Emitter series resistance e�ect of multiple heterojunctioncontacts for Pnp heterojunction bipolar transistors

S. Datta, K.P. Roenker*, M.M. Cahay

Department of Electrical and Computer Engineering and Computer Science, University of Cincinnati, Cincinnati, Ohio 45221-0030,

USA

Received 1 February 1999; accepted 3 March 1999

Abstract

For InP-based Pnp heterojunction bipolar transistors (HBTs), a set of epitaxial layers, frequently incorporatingquaternaries, is used to make a low resistance electrical contact to the emitter layer. We describe an analytical

approach to investigate the nonlinear e�ects of the multiple heterojunction interfaces on the emitter series resistanceand emitter junction current±voltage characteristics of the device. The simulation results show that heterojunctioninterfaces can contribute a substantial portion (up to 20%) to the total emitter series resistance, especially at highlevels of emitter current. # 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction

For InP-based heterojunction bipolar transistors(HBTs), a set of epitaxial layers (including quaternarylayers) are frequently used to make low resistance elec-

trical contacts to the wide bandgap emitter layer. Thee�ects of the heterojunctions between layers are usuallyneglected or incorporated as a ®xed resistance in the

emitter series resistance of the device. However, thepresence of these heterojunctions in the multilayeremitter contact may introduce barriers to carrier ¯owthat produce parasitic voltage drops across the inter-

faces and introduce nonlinearity in the emitter cur-rent±voltage characteristics. They may also modify thehigh frequency performance of the device through the

emitter charging time. These e�ects are of particularconcern for Pnp HBTs since the valence band disconti-nuities may be large (00.2 eV) and the large hole e�ec-

tive mass makes tunneling more di�cult. The thrust ofthis paper is to investigate the e�ects on the emitter I±

V characteristics of such heterojunctions in the multi-layer emitter contact taking into account hole thermio-nic-®eld-emission across the valence band spike, and to

determine its importance relative to the bulk series re-sistances associated with the individual layers. Whilevarious experimental techniques have been reported

for evaluating the emitter series resistance [1±3], themodel developed here is intended for use in calculatingthe potential drops associated with each heterojunctionin comparison with those associated with the bulk

parasitic resistances and to incorporate the combi-nation of these e�ects in the emitter current±voltagecharacteristics. The semi-analytical nature of the model

makes it useful for both the design of the multi-layerepitaxial structure of the emitter contact for the PnpHBT as well as for compact device modeling for equiv-

alent circuit design. The model is easily adapted to theanalysis of the Npn HBT's emitter contact with appro-priate changes. In Section 2 we describe the epitaxialstructure of an example InP/InGaAs Pnp HBT [4] and

brie¯y describe the device physics employed here to

Solid-State Electronics 43 (1999) 1299±1305

0038-1101/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved.

PII: S0038-1101(99 )00117-3

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

513-556-7326.

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

describe the I±V characteristics of the heterojunction

interfaces. In Section 3, we present the simulationresults for the example multilayer emitter contact andcompare the e�ects of the heterojunctions and theparasitic resistances on the emitter junction character-

istics. A comparison of the characteristics with the ex-perimentally reported results is also presented in thissection. In Section 4, we draw conclusions regarding

the e�ect of the emitter series resistances on the per-formance of the device in terms of the collector cur-rently ideality factor and comment on the design of

the epitaxial structure in order to minimize these para-sitic e�ects.

2. Approach

The epitaxial layer structure for an InP/InGaAs PnpHBT is shown in Fig. 1, which is the same structure asreported by Lunardi et al. [4]. The structure incorpor-

ates a quaternary layer of InGaAsP between the p-typeInP emitter layer and the highly doped InGaAs contactlayer, which introduces a pair of parasitic heterojunc-

tions into the contact to the emitter. Fig. 2 shows aschematic of the energy band diagram of the three-layer system and the resistances associated with the

layers and the heterojunction interfaces. For the latter,the valence band discontinuity may introduce a nonli-nearity in the I±V characteristics so that these equival-

ent resistances may in fact be a function of the biaslevel. Rm is the metal resistance associated with themetal contact on the InGaAs cap layer, and, for allpractical purposes, can be ignored. The rc is the con-

tact resistance associated with the metal-semiconductorinterface and can be calculated using [5],

rc � rec

ZELE

�1�

Fig. 1. Epitaxial structure of InP/InGaAs Pnp HBT after

Lunardi et al. [4].

