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Modelling the d.c. performance of GaAs homojunction bipolar transistors
Solid-Stare Electronics Vol. 29, No. 7, pp. 713-723, Printed in Gnat Britain
1986
0038-1101186 $3.&l + 0.00 Pergamon Journals Ltd
MODELLING THE d.c. PERFORMANCE OF GaAs HOMOJUNCTION BIPOLAR TRANSISTORS S.-P. LEE and D. L. PCJLFREY Department of Electrical Engineering, University of British Columbia, Vancouver, British Columbia, V6T lW5 Canada (Received 15 August 1985; in revised form 2 November 1985)
Abstract--Two models, one analytical and one numerical, have been developed to predict the d.c. performance of GaAs homojunction bipolar transistors. In each case the minority carrier properties of lifetime and mobility have been described by polynomial fits to recent data. Bandgap narrowing in the emitter and base regions has also been taken into account. The analytical model assumes uniform doping in the three regions of the transistor and is thus appropriate to predicting the performance of devices fabricated using epitaxial process technologies. This model is also useful for carrying out sensitivity analyses. The importance of parameters such as regional widths and doping densities, minority carrier lifetimes and surface recombination velocity is examined here. The numerical model is useful for describing the performance of ion-implanted devices. Good agreement is obtained between results from the model and recent experimental data.
INTRODUCTION The high electron mobility and the large bandgap of GaAs make it an attractive material for device applica-
tions where operation at high frequency or high temperature is important. To exploit these desirable properties, GaAs-based transistors in the form of MEWETs and bipolar heterojunctions are being investigated widely. In contrast, the GaAs bipolar homojunction transistor is receiving relatively little attention. The major difficulty in this device is obtaining the extremely thin base region which is demanded by the short minority carrier lifetime of GaAs. Presumably suitable base regions could be obtained by using molecular beam epitaxy, which is the method of fabrication employed in many heterojunction transistor structures. In fact, a recent analysis of homojunction and heterojunction GaAs transistors, using parameters appropriate to MBE-fabricated devices in both cases [ 11, indicates that the difference in high frequency performance between the two types of device should be only about 10%. Even though inverted [47] and optimized [48] heterostructures will increase this relative superiority of heterojunctions, and also lead to higher d.c. gains [48], the attraction of GaAs homojunction bipolar transistors is their potential compatibility with the much simpler and more developed fabrication techniques of diffusion and ion implantation which, by themselves, are not sufficient for the fabrication of heterojunction devices. To exploit this feature of relative processing simi plicity, it would help to have a model for the GaAs homojunction transistor which could be used to examine the sensitivity of device performance to processdependent parameters such as minority carrier mobility and lifetime, doping profiles and regional thicknesses. The difficulty in providing such a useful model arises from the wide variation in published data for such factors as: the dependence of mobility and lifetime on doping density; the relative importance of Shockley-Read-Hall,
radiative and Auger recombination prkesses; the surface recombination velocity and, in the case of ion implantation, the activation efficiency of implanted species. These variations are often the result of the use of widely differing GaAs substrates, epitaxial growth procedures and doping conditions. As a first attempt at providing useful models for GaAs homojunction bipolar transistors we have addressed the above points in the following way: recent data on the dependence of minority carrier mobility and lifetime on doping density has been collected together and curve fitted using appropriate polynomial expressions; radiative and Auger recombination have been argued to be unimportant in the devices of interest; surface recombination velocity and dopant activation have been taken as adjustable parameters. In this manner it has proved possible to develop meaningful models for the prediction of the d.c. performance of GaAs bipolar transistors. The first model is analytical, one-dimensional and treats the various regions of the transistor as being uniformly doped. As such, the model is directly applicable to devices fabricated by the sequential growth of epitaxial layers. Good agreement is obtained between predicted results and data from devices utilizing VPE[2], LPEP], and MBE[ l] fabrication techniques. In addition, the model is well-suited to performing sensitivity analyses on factors likely to affect device performance, e.g. lifetime in the base and emitter, emitter surface recombination velocity, widths and doping densities of the various regions of the device. The second model is the one-dimensional numerical model SEDAN [4], suitably modified to render it applicable to GaAs. The required changes concern the mobility and lifetime dependence on doping density and the treatment of bandgap narrowing in the emitter [3]. This model is used here to simulate the performance of recent ion-implanted transistors for which the doping profiles are decidedly non-uniform [5-81. Good agreement between the measured and simulated values of dc current gain is obtained.
713
714
S.-P. LEE and D. L. 2. THE ANALYTICAL MODEL
2.1
Current flows The current components that are included in this model are shown schematically in Fig. 1. The base cur-
PLILFREY
taken to be given by Choo’s expression [9] which takes into account the asymmetry of the doping density between the emitter and the base, namely:
rent density is given by (4)
JB = .J,(-X,)
+ J”(0) - J”(XB) - &(X,) +
JREC
-
JGEN
(1)
where J,(-X,) is the hole current density “back-injected” into the quasi-neutral emitter, the term [J”(O) - J,(X,)] represents the current density due to recombination in the quasi-neutral base, JP(Xc) is the hole component of the base-collector diode saturation current density, JREC is due to recombination in the emitter-base depletion region and JoENis the generation current density in the collector-base depletion region. The collector current density is given by Jc = J,(Xe) + J,(Xc) +
JC~EN
J GEN= $+o&((~)
(2)
where J.(X,) is the electron current density entering the base-collector depletion region and also includes the electron component of the saturation current density of the base-collector diode. The results presented in this paper are expressed in terms of the d.c. current gain, namely
P = JcIJB.
where W,, is the width of the emitter-base junction across which there is an applied voltage V,, and a builtin voltage VbiE, and the minority carrier lifetimes in the base and emitter are given by TV and rE, respectively. The parameters b andf(b) are given in Choo’s paper [9] and depend on the trap level E,. JGeN is given by the usual Sah-Noyce-Shockley expression [lo]:
(3)
The current densities J,(O), J.(XB) and Jp(-XE) appearing in (1) and (2), and the hole current density at the emitter surface J,(- WE - X,), are given by the usual expressions derived from the continuity equations under low-level injection conditions and assuming constant doping in each of the three regions of the npn transistor. JREc for the forward biased emitter-base junction is
where WBc is the width of the base-collector depletion region, E, is the energy level of the generation centers and rc is the minority carrier lifetime in the collector. In eqns (4) and (5) E, is considered to be a single level located at the intrinsic Fermi level E, . The minority carrier lifetimes r&, TV, T= used in eqs (4) and (5) are all taken to be appropriate to a recombination-generation mechanism of the Shockley-Read-Hall type. The dominance of this mechanism of recombination in the GaAs material considered here is supported by minority carrier diffusion length studies in GaAs by various authors. Sekela et al. [ll] showed in their studies of hole diffusion length in n-type GaAs that the largest L, measured is about one third of the theoretical value predicted by Ryan and Eberhardt [12] for radiative recombination, which implies that the hole lifetime due to indirect re-
Fig. 1. Schematic of current flows in a homojunction bipolar transistor.
Modelling GaAs bipolar transistors
combination is typically an order of magnitude lower than that due to direct radiative recombination. The studies on electron diffusion length in p-type GaAs by Casey et al. [ 13, 141 also indicated that the electron lifetime is dominated by nonradiative recombination for hole concentrations less than 1 X lOI* cme3. This insignificant contribution of radiative recombination to the total recombination mechanism, despite the fact that GaAs is a direct bandgap semiconductor, can be attributed to the presence of a large number of recombination centers and defects in GaAs. The Shockley-Read-Hall recombination is assumed to be the dominant component of the indirect recombination mechanism since it is believed that Auger recombination is important in GaAs only at very high doping densities (greater than lOI cmW3)[ 151. 2.2
Model parameters
Carrier concentrations are calculated in the model using the full Fermi-Dirac statistics. The required Fermi-Dirac integrals were approximated by accurate, short-series polynomials [ 161. The electron and hole effective masses, which appear in the expressions for the effective densities of states in the conduction and valence bands, were computed from the detailed equations given by Blakemore [ 171, taking into account the effect of band gap narrowing. This latter effect is described by E,(eV) = 1.42248 - AE,
(6)
where AE, = kT ln(n;/n:)
.
