GaAs abrupt HBTs with a setback layer

Solid-State

Electronics

Vol. 36, No. 6, pp. 819-825,

0038-l lOlj93

1993

$6.00 + 0.00

Copyright 0 1993 Perpmon PressLtd

Printed in Great Britain. All rights reserved

AN ANALYTICAL MODEL FOR CURRENT TRANSPORT IN AlGaAs/GaAs ABRUPT HBTs WITH A SETBACK LAYER J. J. LIOU and C.-S. Ho Electrical and Computer Engineering Department, University of Central Florida, Orlando, FL 32816, U.S.A.

L. L. LIOU and C. I. HUANG Solid State Electronics Directorate, Wright-Patterson Air Force Base, OH 45433-6543, U.S.A. (Received 2 November 1992) Abstract-An intrinsic setback layer (or spacer) is frequently used in abrupt heterojunctions to improve the emitter injection efficiency and to reduce the impurity out-diffusion from the heavily doped base to the emitter. We have developed an analytical model to predict the d.c. performance of the AlGaAs/GaAs abrupt heterojunction bipolar transistor (HBT) with a setback layer. The effects of different setback layer thicknesses on the collector and base currents are studied in detail. Our results suggest that the presence of the setback layer can improve injection efficiency, but it can also increase the base current. Furthermore, for the device considered and parameters used, it was shown that a setback la er with a 100 A thickness can yield the highest current gain and that a setback layer thicker than 100 K can actually degrade the HBT performance. The model predictions compare favorably with the results obtained from solving numerically the Poisson and continuity equations including the nonuniform spatial band distribution as well as carrier degeneracy.

1. INTRODUmION The emitter injection efficiency in an AlGaAs/GaAs abrupt heterojunction bipolar transistor (HBT) is often hindered by the conduction band discontinuity (or spike) at the hetero-interface. The presence of the

spike necessitates the inclusion of thermionic and tunneling mechanisms in describing the free-carrier transport from the emitter to base[l], as opposed to the conventional drift-diffusion model used in homojunction devices. Two methods have been frequently utilized to improve the injection efficiency. One is to make a grading on the Al mole fraction of AlGaAs over a thin region adjacent to the emitter-base hetero-interface. This can effectively reduce the spike. The other approach is to insert a thin layer of intrinsic GaAs (setback layer) between the emitter and base. The setback layer can alter the barrier potentials on both sides of the heterojunction, thus reducing the importance of thermionic and tunneling mechanisms on the free-carrier transport across the heterojunction[2]. An additional advantage of the setback layer is that it can prevent impurity out-diffusion from the heavily doped base to emitter[3]. Many studies on the effects of the graded junction on the HBT current-voltage characteristics have been reported[l-2,4-S], but few have focused on the HBT with a setback layer. For example, Grinberg ef a[.[ l] developed a thermionic-field-diffusion

model for abrupt and graded HBTs. Very recently, Parikh and Lindholm[rl] developed a comprehensive collector and base current model for both abrupt and graded HBTs based on the charge-control concept. A Gummel-Poon-like model for the HBT was also developed by Ryum and Abdel-Motaleb[S]. The current transport in the p/N heterojunction diode with a setback layer, among other types of junction, was investigated by Chen et al.[2]. In their of the Shrodinger work, an exact solution equation was used to calculate the free-carrier tunneling coefficient in the abrupt junction with a setback layer. However, the effects of such a junction structures on the base current components (e.g. recombination current in the space-charge region) were not investigated. In this paper we develop an analytical and detailed model for the collector and base current characteristics in abrupt HBTs with a setback layer. First, equations for the barrier potentials and space-charge region (SCR) thicknesses on both sides of the junction including the setback layer are derived from the Poisson equation. Then a model for the collector current is developed based on the thermionic-fielddiffusion model proposed by Grinberg et al.[l]. This is followed by the study of the different components of the base current. Several setback-layer thicknesses will be considered, and the corresponding collector currents, base currents, and d.c. current gains will be calculated and compared. 819

820

J. J. LIOUet al. 2. THEORY

tration. Note that if 1 = 0, then (6) reduces to

Consider an N/p/n Ab,,Ga,,, As/GaAs HBT in which an undoped GaAs layer is inserted between the emitter and base layers (between x = 0 and x = A), as shown in Fig. 1. In deriving the model, Boltzmann statistics is used throughout and the free carriers are assumed resided and transport primarily in the r valley. 2.1. Barrier thickness

potential

and

space-charge

layer

Solving the Poisson equation including the effects of the setback layer and assuming the setback layer is fully depleted, the electric fields t(x) in the space-charge layer are given by: 5(x) = -(q&/+)(x r(x)=

