MODELING AND CHARACTERIZATION OF ADVANCED BIPOLAR
TRANSISTORS AND INTERCONNECTS FOR CIRCUIT SIMULATION
BY
JIANNSHIUN YUAN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1988
1U OF F LIBRARIES
ACKNOWLEDGMENTS
I wish to express my sincere appreciation to the chairman of my
supervisory committee, Professor William R. Eisenstadt, for his
guidance and encouragement during the course of this study. I also
thank Professors Sheng S. Li, Arnost Neugroschel, Gijs Bosman, and C.
K. Hsieh for their valuable comments and participation on my
supervisory committee.
I am grateful to my colleagues, Dr. S. Y. Yung, Mr. H. Jeong for
their helpful discussions, J. Atwater, G. Riddle for photoconductive
switch measurements and sample preparation. Special thanks are extend
to Dr. Juin J. Liou; his participation on the qualifying exam and on
the final defense merits a note of gratitude.
I am greatly indebted to my wife, HuiLi, my parents and parents
inlaw for their love, patience, and encouragement.
The financial support of the Semiconductor Research Corporation
and the National Science Foundation is acknowledged.
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ................. ..................... .................. ii
LIST OF SYMBOLS ............. ..... ................................. vi
ABSTRACT ............ ..... .......................... ............. xiv
CHAPTER
ONE INTRODUCTION.... ................. ...... ...............1
TWO TWODIMENSIONAL COLLECTOR CURRENT SPREADING EFFECTS
IN QUASISATURATION ............ ......................... 5
2.1 Introduction. .............. ....... ...................... 5
2.2 Multidimensional Collector Current Spreading............7
2.3 SPICE Modeling Including Collector Spreading Effects...17
2.4 Model Verification with Experiments and Device
Simulations ................ .. ......... ........ ......21
2.5 Conclusions ............................ ............... 27
THREE PHYSICSBASED CURRENTDEPENDENT BASE RESISTANCE.............30
3.1 Introduction................................. ........... 30
3.2 Physical Mechanisms for Current Dependency .............31
3.2.1 Base Width Modulation .......................... 32
3.2.2 Base Conductivity Modulation.....................35
3.2.3 Emitter Current Crowding ........................37
3.2.4 Base Pushout....................................44
3.2.4 The Coupling Effects ................ ...........47
3.3 The Nonlinear Base Resistance Model.................... 48
3.4 Model Verification with Experiments.................... 49
3.5 Application. ............. ..... ......................... 52
3.6 Summary and Discussion .................. .............. 52
FOUR CIRCUIT MODELING FOR TRANSIENT EMITTER CROWDING AND TWO
DIMENSIONAL CURRENT AND CHARGE DISTRIBUTION EFFECTS.......55
4.1 Introduction ................ ......... ........... .... 55
iii
4.2 Model Development..................... .............56
4.2.1 Transient Emitter Crowding......................56
4.2.2 Sidewall Injection Current and Junction Charge
Storage Effects...............................61
4.3 Model Verification with Experiments and Transient
Device Simulation....................................67
4.4 Summary and Discussion.................... .............72
FIVE SPARAMETER MEASUREMENT PREDICTION USING A PHYSICAL DEVICE
SIMULATOR................................................. 75
5.1 Introduction........................................... 75
5.2 Bipolar Test Structure Modeling........................ 77
5.3 Bipolar Test Structure SParameter Response............90
5.4 Conclusions .......................................... 98
SIX INTEGRATED CIRCUITS INTERCONNECT MODEL FOR SPICE...........102
6.1 Introduction.......................................... 102
6.2 Interconnect Modeling Topology Development ............103
6.3 Advanced IC Interconnect Crosssection Analysis........111
6.4 Interconnect Model Verification.......................115
6.5 MixedMode Circuit Simulation.........................118
6.6 Summary and Discussion................................128
SEVEN MODELING FOR COUPLED INTERCONNECT LINES....................129
7.1 Introduction........................................ 129
7.2 Even Mode and Odd Mode Analyses for Two Parallel
Lines ................................................130
7.3 Signal Dispersion, Loss and Coupling for Coupled
Transmission Lines ...................................136
7.4 Mode Transition in Photonic Picosecond Measurement....145
7.5 Equivalent Circuit Model for SPICE.....................148
7.6 SPICE simulations and Discussions .....................152
7.7 Conclusions ........................................... 154
EIGHT SUMMARY AND DISCUSSIONS .................................... 161
APPENDICES
A TWODIMENSIONAL NUMERICAL SIMULATION WITH PISCES...........164
A.1 Introduction..........................................164
A.2 Physical Mechanisms in PISCES II....................164
A.3 Discussion...........................................166
B BIPOLAR TRANSISTOR MODELING IMPLEMENTATION TECHNIQUES
IN SLICE/SPICE..............................................168
B.1 Introduction..........................................168
B.2 UserDefinedControlledSources.......................168
B.3 UDCS Implementation of the BJT Model. ................. 173
B.4 Conclusions ............. ... ...........................175
REFERENCES ............ ............................. ............... 178
BIOGRAPHICAL SKETCH ........................ ......... .... .......... 188
v
LIST OF SYMBOLS
AC collector area
AE emitter area
AEeff effective emitter area
a emitterbase junction gradient
CC Coupling coefficient for signal crosstalk
CjC collectorbase junction capacitance
CJCO collectorbase junction capacitance at VBE = 0 V
CJE emitterbase junction capacitance
CJEX extrinsic emitterbase junction capacitance
C'JE derivative of emitterbase junction capacitance
CJEO emitterbase junction capacitance at VBE = 0 V
CSCR spacecharge region capacitance
CSiO2 Si02 capacitance
Ce even mode capacitance for coupled transmission lines
Cea even mode capacitance for coupled transmission lines
without dielectric interface
Cf fringing capacitance
Cf' modified fringing capacitance
Cgt gate capacitance due to finite metal thickness
Co odd mode capacitance for coupled transmission lines
Coa odd mode capacitance for coupled transmission lines
without dielectric interface
Cp plate capacitance
Csub substrate capacitance
C2 forward low current nonideal base current coefficient
C4 reverse low current nonideal base current coefficient
c speed of light
cn Auger coefficient for electron in heavy doping effects
Cp Auger coefficient for hole in heavy doping effects
EFN electron quasiFermi level
EFP hole quasiFermi level
Ei intrinsic Fermi level
Et trap energy level
f frequency
fBWM base width modulation factor
fC critical frequency in frequencydependent permittivity
fCR(t) timedependent emitter crowding factor
fCM base conductivity modulation factor
fCROWDING emitter crowding factor without the coupling effects
f'CROWDING emitter crowding factor with the coupling effects
fc parameter incorporating the second order effects in
the emitter crowding mechanism
fD critical frequency for frequencydependent permittivity
of coupled transmission lines
fPUSHOUT base pushout factor
fT bipolar transistor cutoff frequency
Gn+ conductance of n+ buried layer
hI height of the SiO2 layer
h2 height of the substrate
IB base current
vii
IBideal ideal base current with ohmic drops in the base and
emitter regions
IBj base current in the partitioned region j
IC collector current
ICQNB collector current in the base quasineutral region
ICQNR collector current in the collector quasineutral region
ICSCR collector current in the collector spacecharge region
IE emitter current
IEj emitter current in the partitioned region j
ILQNR lateral diffusion current in the collector quasineutral
region
ILSCR lateral diffusion current in the collector spacecharge
region
IK knee current
IKR reverse knee current
IS collector current at VBE = 0 V
ISB preexponential base current
ISE emitter current at VBE = 0 V
LE emitter length
JC collector current density
JE(x) positiondependent emitter current density
Jn electron current density
JO onset of the collector current density for base pushout
k Boltzmann's constant
LE emitter length
1 transmission line length
mc collectorbase junction gradient coefficient
me emitterbase junction gradient coefficient
viii
NA acceptor doping density of ptype Si
Ng(x) base doping density at depth x
NBeff effective base doping density
ND donor doping density of ntype Si
NEPI epitaxial layer doping density
n nonideal base coefficient
nc nonideal collectorbase emission coefficient
ne nonideal emitterbase emission coefficient
ni intrinsic carrier density
nie effective intrinsic carrier density
no electron concentration normalized by Ng(0)
An excess electron density
PE emitter perimeter
p(x,y) position dependent hole mobility
p average excess hole density
QBC basecollector charge
QBCX extrinsic basecollector junction charge
QBCj basecollector charge in the partitioned region j
QBE baseemitter charge
QBEX baseemitter sidewall junction charge
QBEj baseemitter charge in the partitioned region j
QBO intrinsic base charge at VBE = 0 V
QQNR charge in the collector quasineutral region
QSCR charge in the collector spacecharge region
AQB incremental intrinsic base charge due to base width
modulation
6QB incremental intrinsic base charge due to base
conductivity modulation
q electron charge
qb normalized base charge
RB base resistance
RBI intrinsic base resistance
RBIO intrinsic base resistance at VBE = 0 V
RBj base series resistance in the partitioned region j
RBX extrinsic base resistance
RC collector resistance
RCON base contact resistance
RE emitter resistance
REj emitter series resistance in the partitioned region j
R'EPI currentdependent epilayer resistance
T absolute temperature
t' interconnect line thickness
t time
tI height of the Si02 layer
t2 height of the Si buried layer
t3 height of the Si substrate
VA Early voltage
VB "late" voltage
VBC applied basecollector voltage
VBC' basecollector junction voltage
VBCI basecollector voltage at the moving boundary between
the collector quasineutral region and the collector
spacecharge region
VBCj basecollector charge in the partitioned region j
x
VBCO basecollector voltage at the metallurgical base
collector region
VBE applied baseemitter voltage
VBEj baseemitter junction voltage in the partitioned region j
VBE' baseemitter junction voltage
Vbi junction builtin voltage
VCB applied collectorbase voltage
VCE applied collectoremitter voltage
VDQNR lateral diffusion velocity in the collector quasineutral
region
VDSCR lateral diffusion velocity in the collector spacecharge
region
VT thermal voltage kT/q
V* effective junction builtin voltage
AV ohmic drops in the emitter and base regions
Vpe evenmode phase velocity of propagated signal in
coupled transmission lines
Vpo oddmode phase velocity of propagated signal in
coupled transmission lines
vs electron saturation velocity
WE emitter width
WQNR collector quasineutral region width
WSCR collector spacecharge region width
WEPI epitaxial collector width
XB base width
XEPI epitaxial layer depth
XJB base junction depth
XJE emitter junction depth
AXB current induced incremental base width due to base
pushout
w interconnect width
We effective interconnect width (TEM mode)
weff(f) frequencydependent effective interconnect width
Z transmission line impedance
ZOe evenmode characteristic impedance of coupled
transmission line
Zo0 oddmode characteristic impedance of coupled transmission
line
Zoe(f) frequencydependent evenmode characteristic impedance
of coupled transmission line
Zo0(f) frequencydependent oddmode characteristic impedance
of coupled transmission line
a interconnect attenuation constant
ac interconnect conductor loss
ace conductor loss of coupled transmission lines in even mode
aco conductor loss of coupled transmission lines in odd mode
ad interconnect dielectric loss
ade dielectric loss of coupled transmission lines in even
mode
ado dielectric loss of coupled transmission lines in odd mode
f bipolar transistor current gain
PF maximum forward current gain
PR maximum reverse current gain
Op phase constant
y propagation constant
e permittivity of silicon
eSi relative permittivity of silicon
xii
ESiO2 relative permittivity of silicon dioxide
Er relative permittivity
Ere effective relative permittivity
eree effective permittivity of coupled transmission lines in
even mode
creo effective permittivity of coupled transmission lines in
odd mode
C0 permittivity of free space
Oc collectorbase junction potential
Oe emitterbase junction potential
r effective base doping gradient
rF bipolar transistor forward transit time
rn dopingdependent electron recombination lifetime
Tn0 electron recombination lifetime at low doping
7p dopingdependent hole recombination lifetime
Tp0 hole recombination lifetime at low doping
rQNR injectionleveldependent hole recombination lifetime in
the collector quasineutral region
TR bipolar transistor reverse transit time
PnO electron mobility
Pp(xy) positiondependent hole mobility
P~ permeability of free space
p resistivity of the conducting microstrip
Pb intrinsic base sheet resistivity at VBE 0 V
UMETAL conductivity of metal line
aSi conductivity of silicon
Osub conductivity of substrate
xiii
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
MODELING AND CHARACTERIZATION OF ADVANCED BIPOLAR
TRANSISTORS AND INTERCONNECTS FOR CIRCUIT SIMULATION
BY
JIANNSHIUN YUAN
December 1988
Chairman: William R. Eisenstadt
Major Department: Electrical Engineering
This dissertation discusses the modeling of twodimensional
effects in advanced bipolar transistors (BJT's) and interconnects. The
goal is to develop accurate and compact models for SPICE circuit
simulation of advanced bipolar technologies. After reviewing base
pushout mechanism in the bipolar transistor, the collector current
spreading effects in quasisaturation have been presented. A two
dimensional circuit model including collector spreading effects in the
epitaxial collector is developed based on the physical insights gained
from PISCES device simulations. Illustrative measurements and
simulations demonstrate the bipolar circuit modeling accuracy.
xiv
Then a physicsbased currentdependent base resistance model for
circuit simulation is developed. Physical mechanisms such as base width
modulation, base conductivity modulation, emitter crowding, and base
pushout are accounted for in the comprehensive currentdependent base
resistance model. Comparisons of the model predictions with
measurements and device simulations show excellent agreement.