(7)
For the intrinsic carrier concentration, ni, a value of 2.0 X lo6 crne3 was taken. For the effective intrinsic carrier concentration ni,, the following empirical relations were used [3]:
715
for n-type material n.(cm-‘)
= 3.38 X 10W3m
+ 9 x 10”
lo’*
(8)
for p-type material n.(cm-‘)
= 3.38 X 10--3a
- 6.72
X 105 In -$j + 9 X 10”. ( 1
(9)
To complete the information required to estimate the position of the Fermi energy, it is necessary to know the activation energy of the dopants. This quantity was taken as being adequately described by the empirical relation: Ea = E: - AN:l3
(10)
where E.$is the ionization energy at infinite dilution, N, is the dopant concentration (cmm3) and A is a constant. For n-type and p-type dopants the values of A in cm.eV were taken as 1.9 X 10m8[18] and 2.34 X low8 [19], respectively. The above information, when coupled with the doping densities and widths of the emitter, base and collector regions allows the equilibrium carrier concentration profiles to be established. To proceed to a calculation of the diffusion current flows, data on the electron and hole diffusion constants is required. This follows from the Einstein relatibnship, suitably modified to allow for degeneracy [20], providing the minority carrier mobilities are known. From Hall effect measurements a wealth of data on majority carrier mobility values is available. For electrons, data from [18, 21-261 are plotted in Fig. 2,
A
Emal’yonanko
X
Hill 121)
0
Ovoryonkin
ra
Kotodo
P
Wolukiericz
x
Cox & DiLorsnzo
‘3
Ashen
-
Electron
- 3.47
10” Concentration
01 .I 1221
el al IlS]
k Sugono
(231
el 01 [24] [25]
sl (111261
compufer
lit
10’” [ cm-’
]
Fig. 2. Experimental data and best curve fit for the dependence of electron mobility on majority carrier concentration.
S.-P.
716
LEE
and D. L.
along with a best-fit curve given by p,(cm2V1sec-‘)
F'ULFREY
~h(cm2V-1sec-1) = 502511.268 - 156107~
= 0.053 - 69783.160~
+ 19205.6~~ - 1168.926~~
+ 17348.328~~ - 1579.599~~
+ 35.209~“ - 0.420~~
+ 63.036~“ - 0.935~~
(11)
where y = log&/cm-3), with n being the electron concentration in cmm3. To convert this data to drift mobility data a weak field Hall factor of 1.175 was assumed 1171and the ratio of minority carrier to majority carrier mobility was taken to be /*: = f(n)&
(12)
where Y =
log&p/cm-3)
.
Curve fittings were also performed on published data for electron [31-351 and hole [32, 36-391 minority carrier lifetimes. The data are shown in Figs. 4 and 5, and the fitted curves are given by log,,(r,,/sec)
wheref(n) represents a curve fitted to the data of [27], namely:
= -678.5724587x
+ 157.93508506~~
- 13.7579663247~’ + 0.531235178933~~ 0.0076716569056~~
f(n) = 684.327 - 168.175~ + 15.497y2 - 0.633~’ + 0.009~~
(13)
(14)
(15)
and log,O(rP/sec) = 545.075507209 - 99.5742908474~
where y = log10(n/cm-3).
+ 5.96752406063~~ - 0.11903779718~~
To our knowledge, a corresponding expression relating the minority and majority carrier hole mobilities does not exist. The hole Hall mobility data, operated on by a low field Hall factor of 1.25 [ 171, was thus taken as being the minority carrier hole mobility. Some representative Hall data from [19, 21, 22, 28-311 is shown in Fig. 3, along with the fitted curve used in the present work. The curve is given by
where x = logl,(p/cmW3)
and
z = log,0(n/cm-3).
Finally, the model parameter set uses a value of 13.1 for the relative permittivity of GaAs and, except where specified to the contrary, uses a value of 2 X lo6 cm set-’ [38] for the emitter surface recombination velocity.
R0Si et al [28] Vilms k Spicer 1311 Hill (211 Hill [19] Cosonli sl 01 [29] “ilmr
k Garrett [30]
Emsl’yonenko et 01 [22] computer
0 1
10"
lOI6
10"
Hole Concentration
Fig.
3.
fit
1oae 11 lOI ] Experimental data and best curve tit for the dependence of hole mobility on majority carrier 1
(16)
concentration.
[ cm“
Modelling GaAs bipolar transistors 10000
1000
-
I
Ixi
717
A X
Hilrum d 01 [32]
Lx
Nelson *I 01 [33]
n e
Ellrnbwg 01 al [34] Scoff et 01 134
’
Vilmr & Spicsr [31]
-
comp”ler
111
Le
o.oll 10"
A
10"
10" Hole
10’
1olP
10”
Concentration [ cm-’ ]
Fig. 4. Experimental data and best curve fit for the dependence of electron lifetime on majority carrier concentratibn.
100
w
-
X
Ashley k Baird [36]
&I
Hwang 1371
a
Lagowrki
$
Aeke, at 01 1391 computar
et .I 1381
fif
0 : : 0 ;i
‘O
n
10”
10”
Electron Concentration
0'
10” [ cm-’
]
Fig. 5. Experimental data and best curve fit for the dependence of hole lifetime on majority carrier concentration.
2.3
Results The analytical model is well-suited to the task of establishing the sensitivity of the performance of GaAs homojunction transistors to changes in device and material parameters. For this investigation, the d.c. gain vs collector current dependency was used as the measure whereby the effect of the following changes could be examined: the widths, doping densities and minority carrier lifetimes of the emitter and base regions, and the emitter surface recombination velocity. Results are shown in Figs. 6-9. The baseline parameter values, as
used in all the figures, except when the stated parameter is being varied, are listed in Table 1. Attainment of long minority carrier lifetimes, particularly in the base, has long been recognized as a major difficulty in GaAs bipolar devices. Yuan et al. [S] estimated a base lifetime of lo-” set and held this low value responsible for the poor dc gain of their transistors. Certainly, as Fig. 6 indicates, gains in excess of 20 cannot be expected with such low lifetimes and a basewidth of 0.4 pm. For a base region of this thickness, Fig. 6 also shows that a lifetime of 5 X 10e8 set, which would be
S.-P. LEE and D. L.