-(q&&,)(X,-1)

5(x) = -(qNslce)(X,

< x < 0,

-X,

+ X,)

O
(3)

where subscripts E and B represent the emitter and base, respectively, L is the dielectric permittivity, N is the impurity doping concentration, 1 is the setback layer thickness, and X, and X, are the thicknesses on emitter and base sides of the space-charge region, respectively (Fig. 1). Integrating (1), (2) and (3) over their boundaries, the barrier potentials V,, and Vsz on the emitter and base sides (Fig. 2), respectively, can be derived as: vB,

=

4%

X:

(4)

/CW,

VIJZ= qNB(& - ~)%J + qN,(x,

- i)2/(2%).

(5)

Note that the first term on the right of (5) is the barrier potential associated with the setback layer. Using the conditions that the electrostatic potential must be continuous at x = 0 and that the charge neutrality exists over the space-charge region, the space-charge region thicknesses X, and X2 can be solved as: & = +

[lcB

NB /@E

{~NB/@E%

+

LB NB 11 +

+~EIz~EI(~~~,BE[qN&,N,

NE

+

VBd%/[q’&(%N~

+

wWII~~~,

VBEWBI

Following the thermionic-field-diffusion approach developed by Grinberg et al.[l], the electron current density J,, across the hetero-interface (x = 0) is the difference between two opposing fluxes: J,(O) = qa,y]n(O-) - n(O+)exp(-

AEclkT)],

n(O-) = Kexp(-

Ve,/V,)

and n(“+)=n(X2)exp(VB2/V,).

(10)

At this point, the only unknown parameter is n(X,), which can be solved using the relation: J” (0) = Jscru + JsCRtl+ J,

(X2

1,

-0.6 AE,/q + 0.5 AE,/q + VT ln(NENB /% % ).

(8)

Here AEo = EGE- EoB is the energy bandgap difference (=0.37 eV for the Ab,,G&,,As/GaAs heterojunction under study[7]), V, = kT/q is the thermal voltage, and ni is the intrinsic free-carrier concen-

(11)

where JsCR, is the recombination current density in the setback layer (x = 0 and x = A), JscRB is the recombination current density in the space-charge layer associated with the base layer (x = 2 and x = X2) (the models for &,-a, and JscRe will be developed in the next section), and J,(X,) is the diffusion-only current in the quasi-neutral base (QNB). For a very thin base: J,(x,)

= Jc = qD,W,)/(B’,

+ AB’r, + Dniasa,), (12)

where Jc is the collector current density, D, is the electron diffusion coefficient in the QNB, WB= X, - X, (Fig. 1) is the QNB thickness, A W, is the current-induced base pushout, and v,, (= 10’ cm/s) is the saturation drift velocity caused by the high field at the base-collector junction. An empirical expression can be used to describe D,[9]:

AwB

=

wc{l

-[(Jo

-

qvsa,NcMl

(13)

is given by[lO]: -

(7) built-in voltage.

(9)

where u, is the electron thermal velocity, y is the tunneling coefficient (see Appendix A), n is the electron concentration, and AEc % 0.6 AEo[8] is the conduction band discontinuity (spike). In (9):

The current induced base pushout (6)

~BNB)I~~‘~,

thick-

2.2. Collector current

D, = VT[7200/( + 5.5 x 10~‘7N,)0233].

~~=(~B/~,)(~,N,INB)+~,

Vbi,BE =

-

which is the conventional space-charge-region ness model for an abrupt heterojunction.