Fig. 2. Qualitative energy band diagram of the multi-layer heterojunction system incorporated in the emitter contact including the

p+ cap layer, the intervening quaternary layer and the emitter layer, and the bulk and interface resistances associated with each.

S. Datta et al. / Solid-State Electronics 43 (1999) 1299±13051300

where rec is the speci®c contact resistivity, ZE is the

width and LE the depth of the emitter contact. Rc+ isthe bulk resistance of the p+ InGaAs contact layerand is given as,

Rc� � Wp��qmp�Np��ZELE

�2�

where mp+ is the majority carrier hole mobility, Np+ isthe doping concentration of the InGaAs cap layer and

Wp+ is the thickness of the InGaAs contact layer.Similarly, the bulk resistance of the quaternary layer,Rq, and the emitter bulk resistance, RE, are written as

Rq � 1

qmpqNq

Wq

ZELe

�3�

RE � 1

qmpeNe

We

ZELE

�4�

where mpq and mpe are the hole mobilities, Nq and Ne

are the doping concentrations, and Wq and We are the

thicknesses of the quaternary and emitter layers, re-spectively.In the energy band diagram seen in Fig. 2, since the

InP is much less heavily doped than the InGaAsP qua-

ternary, the majority of the band bending takes placein the InP and the band bending in the quaternary isneglected. Similarly, for the InGaAs/InGaAsP hetero-

junction interface, the band bending takes place largelyon the quaternary side since it is more lightly dopedthan the InGaAs contact layer. On application of a

forward bias to the emitter base-junction, holes will bedriven from the contact across the interfaces to theemitter-base heterojunction. Because of the relative

Table 1

Summary of parameter values for the multiple layer emitter contact for the InP/InGaAs Pnp HBT

Parameters Units Contact Quaternary Emitter

Composition InGaAs InGaAsP InP

Doping cmÿ3 2�1019 1� 1019 1� 1018

Hole mobility mp cm2/Vÿ1 sÿ1 76 86 76

Hole e�ective mass m �p/mo 0.47 0.47 0.50

Contact resistivity rec O cmÿ2 7�10ÿ7 InGaAsP/InP InGaAsP/InGaAs

Valence band discontinuity DEV eV 0.21 0.14

Fig. 3. Current±voltage characteristic of the InP/InGaAsP (*) and the InGaAsP/InGaAs (w) heterojunctions predicted by the

thermionic-®eld emission model.

S. Datta et al. / Solid-State Electronics 43 (1999) 1299±1305 1301

magnitudes of the dopings in the layers(Np+>Nq>Ne), the barrier heights to the holes at the

heterojunctions remain nearly ®xed independent of thebias level and equal to the corresponding valence banddiscontinuity (DEV). The carrier transport situation is

then very similar to that of a reverse bias across aSchottky contact and, hence, we employ a thermionic-®eld-emission model to calculate the I±V characteristic

of the heterojunction interfaces. The current densityacross the heterojunction is approximated by the well-known Schottky equation which can be written for

reverse bias as [6,7].

j � gA�T 2eÿDEV

kBT e

qkBT

���������������qF�Va�mpes

r�5�

where A� is the Richardson±Dushman constant, DEV

is the barrier height and F�Va� is the electric ®eld

strength at the heterojunction. The g factor accountsfor the quantum-mechanical tunneling of holes acrossthe triangular potential barrier in the valence band (see

Appendix A) and is given as [7],

g � 1�� qkBT�Vbi�Va�

0

e yeÿCy3=2

dy �6�

where Va is the applied bias across the heterojunction,Vbi is the built-in potential of the junction, and C is a

constant independent of y de®ned as,

C � 4���������2m�p

p �kBT �3=23qhÿ F�Va� �7�

3. Results

The simulations were performed using the InP/InGaAs Pnp HBT depicted in Fig. 1 having an emitterarea of 3� 8 mm2. Table 1 shows the values of the par-

ameters used for the materials in the multiple layeremitter contact. Fig. 3 shows the current±voltagecharacteristics of the two heterojunction interfaces cal-

culated using Eq. (5). As is evident from the very highcurrent densities achievable at very low bias, the het-erojunction between the InGaAs contact layer and theInGaAsP quaternary does not appreciably limit the

hole transport and, hence, we can safely ignore thee�ect of the associated interface resistance Ri2. This isdue to the heavy doping concentrations on both sides