718
PULFREY
1000
100
.E
s 2 p1
5
0
x
IO
m
I
lo-’
10“
lo-’
lo-’
1
10’
Collector Current Density
10’
[
Amp/cm’
10’
10’
10’
]
Fig. 6. The effect of electron lifetime in the base on gain, as predicted by the analytical model using the parameters listed in Table 1. 1000:
lo-’
lo-’
10“
10“
10-l
1
10’
10’
Collector Current Density [ Amp/cm’
10’
10’
10’
]
Fig. 7. The effect of basewidth on gain, as predicted by the analytical model using the parameters (other than Ws)listed in Table 1. Table 1. Baseline values for parameters used in the model Emitter NB
Base
doping
doping
Collector w
E
wB
Emitter Base
layer
Collector
S
Emitter
”
F CE BE
doping layer
W C
”
density
density
thickness
thickness layer
surface
Emitter-collector Emitter-base
1
density
thickness recombination reverse
forward
bias
velocity bias voltage
voltage
x 1018 cm-3
1 x
101’
cm-3
1 x
1016
cm-3
0.25
&LID
0.40
pm
2.00
)Im
2 x
106
5.0
v
0.6
-
cm *.x-l
1.30
v
Modelling
Collector
GaAs bipolar transistors
Current Density [ Amp/cm’
719
]
Fig. 8. The effect of hole lifetime in the emitter on gain, as predicted by the analytical model using the parameters listed in Table 1. 1000
* =0
cm/s*c
lxlO’cm/s*c lrlO’cm/tec
100
ZxlO’cm/s*c fxlO”cm/ssc
.c :: E ?! ”
5
x
10
1;
lo-’
10-l
lo-’
1
10’
10’
10’
Collector Current Density [ Amp/cm’
10’
10’
10’
]
Fig. 9. The effect of emitter surface recombination velocity on gain, as predicted by the analytical model using the parameters (other than S,) listed in Table 1.
close to the longest ever measured in GaAs for this degree of doping density (see Fig. 4), is needed to realize gains in the neighbourhood of 100. To extend this gain up to around 500, requires a base thickness of less than 0.2 pm (Fig. 7); this is appreciably narrower than the widths that have been reported thus far. The combination of a high lifetime (5 X 10e8 set) and narrow base width (0.2 pm) would lead to a base transport factor in the neighbourhood of 0.9999. Such values are commonplace in silicon bipolar devices where the gain is limited principally by the hole current back-injected into the emitter, i.e. J,(-XE) in Fig. 1. If the conditions in the base of a GaAs homojunction device could be improved such that J,(-X,) became an important parameter in affecting
gain in GaAs bipolar transistors, then the emitter properties of doping, width, minority carrier lifetime and surface recombination would need addressing. The effect of lifetime is shown in Fig. 8. At low collector current densities the effects of 7E and 7B are similar. This follows from the dbminant role of emitter-base space charge region recombination in determining the base current under these conditions. The expression for this current, JREc, is given in eqn (4). With regards to the maximum gain that can be attained, TV is not as critical as TV. Over the range of 1 X lo-” to 1 X lo-’ set for 7E, Fig. 8 indicates that Pmax only changes from 50 to 90. The comparative insensitivity of gain to changes in ?= is to be expected from the lack of dependence on 78
120
S.-P. LEE
and D. L.
RJLFREY
indicate gains in the range of 12-25, somewhat higher than the values of 7-10 predicted in Fig. 10.
of the emitter Gummel number at high doping densities and from the relative widths of the base and emitter regions. In the generally much narrower emitter, a significant portion of the back-injected current is due to recombination at the emitter surface. A value of surface recombination velocity of 2 X lo6 cm/set has been measured in GaAs [38] and, as can be seen from Fig. 9, this is little better than an ohmic contact for emitter widths of a few tenths of a micron. To improve the emitter injection efficiency thus demands both a reduction in emitter width (to about 0.1 pm), and a reduction in surface recombination velocity. Values of S, of 15 cm/set have recently been reported for polysilicon contacts to silicon emitters [40], but such low values have not yet been approached in GaAs homojunctions. A heterojunction contact of the GaAlAs/GaAs type would be capable of attaining this value but, from a practical point of view, if such a heterojunction needs to be employed then the entire emitter might just as well be made of GaAlAs. While the analytical model is very useful for performing sensitivity analyses, it has limited applicability to practical devices, as these rarely can be approximated by uniformly doped regions. This situation will change as MBE becomes more widely used. Figure 10 shows model results for the device studied by Milnes and Tan [l], which was appropriate to a structure that could be realized by MBE. The model predicts a maximum gain of 400, which is in accord with the estimate of “some hundreds” given in [ 11. The devices of Bailbe et al. [3], prepared using LPE, and of Neuse er al, [2], prepared using VPE, can also be viewed as having uniformly doped regions. Simulations of these devices are also presented in Fig. 10. The agreement between measured and calculated values of maximum gain is also reasonable for the case of the VPE devices. Neuse et al. [2] measured gains in the range of 30-90, and the model gives a value of 25. The results of Bailbe et al. [3]
3. NUMERICAL
ANALYSIS
The model
3.1
Ion implantation is a doping technique which may allow attainment of the narrow basewidtbs and long minority carrier lifetimes which the results of Section 2 have shown to be necessary for high gain devices. It is well known that ion implantation affords close control of impurity profiles, and there is some evidence that long minority lifetimes in implanted GaAs can be restored by suitable annealing schedules [8]. The latest GaAs homojunction bipolar transistors, which attempt to exploit these desirable properties of ion-implantation, cannot be satisfactorily modelled analytically because of the nonuniform nature of the doping profiles. Accordingly, the well-known numerical analysis program, SEDAN [4], has been implemented to allow modelling of GaAs devices. The doping profiles were calculated from the classical LSS theory, using data on the projected range and straggle of various species from [41,42]. The effects of masking on the range [43] and of diffusion on the standard deviation [44] were also taken into account. The minority carrier lifetimes used in the model are given by equations (15) and (16). As in the analytical model, Shockley-Read-Hall recombination is considered to be the dominant recombination process. The dependence of the mobility on doping concentration is as derived in eqns (ll)-( 14). These expressions give the low field mobility p* which is used to compute the field-dependent mobility according to:
(17)
1000;
,A-Boilbs
et al.. Series
Bailba -_..I..
et al.
A /’
Series _ B
,
Ton k Milnes -----_____ too-
Nucss -.-.-._
et al.
_
.rr 8 E e 5 0
---
/’
/
/
/
/’
/
/
/
,._-
,’
,’
/
,’
/’
I’
--.--------
x to-
Collector
Current
Density
[ Amp/cm*
]
Fig. 10. The gain predicted by the analytical model using data for devices given by Bailbe er al. [3], Tan and Milnes [l] and Nuese et al. [2].
Modelling GaAs bipolar transistors where E is the electric field and the saturation velocity v, for electrons and holes is taken as 1.O X lo7 cm/set. The effect of band gap narrowing due to heavy doping effects is incorporated in the model by using the empirical relations described in eqns (6)-(9). In implementing the above modifications to SEDAN it was assumed that all dopants have zero activation energy. This is in keeping with the version of SEDAN that is used in modelling silicon devices. However, the activation efficiency for implanted species cannot be treated so perfunctorily as this parameter depends markedly on annealing conditions, and these vary widely from laboratory to laboratory. Activation efficiency is thus an important parameter used in seeking agreement between measured and modelled impurity profiles and d.c. gains. 3.2
Results
In the Hughes fabrication process [S], evaporated metal masks were used to allow selective implants into an n-type epitaxial GaAs layer deposited onto a n + substrate. A triple Be implant was used for the base and a single Si implant for the emitter. Annealing was carried out at 850°C for 30 min. This step should lead to 100% activation of the Be species [45], but the corresponding figure for the Si species cannot be so definitely stated. Previous work indicates that values in the range of 3.2% to 30% are possible [48]. The effect of Si activation and in-diffusion, using a diffusion constant of 3.3 X lo-l4 cm’/sec (at 850°C) [48], on the doping profile for the Hughes fabrication sequence is illustrated in Fig. 11. The principal effect of these variations is to change the effective widths of the emitter and base regions. From Fig. 7 it can be appreciated that variations in base width could have a very significant effect on the d.c. gain. The predicted results from the numerical model are presented in Fig. 12, from which it can be seen that pmbxcan vary over the range of 8-30. This is in good accord with the range of 7-25 which was measured by the Hughes group
lo”
1 0
0.2
0.4
0.6
721
for experimental devices [8]. The latter workers attributed the low gain of their devices to “surface leakage” effects. However, the agreement between measured data and model results shown here suggests that it is not necessary to invoke any such extraneous effects to explain the low values of gain. Instead, it appears that the results are a natural consequence of the device geometry, doping densities and material properties. Particularly significant among the latter is the effect of bandgap narrowing. If this phenomenon is not accounted for then predicted gains are likely to be very optimistic. For example, for the case of 15% silicon activation, neglect of bandgap narrowing causes the predicted value of Pmaxto increase from 14 to 80, see Fig. 12. In contrast to the fabrication procedure used by Hughes, workers at Texas Instruments [5-71, have used blanket implantations for the emitter and base regions and boron implants for device isolation. In TI’s first reported devices [5,6] a single Se implant was used for the emitter, but in later work [7] two Se implants were used. In both instances a single Be implant was used for the base. Separate anneals for the Be and Se were employed. The doping profile based on our calculations for the double Se implant device is shown in Fig. 13, for the case of activation efficiencies of 100% for Be and 70% for Se. The essential features of Fig. 13, namely: peak doping concentrations and emitter and base widths, are in agreement with the calculated profile presented by Doerbeck et al. [7], who used the LSS-theory modified by experimentally observed, but unspecified, activations. The thrust of the later TI work [7] was to ascertain the high temperature performance of GaAs bipolar devices. However some room temperature measurements of d.c. gain were recorded and these can be compared with predictions from the model. Using the profile of Fig. 13 the computed maximum value of d.c. gain was 35. This is in good agreement with the measured values of
0.6
Depth [ microns ]
1.2
1.4
5
’
Fig. 11. The computed doping profile for the Hughes device structure [81, showing the effect of activation efficiency and in-diffusion for the implanted Si species.