~BNB)I~

where V,,, is the base-emitter junction potential and VeE is the applied base-emitter V,,i,BEis given by[6]:

{26EcB(Vbi.BE

(2)

1 < x 6 X,,

- x)

(1)

X1 =

mat&)1°.5)

for Jc > Jo,

(14)

and A W, = 0 otherwise. Here W, is the collector layer thickness, Nc is the collector doping concentration, and Jo is the onset current density for base pushout: Jo = q%.,[Nc +

~~c(~~,.Bc

-

VBC)/~~~]~

(15)

where ~~ is the dielectric permittivity in the collector, Vbi.ecis the base-collector junction built-in potential, and Vet is the base-collector applied voltage. Putting (12) into (11) and (10) into (9) and equating

821

AlGaAs/GaAs current transport

tzzl

Intrinsic

setback

B

layer

1 I

I

I

I I I

N

E-

7

I

I

I

I

I I I

I I I I I I I I

I I I I I I I I I

x2

x3

X4

I I I

I I I I

/ h

-X1

-XE

I

P+

n

-c

X

t0

Fig. 1. Schematic illustration of the HBT structure including a setback layer the resulting equations,

n(S)

we obtain:

= [qru,yNsexp(-

Vs,IVT)

- JXRI- JSCR&~ (16) where v =qR/(B’s+AB’,+Wn,,) + q&Y exp[(VB2 - A&/q)/vTI. Thus Jc can be calculated from (12) after n(X,) is found from (16). 2.3. Base current The components of the base current density Je of the HBT include (1) injection of hole current density JRE from the base to emitter; (2) electron-hole recombination current density JR9 in the quasi-neutral base; (3) electron-hole recombination current density JxR in the emitter-base space-charge layer; and (4) electron-hole recombination current density JRs at the hetero-interface as well as the emitter and base

surfaces. (1) JRE This current can be modeled using the conventional diffusion-current only approximation:

JRE= @,NB

exP[-(VBI

+ vB2

+AEv/q)/vr]/w,,

(17)

where Dp is the hole diffusion coefficient in the emitter, AE, = AEo -- AEc = 0.4 AEG is the valence band discontinuity (Fig. 2), and IV, = X, - X, is the thickness of the quasi-neutral emitter. The doping-concentration dependent Dp is given by[9]: Dp= VT[380/(1 + 3.2 x 10-‘7N,)02666].

(2) JRB The recombination neutral base is[ 111:

(18)

current density in the quasi-

Jm = J,,V,)U

-Co,

Fig. 2. Qualitative illustration of the energy band diagram of the HBT without the setback layer (solid lines and parameters denoted by subscript 0) and with the setback layer (dashed lines).

(19)

J. J. LIOUet

822

where c( is the base transport

Table 1. HBT device in structure

factor:

Thickness (A)

l/cosh[W,/(D,r,)0.5],

CI =

r,, is the electron lifetime in the base (T,= 1 ns is used in calculations). (3)

al.

Emitter Spa03 Base

Collector

JSCR

J sea consists of three recombination current densities occurred in the emitter-side of the space-charge layer (JSCRE), in the intrinsic layer (JSCRI), and in the base-side of the space-charge layer (JSCR,,). Thus:

(21)

JSCR = JXRE+ Jmr + JSCRB 0 =4

s -X1

+

uS,H,I

4

AlAs fraction in AI,Ga, ,As

n

5 x IO”

0.3

PI+ ‘n

I x:019 5 x 10’6

0

1,

3

‘2

I

0.1

8 CI

::

X2

0.01

d uSRH,B

0 0

Y v-z

dx

s 0

+ 4

Type

&

.a u SRH,E dx

17Oil 1 1000 7500

used in calculations

Doping density Cc4

A-oA

--

(22)

dx>

s 1

where Us, is the Shockley-Read-Hall recombination rate. Assuming a single-level trap located at the middle of the bandgap yields: uSRH,E =

u SRHJ -

0.5aunNtnil

(23)

w(~BE/2~T)

0.5au,N,ni2exp(Vr,,/2Vr).

uSRH~B =

JRS

This current density is influenced strongly by the fabrication process. It includes electron-hole recombination taking place at the hetero-interface (JRs,) as well as at the emitter and base surfaces (JRsz):

JRS= JRS,+ JRSZ = ~“S,H(x

=

0) +

J* exP(V,,/V,)

= q0.5au,Nt,ni, exp(Va/,,/2V,)

1 E-CC,

lE-Cd 0.8

1

0.9

1.1

1.2 v,,

Fig.