Twodimensional circuit modeling is developed for the nonuniform
current and charge distribution effects at the emitterbase sidewall
and under the emitter during switchon transients. The charge and
current partitioning implemented in the bipolar transistor model treats
the transient emitter crowding and currentdependent base resistance in
a unified manner. Good agreement is obtained between model predictions
and experimental results and transient device simulations.
In parallel to the work on fast BJT digital transients, the
bipolar transistor highfrequency smallsignal sparameter prediction
using a physical device simulator is developed. This is a novel result
which includes the effects of the intrinsic bipolar response as well as
the parasitics of interconnects, discontinuities, and bonding pads.
This modeling technique can be used for sophisticated threeport or
fourport network characterization and for predicting the high
frequency smallsignal parameters other types of transistors.
The dissertation examines the improvement of IC interconnect
models. Interconnect models including losses and dispersion are
developed for advanced BJT IC doping profiles. In addition, signal
crosstalk between adjacent interconnects is discussed. An ECL ring
oscillator with interconnection line in mixedmode circuit simulation
demonstrates the utility and necessity of accurate interconnect
modeling.
In summary, the dissertation provides a comprehensive two
dimensional circuit and interconnect modeling for advanced bipolar IC
techniques useful in computeraided device and circuit design.
CHAPTER ONE
INTRODUCTION
The bipolar transistor (BJT) circuit model implemented in SPICE
(the GummelPoon model) is derived based on onedimensional device
physics. Recently, the bipolar transistor has been scaled down to one
micrometer emitter width. It exhibits the multidimensional current
flow, especially when operated in high current transients rendering
onedimensional analysis inadequate. Thus, accurate device
characterization and optimal integrated circuit (IC) fabrication
process enhancement, through device and circuit simulations require
better modeling of the advanced bipolar transistor. In addition, the
interconnect delay in the submicrometer integrated circuits becomes
increasing important during high speed transients. To precisely predict
the BJT circuit performance, an accurate modeling of interconnect is
essential. These facts motivate this study.
The general topology of this study is, first, to explore the
importance of the multidimensional current flow by investigating the
physical insight into the twodimensional device simulations, and,
second, to develop a representative twodimensional circuit model for
circuit simulation. The model developed describes the nonuniform
current and charge distribution in the quasineutral base, the emitter
base sidewall, and the collector. The model shows good agreement when
compared with measurements and device simulations.
2
Then, an interconnect model is developed based upon the first
order approximation and physical device simulation. The BJT circuit
model and the IC interconnect model are integrated together for digital
circuit simulation. The results of this study are directly applicable
to advanced bipolar transistors and BiCMOS devices.
In Chapter Two, we developed a circuit model of the collector
current spreading effects in quasisaturation for advanced bipolar
transistors. The discussion in this chapter reveals the importance of
lateral current spreading in the epitaxial collector when base pushout
occurs. The lateral diffusion currents ameliorates the quasisaturation
effects compared to one dimensional BJT model. Physical insight into
the charge dynamics in the collector is shown by examining the current
gain and hole concentration plots in PISCES simulations for 1D
collector and 2Dcollector BJT's. Also, dc and transient circuit
simulations at high currents are compared with measurements to
demonstrate the model utility and accuracy.
Chapter Three presents a physicsbased currentdependent base
resistance model for all levels of injection. The model includes the 1
D and 2D physical mechanisms of base width modulation, base
conductivity modulation, emitter current crowding, and base pushout; it
describes a current and voltagedependent base resistance. Various
measurement results and device simulation data are compared with the
model predictions to demonstrate the model accuracy. For an emitter
coupled logic circuit, the BJT with a currentdependent Rg model
results in a more realistic transient response compared with a BJT with
constant base resistance model.
3
In Chapter Four, the author develops a partitioned circuit model
taking into account the emitter crowding, sidewall current injection,
and currentdependent base resistance in a unified manner. The model
describes a nonuniform transient current and charge distribution under
the emitter and at the emitterbase sidewall. This current and charge
partitioning accurately represents the charge dynamics of the BJT
during switchon transient. The model predictions shows good agreement
when compared with measurements and transient device simulations.
Chapter Five describes the sparameter measurement prediction
using a physical device simulator for advanced bipolar transistors. The
prediction not only includes the intrinsic BJT small signal responses,
but also accounts for the parasitic effects resulting from the
interconnects, bends and pads. The intrinsic BJT small signal s
parameters are converted from yparameters simulated in PISCES. The
terminal responses are obtained by multiplying the cascaded Tmatrix
components representing the intrinsic BJT and extrinsic layout
parasitic effects. Two interconnect crosssections are compared to
evaluate which is a superior test structure that introduces less signal
attenuation and phase. In general, this technique can be used for three
or four port network analysis and for the devices other than the BJT,
such as GaAs heterojunction bipolar transistors in high frequency
characterization.
In Chapter Six, the conventional interconnect model is improved.
A new interconnect model which accounts for signal loss and dispersion
is introduced for advanced IC crosssection profiles. An inverse
Fourier transform is used for modeling transients. The prediction of
4
the interconnect model shows good agreement when compared with
measurement. The model is implemented in SLICE/SPICE for mixedmode
circuit simulation. The utility of the interconnect model is
demonstrated in a fivestage ECL ring oscillator transient simulation.
In Chapter Seven, the single interconnect model is extended to
include crosstalk for coupled interconnect lines in close proximity.
Signal crosstalk is important in digital switching. The model is
developed from even mode and odd mode interconnect capacitance
analysis. The picosecond transient measurement of photoconductive
circuit element technique has been used to demonstrate the even mode
and odd mode pulse splitting. An equivalent distributed, lumped circuit
model for coupled interconnect lines is also developed. Circuit
simulations employing the coupled transmission lines in digital
switching have been used to demonstrate the signal crosstalk between
interconnects. The discussion in this chapter supplements Chapter 6,
thus providing a more complete interconnect modeling analysis.
Chapter Eight summarizes the contributions of this dissertation
and presents recommendations for extension of this study.
CHAPTER TWO
TWODIMENSIONAL COLLECTOR CURRENT SPREADING EFFECTS IN QUASISATURATION
2.1 Introduction
Advanced selfaligned bipolar transistors based on a double
polysilicon technology show multidimensional current flow in the
collector, especially when operated at high currents. The
multidimensional current flow effects are not included in existing
bipolar circuitsimulator models such as the GummelPoon model in
SPICE2 [1]. Recently, a novel 3D BJT circuit model has been developed
by using a 2D device simulator [2]; however, the details of the
collector spreading physical mechanism and the implementation in the
equivalent circuit model have not been treated.
The quasisaturation effects have been investigated by numerous
authors for the past twenty years [38]. In general, two distinct
models (onedimensional and twodimensional) have been developed. In
the 1D model, base pushout or quasisaturation effect occurs when the
current density is high enough that the intrinsic basecollector
metallurgical junction becomes forward biased. Then carriers are
injected into the epitaxial collector [3], [8].
In the twodimensional model, there is a maximum current density,
called spacechargelimited current flow, and any further increase in
collector current results in a 2D base spreading [4], [5]. Detailed
explanations for the operating regions of each mechanism are shown in
[68].
6
For the standard advanced BJT process, however, the heavily doped
extrinsic base resulting from the double polysilicon technology makes
base spreading negligible. In contrast, the base pushout due to high
current in the collector is twodimensional and results in lateral
collector current spreading in the epitaxial collector [9], [10]. This
collector current spreading, which is different from base spreading,
has not previously been modeled.
Recently, Kull et al. [11] extended the GummelPoon model to
include quasisaturation, or base pushout in the BJT circuit model
formulation. Kull's compact extension was modified by Jeong and Fossum
[12] [13] to account for the possible existence of a currentinduced
spacecharge region in the epitaxial collector. The modeling in [11]
[12] is based a onedimensional derivation and does not represent the
twodimensional currents in the collector. Thus, this modeling can
overestimate quasisaturation effects [9], [10].
In this chapter, the model in [12] is extended to take into
account the multidimensional collectorcurrentspreading mechanism that
occurs in quasisaturation. The extension is facilitated by using the
twodimensional device simulator PISCES [14) to perform simulations of
the advanced BJT's (Sec. 2.2). The PISCES simulations reveal the
physical mechanism producing 2D collector spreading. The mechanism was
not reported in the previous BJT simulations [9], [15]. The modeling of
collector transport in [12] [13] is modified to account for the lateral
diffusion currents in the epitaxial collector region. The development
of this modeling is described in Sec. 2.3. Comparisons of the model
performance with measurements and device simulations are presented in
7
Sec. 2.4. Excellent agreement in dc and transient behavior is observed
over a wide range of operating conditions.
2.2 Multidimensional Collector Current Spreading
An analysis of PISCES simulations of the advanced bipolar
transistor was undertaken to identify the physical origin of the
collector current spreading in the epitaxial collector. The BJT
simulations with PISCES include heavydoping effects (bandgap
narrowing, Auger recombination), doping and field dependent carrier
mobilities, and ShockleyReadHall (SRH) recombination. A generic
advanced BJT crosssection was constructed by incorporating common
features of many stateoftheart transistors reported in the
literature [16], [17].
The advanced bipolar transistor is illustrated in Fig. 2.1, where
only half crosssection and doping profile need to be simulated due to
the crosssection's symmetry. The emitter and base doping profiles and
the emitterbase spacing were designed to avoid sidewall tunneling and
perimeter punchthrough in the BJT [18]. Polysilicon contacts are
simulated for the emitter and the base by using an effective surface
recombination velocity of 3 x 104 cm/s [19]. The substrate contact is
situated at the bottom of the buried collector. It is found that only a
negligible perturbation on the lateral current flow in the lightly
doped epitaxial collector results when a sidecollector contact is
used; this is discussed later in the paper.
A PISCES simulation predicted the multidimensional current flow in
the collector and this is shown in Fig. 2.2. This diagram displays the
E
(0,0)
(0,1.0)
Figure 2.1.1
A right half crosssection of an advanced bipolar
transistor used for multidimensional current studies.
Dimensions of the crosssection are indicated in
micrometer.