S.-P.
122
LEE and D. L. PULFREY
_--------_
-.
\
__ __,___.._-...-...-...__._ -I,
“‘\
_--2,
30% SiAct., -----------_ 15%
\
SI Act
BGN BGN
-...-...-‘..._..._..._.
15%SI Act., no BGN l;Z St r+., BGtj & Indlff. 3.27. Si Act..BGN --_-
lo-’
lo-’
10-Z
lo-’
1
10’
Collector Current Density
[
10’
Amp/cm’
10’
10’
10’
]
Fig. 12. The effect of silicon activation efficiency, silicon in-diffusion and bandgap narrowing (BGN) on gain for the Hughes device structure [8], as predicted by the numerical model.
0.1
012
0.3
0.4
Depth
0.5
[
0.6
microns
0.7
0.8
0.9
]
Fig. 13. The computed doping profile for the Texas Instruments device structure [7], assuming 70% activation of the implanted selenium and 100% activation of the implanted beryllium. The redistribution of impurities in
the epitaxial collector is representedby an abrupt profile.
20-30 [7] and, again, indicates that device performance is limited by intrinsic rather than extrinsic phenomena. The higher emitter peak doping level and the narrower base width would have been expected to give the TI device a much superior d.c. gain to that of the Hughes device. In fact the gains are not markedly different, which suggests that the emitter is playing an important role in determining the gain of TI’s devices. The narrower emitter, combined with the suggested surface recombination velocity of 2 X lo6 cm/set apparently leads to appreciable back-injected current. Attention
should therefore be paid to this part of the device in seeking to improve the gain.
4.
CONCLUSIONS
The analytical model derived here for n-p-n
GaAs homojunction transistors has been shown to be useful in predicting gains for devices fabricated in such a way that the assumption of uniformly doped emitter, base and collector regions is reasonable. For previously reported devices utilizing MBE, VPE or LPE processing, it has
Modelling GaAs bipolar transistors
been shown that the measured gains of around 10-90 are to be expected from the device geometries and doping densities employed. The analytical model has also proved useful in examining the sensitivity of the gain to changes in various device parameters. A high gain, of the order of 1000, demands not only a narrow (CO.2 pm), lightly doped (< 10” cme3) base, but requires also, at least for emitter widths SO.25 pm, an emitter surface recombination velocity of less than lo4 cm/set. The numerical model presented here has been shown to be useful in predicting gains for ion-implanted GaAs transistors. Agreement with recent experimental data is good, provided that bandgap narrowing effects are taken into account. This good agreement suggests that the experimental devices considered here are limited in d.c. performance by intrinsic phenomena, and not by previously postulated extrinsic effects such as surface leakage. Surface effects at the emitter, however, appear to be important in devices with good base properties. Enhanced passivation of this surface is necessary for significant improvements in gain to be realized. Acknowledgement -The
financial assistance of the Natural Sciences and Engineering Research Council of Canada is gratefully acknowledged. REFERENCES S. S. Tan and A. G. Milnes, IEEE Trans. Electron Dev.
ED-SO, 1289-1294 (1983). C. J. Nuese, J. J. Gannon, R. H. Dean, H. F. Gossenberger and R. E. Enstrom, Solid-St. Electron. 15, 81-91 (1972). J. P. Bailbe, A. Marty and G. Rey, Electron. Lett. 20, 258-259
(1984).
M. Vanzi, Semiconductor Device Analysis Program, Integrated Circuits Laboratory, Stanford University, January 1980 Version. 5. H. T. Yuan. F. H. Doerbeck and W. V. McLevige, Electron. Lett. 16, 637-638
(1980).
6. H. T. Yuan, W. V. McLevige, F. H. Doerbeck and E.G. Dierschke, Tech. Dig. IEEE IEDM 398-400 (1980). 7. F. H. Doerbeck, W. M. Duncan, W. V. McLevige and H. T. Yuan, IEEE Trans. Znd. Electron. IE-29, 136-139 (1982). 8. K. V. Vaidyanathan, R. A. Jullens, C. L. Anderson and H. L. Dunlap, Solid-St. Electron. 26, 717-721 (1983). 9. S. C. Choo. Solid-St. Electron. 11. 1069-1077f19681. 10. C. T. Sah, R.N. Noyce and W. Shockley, Proc: IRE’ 45, 1228-1243 (1957). 11. A.M. Sekela, D. L. Feucht and A. G. Milnes, Gallium Arsenide and Related Compounds [Conf. Ser.-Inst. Phys.] 24, 243-253 (1975). 12. R. D. Ryan and J. E. Eberhardt, Solid-St. Electron. 15,
865-868 (1972). 13. H. C. Casey, Jr., B. I. Miller and E. Pinkas, J. Appl. Phys. 44, 1281-1286 (1973).
14. H. C. Casey, Jr. and F. Stem, J. Appl. Phys. 47, 631-643 (1976). 15. H. Kressel and J. K. Butler, Semiconductor Lasers and Heterojunction LEDs, pp. 46-47, Academic Press, New York, 1977. 16 P. Van Halen and D. L. Pulfrey, J. Appl. Phys. 57, 5271-5274
(1985).
723
17. J. S. Blakemore, J. Appl. Phys. 53, 123-181 (1982). 18. V. F. Dvoryankin, 0. V. Emel’yanenko, D. N. Nasledov, D. D. Nedeoglo and A. A. Telegin, Sov. Phys.-Semicond. 5, 1636-lti(1972). . 19. D. E. Hill. J. At&. Phvs. 41. 1815-1818 11970) 20. S. M. Sze; Physics of Semiconductor Devices, pp. 22-27, 2nd ed., John Wiley & Sons, New York, 1981. 21. D. E. Hill, Phys. Rev. 133, 866-872 (1964). 22. 0. V. Emel’yanenko, T. S. Lagunova and D. N. Nasledov, Sov. Phys.-Solid State 2, 176-180 (1960). 23. T. Katoda and T. Sugano, J. Electrochem. Sot. 121, 1066- 1073 (1974). 24. W. Walukiewicz, L. Lagowski, L. Jastrzebski, M. Lichtensteiger and H.C. Gatos, J. Appl. Phys. 50, 899-908
(1979).
