J~. If J~ is the emitter injection current density which crosses the base-emitter junction boundary, then:

1 f a Jl(x) = ~ Je(x')dx'. (1)

(a)

Yo

- - - 7 - " - - - ' , " - " - - - . . . . . . . . - -" - - r ~ Not Fully Depleted

' Passivafion Ledge Emitter ~ Base Contact / . . . . . . . . . . . .

0'~ J n d 1 J e (x) d 2 X o

Base

Y Collector

X

(b) an + fn = - - -

0 .a... o]- - - = 0

Yo _1__

Y

Jn an Sa J e (x) qDn ~)~ + fn = Dnn n - qD n

| | ! !

dl d 2

Smax ~-+ fn = ~ 7 - n

On Sl L I - ~JX - D n n

n(x ,Y o ) = 0

x

Fig. 2. (a) A schematic diagram of an emitter-up HBT. Note only half of the transistor is shown; the boundary conditions are reflective across the plane bisecting the emitter mesa. (b) Schematic diagram for

the base surface boundary conditions.

Parasitic conduction currents in HBTs 893

It is assumed that the emitter current density depends only on the junction voltage at given position x. Therefore:

Je( x ) -= .,Is exp[V(x)/ Vt], (2)

V(x) = V(O) - J~(x')p dx', (3)

where J~ is the reverse saturation current of the base-emitter junction, Vt is the thermal voltage, V(0) is the voltage at x = 0 and p is the resistivity of the undepleted portion of the passivation ledge (f~. cm). After substituting eqns (2) and (3) into eqn (1) and taking the derivative of the resultant equation twice, one obtains:

d2Jl(x) d~(xX) Jl(x) = 0. (4) P

dx ~ + Vt

A solution to this differential equation which satisfies one of the boundary conditions, Jl(d) = 0, is,

Jr(x)= c tan c 1 (5) p 2 - ~ '

where d is the passivation ledge distance and c is an unknown constant. This constant is determined from the remaining boundary condition, namely, at x = 0, Je(x) = Je(0), where Je(0) is the given emitter current density flowing through the intrinsic emitter mesa (Fig. 1). Taking the derivative ofeqn (1), one obtains, dJl(x)/dxl.~=o=-Je(O)/A. Substituting Jl(x) from eqn (5) into this equality, one then finds that the constant c is obtained from the solution to the following transcendental equation:

p d 2 c 2 sec(c 2) = ~ ~- Je(0). (6)

We shall hereafter refer the right-hand side of eqn (6) as the Product. Therefore, in addition to the emitter current which flows through the intrinsic emitter area [J~(0) x emitter area], there is another component of emitter current, /ledge, which first flows through the undepleted ledge and then injects into the base. This additional emitter current is simply J~(0) times the cross-section area, or from eqn (5):

2Vt A llodge=hc P ~ tan c. (7)

In addition to the solution l~ed,o, we are interested in determining the various base current components in order to calculate the current gain for HBTs with an undepleted passivation ledge such as shown in Fig. 2a. The approach here is similar to the approach used in Ref. [8]; that is, to first solve the following 2-D minority electron continuity equation in the base:

7 2 n(x, y) + f ~ n ( x , y) n(x, y ) = 0. (8) c3y z ,D,

In the above equation, n(x , y ) is the 2-D electron concentration in the entire base, including both the intrinsic and extrinsic base regions; f is an electric field

factor, equal to the base electric field divided by the thermal voltage; z. and D. are the minority electron lifetime and diffusion coefficient, respectively. After solving n (x, y) with appropriate boundary conditions, the base current, which includes the base bulk recom- bination current, extrinsic base surface recombination current and base contact recombination current, is then determined. In general, a solution of n(x, y) in eqn (8) can be written as[8]:

e x fy'2 n ( x , y ) = p( ' )~ f f , ,K , , m

x sinh[?,,(y - Y0)]cos(2,,x), (9)

where 2m, 7,, and Km are related to the Eigen- coefficients of the associated Eigen-solutions when one applies the technique of separation of variables to solve the 2-D base minority carrier continuity equation[8]. ~m, in contrast, is specifically related to the boundary conditions of a given device structure. In Ref. [8], the solution of ~k,,, and thus, n(x, y), was determined with a set of boundary conditions which assumed Je(x) =- O. In this investigation, we solve for the if,, specific to the new set of boundary conditions which include the effects of non-zero Je(x). With this new set of boundary conditions (Fig. 2b), the equation for ~O,, is given as[7,8]:

- J , / q D , , 0 < x <dl,

~,, cos(2, ,x)= - J¢ (x ) /qD ,+ns , /D , , dl < x < d 2, m

nSm.x / D . , dz < x < Xo ,

(10)

where the non-zero emitter current density which crosses the base-emitter junction under the un- depleted ledge Je(x), is readily determined from eqns (1) and (5):

Je(x) = c2 2 V T A 1

In eqn (10), all variables and geometries correspond to those of Ref. [8]. [In fact, eqn (10) is identical to eqn (8) of Ref. [8], except that J~(x) in the latter is 0.]