(0.5,0)
n+
p+
n
(EPITAXIAL LAYER)
n*
I (1.0,0)
(1.0,1.0)
1x1021
S1x1020
E
S1x1019 
Z ,EXTRINSIC BASE
O p PROFILE
S1x1018 
S 170 
O
Z 1x1016 \
0.
o 614
o lxlO10
l 1x1014 I
1x1013 1 11 
0.0 0.2 0.4 0.6 0.8 1.0
DEPTH INTO SILICON (gm)
Figure 2.1.2 The doping profiles of the bipolar transistor shown in
Figure 2.1.1. The solid line is the doping profile at
the center of the emitter and the dashed line is the
doping profile below the extrinsic base region.
E
(0,0)
(0,1.0)
B
I (1.
(0.5,0)
(1.0,
),0)
1.0)
Figure 2.2 Plot of electron current vectors in the advanced BJT
shown in Figure 2.1. In this PISCES simulation the
collector contact is at the bottom of the buried
collector at VCE 2.0 V and VBE 0.9 V.
Jr Jr r r \\V \ I \ \ \ \ +
 <  t  ' t*
Jr Jr Jr \\\\\\' \JrI \ \ \ \ \
SI Jr r \\\\\\VIAI \ \ \ \ \ Jr
S t 4 4 "
t t t I I At" I
t t t tt" *
i i I I 1111~11141 1 1 1 1 I I
I( t I t I 1tt111 1 1 1 I I
i t 1 1) )1 nniu \ : .
I I I \ \ \~!II \ \\\\ \
11
PISCES simulation of the electroncurrentdensityvector plot, Jn, of
the advanced BJT biased at applied collectoremitter voltage, VCE = 2.0
V and applied baseemitter voltage, VBE = 0.9 V (IC = 0.5 mA/pm). In
the quasisaturation region depicted in Fig. 2.2, excess carriers are
injected into the epitaxial collector (base pushout). These excess
electrons diffuse laterally in the epitaxial collector region under the
extrinsic base due to the high carrier concentration gradient in the
horizontal direction. Collector current spreading is indicated by the
horizontal component of currentdensity vectors underneath the
extrinsic base.
Note that Fig. 2.2 qualitatively shows where the multidimensional
collector currents occur, but it does not lend itself to a quantitative
estimation of the magnitude of these currents. The grid in Fig. 2.2 is
nonuniform (for better simulation accuracy and convergence) and dense
at emitter, base, and emitterbase junction because of the position
dependent doping density at these regions. The magnitudes of the
currentdensity vectors at the grid points which are sparsely located
are enhanced when compared to those of dense grid points.
The effect of electric field in the buried collector on the
current distribution in the epitaxial collector can be seen by shifting
the collector contact to the rightside of the BJT. Figure 2.3 shows a
BJT simulation from PISCES of the currentdensity vectors for a right
sidecollector contact, with VCE 2.0 V and VBE = 0.9 V, the same bias
as that of Fig. 2.2. Although there is a great difference in the
current vectors in the buried collector (due to lateral ohmic drop),
all the currents in the intrinsic BJT remain virtually the same. The
E
(0,0) I
(0,1.0)
(0.5,0)
B
S(1.0,0o)
(1.0,1.0)
Figure 2.3 Plot of electron current vectors in the advanced BJT
shown in Figure 2.1. In this PISCES simulation the
collector contact is at the side of the buried collector
at VCE 2.0 V and VBE 0.9 V.
: ii,,,,,::
t t f t tfr *t*
S ttt
4 4 4 4 4 *444*4*44
t ,4 + 4 4 t tt4 '4
; I n, s'mI :iiii *
 t J \ i ;\ 15515; +
l i n m11\\ \ \ \ \ '
J r i, l l\\\\\\w\ \ \ \ \ ,
\ 4 \ \ \\\\\4\\\\ \ \ \ \ \
1 \ \ \ \\\ \\1 \ \ \ \ \
S \ \\\ \\4\\ \ \ \ \'
\ \ \ \\ VS\\ ^ * O
13
magnitudes of the vertical and lateral currentdensity vectors in Fig.
2.2 and Fig. 2.3 are typically within 0.5% of each other. This
indicates that the electric field from the rightside collector contact
only controls the current flow in the buriedcollector region, and that
it does not significantly affect the lateral flow. Thus, there is no
significant drift component in the collector spreading mechanism.
A 1Dcollector transistor was simulated in order to isolate the
effects of collector spreading in the advanced BJT operation. This 1D
collector BJT, shown in Fig. 2.4, has the same emitter and base regions
as the 2D BJT in Fig. 2.1; however, below the extrinsic base region of
the 1Dcollector transistor, the epitaxial and buriedcollector
regions are replaced with SiO2. This forces the collector current to
flow solely in the vertical direction below the intrinsic base, hence
the name lDcollector transistor.
Comparing the current gain, f and cutoff frequency, fT of the 2D
BJT to those of the 1Dcollector BJT at high currents is one of the
keys to understanding the role of collector currentspreading. The 2D
BJT exhibits a larger p (see Fig. 2.5) and fT than the 1Dcollector
BJT as both transistors are driven further into saturation [10].
Figure 2.6 indicates how quasisaturation is ameliorated by
lateral diffusion in the collector. This figure displays a hole
concentration plot for a vertical slice along the center of the emitter
of both the 2D BJT and lDcollector BJT. This simulation is performed
for BJT's with emitter width, WE 1 pm, VBE = 0.9 V, and VCE 2.0 V.
The base in the 1D BJT displays significantly more base widening than
the 2Dcollector BJT, which results in an enhanced 2DBJT P, and fT
E
(0,0) I
B
I (1.0,0)
(0.5,0)
(0,1.0o)
C
(1.0,1.0)
Figure 2.4 An advanced bipolar transistor crosssection designed
with a 1Dcollector. This transistor is used to isolate
the 2D collector spreading effects.
n+
P+
p
n
Si02
n+
300
z 200
u
100
0.4 0.5 0.6 0.7 0.8 0.9
VBE (V)
Figure 2.5 Plot of the current gain versus VBE. The solid line
represents the 2D BJT and the dashed line represents
the 1Dcollector BJT.
E 20
E.1 0 
z
O 
10 
F
0 10\
0 4
=1014
0 0.2 0.4 0.6 0.8 1.0
DEPTH (grm)
Figure 2.6 Plot of hole concentration from the center of the emitter
to the collector at VCE 2.0 V and VBE 0.9 V. The
solid line represents the 2D BJT and the dashed line
represents the lDcollector BJT.
at high currents. The reduced quasisaturation effects in 2DBJT are
due to the lateral diffusion current which results from the high
carrier concentration gradient in the horizontal direction. Further
simulation of current spreading at different emitter widths, with the
same doping profiles and boundary conditions as in Fig. 2.2, indicates
that the lateral diffusion current is not a function of WE, but a
function of normalized charge Q(IC,VCE,WE)/WE or the charge below the
emitter periphery.
2.3 SPICE Modeling Including Collector Spreading Effects
A semiempirical model was developed using PISCES simulation to
suggest analytical approximations that would predict collector current
spreading. This modeling of the collector spreading effect was
incorporated into an existing chargebased 1D BJT model [12] to yield
a quasi2D model. The 1D BJT model accounts for quasisaturation
ohmicc and nonohmic) by describing the collector current in terms of
the quasiFermi potentials at the boundaries of the epitaxial collector
which, in conjunction with the base transport, characterizes
IC(VBE,VBC). Since this chargebased 1D model correctly accounts for
the 1D BJT physics [12] it can be modified to incorporate the
multidimensional current effects in the advanced BJT.
In the formulation of the 2D model, we estimate the lateral
diffusion currents in the collector quasineutral region and the
collector spacecharge region (ILQNR and ILSCR) as a function of the
normalized 1Dcollector quasineutral region charge and spacecharge
region charge (QQNR/AE and QSCR/AE, AE is the emitter area). These
18
normalized excess charges are the sources of the lateral diffusion
currents. Empirical lateral diffusion velocities (VDQNR and VDSCR) are
estimated from the collector lateral current flow predicted by PISCES
BJT simulation. These lateral diffusion velocities multiplied by the
respective normalized charges and emitter perimeter, PE form the
lateral diffusion currents. The current and voltage dependence of the
lateral diffusion currents are implicitly accounted for in the model by
the collector charges QQNR(IC,VCE) and QSCR(IC,VCE). Figure 2.7 shows
the base transport current, ICQNB in the quasineutral base, collector
transport currents, ICQNB and ILQNB in the collector quasineutral
region, and ICSCR and ILSCR in the collector spacecharge region. In
Fig. 2.7 a moving boundary between collector quasineutral region and
collector spacecharge region defines the collector quasineutral
region width, WQNR and the collector spacecharge region width, WSCR
(WSCR WEPIWQNR, and WEPI is the epitaxial collector width).
The following equations incorporate the collectorspreading
mechanism into the 1D model and make it a 2D model:
ICQNB = ICQNR + ILQNR (2.1)
ICQNR ICSCR + ILSCR (2.2)
ICQNB = IS/qb [exp(VBE'/VT) exp(VBCO/VT)]
+ C21S exp[VBE'/(neVT)] (2.3)
VT 1+F(VBCO) VBCOVBCI
ICQNR  F(VBCO) F(VBCI) In[] + )
R'EPI 1+F(VBCI) VT (2.4)
ICSCR q AE (NEPI + An) v,
(2.5)
1/2 R 1/2 SCR
L L
E O I  C
IQNB QNR ISCR
C C C
0 WONR WEPI
QNR SCR
B 1/2 IL 1/2 1
Figure 2.7 Regional BJT schematic used to show the transport
currents associated with their regions and boundaries.
ILQNR VDQNR (QQNR/AE) PE (2.6)
ILSCR VDSCR (QSCR/AE) PE (2.7)
where R'EPI QQNR/(nONEPIAE), F(V) [1 + aexp(V/VT)]1/2,
VBCO [EFN(0)EFP]/q, a 4ni2/NEPI2
VBCI [EFN(WQNR)EFp]/q, VT kT/q,
QQNR, QSCR, WQNR, and An are defined in [12].
The notation used in the equations above is as follows: NEPI is the
epitaxial collector doping concentration, ni is the intrinsic carrier
concentration, vs is the saturation velocity, PnO is the electron
mobility, EFN is the electron quasiFermi level, EFP is the hole quasi
Fermi level, VBE' is the baseemitter junction voltage, and IS, qb, C2,
and ne retain their meanings given in the GummelPoon model [1].
Figure 2.8 displays the overall SPICE model topology of the 2D
model for collector spreading. Two new current sources which are
highlighted in the figure have been added to the 1DBJT model [12] to
account for the lateral diffusion currents in the epitaxial collector.
Note that, since the 2D model modifies the 1D BJT quasistatic charge
in the collector region, the transient currents dQQNR/dt and dQSCR/dt
are effectively refined in terms of this new quasistatic charge
distribution as Eqs. (2.1)(2.7) are solved simultaneously. A lD BJT
model can not represent this collector charge redistribution [12] and
gives erroneous estimates of the BJT transient performance [10]. In
contrast, the 2D BJT circuit model correctly accounts for the charge
21
dynamics in the collector and the moving boundary between the quasi
neutral region and the spacecharge region in the epitaxial collector.
In addition, collector conductivity modulation, which makes the
collector resistance small, is accounted for in the modified R'EPI that
is a function of the varying quasineutral collector width,
WQNR(IC,VCE). A component of base recombination current, QQNR/rQNR due
to a finite recombination lifetime, rQNR in the collector quasineutral
region [20] is also included in the base current, IB. The injection
leveldependent lifetime (TQNR) can be modeled as [21]:
p
'QNR rpO + 'nO (2.8)
p+ NEPI
QQNR
p (2.9)
q AE WQNR
where rnO is the electron recombination lifetime, and rp0 is
the hole recombination lifetime in SRH recombination model.
