Technical Note

Analytical modeling of pnp InP/InGaAs heterojunctionbipolar transistors

S. Datta a, K.P. Roenker a,*, M.M. Cahay a, L.M. Lunardi b

a Department of Electrical and Computer Engineering and Computer Science, University of Cincinnati, P.O. Box 210030, Cincinnati, OH

45221-0030,USAb AT&T Labs ± Research, Red Bank, NJ 07701,USA

Received 20 January 2000; accepted 21 February 2000

Abstract

Pnp InP/InGaAs heterojunction bipolar transistors have been modeled using a modi®ed Gummel±Poon model, and

the results are compared with experimental measurements and results from a commercial simulator. The model pro-

vides a good description of the transistorÕs high frequency performance and describes the fallo� in device performance

at high current densities. The model overestimates the current gain at low current densities by neglecting hole re-

combination in the base side of the emitter±base space charge region. Ó 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Pnp; Heterojunction; Bipolar; Transistor; InP

1. Introduction

Recently, Pnp heterojunction bipolar transistors

(HBTs) have been demonstrated in InP-based materials

operating at microwave frequencies [1±6]. Lunardi et al.

[1] have reported InP/InGaAs Pnp HBTs with a current

gain as high as 420, a cuto� frequency fT of 10.5 GHz

and a maximum frequency of oscillation fmax of 25 GHz.

Stanchina et al. [2,3] have reported comparable results

for InAlAs/InGaAs Pnp HBTs. The devices are of in-

terest for integration with Npn HBTs in complementary

HBT (CHBT) based circuits [2±8] and for power appli-

cations [9]. Previously, we reported the development of a

modi®ed Gummel±Poon model for Pnp HBTs and

compared the modelÕs results with experimental mea-

surements for InAlAs/InGaAs HBTs [10]. In this work,

we compare the results of the analytical model for InP/

InGaAs Pnp HBTs with the experimental reports [1],

and the results from a commercial numerical simulator

for Ref. [11]. In Section 2, we brie¯y summarize the

device physics included in the analytical model. A

comparison of the experimental and simulation results is

presented in Section 3. In Section 4, we draw conclu-

sions regarding the limitations of the analytical model

and means for improving it, and factors limiting the

deviceÕs performance.

2. Device modeling

To study the performance of the InP/InGaAs Pnp

HBT, the analytical model recently reported [10] was

employed. The modelÕs development follows that pre-

viously reported for the Npn HBT [12,13] by matching

the carrier thermionic-®eld-emission current across the

emitter±base heterojunction with the drift-di�usion

current in the base to derive the excess carrier concen-

tration at the emitter end of the quasi-neutral base. The

drift-di�usion of holes across the emitter space charge

region is included and found to be as important as

thermionic emission in limiting hole injection into the

base [10]. In addition, the model incorporates a more

realistic boundary condition for the hole concentration

at the collector end of the quasi-neutral base, i.e. a ®nite

concentration su�cient to carry the hole collector cur-

rent. Derived from this model is the primary hole cur-

rent ¯ow from the emitter to the collector. To obtain

Solid-State Electronics 44 (2000) 1331±1333

* Corresponding author. Tel.: +1-513-556-4761; fax: +1-513-

556-7326.

E-mail address: kroenker@ececs.uc.edu (K.P. Roenker).

0038-1101/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 3 8 - 1 1 0 1 ( 0 0 ) 0 0 0 5 5 - 1

realistic terminal currents for the device, the recombi-

nation currents are incorporated [10]. Series resis-

tance and base pushout e�ects are also included to

describe the fallo� in device performance at high

current densities [14]. The material parameters em-

ployed in the simulation have been described in detail

elsewhere [15].

For comparison with the results of the analytical

model and available experimental results, the device was

also modeled using a commercial device simulator [11].

The same material parameters employed in the analyti-

cal model were used. Performance analysis was achieved

by self-consistent numerical solution of the Poisson,

carrier continuity and current density equations in two

dimensions subject to the device's geometry and

boundary conditions imposed by the device's contacts

and biasing.

3. Results

The epitaxial layer structure for the InP/InGaAs Pnp

HBT modeled is similar to that previously reported by

Lunardi et al. [1]. To provide grading of the valence

band discontinuity, the device structure incorporates an

InGaAsP quaternary layer between the emitter and the

base. Fig. 1 shows the current gain as a function of the

collector current density calculated using the analytical

model, and compared with the experimental and nu-

merical modeling results. Near the current density cor-

responding to the peak experimentally observed gain,

good agreement of the analytical and numerical mod-

eling results is seen, but both overestimate the observed

current gain. This may be due to an overestimation of

the minority carrier lifetime in the base, since both

modeling approaches assume the same lifetime, and

yield very similar results. The fallo� at high current

densities, which can be attributed to the base pushout

and series resistance e�ects, is seen in the experimental

results and is incorporated in both the analytical and

numerical models. However, the experimental results

show a fallo� in gain above � 104 A/cm2, which is

somewhat earlier than that predicted by either of the

models. However, both the analytical and numerical

models neglect self-heating e�ects, which are known to

be important at high current densities and which de-

grade the device performance. At low current densities,

both the analytical and numerical models overestimate

the current gain. In the case of the analytical model, the

e�ect is believed to be due to neglecting the recombi-

nation of holes in the base side of the emitter±base space

charge region, which numerical modeling has recently

shown to be important for Pnp AlGaAs/GaAs HBTs

[16]. That is, in our analytical model the level of hole

injection into the base is determined by matching

thermionic-®eld-emission from the emitter with drift-

di�usion in the base while neglecting the loss of holes to

recombination in the space charge region on the base

side. Ekbote et al. [16] have shown that this overesti-

mates the holes available for drift-di�usion in the base.

Searles and Pulfrey [17] have also addressed this issue.

The cuto� frequency fT and maximum frequency of

oscillation fmax as a function of the collector current

density are seen in Fig. 2. In this case, both the analytical

and numerical modeling results are in excellent agree-

ment with the available experimental results near the

current density corresponding to the peak current gain.

Fig. 1. Measured (d) DC current gain as a function of the

collector current density for VEC � 5 V compared with simula-

tion results from the analytical (s) and numerical (h) models.

Fig. 2. Measured cuto� frequency (n) as a function of the

collector current density compared with simulation results from

the analytical (h) and numerical (*) models for VEC � 5 V.

Measured maximum frequency of oscillation (d) compared

with simulation results from the analytical (s) and numerical

(D) models.

1332 S. Datta et al. / Solid-State Electronics 44 (2000) 1331±1333

At higher current densities, base pushout and other high

current e�ects degrade both fT and fmax, which are seen

in the analytical modeling results. As in the case of the

current gain, the fallo� is predicted at higher current

densities than expected since self heating e�ects have not

yet been incorporated. More experimental results are

needed at high current densities for further comparison

with the simulation results.

4. Conclusion

In summary, we have compared results from an an-

alytical model for Pnp InP/InGaAs HBTs with the ex-

perimental results and results from a commercial

numerical device simulator. Reasonable agreement has

been found for the deviceÕs high frequency performance.

The results suggest that the analytical model provides a

useful tool for device design and development that

complements the capabilities provided by commercial

device simulators. In particular, the model has been used

to examine the e�ects of linear compositional base

grading [6], which suggests that improved high fre-

quency performance and current gain are possible. Fi-

nally, the results reported here for InP/InGaAs Pnp

HBTs are similar to those reported previously for In-

AlAs/InGaAs PnpÕs [2,3].

Acknowledgements

This work was supported by the National Science

Foundation under Grant no. ECS-9525942.

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