25. H. M. Cox and J. V. DiLorenzo, Gallium Arsenide and Related Compounds [Conf. Ser.-Inst. Phys.] 33b, 11-22, 1977. 26. D. J. Ashen, P. J. Dean, D. T. J. Hurle, J. B. Mullin, A. Royle and A. M. White, Gallium Arsenide and Related Compounds [Conf. Ser.-Inst. Phys.] 24, 229-244
(1975).
27. W. Walukiewicz, L. Lagowski, L. Jastrzebski and H. C. Gatos, J. Appl. Phys. 50, 5040-5042 (1979). 28. E D. Rosi, D. Meyerhofer and R. V. Jensen, J. Appl. Phys. 31, 1105-1108 (1960). 29. Sh. M. Gasanli, 0. V. Emel’yanenko, V. K. Ergakov, F. P. Kesamanly, T. S. Lagunova and D. N. Nasledov, Sov. Phys.-Semicond. 5, 1641-1644 (1972). 30. J. Vilms and J. P. Garrett, Solid-St. Electron. 15, 443-455 (1972).
31. J. Vilms and W. E. Spicer, J. Appl. Phys. 36, 2815-2821 (1965). 32. C. Hilsum and B. Holeman, Proc. Int. Conf. on Semicond. Phys. 962-966 (1960). 33, R. J. Nelson and R. G. Sobers, .I. Appl. Phys. 49,
6103-6108 (1978). 34. M. Ettenberg, H. Kressel and S. L. Gilbert, J. Appl. Phys. 44, 827-831 (1973). 35. G. B. Scott, G. Duggan and P. Dawson, J. Appl. Phys. 52, 6888-6894 (198 1). 36. K. L. Ashlev and J. R. Biard, IEEE Trans. Electron Dev.
ED-14, 4291432 (1967). 37. C. J. Hwang, J. Appl. Phys. 42.4408-4413 (1971). 38. L. Lagowski, L. Jastrzebski and H. C. Gatos, Awl. Phys. . Lett. 27, 537-539 (1975). 39. G. A. Acket and J. J. Scheer. Solid-St. Electron.
14.
167-174 (1971). 40. A. Neugroschel, M. Arienzo, Y. Komen and R. D. Isaac, IEEE Trans. Electron Dev. ED-32. 807-816 (1985). 41. J. F. Gibbons, W. S. Johnson and S.‘W. Mylroie, Projected Range Statistics, 2nd ed. Dowden, Hutchinson, and Ross, Stroudburg, Pennsylvania, 1975. 42. H. Ryssel and I. Ruge, lonenimplantation, Teubner, Stuttgart, 1978. 43. T. H. Chen and M. S. Shur, IEEE Trans. Electron Dev. ED-32, 18-27 (1985). 44. S.K. Ghandhi, VLSI Fabrication Principles, pp. 345346, John Wiley & Sons, 1983. 45. C. L. Anderson and H. L. Dunlap, Appl. Phys. Lett. 35, 178-180 (1979). 46. C. A. Stolte, in Semiconductors and Semimetals 20, 89-159, Academic Press, New York, 1984. 47. C. G. Fonstad, IEEE Electron Dev. Len. EDL-5, 99-100
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1986
0038-1101186 $3.&l + 0.00 Pergamon Journals Ltd
MODELLING THE d.c. PERFORMANCE OF GaAs HOMOJUNCTION BIPOLAR TRANSISTORS S.-P. LEE and D. L. PCJLFREY Department of Electrical Engineering, University of British Columbia, Vancouver, British Columbia, V6T lW5 Canada (Received 15 August 1985; in revised form 2 November 1985)
Abstract--Two models, one analytical and one numerical, have been developed to predict the d.c. performance of GaAs homojunction bipolar transistors. In each case the minority carrier properties of lifetime and mobility have been described by polynomial fits to recent data. Bandgap narrowing in the emitter and base regions has also been taken into account. The analytical model assumes uniform doping in the three regions of the transistor and is thus appropriate to predicting the performance of devices fabricated using epitaxial process technologies. This model is also useful for carrying out sensitivity analyses. The importance of parameters such as regional widths and doping densities, minority carrier lifetimes and surface recombination velocity is examined here. The numerical model is useful for describing the performance of ion-implanted devices. Good agreement is obtained between results from the model and recent experimental data.
INTRODUCTION The high electron mobility and the large bandgap of GaAs make it an attractive material for device applica-
tions where operation at high frequency or high temperature is important. To exploit these desirable properties, GaAs-based transistors in the form of MEWETs and bipolar heterojunctions are being investigated widely. In contrast, the GaAs bipolar homojunction transistor is receiving relatively little attention. The major difficulty in this device is obtaining the extremely thin base region which is demanded by the short minority carrier lifetime of GaAs. Presumably suitable base regions could be obtained by using molecular beam epitaxy, which is the method of fabrication employed in many heterojunction transistor structures. In fact, a recent analysis of homojunction and heterojunction GaAs transistors, using parameters appropriate to MBE-fabricated devices in both cases [ 11, indicates that the difference in high frequency performance between the two types of device should be only about 10%. Even though inverted [47] and optimized [48] heterostructures will increase this relative superiority of heterojunctions, and also lead to higher d.c. gains [48], the attraction of GaAs homojunction bipolar transistors is their potential compatibility with the much simpler and more developed fabrication techniques of diffusion and ion implantation which, by themselves, are not sufficient for the fabrication of heterojunction devices. To exploit this feature of relative processing simi plicity, it would help to have a model for the GaAs homojunction transistor which could be used to examine the sensitivity of device performance to processdependent parameters such as minority carrier mobility and lifetime, doping profiles and regional thicknesses. The difficulty in providing such a useful model arises from the wide variation in published data for such factors as: the dependence of mobility and lifetime on doping density; the relative importance of Shockley-Read-Hall,
radiative and Auger recombination prkesses; the surface recombination velocity and, in the case of ion implantation, the activation efficiency of implanted species. These variations are often the result of the use of widely differing GaAs substrates, epitaxial growth procedures and doping conditions. As a first attempt at providing useful models for GaAs homojunction bipolar transistors we have addressed the above points in the following way: recent data on the dependence of minority carrier mobility and lifetime on doping density has been collected together and curve fitted using appropriate polynomial expressions; radiative and Auger recombination have been argued to be unimportant in the devices of interest; surface recombination velocity and dopant activation have been taken as adjustable parameters. In this manner it has proved possible to develop meaningful models for the prediction of the d.c. performance of GaAs bipolar transistors. The first model is analytical, one-dimensional and treats the various regions of the transistor as being uniformly doped. As such, the model is directly applicable to devices fabricated by the sequential growth of epitaxial layers. Good agreement is obtained between predicted results and data from devices utilizing VPE[2], LPEP], and MBE[ l] fabrication techniques. In addition, the model is well-suited to performing sensitivity analyses on factors likely to affect device performance, e.g. lifetime in the base and emitter, emitter surface recombination velocity, widths and doping densities of the various regions of the device. The second model is the one-dimensional numerical model SEDAN [4], suitably modified to render it applicable to GaAs. The required changes concern the mobility and lifetime dependence on doping density and the treatment of bandgap narrowing in the emitter [3]. This model is used here to simulate the performance of recent ion-implanted transistors for which the doping profiles are decidedly non-uniform [5-81. Good agreement between the measured and simulated values of dc current gain is obtained.