2.4 Model Verification with Experiments and Device Simulations
The circuit model which includes collector current spreading was
implemented in the userdefined controlledsources (UDCS's) available
in SLICE, the Harris Corporation enhanced version of SPICE. In the
SPICE circuit analysis, UDCS's are userdefined subroutines that use
the implicit nonlinear model equations to compute both charging current
(dQ/dt) and transport (I) currents [22] (see Appendix B) in the model
as depicted in Fig. 2.8. The underlying transport currents in Sec. 2.3
dQQNR/dt
B R dQB/dt RC
*Ar  n 
SCR C
QNR
'B L lQNR dQscR/dt
dQBE/dt
I QNB
Co,).
RE
*E
Figure 2.8 Network representation of the circuit model including
collector current spreading effects. The bold lines are
lateral diffusion currents in the collector.
23
are solved simultaneously to account for the correct charge dynamics in
the collector. The time derivatives of the quasistatic stored charges
thus properly represent the distributed charging currents. Also the
inherent nonreciprocal transcapacitance of the BJT are simulated
directly, without the use of equivalentcircuit capacitors [23].
Test devices representative of the advanced BJT were used to
verify the model and to define a parameterextraction scheme [24). Some
of the parameters can be defaulted directly from geometrical and
process information such as AE, PE, NEPI, and WEpI. Empirical
parameters of RE, RB, IS, F, PR, VA, VB, C2, C4, ne, nc, CJEO, CJCO,
me, mc, e, Oc, TF, rR are measured by standard methods [1]. Other
parameters which related to device physics are known in [25] (ni, PnO,
vs), by fitting measured and simulated IB (rnO, rpO), by estimating
PISCES results (VQNR, VDSCR).
The physical parameters of the lateral diffusion velocities
calculated from the collector lateral flow in PISCES 2D simulation (WE
SLE) are:
AWE [Jn(x,y=O) + Jn(x,yWE)] dx
AE ILQ(R 0
VDQNR = (2.10)
PE QQNR
AE ILSCR
VDSCR
PE QSCR
FWE[WQNR
2 WE q[n(x,y) NEPI] dxdy
Jo Jo
EPI
WE [Jn(x,y=O) + Jn(x,yWE)] dx
JWQNR
[WE WEPI
2 JE q[n(x,y) NEPI] dxdy
J0 JWQNR
(2.11)
24
where n is the positiondependent electron carrier concentration, the x
axis is in the vertical direction, the y axis is in the horizontal
direction, y 0 stands for the leftside emitter edge, and y WE
stands for the rightside emitter edge.
The lateral diffusion velocities are in the range of 3 x 106 cm/s
to 5 x 106 cm/s due to the error introduced in the double integration
of discrete data. A fine tuneup of these parameters can be done by
optimizing (or fitting) the measured and simulated results at high IC,
and low VCE.
The simulation results of the collector current versus VCE at
different base currents from 1D [12] and 2D models are compared with
measurements in Fig. 2.9. In this figure, the solid line represents
measurements, the symbol x's represent 2D model simulations, and the
circles represent lD model simulations. It is clear that 1D model
overestimates quasisaturation effects. This is seen in Fig. 2.9 at
high IC and low VCE, where nonohmic quasisaturation dominates. The
test device measured in Fig. 2.9 has the drawn dimension WE = 2 pm, LE
 4 pm and the approximate active emitter area AE = 1.2 x 3.2 pm2 due
to its "bootshaped" sidewall spacer technology [26]. In order to
demonstrate the model's lateral scalability, a test device with active
emitter area AE = 0.7 x 3.2 pm2 was measured and compared with model
simulations in Fig. 2.10. Note that the lateral diffusion velocities
(VDQNR, VDSCR) used in these simulations are the same as in the
previous ones. The predictions of the present model show good agreement
when compared with the experimental results on these two different
emitter size BJT's. However, the 1D model simulation results differ
3.0 IB = 35 A
2.4
IB = 20 mA
< 1.8
 0
1.2
IB = 5 MA
0.6
0,,. 1   
0 0.2 0.4 0.6 0.8
VCE (V)
Figure 2.9 Plot of collector current IC versus VCE at different
IB with test device AE = 1.2 x 3.2 pm. The solid line
represents measurements, "x" represents 2D model
simulations, and "0" represents 1D model simulations.
VCE (V)
Plot of collector current IC versus VCE at different
IB with test device AE = 0.7 x 3.2 pm. The solid line
represents measurements, "x" represents 2D model
simulations, and "0" represents lD model simulations.
Figure 2.10
significantly from measurements in quasisaturation, especially with
the small emitter size BJT.
The 2D and 1D models are used to simulate a BJT (AE 1.2 x 3.2
pm2) inverter with 1.6 KQ load resistor. The input pulse waveform
consists of a 0.9 V, 50 ps ramp followed by a flat pulse of 950 ps
duration and then a falling 0.9 V ramp of 50 ps. The circuit responses
to the input pulse of the 2D and 1D BJT models are shown in Fig.
2.11. Both transistor models yield the same initial delay and falling
waveform for the first 100 ps. After that the 2D BJT model predicts a
faster falling waveform that goes to a lower asymptote on the output
pulse due to higher IC, lower dQQNR/dt and dQSCR/dt. To verify model
prediction in transient operation, transient device simulation is used
for comparison. Transient measurement of a ring oscillator introduces
an extra propagation delay from the interconnect between the first and
last stages of the ring oscillator and the I/O pad capacitances which
lead to the difficulty in measuring the actual transient switching
responses [27]. The 2D model simulations of an inverter show good
agreement with PISCES numerical results (circles in Fig. 2.10) in
transient operation which indicates that 2D BJT model correctly
accounts for the charge dynamics and the time derivatives of the quasi
static stored charges in the collector.
2.5 Conclusions
A circuit model for the advanced bipolar transistor including
collector current spreading effects in quasisaturation has been
developed. The model is defined implicitly by a system of nonlinear
2 t3=l2o0psec
I 1.2 t2=1000psec
0
0.8
0.4 
0 III I I I
0 0.3 0.6 0.9 1.2
TIME (x 109s)
Figure 2.11 Plot of the simulated transient responses of a BJT
inverter (AE = 1.2 x 3.2 pm) with load resistance 1.6 KO
for 2D model (solid line), 1D model (dashed line), and
PISCES simulation (circles).
equations describing base and collector transport. Two lateral
diffusion current sources were added to the lD physical model to
account for the multidimensional currents in the collector. The lateral
diffusion currents due to a carrier concentration gradient between the
collector area under the emitter and the collector area under the
extrinsic base were investigated. It was found that the collector
current spreading mechanism, which is entirely different from the base
spreading mechanism, is independent of the drift component in the
collector, and ameliorates quasisaturation effects in terms of current
gain and transient response. The collector spreading effect is
significant when the BJT is operated at high IC and low VCE, with low
epitaxial collector concentration, large epitaxial collector depth, or
small emitter width. SPICE simulations employing the collector
spreading model are in good agreement with the experimental results and
device simulations. The present model correctly accounts for the charge
dynamics in the collector and is scalable to small geometry BJT
resulting lateral scaling.
CHAPTER THREE
PHYSICSBASED CURRENTDEPENDENT BASE RESISTANCE
3.1 Introduction
The base resistance RB plays a significant role in the switching
speed and frequency response of the bipolar transistors [28] [29]. In
BJT circuit simulator models such as the GummelPoon model in SPICE, RB
is treated as constant with respect to applied bias [1], which in
modern BJT's is inadequate because base resistance is current
dependent.
The characterization and modeling of the BJT base resistance is a
difficult task. For the past twenty years, various methods for deriving
RB have been reported [3034] Recently, Ning and Tang [33] developed an
elegant dc method for measuring the base and emitter resistances.
However, the accuracy of this method depends on having the intrinsic
base resistance RBI linearly proportional to the forward current gain,
3 at high currents. This method may not be applicable to modern
advanced bipolar transistors [35]. Neugroschel [34] presented an ac
method for determining RB at low currents. By varying the baseemitter
voltages, the currentdependent base resistance was characterized at
low currents. However, this ac technique can be sensitive to the
picofarad parasitic capacitances associated with probed measurements on
the integrated circuits and requires skilled experimental techniques.
In this chapter, we propose a physicsbased base resistance model
taking into account a wide range of injection levels. This model, which
30
31
is discussed in Secs. 3.2 and 3.3, includes the physical effects of
base width modulation, base conductivity modulation, emitter crowding,
and base pushout. Good agreement is obtained when the new RB model is
compared with BJT measurements and a 2D device simulations (Sec. 3.4).
In order to illustrate its usefulness, the RB model is also implemented
in the userdefined subroutines in SLICE. Then transient responses are
simulated for an ECL circuit by performing circuit simulation with the
current RB model versus the constant RB model (Sec. 3.5). Conclusions
are given in Sec. 3.6.
3.2 Physical Mechanisms for Current Dependency
In this section, the various physical mechanisms (1D and 2D)
that are involved in the RB determination are treated separately and
then a simple method of estimating their coupled effects is proposed.
The total base resistance of a bipolar transistor, RB is composed
of the following
RB = RBI + RBO + RCON (3.1)
where RBI is the intrinsic base resistance, RB0 is the extrinsic base
resistance, and RCON is the base contact resistance. The intrinsic base
resistance occurs in the base region between the emitter and collector,
the extrinsic base resistance occurs in the lateral extension of the
base from its intrinsic region to the base contact, and the base
contact resistance results from the ohmic contact between IC
interconnect and the base. Generally, RCON < RBI and RCON < RBO. Thus,
RCON will be neglected in this study. In addition, the RBO of a BJT is
32
almost excitation independent [36]. Thus the only current dependent
term in the right hand side of Eq. 1 is RBI. Methods for characterizing
ohmic base resistance behavior (RB0) in the BJT are presented in the
literature [3336]. Therefore, the focus of this chapter will be on
estimating RBI from the physical mechanisms in the active base region.
3.2.1 Base Width Modulation
Figure 3.1 shows a simplified structure of n+pnn+ bipolar
transistor. Using conventional terminology, the base width, Xg is the
vertical dimension between the emitterbase spacecharge region (SCR)
and the collectorbase spacecharge region. The emitter length, LE is
defined as the dimension pointing into the figure. The crosssectional
area of the base (perpendicular to the base current path) is determined
by the product of the quasineutral base width, XB and LE.
Since RBI is inversely proportional to the crosssectional area
of the base, the modulation of the emitterbase or the collectorbase
spacecharge region will change the magnitude of RgB. For example,
assume that the emitterbase junction is forwardbiased and there is a
constant collectorbase applied voltage, VCB. Then XB is modulated by
the moving edge of the emitterbase spacecharge region when VBE
changes. As VBE increases, the emitterbase spacecharge region
contracts, and Xg expands. This reduces RBI because the base cross
sectional area, XB x LE increases resulting in a larger base charge and
a larger effective Gummel number.
The variation in quasineutral base charge can be modeled as
QBO/(QBO+AQB) where QBO is the zerobiased intrinsic base charge
. BASE EMITTER
CONTACT CONTACT
SI02 P P P S 0
1i
n .
n '
/ /
Figure 3.1 Schematic of an advanced bipolar transistor structure.
The dashed lines represent the edges of the spacecharge
region.
34
(QBO AEJNB(X) dx), and AQg is the incremental base charge resulting
from base width modulation effect (AQg AEJCJE(V) dV). AE is the
emitter area, and VBE' is the baseemitter junction voltage (VBE'= the
quasiFermi level separation between the edges of the emitterbase
spacecharge region).