Solving for ~k,, in eqn (10) is seemingly difficult. However, using a matrix technique similar to that discussed in Refs [7,8], one can express if,, as a sum of three different coefficients:

~,,, = ff~, + qJ~ + ~O~. (12)

~k~, ~2 and ~b 3 are given as[7,8]:

[ 1 I / / 2 / = SnmSaf(Sa - - Sma×)

~kJ T.~

Pnra

1 +s .K . sinh(7,. Y0)l

Tnmamax/(amax- aa)

l-' l+sm.xK, sinh()'mYo)lJ L0 J

894 WILLIAM LIU a n d JAMES S. HARRIS JR

2 ~ - . . . . . . . . . . . . . . . . . . . ~ ........ ~ ~ ~ - ~ . . . . ~ 7 L

[

c" ~ r c / 2 1.5 ~ ~ V

Je (d ) / Je(O) = cos2 (c )

0.5

0 --, ....... r ',-~,,,F ........ I ........ i ~ ...... 0 10-3 1 10 ~

T h e P r o d u c t , p d 2 Je(O) /(2 V w A )

Fig. 3. The ratio of J~(d)/J~(O) as a function of the Product, which is defined as the right-hand side of eqn (6). The value 'c', which is the solution to the same transcendental

equation is also shown as a function of the Product.

where

Y,, = 4~,, 2 V T A

22, ,X0+ sin(22,,X0) P d 2

XqD,, _x - d l " ~ l dx" (14)

, c ° s ~ c I 4 - d ~ / J

and P .... S,,,,, T,,,, are the same as those g i v e n in Ref. [8].

N o t e tha t in the der iva t ion in Ref. [8], the paras i t ic ledge c o n d u c t i o n cu r ren t was neglected, then Y,, was s imply 0. The i n t roduc t i on o f a non -ze ro J~(x) in the p resen t analysis leads to a non -ze ro Y,,, which is d e t e r m i n e d f rom eqn (14). Toge the r wi th eqn (13), one can solve for the q6,s, and thus ob ta in a so lu t ion to the 2-D cont inu i ty equa t ion o f e q n (8). The var ious c o m p o n e n t s o f the base current , such as base bulk

curren t ga in

~ L , ] , b , J ; , i i , I i i i ~ _ ~ l , , I i i , ,

103

102

101

/ ~ ~ A = 5 0 ° A = 2 0 0 ° ° - ....

0 0 .5 1 1.5 2 2 .5 p a s s i v a t i o n l edge l eng th ( p m )

Fig. 4. Simulated current gain as a function of passivation ledge length, for various values of undepleted depth A. The emitter width is 2 lam, and the base thickness is 1000 A. The emitter and base dopings are 5 x 1017cm -3 and 5 x 10 ~Scm 3, respectively. The current density is 1 x 104A cm -2. The dots are from the experimental results

of Ref. [3] for a device at the same current density.

curren t ga in

/ ~ = 0 . l a." x °

b. x ° = 0 . 0 5

c: Yo : 0

101 ~ T ~ , i , ~ ~ ~ E ~

0 0.5 1 1.5 2 2.5 3 passivation ledge length ( t-tin )

Fig. 5. Simulated current gain as a function of passivation ledge length, for devices with various base quasi-electric fields, which are established by a linear grading of AI composition from 0% to x0% across the entire base. The undepleted portion of the passivation !edge is assumed to be

A =50A.

r ecombi na t i on current , surface r ecombi na t i on cur- rent at the ledge surface, and surface r ecombi na t i on cur ren t at the base contac t s , are similarly ob ta ined f rom the equa t ions in Ref. [8]. The col lector cu r ren t I~ can also be simi!arly ob ta ined f rom Ref. [8]. The n u m b e r o f t e rms m to be used in the s u m m a t i o n o f eqn (9) depends on the accuracy desi red and the c o m p u t a t i o n t ime available. An es t imate o f the accu- racy o f the so lu t ion can be ob ta ined by c o m p a r i n g I c to le + I~dge -- Ih as the n u m b e r o f t e rms in the sum- ma t ion increases. (Io is the emi t te r cur ren t f lowing t h rough the intr insic emi t te r area only. lh is the sum o f all the r e combi na t i on cur ren t s in the bulk, the extrinsic base surface, and the base con tac t interface.)

3. R E S U L T S AND D I S C U S S I O N S

The relative i m p o r t a n c e o f the parasi t ic ledge c o n d u c t i o n for a given s t ructure is e s t imated f rom the plot o f Je(d)/Je(O) as a func t ion o f the Product , as s h o w n in Fig. 3. Also s h o w n in this figure is the value o f c as a funct ion o f the Product . I f one desires the ledge parasi t ic c o n d u c t i o n cur ren t to be negligible, the rat io o f J~(d)/Je(O) should be smal ler than , for example , 0.01. F r o m Fig. 3, this ratio decreases to 0.01 when the Product increases to grea te r than 200. In o rde r to give an idea to this magn i tude o f the Product , the Product is ca lcula ted for the fo l lowing example . F o r a typical H B T with a pass iva t ion ledge d is tance o f d = I I~m, and emi t te r dop i ng o f 5 × 1017cm 3, and an undep le t ed ledge th ickness o f A = 50 A, the Product is ~ only 32 (which is ,~ 200), at a col lector cur ren t dens i ty o f I × 104 A/cm 2. Such an H B T would have d r ama t i c cur ren t d e g r a d a t i o n due to the parasi t ic c o n d u c t i o n in the undeple ted ledge.