713
714
S.-P. LEE and D. L. 2. THE ANALYTICAL MODEL
2.1
Current flows The current components that are included in this model are shown schematically in Fig. 1. The base cur-
PLILFREY
taken to be given by Choo’s expression [9] which takes into account the asymmetry of the doping density between the emitter and the base, namely:
rent density is given by (4)
JB = .J,(-X,)
+ J”(0) - J”(XB) - &(X,) +
JREC
-
JGEN
(1)
where J,(-X,) is the hole current density “back-injected” into the quasi-neutral emitter, the term [J”(O) - J,(X,)] represents the current density due to recombination in the quasi-neutral base, JP(Xc) is the hole component of the base-collector diode saturation current density, JREC is due to recombination in the emitter-base depletion region and JoENis the generation current density in the collector-base depletion region. The collector current density is given by Jc = J,(Xe) + J,(Xc) +
JC~EN
J GEN= $+o&((~)
(2)
where J.(X,) is the electron current density entering the base-collector depletion region and also includes the electron component of the saturation current density of the base-collector diode. The results presented in this paper are expressed in terms of the d.c. current gain, namely
P = JcIJB.
where W,, is the width of the emitter-base junction across which there is an applied voltage V,, and a builtin voltage VbiE, and the minority carrier lifetimes in the base and emitter are given by TV and rE, respectively. The parameters b andf(b) are given in Choo’s paper [9] and depend on the trap level E,. JGeN is given by the usual Sah-Noyce-Shockley expression [lo]:
(3)
The current densities J,(O), J.(XB) and Jp(-XE) appearing in (1) and (2), and the hole current density at the emitter surface J,(- WE - X,), are given by the usual expressions derived from the continuity equations under low-level injection conditions and assuming constant doping in each of the three regions of the npn transistor. JREc for the forward biased emitter-base junction is
where WBc is the width of the base-collector depletion region, E, is the energy level of the generation centers and rc is the minority carrier lifetime in the collector. In eqns (4) and (5) E, is considered to be a single level located at the intrinsic Fermi level E, . The minority carrier lifetimes r&, TV, T= used in eqs (4) and (5) are all taken to be appropriate to a recombination-generation mechanism of the Shockley-Read-Hall type. The dominance of this mechanism of recombination in the GaAs material considered here is supported by minority carrier diffusion length studies in GaAs by various authors. Sekela et al. [ll] showed in their studies of hole diffusion length in n-type GaAs that the largest L, measured is about one third of the theoretical value predicted by Ryan and Eberhardt [12] for radiative recombination, which implies that the hole lifetime due to indirect re-
Fig. 1. Schematic of current flows in a homojunction bipolar transistor.
Modelling GaAs bipolar transistors
combination is typically an order of magnitude lower than that due to direct radiative recombination. The studies on electron diffusion length in p-type GaAs by Casey et al. [ 13, 141 also indicated that the electron lifetime is dominated by nonradiative recombination for hole concentrations less than 1 X lOI* cme3. This insignificant contribution of radiative recombination to the total recombination mechanism, despite the fact that GaAs is a direct bandgap semiconductor, can be attributed to the presence of a large number of recombination centers and defects in GaAs. The Shockley-Read-Hall recombination is assumed to be the dominant component of the indirect recombination mechanism since it is believed that Auger recombination is important in GaAs only at very high doping densities (greater than lOI cmW3)[ 151. 2.2
Model parameters
Carrier concentrations are calculated in the model using the full Fermi-Dirac statistics. The required Fermi-Dirac integrals were approximated by accurate, short-series polynomials [ 161. The electron and hole effective masses, which appear in the expressions for the effective densities of states in the conduction and valence bands, were computed from the detailed equations given by Blakemore [ 171, taking into account the effect of band gap narrowing. This latter effect is described by E,(eV) = 1.42248 - AE,
(6)
where AE, = kT ln(n;/n:)
.
(7)
For the intrinsic carrier concentration, ni, a value of 2.0 X lo6 crne3 was taken. For the effective intrinsic carrier concentration ni,, the following empirical relations were used [3]:
715
for n-type material n.(cm-‘)
= 3.38 X 10W3m
+ 9 x 10”
lo’*
(8)
for p-type material n.(cm-‘)
= 3.38 X 10--3a
- 6.72
X 105 In -$j + 9 X 10”. ( 1
(9)
To complete the information required to estimate the position of the Fermi energy, it is necessary to know the activation energy of the dopants. This quantity was taken as being adequately described by the empirical relation: Ea = E: - AN:l3
(10)
where E.$is the ionization energy at infinite dilution, N, is the dopant concentration (cmm3) and A is a constant. For n-type and p-type dopants the values of A in cm.eV were taken as 1.9 X 10m8[18] and 2.34 X low8 [19], respectively. The above information, when coupled with the doping densities and widths of the emitter, base and collector regions allows the equilibrium carrier concentration profiles to be established. To proceed to a calculation of the diffusion current flows, data on the electron and hole diffusion constants is required. This follows from the Einstein relatibnship, suitably modified to allow for degeneracy [20], providing the minority carrier mobilities are known. From Hall effect measurements a wealth of data on majority carrier mobility values is available. For electrons, data from [18, 21-261 are plotted in Fig. 2,
A
Emal’yonanko
X
Hill 121)
0
Ovoryonkin
ra
Kotodo
P
Wolukiericz
x
Cox & DiLorsnzo
‘3
Ashen
-
Electron
- 3.47
10” Concentration
01 .I 1221
el al IlS]
k Sugono
(231
el 01 [24] [25]
sl (111261
compufer
lit
10’” [ cm-’
]
Fig. 2. Experimental data and best curve fit for the dependence of electron mobility on majority carrier concentration.
S.-P.
716
LEE
and D. L.
along with a best-fit curve given by p,(cm2V1sec-‘)
F'ULFREY
~h(cm2V-1sec-1) = 502511.268 - 156107~
= 0.053 - 69783.160~
+ 19205.6~~ - 1168.926~~
+ 17348.328~~ - 1579.599~~
+ 35.209~“ - 0.420~~
+ 63.036~“ - 0.935~~
(11)
where y = log&/cm-3), with n being the electron concentration in cmm3. To convert this data to drift mobility data a weak field Hall factor of 1.175 was assumed 1171and the ratio of minority carrier to majority carrier mobility was taken to be /*: = f(n)&
(12)
where Y =
log&p/cm-3)
.
Curve fittings were also performed on published data for electron [31-351 and hole [32, 36-391 minority carrier lifetimes. The data are shown in Figs. 4 and 5, and the fitted curves are given by log,,(r,,/sec)
wheref(n) represents a curve fitted to the data of [27], namely:
= -678.5724587x
+ 157.93508506~~
- 13.7579663247~’ + 0.531235178933~~ 0.0076716569056~~
f(n) = 684.327 - 168.175~ + 15.497y2 - 0.633~’ + 0.009~~
(13)
(14)
(15)
and log,O(rP/sec) = 545.075507209 - 99.5742908474~
where y = log10(n/cm-3).
+ 5.96752406063~~ - 0.11903779718~~
To our knowledge, a corresponding expression relating the minority and majority carrier hole mobilities does not exist. The hole Hall mobility data, operated on by a low field Hall factor of 1.25 [ 171, was thus taken as being the minority carrier hole mobility. Some representative Hall data from [19, 21, 22, 28-311 is shown in Fig. 3, along with the fitted curve used in the present work. The curve is given by
where x = logl,(p/cmW3)
and
z = log,0(n/cm-3).
Finally, the model parameter set uses a value of 13.1 for the relative permittivity of GaAs and, except where specified to the contrary, uses a value of 2 X lo6 cm set-’ [38] for the emitter surface recombination velocity.