4. Barrier

(24)

Here rr (cm-‘) is the capture cross section, N, (#/cm-‘) is the trapping density, n,, and ni2 are the intrinsic concentrations in the emitter and base, respectively. (4)

0.001 0.9

1.3

1.4

1.5

w

potentials calculated for setback layer thicknesses.

three

different

where N,, is the hetero-interface trapping density ( #/cm2) and J* is the empirical parameter that characterized the recombination current at the emitter and base surfaces. Note that the recombination is proportional to current at the interface exp( VBE/2VT)[12]whereas the recombination current at the emitter and base peripherals is a function of current ew(~BE/~TWl. The pre-exponential density J* is a function of the surface recombination velocity S, the value of which depends strongly on the surface states and the location of the Fermi level pinned at the surface (S = lO”cm/s is used in our calculations). Finally the dc. current gain /I of the HBT is defined

I

0.9

1

1.2

1.1 v,,

1.3

1.4

I 1.5

w

Fig. 3. Space-charge region thicknesses vs V,, calculated for three different setback layer thicknesses.

0.9

0.9

1

1.1

1.2 v,,

1.3

1.4

1.5

6

w

Fig. 5. Collector current densities vs V,, calculated from the present model and from the numerical model[l4].

AlGaAs/GaAs current transport

823

I-oA s-IOOA _____ __ a-mA

-

h-mA

-

0.01~ 0.8 0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

v,, 04 Fig. 6. Comparison of the collector current density without tunneling (5;) and with tunneling (A). 3. RESULTS AND DJSCURMON For illustrations we consider a typical HBT makeup listed in Table 1 and three different setback thicknesses: 1 = 0, 100 and 200 A. Figure 3 shows the SCR thicknesses X, and X, vs the applied base-emitter voltage Van. In general, X, is larger than

X, because the doping concentration in the base is higher than that in the emitter, except for the cases of 1 > 0 and Vaa is large. In these cases, X, z 1 and can be larger than X, if Vaa is large. The barrier potential Pa2 on the base-side of the junction is also increased due to the presence of the setback layer, as evidenced by the results in Fig. 4. On the other hand, the barrier potential Pa, on the emitter-side is decreased as I is increased. The collector current densities calculated from the present model for three 1 values are shown in Fig. 5. Also included are the results obtained from a numerical model[l4] which solves numerically the Poisson and continuity equations including the nonuniform spatial band distribution as well as carrier degeneracy. Good agreement is found between the present

Fig. 8. Four base current density components calculated as a function of V,,.

and numerical models. Clearly, the setback layer improves the emitter injection efficiency, particularly when Vsa is relatively low. Also note that there is a smaller increase in Jc when 1 is increased from 100 to 200 A than from 0 to 100 A. We also calculated the collector current density Jc without including the tunneling mechanism. The results of J&/Jc are illustrated in Fig. 6, which indicates that the tunneling current becomes much less important when 1 is increased. This stems from the smaller tunneling probability caused by the decreased barrier potential Vsr (see Fig. 4). Our finding agrees with the numerical results in[2] which suggested that the conventional drift-diffusion model becomes applicable if a relatively thick setback layer is used. The setback layer nonetheless will increase the base current density of the HBT, as shown in Fig. 7. To investigate the origin of this increase, we first calculate the four components of JB. The results in Fig. 8 suggest that JxR and JRB are the dominant components of JB at low and high Paa, respectively. The dependencies of these two current densities on 2 are then calculated and given in Figs 9 and 10,

$ 2

1.1

12

1.3

1.4

1.5

12

V,(v) Fig. 7. Base current densities vs Va, calculated from the present model and from the numerical model[l4].

0.6

0.9

1

1.1

12

1.3

1.4

1.5

5

VBE W) Fig. 9. Space-charge region recombination current densities calculated for three different setback layer thicknesses.

824

,/:...~,* ’ /A J. J. LIOU et al.

100

-_

,/... ,._,./

_______?.-2OOA

10

z

A.oA A-1wA

,.

’

-

..*”

,.I.

,/,y

0.1

,,:/ ./

,I,/' ,/_.. ,,,$.."

,/;., /:.,,:./ 1

0.01 0.001

1,::.

/:..”

,I

,”

,

O.wol.;..,” ,/

lE-09~ 0.9

,

-.-.-

/

0.9

1

1.1

1.2

1.3

1.4

1.5

I 1.6

10 lo-’

10”

10-Z 10-l

V,(V)

Fig. 10. Quasi-neutral densities calculated

base region recombination current for three different setback layer thicknesses.

respectively. Both JscR and Jar, increase as 1 is increased, which lead to the increase in JB. We have also calculated JRE and JRs and found them insensitive to the variation of 1. In Fig. 11, the d.c. current gains /.I vs Jc calculated from the present model for three I are compared. For the device make-up considered and the parameters used, our calculations suggest that while inserting a setback layer between the emitter and base can improve the current gain, a 2OOA layer nonetheless yields a slightly smaller B than a 100 A layer at the low and medium current level. Similar current gains are obtained from 1 = 100 and 200A at the high current region. As a result, using a layer thicker than 100 A actually degrades the HBT performance if the bias condition is relatively low.