F igure 4 shows the cu r ren t gain as a func t ion o f the pass iva t ion ledge dis tance, for var ious values o f

Parasitic conduction currents in HBTs 895

undepleted ledge thickness A. The calculation par- ameters used, such as the surface recombination velocities, are the same as those used in Ref. [8]. In brief, S = 103cms t for passivated surface, S = 106cms-~ for unpassivated surface, S = 2 x 107cms i for base contact surface. The models of Ref. [9] are used for the electron minority carrier mobility and lifetime vs doping. Note however, in the calculation of the emitter resistivity, p [eqn. (3)], the electron majority carrier mobility should be used, rather than the minority carrier mobility. The model of majority carrier mobility as a function of doping in Ref. [10] is used. The device is assumed to have 1000 A base thickness, and a base doping of 5 x 10 ~s cm 3. The emitter width is 2 p.m, and the base contact width is 5 p.m. The current density is 1 × 104A cm -~.

The plot for A = 0 A in Fig. 4 corresponds to a fully depleted device without parasitic ledge conduction. This A = 0 A result closely matches the plot obtained from the solutions in Ref. [8], in which the passivation ledge was assumed to be fully depleted. In contrast, for a device with a thick undepleted ledge (A = 2000 A), a significant portion of the emitter current flows through the ledge. Therefore, many minority carrier electrons recombine at the nearby base con- facts and the resultant base contact recombination current limits the current gain to low values, even though the passivation ledge distance is as long as 3 p.m. It is interesting to note that the passivation ledge distance required for the current gain to saturate at its highest values increases from 3000 A when A = 0A (complete depletion), to 2 p.m when A is only 50 A. The experimental values of Ref. [3] suggest that the minimum passivation ledge distance for gain satura- tion is roughly 2 + 0.5 p,m. This corresponds reason- ably well to the calculated case of A = 50/~, which could easily be the thickness of the undepleted material. The current gain values of Ref. [3] for devices with passivation ledge distances of 0.2 and 2 p.m are also shown in Fig. 4. These experimental results again match closely to the calculated results for the case of , 1 = 50A.

Figure 5 shows the current gain as a function of the passivation ledge length for devices with uniform base quasi-electric fields. In this calculation, the device structure is identical to those used to obtain Fig. 4, and the undepleted portion of the passivation ledge is assumed to be A = 50 A for all cases. A built-in base quasi-electric field can be established by linearly grading the A1 composit ion from 0% at the collector side of the base to x0 % at the emitter side of the base. Linear gradings of AI with x 0 % of 0.05, and 0.1 result in base quasi-electric fields of 6.25, and 12.5 kV cm- ~, respectively, across the 1000 ~, base. As expected from Fig. 5, the current gain increases with increasing base quasi-electric field. This results because the base field propels the minority carriers away from the base-emitter junction toward the collector, reducing both base bulk recombination and base contact re- combination. More importantly, Fig. 5 shows that

when the base quasi-electric field increases, the re- quired passivation ledge length to achieve constant current gain decreases by about 50%. However, even with a base field of 1.25 × 104Vcm -1, the required passivation ledge length is still i .5 p,m for devices with A = 50 A. This is significantly longer compared to the required ledge length of only 3000,~ for devices without base field but having a fully depleted ledge. This observation indicates that there is still dramatic ledge parasitic conduction at high base quasi-electric fields. Hence, the design parameters for thickness and doping to achieve complete depletion of the base-emit- ter passivation ledge for HBTs are essential to achieve very high values of current gain.

4. SUMMARY

In summary, a theoretical analysis describing para- sitic conduction in the passivation ledge of a mesa A1GaAs/GaAs HBT demonstrates the importance of achieving complete depletion of the ledge. A solution of the 2-D diffusion equation which takes this para- sitic ledge conduction into account is developed. Calculations of current gain suggest that mesa A1- GaAs/GaAs HBTs fabricated with the selective etch process of Ref. [3] which stops on the thin AIGaAs emitter might well have about a 50A undepleted ledge. Parasitic conduction through the undepleted ledge causes the current gain of the device to decrease due to contact recombination in the base. This analy- sis indicates that during HBT processing, it is of paramount importance to monitor the base etch by, for example, measuring the current between two emitter mesas through the ledge, thus ensuring that the passivation ledge is fully depleted when under normal forward bias operating conditions.

Acknowledgements The authors would like to thank R. Chan and L. I. Hwang for discussions about the math- ematical equations, and T. Boykin for managing the com- puter workstations. This work was supported by DARPA and ONR through Contracts N00014-K-84-0077 and N00014-90-J-4056. W. Liu was also supported by an AT&T Bell Laboratories Fellowship.

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