To find AQB, a recently reported comprehensive lD model for the
emitterbase junction capacitance, CJE is employed [37]:
CJE(VBE') [qe2a/12(V*VBE')]1/3 for qNB3/(a2 (V*VBE')] > 0.1
= [qeNB/2(V*VBE')]1/2 for qNB3/(a2E(V*VBE')] < 0.1
for VBE' < Vbi 0.3 (3.2)
CJE(VBE') (2qeni/VT)1/2 exp(VBE'/4VT)
for Vbi 7VT S VBE' < Vbi 5VT (3.3)
CJE(VBE') = (2qeni/VT)1/2 exp[(VBE'2Vbi+10VT)/4VT]
for VBE' > Vbi 5VT (3.4)
where q is the electron charge, ni is the intrinsic carrier
concentration, e is the dielectric permittivity of silicon, "a" is the
emitterbase junction impurity gradient, Vbi is the builtin junction
voltage, NBeff is the effective base doping density (NBeff 
JN(x)dx/Xg, XB is the base width), C'JE is the derivative of the
junction capacitance, V* is the effective junction builtin voltage.
For a linearlygraded junction V* (2kT/3q)/n(ckTa2/8q2ni3) [37].
The model defines parameters V1 m Vbi 0.3 and V2 Vbi 7VT. A
polynomial fit calculates the capacitance using (3.2), (3.3) and the
derivative of the capacitance (C'JE) in the region between Vbi 0.3 <
VBE' < Vbi 7VT [37].
CJE(VBE') = CJE(V1) [12(VBE'Vl)/(VlV2)] [(VBE'V2)/(VlV2)12
+ CJE(V2) [12(VBE'V2)/(V2Vl)] [(VBE'Vl)/(V2Vl)]2
+ C'JE(V1) (VBE'Vl) [(VBE'V2)/(VlV2)]2
+ C'JE(V2) (VBE'V2) [(VBE'Vl)/(V2Vl)12
for Vbi 0.3 VI < VBE' < Vbi 7VT = V2 (3.5)
Figure 3.2 shows a plot of a basewidth modulation QBO/(QBO+AQB)
versus VBE'. We define a basewidth modulation factor, fBWM "
QBO/(QBO+AQB) as the vertical axis of the plot in Fig. 3.3. In general,
VBE' < VBE because of ohmic drop in the quasineutral region [38]. The
monotonic decrease of fBWM at low VBE' is due to the contraction of the
emitterbase SCR width shrinking. For VBE' above 0.8 V, the fBWM slope
is zero because the emitterbase SCR width can not contract further.
The base width modulation due to the basecollector SCR edge variation
in the base is neglected because modern BJT's have base doping density
much higher than their epilayer doping density, Nepi. This results in
the SCR edge variation occurring in the epitaxial collector.
3.2.2 Base Conductivity Modulation
When a bipolar transistor (npn) is in high current operation,
the hole concentration (including the excess carrier concentration) in
the base will exceed the acceptor dopantt) concentration to maintain
charge neutrality. As a result, the base sheet resistance under the
emitter decreases as the hole injection level increases. An excess base
charge, 6QB that results from this effect is given as [39]
0 0.2 0.4 0.6 0.8
VB (v)
Figure 3.2 Plot of the basewidthmodulation factor, fBWM versus the
baseemitter junction voltage, VBE'.
(2+Al+no)A2n0
6QB QBO (3.6)
(2+AI)A2/A3+n0
where A1=2[exp(r)l]/[rexp(r)], A21/A1, A3exp[(rl)exp(r)+l]/[exp(r)
1]2, r is the effective base doping gradient (r In[N(O)/N(XB)]), and
no is the electron concentration normalized by base doping N(O) at the
base edge of the emitterbase spacecharge region. Note that no is
determined by no(l+no)ni2/N2(0)exp(VBE'/VT)
The simulated result of baseconductivity modulation versus VBE'
is shown in Fig. 3.3. We define a baseconductivitymodulation factor,
fCM QBO/(QBO + 6QB) as the vertical axis of the plot in Fig. 3.3. The
factor, fCM stays constant at low voltages (low injection) and drops
sharply for VBE' > 0.75 V due to the presence of numerous excess
carriers (high injection) in the quasineutral region.
3.2.3 Emitter Current Crowding
As the base current flows through the active base region, a
potential drop in the horizontal direction causes a progressive lateral
reduction of de bias along the emitterbase junction. Consequently, the
emitter current crowding occurs at the peripheral emitter edges. Figure
3.4 shows emitter current crowding across the active base region in a
plot of the electron current density. This plot is drawn horizontally
from the middle of the emitter (x 0) to the left side emitter edge (x
 WE/2) using the twodimensional device simulator PISCES [14]. In the
PISCES simulations, the physical features of the transistor include a 2
pm emitter width (WE/2 1 pm), a 0.1 pm emitter junction depth, XJE, a
0.2 pm base junction depth, XJB, and a 0.7 pm epilayer depth, XEpI.
0.2 0.4 0.6 0.8
VBE (v)
Figure 3.3 Plot of the baseconductivitymodulation factor, fCM
versus the baseemitter junction voltage, VBE'.
20 x 104
18 x 104
16 x 10'
14 x 104
N 12 x 104
10 x 104
8 x 104 VBE=0.91V
6 6x10'
4x 104 VBE= 0.87V
2 x 104 WE/2
0 0.5 1.0 1.5
X (pm)
Figure 3.4 PISCES simulation of electron current density horizon
tally along the emitterbase junction. In this figure,
x 0 represents the center of the emitter; the
increasing x is closer to the base contact.
40
The doping profiles are assumed Gaussian for the emitter, Gaussian for
the base, and uniform for the epilayer. The peak dopings are 2 x 1020
cm3, 8 x 1017 cm3, and 2 x 1016 cm3 in the emitter, intrinsic base,
and epilayer, respectively. The nonuniform emitter current
distribution (Fig. 3.4) makes the effective emitter width smaller [40
42]. Hence, emitter current crowding reduces the magnitude of RBI.
In order to analytically represent the effects of emitter
crowding, a variable named the emitter crowding factor, fCROWDING is
employed. The emitter crowding factor is defined as the ratio of the
emitter current with emitter crowding to the emitter current without
emitter crowding [40], [41], [43]:
fCROWDING IE with emitter crowding/IE without emitter crowding
WE
JE(x) dx
(3.7)
JE(0) dx
where JE(0) is the emitter current density at the emitter edge.
In general, the integration of JE(x), the nonuniform emitter
current caused by lateral ohmic drops, can not be solved analytically
[4042], [44]. Equation (3.7) is solved numerically by using Simpson's
integration method applied to a circuit network.
The circuit network in Fig. 3.5 is used to model the current
densities at various partitioned regions. The emittercurrent density
at the different emitter sections including the ohmic drops in the
quasineutral base and emitter region are:
EMITTE
Bo
BASE
COLLECT
R IR T RE1 T RE2 T RE3 T RE4 T
IEO IEi E2 E3 lE4l
  
REo I R1 RB RB3 RB4
Io 1 I8 182 183 IB4

TOR
L
I Ic
C
Figure 3.5 Equivalent circuit representing the ohmic drops in the
quasineutral base and emitter regions.
42
IEO ISE/5 exp[(VBEIBORBOIEOREO)/VT] (3.8)
IE1 ISE/5 exp[(VBEIBBORBOIBRBlIElREl)/VT] (3.9)
IE2 = ISE/5 exp[(VBEIBORBOIBlRB1IB2RB2IE2RE2)/VT] (3.10)
IE3 ISE/5 exp[(VBEIBORB01BIRBlIB2RB2IB3RB31E3RE3)/VT]
(3.11)
IE4 ISE/5 exp[(VBEIBORBOIBIRB1IB2RB2IB3RB3IB4RB4
IE4RE4)/VT] (3.12)
where ISE is the emitter current at VBE VBE' 0 V, RBj, REj are the
emitter, base series resistances in the partitioned region j. As a
first order approximation, RBO = RBX, RBj(j1,2,3,4) = RBI/4,
REj(j0,1,2,3,4) 5 RE. The base currents (IBO, IB, IB2, IB3, IB4)
can also be calculated by using (3.8)(3.12) provided ISE/5 is replaced
by ISE/(5(PF+1)]. PF is the maximum forward current gain.
Using the Simpson's integration method, the total emitter current
IE = (IE0+4El1+2IE2+41E3+IE4)/12 is calculated for a singlebase
contact BJT. The method also applies to a doublebasecontact BJT in
which the equations for IE3 and IE4 should be replaced by those of IE1
and IEO due to a symmetry current crowding in the left and right halves
of the BJT. Note that the accuracy can be improved if the structure in
Fig. 3.5 is divided into more sections, but there is a tradeoff in
terms of the increased CPU time. The calculated fCROWDING versus VBE is
shown in Fig. 3.6. The solid line represents the emitter crowding
factor without conductivity modulation. The dashed line represents the
emitter crowding factor with conductivity modulation. This second order
effect lessens the level of emitter current crowding and will be
0.4
0.2
0
0
Figure 3.6
S0.2 0.4 0.6 0.8
VBE (V)
Plot of the emitter crowding factor, fCROWDING versus the
baseemitter applied voltage, VBE with RRI 480 0, RE 
20 0, ISE 10 x 1018 A, ISB 6 x 1022 A for a single
basecontact BJT. The solid line represents the emitter
crowding without baseconductivity modulation and the
dashed line represents the emitter crowding with base
conductivity modulation.
44
discussed later. The emitter current crowding becomes important when
VBE > 0.85 V. In general, emitter crowding is more pronounced at high
currents (see Fig. 3.4) and for devices with large emitter width and
high intrinsic base sheet resistance.
3.2.4 Base Pushout
For bipolar transistors operating at high currents, base pushout
can occur [3]. Based on PISCES simulations, Fig. 3.7 shows hole
concentrations of a n+pnn+ BJT at the emittercollector applied
voltage, VCE 2.0 V and VBE 0.87 V, 0.91 V, and 0.95 V. Base pushout
initiates when VBE is greater than 0.87 V for the doping profile used
in Sec. 3.2.
The currentinduced incremental base width, 6XB is [25]
(JO qsNEPI)/2
6XB = WEPI (1 C q ) ) for JC > J0 (3.13)
(Jc qVsNEpl)I/2
where WEPI is the epitaxialcollector width between the basecollector
junction and collector highlow junction, vs is the saturation
velocity, JC is the collector current density, and JO is the onset
collector current density for base pushout (JO
qvs(Nepi+2VcB/qWEPI2)).
The variation of base resistance due to basewidening is shown in
the plot in Fig. 3.8. We define a basepushout factor, fPUSHOUT as the
ratio of base width, XB without base widening to base width with base
widening (XB + AXB). Thus,
1014
DEPTH (m)
PISCES simulation of hole concentration plot along the
vertical direction at VCE 2 V, VBE 0.87 V, 0.91 V,
and 0.95 V (dashed lines). The solid line is the doping
profile from emitter to collector. Depth zero stands for
emitter surface.
Figure 3.7
1.2
1.0
\\ \\
\\
0.8
\ \
0
'n! 0.6
0a
0.4
0.2
0 T, I IT I I I I I !11
103 104 10s
Jc (A/cm2)
Figure 3.8 Plot of the base pushout factor, fpUSHOUT versus the
collector current density, JC (A/cm ). The solid line
represents the epilayer doping density, Nepi 2 x 1016
cm, the epitaxial collector thickness, Wepi 0.5 pm,
and the collectorbase applied voltage VCB 2.0 V, the
dashed line represents Nepi 0.8 x 1016 cm3, Wepi 0.5
pm, and VCB 2.0 V, and the dotted and dashed line
represents Nepi 2 x 1016 cm3, Wepi 0.5 pm, and VCB 
3.0 V.
fFUSHOUT 1 for JC < JO,
WEPI (JO qvsNEPI)1/2
(1 +  [1 /21 for JC > JO. (3.14)
XB (JC sNEPI)1/2
Figure 3.8 shows a plot of fPUSHOUT versus JC. In Fig. 3.8, the
solid line represents BJT pushout for a collector with NEPI = 2 x 1016
cm3, WEPI 0.5 pm, and VCB 2.0 V, the dashed line represents BJT
base pushout with NEPI 0.8 x 1016 cm3, WEPI 0.5 pm, and VCB = 2.0
V, and the dotted and dashed line represents BJT base pushout with NEPI
 2 x 1016 cm3, WEPI = 0.5 pm, and VCB = 3.0 V. The base widening is
more significant when the epilayer doping density is low, the width of
the epitaxial collector is large, or the collectorbase applied voltage
is small. The basewidening increases dramatically for BJT operated at
high current densities and results in a very low fPUSHOUT
3.2.4 The Coupling Effects
The emittercrowding factor taking into account the conductivity
modulation, base width modulation, and base pushout in the emitter
crowding mechanism is discussed in this section. In general, the high
conductivity from high injection reduces the emitter current crowding
(see dotted line in Fig. 3.6). Also, the base width modulation and base
pushout effects result in a smaller effective base resistance. These
effects lessens the level of emitter current crowding.