4. CONCLUSION

An analytical model has been developed for predicting the current-voltage characteristics of abrupt HBTs with an intrinsic setback layer inserted between the emitter and base. The effects of the different thicknesses of the setback layer on the base and collector currents were studied in detail. It has been shown that the setback layer can alter the barrier potentials on both sides of the heterojunction, thus making the free-carrier tunneling and thermionic mechanisms less important. Furthermore, it was indicated that while the setback layer can improve the emitter injection efficiency, it can also increase the base current of the HBT. The increase in the base current is caused mainly by the increase in the recombination currents in the space-charge region and in the quasi-neutral base region due to the presence of the setback layer. Among the three setback layer thicknesses considered (0, 100, and 2OOA), our calculations show that a setback layer with a 100A thickness can yield the highest curent gain and that a setback layer thicker than 100 8, can

100

J,

10’

10’

A.IOOA

lo3

10’

10’

IO6

(A/cm’)

Fig. 11. Comparison of the d.c. current gains vs Jc calculated from the present model for three different setback layer thicknesses.

actually degrade the HBT performance condition is relatively low.

if the bias

Acknowledgement-One of the authors (JJL) acknowledges the support of the Air Force Office of Scientific Research (Account # 16-22-502).

REFERENCES

1. A. A. Grinberg, M. S. Shur, R. J. Fischer and H. Morkoc, IEEE Trans. Electron Deices ED-31, 1758 (1984). 2. S.-C. Chen, Y.-K. Su and C.-Z. Lee, Solid-St. Electron. 35, 1311 (1982). 3. M. E. Kim, B. Bayraktaroglu and A. Gupta, in HEMTs & HBTs: Devices, Fabrication, and Circuits (Edited by F. Ali and A. Gupta). Artech House, Boston, Mass. (1991). 4. C. D. Parikh and F. A. Lindholm, IEEE Trans. Electron Devices ED-39, 1303 (1992). 5. B. Y. Ryum and I. M. Abdel-Motaleb, Solid-St. Electron. 33, 896 (1990). 6. A. Chatterjee and A. H. Marshak, Solid-St. Electron. 24, 1111 (1981). 7. S. Adachi, J. appl. Phys. 58, RI-R29 (1985). 8. W. I. Wong, Solid-St. Electron. 29, 133 (1986). 9. D. A. Sunderland and P. L. Dapkus, IEEE Trans. Electron Devices ED-34, 367 (1987). 10. C. T. Kirk Jr, IRE Trans. Elecfron Devices ED-9, 164 (1962). 11. A. Furukawa, K. Ohta and T. Baba, IEEE IEDM, p. 615 (1987). 12. C. H. Henry, R. A. Logan and F. R. Merritt, J. appl. Phys. 49, 3530 (1978). 13. J. J. Liou and J. S. Yuan, Solid-St. Elecfron. 35, 805 (1992). 14. L. L. Liou and C. I. Huang, Electron Left. 26, 1501 (1990).

APPENDIX

A

The tunneling coefficient y for an abrupt junction can be obtained by integrating over the range of barrier energies available for tunneling[ I]: Y=

1+ev(~B,l~T)YI~T,

641)

AlGaAs/GaAs current transport where:

825

where VU1 Y= D(X)exp(sr

V/V,)dV.

Here V* = VB, - AEdq if VB, > AEdq and V* = 0 otherwise, x = v/v,,, and D(X) is the barrier transparency. For a triangular barrier: D(X)=exp[(-V,,/V,){(l

-X)o.s

+0.5X In X -X ln[l + (1 - ,?J”,)}],

v, = 100(h/4n)[N,/(m,+t,)]0.5.

(A2)

(A3)

(A4)

Here h is the Planck constant and rn.’ = O.O&‘m, is the

effecti.e

electron

maSS

It should be pointed out that the above model is the same as that given in [l], except for two minor corrections. In [I], it was stated that V* = V,, - AE,/q if VbiTaE> AE,-/q and that V, = (h/4n)N,/(m:g).