R0Si et al [28] Vilms k Spicer 1311 Hill (211 Hill [19] Cosonli sl 01 [29] “ilmr
k Garrett [30]
Emsl’yonenko et 01 [22] computer
0 1
10"
lOI6
10"
Hole Concentration
Fig.
3.
fit
1oae 11 lOI ] Experimental data and best curve tit for the dependence of hole mobility on majority carrier 1
(16)
concentration.
[ cm“
Modelling GaAs bipolar transistors 10000
1000
-
I
Ixi
717
A X
Hilrum d 01 [32]
Lx
Nelson *I 01 [33]
n e
Ellrnbwg 01 al [34] Scoff et 01 134
’
Vilmr & Spicsr [31]
-
comp”ler
111
Le
o.oll 10"
A
10"
10" Hole
10’
1olP
10”
Concentration [ cm-’ ]
Fig. 4. Experimental data and best curve fit for the dependence of electron lifetime on majority carrier concentratibn.
100
w
-
X
Ashley k Baird [36]
&I
Hwang 1371
a
Lagowrki
$
Aeke, at 01 1391 computar
et .I 1381
fif
0 : : 0 ;i
‘O
n
10”
10”
Electron Concentration
0'
10” [ cm-’
]
Fig. 5. Experimental data and best curve fit for the dependence of hole lifetime on majority carrier concentration.
2.3
Results The analytical model is well-suited to the task of establishing the sensitivity of the performance of GaAs homojunction transistors to changes in device and material parameters. For this investigation, the d.c. gain vs collector current dependency was used as the measure whereby the effect of the following changes could be examined: the widths, doping densities and minority carrier lifetimes of the emitter and base regions, and the emitter surface recombination velocity. Results are shown in Figs. 6-9. The baseline parameter values, as
used in all the figures, except when the stated parameter is being varied, are listed in Table 1. Attainment of long minority carrier lifetimes, particularly in the base, has long been recognized as a major difficulty in GaAs bipolar devices. Yuan et al. [S] estimated a base lifetime of lo-” set and held this low value responsible for the poor dc gain of their transistors. Certainly, as Fig. 6 indicates, gains in excess of 20 cannot be expected with such low lifetimes and a basewidth of 0.4 pm. For a base region of this thickness, Fig. 6 also shows that a lifetime of 5 X 10e8 set, which would be
S.-P. LEE and D. L.
718
PULFREY
1000
100
.E
s 2 p1
5
0
x
IO
m
I
lo-’
10“
lo-’
lo-’
1
10’
Collector Current Density
10’
[
Amp/cm’
10’
10’
10’
]
Fig. 6. The effect of electron lifetime in the base on gain, as predicted by the analytical model using the parameters listed in Table 1. 1000:
lo-’
lo-’
10“
10“
10-l
1
10’
10’
Collector Current Density [ Amp/cm’
10’
10’
10’
]
Fig. 7. The effect of basewidth on gain, as predicted by the analytical model using the parameters (other than Ws)listed in Table 1. Table 1. Baseline values for parameters used in the model Emitter NB
Base
doping
doping
Collector w
E
wB
Emitter Base
layer
Collector
S
Emitter
”
F CE BE
doping layer
W C
”
density
density
thickness
thickness layer
surface
Emitter-collector Emitter-base
1
density
thickness recombination reverse
forward
bias
velocity bias voltage
voltage
x 1018 cm-3
1 x
101’
cm-3
1 x
1016
cm-3
0.25
&LID
0.40
pm
2.00
)Im
2 x
106
5.0
v
0.6
-
cm *.x-l
1.30
v
Modelling
Collector
GaAs bipolar transistors
Current Density [ Amp/cm’
719
]
Fig. 8. The effect of hole lifetime in the emitter on gain, as predicted by the analytical model using the parameters listed in Table 1. 1000
* =0
cm/s*c
lxlO’cm/s*c lrlO’cm/tec
100
ZxlO’cm/s*c fxlO”cm/ssc
.c :: E ?! ”
5
x
10
1;
lo-’
10-l
lo-’
1
10’
10’
10’
Collector Current Density [ Amp/cm’
10’
10’
10’
]
Fig. 9. The effect of emitter surface recombination velocity on gain, as predicted by the analytical model using the parameters (other than S,) listed in Table 1.
close to the longest ever measured in GaAs for this degree of doping density (see Fig. 4), is needed to realize gains in the neighbourhood of 100. To extend this gain up to around 500, requires a base thickness of less than 0.2 pm (Fig. 7); this is appreciably narrower than the widths that have been reported thus far. The combination of a high lifetime (5 X 10e8 set) and narrow base width (0.2 pm) would lead to a base transport factor in the neighbourhood of 0.9999. Such values are commonplace in silicon bipolar devices where the gain is limited principally by the hole current back-injected into the emitter, i.e. J,(-XE) in Fig. 1. If the conditions in the base of a GaAs homojunction device could be improved such that J,(-X,) became an important parameter in affecting
gain in GaAs bipolar transistors, then the emitter properties of doping, width, minority carrier lifetime and surface recombination would need addressing. The effect of lifetime is shown in Fig. 8. At low collector current densities the effects of 7E and 7B are similar. This follows from the dbminant role of emitter-base space charge region recombination in determining the base current under these conditions. The expression for this current, JREc, is given in eqn (4). With regards to the maximum gain that can be attained, TV is not as critical as TV. Over the range of 1 X lo-” to 1 X lo-’ set for 7E, Fig. 8 indicates that Pmax only changes from 50 to 90. The comparative insensitivity of gain to changes in ?= is to be expected from the lack of dependence on 78
120
S.-P. LEE
and D. L.
RJLFREY
indicate gains in the range of 12-25, somewhat higher than the values of 7-10 predicted in Fig. 10.
of the emitter Gummel number at high doping densities and from the relative widths of the base and emitter regions. In the generally much narrower emitter, a significant portion of the back-injected current is due to recombination at the emitter surface. A value of surface recombination velocity of 2 X lo6 cm/set has been measured in GaAs [38] and, as can be seen from Fig. 9, this is little better than an ohmic contact for emitter widths of a few tenths of a micron. To improve the emitter injection efficiency thus demands both a reduction in emitter width (to about 0.1 pm), and a reduction in surface recombination velocity. Values of S, of 15 cm/set have recently been reported for polysilicon contacts to silicon emitters [40], but such low values have not yet been approached in GaAs homojunctions. A heterojunction contact of the GaAlAs/GaAs type would be capable of attaining this value but, from a practical point of view, if such a heterojunction needs to be employed then the entire emitter might just as well be made of GaAlAs. While the analytical model is very useful for performing sensitivity analyses, it has limited applicability to practical devices, as these rarely can be approximated by uniformly doped regions. This situation will change as MBE becomes more widely used. Figure 10 shows model results for the device studied by Milnes and Tan [l], which was appropriate to a structure that could be realized by MBE. The model predicts a maximum gain of 400, which is in accord with the estimate of “some hundreds” given in [ 11. The devices of Bailbe et al. [3], prepared using LPE, and of Neuse er al, [2], prepared using VPE, can also be viewed as having uniformly doped regions. Simulations of these devices are also presented in Fig. 10. The agreement between measured and calculated values of maximum gain is also reasonable for the case of the VPE devices. Neuse et al. [2] measured gains in the range of 30-90, and the model gives a value of 25. The results of Bailbe et al. [3]
3. NUMERICAL
ANALYSIS
The model
3.1
Ion implantation is a doping technique which may allow attainment of the narrow basewidtbs and long minority carrier lifetimes which the results of Section 2 have shown to be necessary for high gain devices. It is well known that ion implantation affords close control of impurity profiles, and there is some evidence that long minority lifetimes in implanted GaAs can be restored by suitable annealing schedules [8]. The latest GaAs homojunction bipolar transistors, which attempt to exploit these desirable properties of ion-implantation, cannot be satisfactorily modelled analytically because of the nonuniform nature of the doping profiles. Accordingly, the well-known numerical analysis program, SEDAN [4], has been implemented to allow modelling of GaAs devices. The doping profiles were calculated from the classical LSS theory, using data on the projected range and straggle of various species from [41,42]. The effects of masking on the range [43] and of diffusion on the standard deviation [44] were also taken into account. The minority carrier lifetimes used in the model are given by equations (15) and (16). As in the analytical model, Shockley-Read-Hall recombination is considered to be the dominant recombination process. The dependence of the mobility on doping concentration is as derived in eqns (ll)-( 14). These expressions give the low field mobility p* which is used to compute the field-dependent mobility according to:
(17)
1000;
,A-Boilbs
et al.. Series
Bailba -_..I..
et al.