To model a better emittercrowding factor, f'CROWDING which
accounts for the second order effects (base conductivity modulation,
base width modulation, and base pushout) in the emitter crowding
mechanism, a parameter fc (fc, fBWM x fCM x fPUSHOUT) is incorporated
48
into (3.8)(3.12). The parameter fc modifies the base resistance in
each partitioned region of the intrinsic base. Thus if base resistance
is lower due to base conductivity modulation, base width modulation, or
base pushout, the IBRBI drop due to intrinsic base resistance is
reduced in the current crowding calculation.
IEO 1SE/5 exp[(VBEIBORBOIEOREO)/VT] (3.15)
IEl ISE/5 exp[(VBEIBORBOIBlRBlfcIE1RE1)/VT] (3.16)
IE2 ISE/5 exp[(VBEIBORBOBIlRBlfcIB2RB2fcIE2RE2)/VT] (3.17)
IE3 ISE/5 exp[(VBEIBORBO^BlRBfc^B2RB2fcB3RB3fc
IE3RE3)/VT] (3.18)
IE4 = ISE/5 exp[(VBEIBORBO1BlRBlfcIB2RB2fcB3RB3f
IB4RB4fcIE4RE4)/VT] (3.19)
Using (3.7), (3.15)(3.19) together with the Simpson's method,
f'CROWDING can be calculated numerically.
3.3 The Nonlinear Base Resistance Model
The physical mechanisms for modeling the currentdependent base
resistance have been discussed in Sec. 3.2. A simple method of
estimating the combined effects of all the contributing factors in the
base resistance is to multiply then together in a liner fashion. In
fact, the multiplication of those physical factors produces a very
acceptable first order model of the currentdependent base resistance
that agrees with experiments. Thus,
49
RBI RBIO x fBM x fCM x f'CROWDING x fPUSHOUT (3.20)
where RBIO is the intrinsic base resistance at VBE 0 V. RBIO equals
WEPb/12LE for a rectangular emitter with base contact on two sides, and
WEPb/3LE for a rectangular emitter with single base contact [45]. pb is
the intrinsic base sheet resistivity at VBE 0 V.
The solid line in Fig. 3.9 represents Rg (RB = RBI + RBO)
calculated from the present model, where RB0 can be obtained through
measurements [33], [34], circuit simulation [36), or device
simulations. The gradual reduction of RB at low VBE is caused by the
emitterbase spacecharge region shrinkage. The sharp decrease of RB at
high VBE is due to base conductivity modulation, base pushout, and
emitter current crowding effects.
3.4. Model Verification with Experiments
A method is developed in this section for obtaining RB at high
voltages. An ideal base current, IBideal without ohmic drops in the
quasineutral base and emitter regions can be defined
IBideal ISB exp(qVBE/nkT) (3.21)
where ISB is the preexponential base current (ISB ISE/(F+1)),
n is the nonideal base coefficient. n = 1 for metal emitter contact,
and n > 1 for a polysilicon contact BJT in the current technologies
[35].
The actual base current from measurement is [1]
IB ISB exp[q(VBEAV)/nkT]
(3.22)
600
500 O
400
" 300
r0
200
100
0
0 
0 0.2 0.4 0.6 0.8 1.0 1.2
VBE (V)
Figure 3.9 Plot of the base resistance, RB versus the baseemitter
applied voltage, VBE. The solid line represents the
simulation result from the present RB model, squares
represent PISCES simulation data, triangle represents
Ning and Tang's method data, and circles represent DC
measurement data at high currents.
51
From (3.21), (3.22) the ohmic drop AV (AV IERE + IBRB) is
AV (nkT/q)[ln(IBideal/IB)] (3.23)
1 nkT IBideal
thus RB(VBE) = ( ln( ) IERE) (3.24)
IB q IB
Since Ig, ISB, and IE are known from measurement directly, n is
extracted in the intermediate current level (prior to ohmic drop
region) by (3.21), RE can be extracted from open collector method [46]
or ac method [34], and IBideal can be calculated from (3.21), the
excitationdependent base resistance RB can be computed from (3.24).
When emitter current crowding occurs, however, the emitter resistance
RE increases due to a smaller effective emitter area. Thus, emitter
crowding factor, f'CROWDING must be included in the RE term in (3.24)
to obtain a more accurate Rg:
1 nkT IBideal IERE
RB(VBE)  ( ln( ) ) (3.25)
IB q IB f'CROWDING
The low current base resistance value, on the other hand, is
extracted from device simulations because AV is negligible compared to
VBE in low current and difficult to measure. RBI in low currents is
computed as WE2/mLE S qpp(x,y)p(x,y)dxdy where the positiondependent
hole mobility pp(x,y) and hole concentration are known from PISCES
simulations. Here, m 3 for a rectangular emitter with one base
contact, and m = 12 for a rectangular emitter with two base contacts.
Combining the above methods for RB characterization and a dc
method [33], the base resistance is obtained (Fig. 3.9). The results
52
from the present model are in good agreement with measurements. A small
derivation is present at low VBE and this is due to the fuzzy
boundaries of the moving spacechargeregion edges in the PISCES
simulations.
3.5 Application
In order to demonstrate the utility of the currentdependent base
resistance model, the present model was implemented in SLICE using
userdefined subroutines [10]. Transient simulations from GummelPoon
model with currentdependent base resistance for an ECL circuit are
illustrated in Fig. 3.10. The ECL gate has the load resistances, RL1 
270 0, RL2 290 0, and the current source resistance, RI = 1.24 Kn.
The input pulse waveform has logic swing from 1.55 V to 0.75 V with
20 ps ramp followed by a flat pulse of 400 ps, and then a falling ramp
of 20 ps from 0.75 to 1.55 V. Figure 3.10 indicates that the constant
base resistance chosen at low injection (dashed line) overestimates the
propagation delay of ECL logic and that the nonlinear base resistance
model (solid line) yields a more realistic switching transient in which
the base resistance changes drastically during the largesignal
transition. These simulations indicate that the existing constant RB
model is inadequate for predicting the transient performance of
advanced bipolar technologies and the currentdependent base resistance
model is superior for BJT predicting transients.
0.9
1.0 RLI1 R2
0 \ 270S 290S
1.1 VIN (v) \ VI 1.15V
1.1 5V
/ 0.75 VOUT
1.2 \ Ri RI=
1.55 1.24K1 1.24K6
/ t t2 t \t
1.3 /t = 20 PS \ 5.2V
/ t2= 420 PS \
t3= 440 PS \
1.4 \
/ \
/ \
/ \
1.5 / \
1 \
1.6 / \
1.7
0 1 2 3 4 5 6 7 8
TIME ( x 10s)
Figure 3.10
Transient responses from GummelPoon model with constant
base resistance model (dashed line) and currentdepend
ent base resistance model (solid line) for an emitter
coupled logic inverter with an emitter follower.
54
3.6 Summary and Discussion
A physicsbased currentdependent base resistance model of
bipolar junction transistors has been presented. The model is
applicable for all injection levels and accounts for the effects of
base width modulation, base conductivity modulation, base pushout, and
emitter crowding. Interactions among these effects are also treated.
The results obtained from the present model, from the twodimensional
device simulator PISCES, and from measurement data show excellent
agreement.
We have implemented this physicsbased base resistance model in
SLICE/SPICE using userdefined subroutines. For an emittercoupled
logic circuit, the GummelPoon model with the present Rg model results
in a more realistic transient response compared with that of the
constant base resistance model. It is anticipated that the present
model is useful for accurate bipolar integratedcircuit simulation in
advanced IC technologies.
CHAPTER FOUR
CIRCUIT MODELING FOR TRANSIENT EMITTER CROWDING AND
TWODIMENSIONAL CURRENT AND CHARGE DISTRIBUTION EFFECTS
4.1 Introduction
Today's advanced bipolar transistors, resulting from double
polysilicon selfaligned technology, have been scaled down to
submicrometer emitter widths and exhibit multidimensional current flow,
especially when operated during high current transients. The one
dimensional BJT model [12] has been extended into a quasi2D model,
useful for quasisaturation, to account for the twodimensional
collector current spreading effects. In forward active mode the emitter
current crowding will be significant if the base resistance is large
and the collector current is high. In addition, this current crowding
is enhanced during the BJT switchon transient.
The emitter current crowding and sidewall injection effects have
been investigated by numerous authors [4045], [4755]. Analytical
solutions for emitter crowding were derived to formulate a distributed
circuit model [42]. The assumption of a negligible emitter ohmic drop,
IERE in [42] is not generally valid for the polysilicon bipolar
transistors since IERE can be nonnegligible compared to the base ohmic
drop, IBRB. It is the author's experience that neither the distributed
model [42] nor the twolump empirical models [48] [49] are optimal for
parameter extraction and circuit simulation in terms of CPU time. In
addition, emitterbase sidewall injection and its junction charge
56
storage effects, usually neglected in the lumped circuit models, can be
quite significant in small emitterwidth VLSI BJT's.
In this chapter, an improved circuit model including nonuniform
transient current and charge distribution effects is developed. The
details of the model formulation are described in Section 4.2. In
Section 4.3 the model is verified by measurements and transient device
simulations. Conclusions are given in Section 4.4.
4.2. Model Development
A circuit model for the nonuniform current and charge
distribution resulting from transient emitter crowding and emitterbase
sidewall injection effects is discussed in this section.
4.2.1. Transient emitter crowding
As the base current flows through the active base region, a
potential drop in the horizontal direction causes a progressive lateral
reduction of dc bias along the emitterbase junction. Consequently,
emitter current crowding occurs at the peripheral emitter edges. This
nonuniform current distribution effect is enhanced in transient
operation [55], in which the base resistance and junction capacitance
contribute finite RC time constant (delay) in the base region. Thus the
emitter edge of a BJT turns on earlier than the emitter center during a
switchon transient. Also, the charge (QBE) at the emitter edge is
larger than at the center during switching.
In order to analytically represent the emitter crowding effect, a
variable, emitter crowding factor fCR, was defined as the ratio of the
57
emitter current with emitter crowding to the emitter current without
emitter crowding (see Cahpter 3). In this Chapter, fCR is treated as
timedependent for transient as well as steady state operation:
JE[V(x,t)]dx
fCR(t) (4.1)
JWE
0EJE[V(0,t)]dx
where JE is the position and timedependent emitter current density, x
is the horizontal direction (x 0 is the emitter edge), t is time, and
V is the position and timedependent junction voltage.
In general, JE(x,t), the nonuniform transient emitter current,
can not be integrated analytically [41] [46]. Equation (4.1) is solved
numerically using Simpson's integration method as
WE n/2 n/21
JE(0,t)+JE(WE,t)+4 X JE[(2jl)WE/n,t]+2 X JE(2jWE/n,t))
3n j1 j=1
fCR 
JE(0,t)WE
(4.2)
A circuit network is used to model the current densities at
various partitioned boundaries in a threedimensional bipolar structure
shown in Fig. 3.1. The concept of chargebased model was developed by
Jeong and Fossum [12]. This work extends the development of Chapter 3
using this chargebased concept for regional BJT partitioning. The
timedependent lateral voltage drop, IBI(t)RBI in the intrinsic base
region is calculated using the partitioned intrinsic base series
resistance, RBj, base current, IBIj(t), and charging currents,
58
dQBEj(t)/dt and dQBCj/dt at the partioned region j.