of the junction which facilitates hole tunneling andenhances the magnitude of the electric ®eld at theinterface, thereby causing further lowering of the bar-

rier to the hole ¯ow through the image force e�ect.However, for the other heterojunction (InGaAsP/InP),the thermionic-emission-model predicts a signi®cant

potential drop (10.1 V) when the magnitude of the

emitter current density exceeds 1� 105 A/cm2, which is

the region of interest for high gain and high frequency

device operation. This implies that the e�ect of the

interface resistance associated with this heterojunction,

Ri1, must be incorporated in the calculation of theemitter series resistance in addition to that of the bulk

parasitic resistances. The importance of this interface

resistance is attributed to the higher valence band dis-

continuity (DEV=0.2 V) [8] associated with the InP/

InGaAsP junction as compared to the InGaAs/

InGaAsP junction (DEV=0.14 V) [9] and a reduction

in the extent of hole tunneling due to the lightly dopednature of the InP emitter layer.

Fig. 4 shows a comparison of the potential drops

across the various bulk resistances and the interface re-sistance, Ri1, as a function of the emitter current for

the InP/InGaAs HBT structure [4] depicted in Fig. 1.

The largest parasitic resistance arises from the emitter

bulk resistance which is estimated to be around 3.0 O.This arises from the low emitter doping employed for

high frequency devices to reduce the emitter-base de-pletion capacitance. The second most important contri-

bution comes from the emitter contact resistance (2.9

O for rec=7� 10ÿ7 O cm2) [10] which causes a poten-

tial drop of 44 mV when the emitter current is 15 mA.

The interface resistance arising from the thermionic-

®eld-emission of holes across the InGaAsP/InP hetero-

junction causes a potential drop of 11 mV at this emit-ter current (15 mA) which translates to an equivalent

interface resistance, Ri1, of 0.78 O. The parasitic bulk

resistances associated with the quaternary layer and

the InGaAs cap layer (0.1 and 0.3 O, respectively)

cause drops of 1.8 and 4.5 mV, respectively, at this

current level. Thus, it is evident that when an externalbias is applied to the emitter-base junction in the Pnp

HBT with multiple heterojunctions, a signi®cant por-

Fig. 4. Calculated potential drops across the emitter contact

resistance (w), cap layer bulk resistance (r), quaternary bulk

resistance (*), emitter bulk resistance (q), and InP/InGaAsP

heterojunction interface resistance (solid line).

S. Datta et al. / Solid-State Electronics 43 (1999) 1299±13051302

tion of it, depending on the emitter current densityand the heterojunction barrier (DEV), can be lost as aparasitic voltage drop across a heterojunction inter-

face. This e�ect will contribute to the emitter's para-sitic series resistance and can a�ect deviceperformance.

The e�ects of the emitter resistance become import-ant at high currents and contribute to a saturation inthe Gummel characteristics at a high bias level, therebya�ecting the ideality factor of the collector current of

the device. This is illustrated in Fig. 5, where the emit-ter current with the e�ect of the emitter series resist-ance including the parasitic heterojunction e�ects is

plotted vs the applied emitter-base bias. The idealityfactor is plotted in Fig. 6 as a function of the collectorcurrent. For comparison, we have also shown in Fig. 5

the collector current measured experimentally by

Lunardi et al. [4]. In our calculation of the emitter cur-rent and, hence the collector current, we have incor-porated the thermionic-emission of holes along with

tunneling across the emitter-base interface and also thedrift-di�usion of holes across the emitter base spacecharge region [11,12]. Although our analysis showsthat the parasitic heterojunction interfaces in the emit-

ter contact add to the emitter series resistance, they donot explain the observed discrepancy in magnitude andideality factor in the collector currents between the

simulated and the measured values. The origin of thisdiscrepancy may be due in part to the nature of holetunneling taking place at the emitter-base interface.

Preliminary results of Ekbote et al. [13] suggest thatthe hole ¯ux injected from the emitter into the basedepends on the extent of band mixing between holes inthe heavy, light and split-o� bands. This band mixing

e�ect has been ignored in this analysis since we assumea single type of hole in describing the carrier transportand use the density of states e�ective mass of holes to

calculate the tunneling factor. Future work will incor-porate a more accurate description of hole tunneling atthe emitter-base junction including the e�ects of light,

heavy and split-o� band mixing and hole conversionduring tunneling.