A /’
Series _ B
,
Ton k Milnes -----_____ too-
Nucss -.-.-._
et al.
_
.rr 8 E e 5 0
---
/’
/
/
/
/’
/
/
/
,._-
,’
,’
/
,’
/’
I’
--.--------
x to-
Collector
Current
Density
[ Amp/cm*
]
Fig. 10. The gain predicted by the analytical model using data for devices given by Bailbe er al. [3], Tan and Milnes [l] and Nuese et al. [2].
Modelling GaAs bipolar transistors where E is the electric field and the saturation velocity v, for electrons and holes is taken as 1.O X lo7 cm/set. The effect of band gap narrowing due to heavy doping effects is incorporated in the model by using the empirical relations described in eqns (6)-(9). In implementing the above modifications to SEDAN it was assumed that all dopants have zero activation energy. This is in keeping with the version of SEDAN that is used in modelling silicon devices. However, the activation efficiency for implanted species cannot be treated so perfunctorily as this parameter depends markedly on annealing conditions, and these vary widely from laboratory to laboratory. Activation efficiency is thus an important parameter used in seeking agreement between measured and modelled impurity profiles and d.c. gains. 3.2
Results
In the Hughes fabrication process [S], evaporated metal masks were used to allow selective implants into an n-type epitaxial GaAs layer deposited onto a n + substrate. A triple Be implant was used for the base and a single Si implant for the emitter. Annealing was carried out at 850°C for 30 min. This step should lead to 100% activation of the Be species [45], but the corresponding figure for the Si species cannot be so definitely stated. Previous work indicates that values in the range of 3.2% to 30% are possible [48]. The effect of Si activation and in-diffusion, using a diffusion constant of 3.3 X lo-l4 cm’/sec (at 850°C) [48], on the doping profile for the Hughes fabrication sequence is illustrated in Fig. 11. The principal effect of these variations is to change the effective widths of the emitter and base regions. From Fig. 7 it can be appreciated that variations in base width could have a very significant effect on the d.c. gain. The predicted results from the numerical model are presented in Fig. 12, from which it can be seen that pmbxcan vary over the range of 8-30. This is in good accord with the range of 7-25 which was measured by the Hughes group
lo”
1 0
0.2
0.4
0.6
721
for experimental devices [8]. The latter workers attributed the low gain of their devices to “surface leakage” effects. However, the agreement between measured data and model results shown here suggests that it is not necessary to invoke any such extraneous effects to explain the low values of gain. Instead, it appears that the results are a natural consequence of the device geometry, doping densities and material properties. Particularly significant among the latter is the effect of bandgap narrowing. If this phenomenon is not accounted for then predicted gains are likely to be very optimistic. For example, for the case of 15% silicon activation, neglect of bandgap narrowing causes the predicted value of Pmaxto increase from 14 to 80, see Fig. 12. In contrast to the fabrication procedure used by Hughes, workers at Texas Instruments [5-71, have used blanket implantations for the emitter and base regions and boron implants for device isolation. In TI’s first reported devices [5,6] a single Se implant was used for the emitter, but in later work [7] two Se implants were used. In both instances a single Be implant was used for the base. Separate anneals for the Be and Se were employed. The doping profile based on our calculations for the double Se implant device is shown in Fig. 13, for the case of activation efficiencies of 100% for Be and 70% for Se. The essential features of Fig. 13, namely: peak doping concentrations and emitter and base widths, are in agreement with the calculated profile presented by Doerbeck et al. [7], who used the LSS-theory modified by experimentally observed, but unspecified, activations. The thrust of the later TI work [7] was to ascertain the high temperature performance of GaAs bipolar devices. However some room temperature measurements of d.c. gain were recorded and these can be compared with predictions from the model. Using the profile of Fig. 13 the computed maximum value of d.c. gain was 35. This is in good agreement with the measured values of
0.6
Depth [ microns ]
1.2
1.4
5
’
Fig. 11. The computed doping profile for the Hughes device structure [81, showing the effect of activation efficiency and in-diffusion for the implanted Si species.
S.-P.
122
LEE and D. L. PULFREY
_--------_
-.
\
__ __,___.._-...-...-...__._ -I,
“‘\
_--2,
30% SiAct., -----------_ 15%
\
SI Act
BGN BGN
-...-...-‘..._..._..._.
15%SI Act., no BGN l;Z St r+., BGtj & Indlff. 3.27. Si Act..BGN --_-
lo-’
lo-’
10-Z
lo-’
1
10’
Collector Current Density
[
10’
Amp/cm’
10’
10’
10’
]
Fig. 12. The effect of silicon activation efficiency, silicon in-diffusion and bandgap narrowing (BGN) on gain for the Hughes device structure [8], as predicted by the numerical model.
0.1
012
0.3
0.4
Depth
0.5
[
0.6
microns
0.7
0.8
0.9
]
Fig. 13. The computed doping profile for the Texas Instruments device structure [7], assuming 70% activation of the implanted selenium and 100% activation of the implanted beryllium. The redistribution of impurities in
the epitaxial collector is representedby an abrupt profile.
20-30 [7] and, again, indicates that device performance is limited by intrinsic rather than extrinsic phenomena. The higher emitter peak doping level and the narrower base width would have been expected to give the TI device a much superior d.c. gain to that of the Hughes device. In fact the gains are not markedly different, which suggests that the emitter is playing an important role in determining the gain of TI’s devices. The narrower emitter, combined with the suggested surface recombination velocity of 2 X lo6 cm/set apparently leads to appreciable back-injected current. Attention
should therefore be paid to this part of the device in seeking to improve the gain.
4.
CONCLUSIONS
The analytical model derived here for n-p-n
GaAs homojunction transistors has been shown to be useful in predicting gains for devices fabricated in such a way that the assumption of uniformly doped emitter, base and collector regions is reasonable. For previously reported devices utilizing MBE, VPE or LPE processing, it has
Modelling GaAs bipolar transistors
been shown that the measured gains of around 10-90 are to be expected from the device geometries and doping densities employed. The analytical model has also proved useful in examining the sensitivity of the gain to changes in various device parameters. A high gain, of the order of 1000, demands not only a narrow (CO.2 pm), lightly doped (< 10” cme3) base, but requires also, at least for emitter widths SO.25 pm, an emitter surface recombination velocity of less than lo4 cm/set. The numerical model presented here has been shown to be useful in predicting gains for ion-implanted GaAs transistors. Agreement with recent experimental data is good, provided that bandgap narrowing effects are taken into account. This good agreement suggests that the experimental devices considered here are limited in d.c. performance by intrinsic phenomena, and not by previously postulated extrinsic effects such as surface leakage. Surface effects at the emitter, however, appear to be important in devices with good base properties. Enhanced passivation of this surface is necessary for significant improvements in gain to be realized. Acknowledgement -The
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