The regional intrinsic base current IBgj(t) can be written as
IS VBEj(t) C21S VBEj(t)
IBIj [exp( )1] + [exp( )1]
(n+l)BF VT (n+l) VT
IS VBCj(t) C41S VBCj(t)
+  [exp( )l] + [exp( )l]
(n+l)>R VT (n+l) VT (4.3)
VBEj(t) VBE(t) IB(t)RBX IE(t)RE IBI(k1)(t)RBk (4.4)
k=l
VBCj(t) VBC(t) IB(t)RBX IC(t)RC IBI(k1)(t)RBk (4.5)
k=l
where RBX is the extrinsic base resistance, RBk is the regional
intrinsic base resistance (RBk 1/n RBIO x fBWM x fCM), VT is the
thermal voltage kT/q, and IS, IB, IE, IC, OF, R, RC, RE, ne, nc, C2,
and C4 retain their usual meanings in the GummelPoon model.
The regional baseemitter charging (transient) current is
dQBEj(t) 1 d VBEj(t)
 (rFIs[exp( )1] + AEfCJE[VBEj(t)]dV)
dt n+l dt VT
(4.6)
where CJE is the voltagedependent emitterbase junction capacitance,
AE is the emitter area, and TF is the forward transit time. Similarly,
the regional basecollector charging current, dQBCj(t)/dt can be found.
The junction capacitance model in SPICE2 is based on the
depletion approximation. This simple model holds for CJC, the
collectorbase junction capacitance, in which the collectorbase
59
junction is reversebiased when the BJT is at the forward active mode.
When emitter crowding occurs, however, the junction voltage across the
emitterbase spacecharge region is usually high enough to invalidate
the depletion approximation for finding the emitterbase junction
capacitance. A recently developed junction capacitance model [37] which
takes into account the free carrier charges in the spacecharge region
in high forward bias is therefore used in this circuit model to
determine emitterbase charging currents. The biaseddependent CJE
model can be found in Section 3.2.1.
Through the regional voltage drops which define the position and
timedependent junction voltages, the nonuniform currents and charges
under the emitter are determined. For example, the nonuniform quasi
static charges under the emitter are described by the position and
timedependent regional charge, Qj(x,t) which is a function of its
junction voltage, V (x,t).
Figure 4.1 shows a partitioned circuit model including the
transient crowding effects using chargebased circuit modeling approach
[12] [23]. In Fig. 4.1 the collector current under the emitter is the
product of the current crowding factor fCR and the collector current
without emitter current crowding. The current crowding factor is
equivalent to the effective emitter area ratio (AEeff/AE) in [40] [41]
[45]. Applying (4.1)(4.2) to the partitioned model for n = 2 yields
VBE(t)IB(t)RBXIE(t)RE
IC = fCR {ISexp[]
VT
VBE(t)IB(t)RBXIE(t)RE
+ C21Sexp[ ]) (4.7)
neVT
dOBC2 V = VBO V
di VBE1 = VB;. VE
RB RB 81 RB2 B VBE2=VB2VE
dOBEx dE dOBO dC3El d02
di bb 1 d o i c
'Ax r o iY '62 Ic (VBEO VBE1 VBE2)
E'
RE
E
Figure 4.1 Network representation of the chargebased bipolar model
including the nonuniform transient current and charge
distribution effects.
61
exp[VBEO(t)]+4exp[VBEl(t)]+exp[VBE2(t)]
fCR (4.8)
6exp(VBEO(t))
where VBEO, VBEl, and VBE2 are the position and timedependent base
emitter junction voltages at the emitter edges (VBEO, VBE2) and emitter
center (VBEI). Note that the present model takes into account both dc
and transient emitter crowding and it can be easily reduced to a dc
model by removing the transient current sources in Fig. 4.2. In
addition, the equivalent distributed twodimensional circuit model
avoids the convergence, grid, and cost problems associated with
transient numerical device simulations while still providing an
accurate prediction of transient current crowding (see Fig. 4.7) with
much less CPU time.
4.2.2. Sidewall Iniection Current and Junction Charge Storage Effects
When the lateral dimensions of the emitter are in the same order
of magnitude as the emitter width, the emitterbase sidewall plays a
significant role in the performance of the bipolar transistor [52]. To
accurately model the nonuniform current and charge distribution in the
advanced BJT, the emitterbase sidewall injection current and its
associated junction stored charge should be modeled. An analysis of a
PISCES simulation of an advanced bipolar transistor is performed to
identify multidimensional currents. In PISCES simulations, the BJT has
a 1.2 pm emitter width, a 0.1 pm emitter junction depth, a 0.25 pm base
junction depth, and a 0.7 pm epilayer depth. The doping profiles are
assumed Gaussian for the emitter, Gaussian for the base, and uniform
for the epilayer. The emitter dopant lateral straggles are assumed 75%
62
of the vertical straggles for the emitter sidewall lateral diffusion
[18]. The peak dopings are 2 x 1020 cm3, 8 x 1017 cm3, and 2 x 1016
cm3 in the emitter, intrinsic base, and epilayer, respectively. The
physical mechanisms used in PISCES simulations include ShockleyRead
Hall recombination, Auger recombination, bandgap narrowing, and doping
and fielddependent mobility.
PISCES 2D simulation readily shows the multidimensional current
paths as illustrated in Fig. 4.2. The figure displays the electron
currentdensity and holecurrentdensity vector plots of the advanced
BJT biased at VBE 0.85 V and VCE 3.0 V. The current vectors suggest
that the sidewall injection contributes an important component of the
base current. A quantitative measure of the sidewall current is given
by integrating the electron current density and hole current density
along the emitterbase junction sidewall. Simulation of the current
gain versus emitter width also indicates the significance of the
sidewall injection current and the emitterwidth size effect on the
current gain.
Figure 4.3 shows the f plots of three advanced BJT's with
different emitter widths. The peak P of the BJT with the 1.5 pm emitter
width is the highest followed by the peak P of the 1.0 pm emitter, and
then the peak P of the 0.5 pm emitter. The PISCES 2DBJT simulations
indicate the peakcurrent gains of the submicrometer advanced BJT's
will be reduced significantly with scaling. Since the normalized
collector currents (IC/WE) are approximately the same in these three
structures, the primary reason for peak P reduction is the emitterbase
sidewall injection current, which makes Ig not scalable. The f falloff
E B
+ n+ +
#* 4 *
+ 4 4, +1,
+ +, 4 4 4 
4, + 4 + 4 4,
4 4, 4, 4, 4, .4, 4' 4
C
P ~*)*+Cc
Figure 4.2.1 PISCES electroncurrentdensity vector plot at VBE 
0.85 V and VCE 3.0 V.
E B
t t t 
S i
P p  p+
n
C
Figure 4.2.2 PISCES holecurrentdensity vector plot at VBE 0.85 V
and VCE 3.0 V.
300
Z 200
< / /*'' ~" ^.
, ,,
I
0 I I I I
S100 l i
0.4 0.5 0.6 0.7 0.8
VBE (V)
Figure 4.3 Plot of current gain versus VBE at different emitter
width, WE. The solid line represents WE 0.5 Am, the
dashed line represents WE 1.0 Am, and the dashed and
dotted line represents WE 1.5 pm.
66
at the intermediate current level before high injection occurs is due
to basewidth modulation at the emitterbase junction; this effect is
significant in narrowbase BJT's [56].
Based on device simulation and analytical approximation [52]
[53], the emitterbase sidewall base current, IBX is modeled using the
ratio of the emitter perimeter to the emitter area:
PE XJE IS VBE(t)IB(t)RBX VBE(t)IB(t)RBX
IBX (exp[ ] + C21Sexp[ ])
AE F VT VT
(4.9)
where PE is the emitter perimeter and XJE is the emitter junction
depth. Note that the lateral voltage drop under the emitter is defined
as IBIRBI in the emitter crowding mechanism. The use of voltage drop
IBRBI in emitter crowding would overestimate the level of current
crowding since the base current under the emitter (IBI) can be quite
different than the base terminal current (Ig) if the base sidewall
current (IBX = IBIBI) is significant.
As a firstorder approximation, the collector current flow out of
the emitterbase sidewall can be neglected [52]. Thus the charge stored
at the emitterbase junction sidewall, QBEX is determined by the
sidewall junction capacitance, CjEX so that QBEX = PEXJEGCjEX(V)dV.
CJEX is the same as Eqs. (3.2)(3.5) providing different values for the
junction gradient "a" and the effective junction builtin voltage V*.
Similarly, the extrinsic basecollector junction charge, QBCX
associated with the collectorbase junction outside the intrinsic
emitter region is (ACAE)fCjC(V)dV because the collector current flows
mainly in the intrinsic emitter region (see Fig. 4.3.1).
67
By combining the modeling methodologies in Secs. 4.2.1 and 4.2.2,
the nonuniform transient currents and charges in an advanced BJT can be
determined.
4.3. Model Verification with Experiments and Transient
Device Simulations
The circuit model which includes the emitter crowding (dc and
transient) and sidewall injection effects was implemented as user
definedcontrolledsources in SLICE. In SLICE/SPICE circuit analysis,
UDCS's are userdefined subroutines (see Appendix B) that use the
implicit nonlinear model equations to compute both charging current
(dQ/dt) and transport current (I) in the model depicted in Fig. 4.1.
The time derivatives of the quasistatic stored charges in the base
thus properly represent the charge dynamics in the BJT. The lateral
voltage drops (VBE2(t) < VBEl(t) < VBEO(t) < VBE(t)) are given as the
system of model equations (I and dQ/dt) are solved simultaneously.
Transient current crowding is then accounted for in the collector
current by fcR(VBEO(t),VBEI(t),VBE2(t)).
Test devices representative of advanced BJT's were used to verify
the model and to define a parameterextraction scheme. The devices have
drawn emitter width WE = 2 pm, emitter length LE = 8 pm and the
approximate active emitter area is AE 1.2 x 7.2 pm2 due to sidewall
spacer technology. The intrinsic and extrinsic base resistances are
obtained by Ning and Tang's method [33]. The GummelPoon model
parameters IS, PF, fR, 'F, rR, ne, nc, C2, C4, RE, and RC are extracted
by the methods in [1]. Some of the physical parameters are determined
from the process information (AE, PE, WE, XJE, and NB) and from [25]
(ni, V*).
The BJT is measured from VBE 0.6 V to VBE 1.0 V with VCE 3
V to keep the transistor out of quasisaturation. The simulated results
from the present model and the GummelPoon model show excellent
agreement with the experimental data at low currents; however, the
simulated results from the GummelPoon model deviate significantly from
measurements at high currents (see Fig. 4.4). The discrepancy would be
exaggerated if Fig. 4.4 were shown on a linear scale.
Transient measurement of a ring oscillator introduces an extra
propagation delay due to the interconnect between the first and last
stages of the ring oscillator and the I/O pad capacitances which
complicate measurement of the real inverter transient response [27].
Thus, to demonstrate the model utility in transient operation, the
emitter crowding factor and pulse response of an inverter are simulated
using the present model and compared with transient device simulation
using PISCES. Figure 4.5 shows the emitter current density horizontally
along the emitterbase junction at various times in the PISCES
transient simulation. In Fig. 4.5 emitter crowding is very significant
during the initial turnon transient. The transient crowding factors
obtained from PISCES and the present model are compared in Fig. 4.6.
The model predictions show close agreement with PISCES transient
simulations. This indicates that the lumped model in Fig. 4.1 correctly
accounts for the nonuniform transient current and charge distribution
effects. SLICE implementation employing the present model, which
includes the transient crowding effects, is used to simulate a BJT
inverter with 1.2 KD load resistor. The input pulse waveform consists
102
10"3 IC
104
105
106
10 6
10.8
108
109 I \ I \ I I
0.6 0.7 0.8 0.9 1.