4. Conclusions

In summary, we have shown that the e�ect of para-

sitic heterojunction interfaces should be consideredalong with the parasitic bulk resistances in evaluatingthe emitter series resistance for Pnp HBTs with multi-

layer emitter contacts. The presence of the valenceband discontinuities at the parasitic heterojunctioninterfaces presents barriers to the hole ¯ow and so

a�ects the emitter-base junction current±voltagecharacteristic. In particular, the quaternary layer inbetween the emitter layer and the cap layer must bechosen such that the valence band discontinuity associ-

Fig. 5. Measured collector current±voltage characteristic

(dashed line) compared with the simulated results (solid line)

taking into account the emitter series resistance e�ect for the

InP/InGaAs Pnp HBT.

Fig. 6. Collector current ideality factor (w) as a function of

collector current for the InP/InGaAs Pnp HBT compared

with the ideality factor extracted from the measured charac-

teristics (q) seen in Fig. 5.

Fig. 7. Schematic energy band diagram of p+P heterojunction

with the hole energy plotted vertically along the positive y-

axis.

S. Datta et al. / Solid-State Electronics 43 (1999) 1299±1305 1303

ated with its interface to the InP emitter is reduced sothat the barrier to the hole ¯ow is small.

Acknowledgements

This work was supported by the National ScienceFoundation under Grant No. ECS-9525942.

Appendix A

We consider a p+P heterojunction with the valenceband structure as shown in Fig. 7 where the hole

energy has been plotted vertically. Following Sze [7],we write for the hole current density ¯owing from leftto right as,

J � A�TkB

eÿqfBp

kBT

�10

T�z�eÿzkBT dz

� A�TkB

�q�Vbi�Va�

0

FmT�Z��1ÿ Fs� dZ�A1�

where z and Z are measured upward and downwardfrom the potential maximum at the interface, Fm and

Fs are the Fermi functions for holes on the left handside and the right hand side, respectively. T(z ) andT(Z ) are the transmission probabilities for holes above

and below the potential maximum, respectively, andA � is the Richardson±Dushman constant given by,

A� � pqm�pk2B

2h3�A2�

Assuming, for simplicity, T(z )=1 for hole energiesabove the peak, we get from the ®rst integral,

A�TkB

eÿqfBp

kBT

�1

ÿ1=kBTeÿzkBT

���10� A�T 2e

ÿqfBp

kBT �A3�

For the second integral in Eq. (A1), we use Sze's resultfor tunneling through a triangular barrier [7],

T�Z� � exp

ÿ4 ���������

2m�pp3qhÿ

Z3=2

F�Va�

!�A4�

where F�Va� is the magnitude of the depletion regionelectric ®eld given by,

F�Va� ����������������������������������������������������2qNe

es

�Vbi � Va ÿ kBT

q

�s�A5�

Fm is the Fermi function for the holes given by,

Fm�Z� � 1

1� e

EFp�ÿZkBT

1e

ZÿEFp�kBT �A6�

On the right hand side, similarly, we have

1ÿ Fs�Z� � 1

1� eZÿEFp

kBT

�A7�

Thus, the second integral in Eq. (A1) becomes�q�Vbi�Va�

0

FmT�Z��1ÿ Fs� dZ

��q�Vbi�Va�

0

e

ZÿEFp�kBT e

ÿC�

ZkBT

�3=2

� 1

1� Zÿ EFp�

kBT

dZ �A8�

where we de®ned the constant C (see Eq. (7)). Since

the upper limit for the integral Z � q�Vbi � Va� is stillless than EFp

by more than a few kBT, we can assumethe last fraction in Eq. (A8) is unity, so that the secondintegral becomes,

�q�Vbi�Va�

0

e

ZÿEFp�kBT e

ÿC�

y

kBT

�3=2

1

1� Zÿ EFp�

kBT

dZ

� e

ÿEFp�kBT

�q�Vbi�Va�

0

eZ

kBT eÿC�

ZkBT

�3=2

dZ �A9�

But in the Z coordinate system EFp� � qfBp: So, using

Eq. (A9) in combination with Eq. (A2), we get fromEq. (A1),

J � A�T 2e

ÿqfBp

kBT

"1�

� qkBT�Vbi�Va�

0

e yeÿCy3=2

dy

#

� gA�T 2eÿqfBp

kBT �A10�where we de®ne a tunneling factor g as

g � g�Va� � 1�� qkBT�Vbi�Va�

0

e yeÿCy3=2

dy �A11�

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