VBE (V)
Figure 4.4 Log I versus baseemitter applied voltage, VBE. The solid
line represents the present model simulation, the dashed
line represents the GummelPoon model simulation, and the
circles represents the measurement.
1.2
1.0
t=940 PS
0.8
St=227 PS
0.6
t=126 PS
0.4
t=89 PS
0.2
t=62 PS
o f I jI i I i
0 1.0 2.0 3.0
x (gim)
Figure 4.5 Electron current density distribution horizontally along
the emitterbase junction at various times in PISCES
transient simulation.
1.0
0.8
0.6
0.4
0.2 
0 0.2 0.4 0.6 0.8
TIME (x109S)
Figure 4.6 Plot of the emitter crowding factor versus time. The
solid line represents SPICE simulation employing the
present model, and the circles represent PISCES
simulation.
72
of a 0.85 V, 50 ps ramp followed by a flat pulse of 1200 ps duration
and then a falling 0.85 V ramp of 50 ps. Figure 4.7 shows the inverter
transient responses from SPICE/SLICE (using the GummelPoon model and
the present model) and PISCES. The predictions of the present model are
in good agreement with PISCES results; however, the GummelPoon model
shows a slower turnon transient and a large propagation delay. The
discrepancy between the GummelPoon and PISCES results is due to the
nonuniform transient current and charge distribution in PISCES
simulation which lowers the magnitude of the base impedance during
switching. The use of a lumped base resistance measured at steadystate
in the GummelPoon model predicts more delay than is actually observed.
4.4 Summary and Discussion
A new circuit model for the advanced bipolar transistor including
nonuniform transient current and charge distribution effects has been
developed. The model takes into account the transient emitter crowding
mechanism, emitterbase sidewall injection, and extrinsic junction
charge storage effects. The spatially partitioned model is developed
based on physical insight gained from device simulations (dc and
transient). Although the partitioning technique itself is
straightforward, the present model represents the nonuniform current
and charge distribution at the emitterbase sidewall and under the
emitter in a unified manner. Furthermore, second order effects such as
basewidth modulation and base conductivity modulation, which decrease
the intrinsic base resistance and emitter crowding are easily modeled
in the equivalent circuit through a correction factor for the effective
3.5
Vc = 3V
VIN
3.0 0.85V R L= 1.2 Kf2
0.85V
0 t t VIN VOUT
\ t = 50 ps
S2.5 \ t2= 1250 ps
S\ t3= 1300 ps
>O
2.0 
1 .5 I I I I I I II I I
0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
TIME (xlO 9S)
Figure 4.7 Simulated transient responses for a singletransistor
inverter. The solid line represents the present model
simulation, the dashed line represents the GummelPoon
model simulation, and the circles represents PISCES
transient simulation.
74
base charge. SLICE simulations employing the present model show
excellent agreement with measurements and device simulations. Since the
model correctly represents the charge dynamics of the BJT in transient
operation, it is anticipated that the present model can be useful in
advanced bipolar (or BiCMOS) modeling in technology computeraided
circuit design and process sensitivity diagnosis.
CHAPTER FIVE
SPARAMETER MEASUREMENT PREDICTION USING A PHYSICAL
DEVICE SIMULATOR
5.1 Introduction
Submicrometer emitter bipolar transistors produce small signal
responses that are difficult to characterize with existing sparameter
equipment. State of the art probes, and proper calibration technique
have proven essential in the measurement of sparameters of single BJT
test structure [57]. However, sparameter measurements cannot predict
the teststructure response of new BJT technologies in the "on paper"
development stage.
A new method of predicting sparameter test structure response
from physical device simulator output has been developed. This
predicted sparameter response is particularly useful for examining the
performance of conceptual designs of submicron BJT technologies.
Submicrometer BJT's have significant dc, transient and smallsignal
multidimensional effects which include collector current spreading,
emitter crowding, and emitterbase sidewall injection; these effects
have been evaluated by a 2D physical device simulator previously [58]
[59] and are discussed in Chapters 2, 3, and 4. The new method of
predicting sparameter response provides a direct comparison between 2
D BJT simulations and measurement data from BJT test structures.
Important uses of this simulated sparameter response also
include verifying BJT test structure sparameter measurements and
76
previous BJT characterizations. The derived BJT test structure response
can be used to confirm the accuracy of existing test structures
measurements, potentially reducing the total number of test structures,
measurements, and cost necessary to characterize a BJT technology.
In order to get a complete characterization of a 3port BJT,
three sets of 2port measurements must be taken, generally requiring 3
separate test structures. Since the 3port measurement is time
consuming and IC layout area intensive, often only a single 2port BJT
measurement is made. The sparameter prediction technique can
supplement an existing 2port test structure measurement so that a
complete 3port BJT characterization is possible. The simulated s
parameter response also can be extended beyond sparameter
instrumentation frequency ranges.
This modeling technique is demonstrated using submicrometer BJT
simulations from the PISCES 2D physical device simulator [60]. Other
smallsignal device simulations or characterizations [61) could be
substituted for the PISCES data. Simulated smallsignal BJT yparameter
measurements are converted (via software) to sparameters. Sparameter
measurements are preferred for highfrequency characterizations and
have been demonstrated onchip at frequencies up to 50 GHz [62]. In
addition, sparameter best represent a distributed circuit with high
frequency discontinuities [63], such as a BJT IC test structure
measured at microwave frequencies. The BJT sparameter response is
incorporated into a BJT test structure model which includes the effects
of IC interconnects, discontinuities and bond pads. The predicted s
parameter response for the BJT test structure is then calculated and
77
plots of the BJT test structure responses are presented. This modeling
technique proves extremely useful for evaluating IC test structure
characteristics.
This is the first time that the high frequency BJT test structure
circuit modeling has been combined with a 2D device simulation output
in order to predict test structure sparameter response. In addition, a
novel twolayer metalbased BJT test structure with low attenuation is
examined using this modeling. The modeling algorithms presented here
may be applied in inverse fashion to extract accurate BJT small signal
characteristics from sparameter measurements or evaluate the accuracy
of sparameter calibration algorithms.
5.2 Bipolar Test Structure Modeling
In order to demonstrate the utility of the bipolar test structure
modeling, an npn BJT smallsignal response was simulated using the
PISCES program. The physical features of the BJT include a 1 pm emitter
width (WE 0.5 pm), a 0.1 pm emitterdepth, a 0.2 pm basedepth, and a
0.8 pm epitaxial collectordepth shown in Fig. 2.1.1. The doping
profiles are shown in Fig. 2.1.2. Smallsignal parameters from lD, 2
D, or 3D simulator may be used for input in this test structure
modeling technique.
A 2D simulation typically provides BJT yparameter response up
to the emitter contact, base contact, and collector contact. During y
parameter simulations the BJT is biased at VBE = 0.8 V. and VCE = 2.0 V
and the frequency is varied from 10 MHz to 7 GHz. The yparameters are
normalized by the distributed circuit admittance (frequency dependent
78
interconnect admittance) and then converted to sparameters. The y
parameter to sparameter conversion equations are [64]:
(1yll)(1+y22) + Y12Y21
S11 (5.1)
(I+yll)(+y22) Y12Y21
2y12
s12 (5.2)
(1+yll)(l+y22) Y12Y21
2y21
s21 (5.3)
(1+Yll)(I+Y22) Y12Y21
(1+yll)(1y22) + Y12Y21
s22 = (5.4)
(1+yll)(l+y22) Y12Y21
In order to predict the sparameter response of a specific BJT
test structure layout, an equivalent high frequency circuit must be
constructed. An example BJT test structure layout which is frequently
used for sparameter measurements is presented in Fig. 5.1. Here, the
BJT is positioned between three bond pads that are connected to the
transistor by IC interconnect. The bond pads are 100 pm by 100 pm and a
bend is added to the IC interconnect between the base terminal and the
base bond pad. The interconnect, the bond pads and the bend exhibit
parasitic responses at microwave frequencies.
A flow chart which outlines the calculation of the BJT test
structure response is shown in Fig. 5.2. The physical dimensions and
doping profiles of the submicron BJT are entered into the device
simulator program and dc and ac simulations are performed in order to
predict yparameters. These yparameters are converted to sparameters
Figure 5.1 BJT test structure layout typically used for sparameter
measurement.
ADVANCED BIPOLAR
TRANSISTOR DESCRIPTION
PIECES DC & AC SIMULATIONS
Y PARAMETERS
CONVERT TO S PARAMETERS
NORMALIZE TO INTERCONNECT IMPEDANCE
CASCADE TEST STRUCTURE LAYOUT DISCONTINUITY
EFFECTS WITH INTRINSIC BJT RESPONSE MODELS
NORMALIZE TO 50Q S PARAMETER
MEASUREMENT ENVIRONMENT
S11 S12
2, S22
Figure 5.2 Flow chart outlining the calculation of the BJT test
structure measurement.
81
after normalization by the onchip interconnect admittance. Then the
BJT sparameters are cascaded with the sparameter responses of the BJT
layout elements (interconnect, bond pads and a bend in interconnect).
Figure 5.3 is a block diagram showing the order in which the
matrix models of the interconnect, bend in interconnect and bond pads
are cascaded. The BJT simulation (shown in the middle of the cascaded
matrices) is multiplied by the surrounding component matrices. In order
to do this, the sparameter data in each component matrix are converted
to readily cascaded high frequency Tparameters which are similar to
low frequency ABCD parameters [63]. The cascaded Tparameter matrices
are multiplied in order to model the BJT test structure response at the
bond pads and the result is converted back to sparameters.
The sparameters at the bond pads, which are normalized by the
onchip interconnect admittance, are converted to a 50 0 system
impedance that is common to sparameter instrumentation. This
conversion employs the following equations [63]:
(Z2 Z02) sinhyl
Sll = S22 = (5.5)
2ZZOcoshyl + (Z2+Z02)sinhyl
2ZZO
S21 = S21 = (5.6)
2ZZ0coshyl + (Z2+Z02)sinhTl
In these equations, Z is the transmission line impedance, ZO is the
system impedance (50 0), is the propagation constant (v a + jip), a
is the attenuation constant, 9p is the phase constant, and 1 is the
transmission line length.
Figure 5.3 Cascade of the BJT test structure components and PISCES
simulations for calculating sparameter response.
83
Analytical circuit models from the microwave literature are used
to represent the effects of IC interconnect and bends. The bond pads
are treated as a section of wide lumped admittance since a probe or
ball bond touches most of the bond pad area. The value of the bond pad
admittance was estimated by calculating the lumped admittance of a
short section of interconnect of the same dimensions as the bond pad.
The microwave model for the bend in the interconnect was taken from the
literature [63].
An IC interconnect crosssection with microstrip metal over Si02
over the Si substrate is used for the BJT test structure layout. Then a
novel twolayermetal IC interconnect is examined as a superior
interconnect alternate. Fig. 5.4 displays a crosssection of a metal
SiO2Si microstrip interconnect crosssection. In Fig. 5.4 the width of
the metal line is 20 pm, the thickness of the metal line is 1 pm, the
thickness of the Si02 layer is 1 pm, the thickness of the Si substrate
is 300 pm, and the resistivity of the Si substrate is 1 0cm.
The transmissionline model for this interconnect system has a
series impedance per unit length and a parallel admittance per unit
length as shown in Fig. 5.5. The series impedance, Z is composed of R,
the interconnectline resistance plus L, the interconnectline
inductance. The parallel admittance of the transmission line includes
the SiO2 capacitance, C1, in series with the parallel combination of
the Si capacitance, C2, and the Si conductance, G2. The IC interconnect
equations presented below are valid when the Si substrate layer is
moderately to lightly doped [65] [66]:
L ~o F(hl+h2)
(5.7)
