Group Title: Modeling and characterization of advanced bipolar transistors and interconnects for circuit simulation /
Title: Modeling and characterization of advanced bipolar transistors and interconnects for circuit simulation
CITATION PDF VIEWER THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00098065/00001
 Material Information
Title: Modeling and characterization of advanced bipolar transistors and interconnects for circuit simulation
Physical Description: xvi, 188 leaves : ill. ; 28 cm.
Language: English
Creator: Yuan, Jiann-Shiun, 1957-
Publication Date: 1988
Copyright Date: 1988
 Subjects
Subject: Bipolar transistors   ( lcsh )
Integrated circuits -- Computer simulation   ( lcsh )
Electrical Engineering thesis Ph. D
Dissertations, Academic -- Electrical Engineering -- UF
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1988.
Bibliography: Includes bibliographical references.
General Note: Typescript.
General Note: Vita.
Statement of Responsibility: by Jiann-Shiun Yuan.
 Record Information
Bibliographic ID: UF00098065
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 001115783
oclc - 19989966
notis - AFL2506

Downloads

This item has the following downloads:

PDF ( 6 MBs ) ( PDF )


Full Text











MODELING AND CHARACTERIZATION OF ADVANCED BIPOLAR
TRANSISTORS AND INTERCONNECTS FOR CIRCUIT SIMULATION
















BY

JIANN-SHIUN 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, Hui-Li, my parents and parents-

in-law 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 TWO-DIMENSIONAL COLLECTOR CURRENT SPREADING EFFECTS
IN QUASI-SATURATION ............ ......................... 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 PHYSICS-BASED CURRENT-DEPENDENT 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 S-PARAMETER MEASUREMENT PREDICTION USING A PHYSICAL DEVICE
SIMULATOR................................................. 75

5.1 Introduction........................................... 75
5.2 Bipolar Test Structure Modeling........................ 77
5.3 Bipolar Test Structure S-Parameter 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 Cross-section Analysis........111
6.4 Interconnect Model Verification.......................115
6.5 Mixed-Mode 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 TWO-DIMENSIONAL 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 User-Defined-Controlled-Sources.......................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 emitter-base junction gradient

CC Coupling coefficient for signal crosstalk

CjC collector-base junction capacitance

CJCO collector-base junction capacitance at VBE = 0 V

CJE emitter-base junction capacitance

CJEX extrinsic emitter-base junction capacitance

C'JE derivative of emitter-base junction capacitance

CJEO emitter-base junction capacitance at VBE = 0 V

CSCR space-charge 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 quasi-Fermi level

EFP hole quasi-Fermi level

Ei intrinsic Fermi level

Et trap energy level

f frequency

fBWM base width modulation factor

fC critical frequency in frequency-dependent permittivity

fCR(t) time-dependent 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 frequency-dependent permittivity
of coupled transmission lines

fPUSHOUT base pushout factor

fT bipolar transistor cut-off 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 quasi-neutral region

ICQNR collector current in the collector quasi-neutral region

ICSCR collector current in the collector space-charge region

IE emitter current

IEj emitter current in the partitioned region j

ILQNR lateral diffusion current in the collector quasi-neutral
region

ILSCR lateral diffusion current in the collector space-charge
region

IK knee current

IKR reverse knee current

IS collector current at VBE = 0 V

ISB pre-exponential base current

ISE emitter current at VBE = 0 V

LE emitter length

JC collector current density

JE(x) position-dependent 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 collector-base junction gradient coefficient

me emitter-base junction gradient coefficient

viii








NA acceptor doping density of p-type Si

Ng(x) base doping density at depth x

NBeff effective base doping density

ND donor doping density of n-type Si

NEPI epitaxial layer doping density

n nonideal base coefficient

nc nonideal collector-base emission coefficient

ne nonideal emitter-base 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 base-collector charge

QBCX extrinsic base-collector junction charge

QBCj base-collector charge in the partitioned region j

QBE base-emitter charge

QBEX base-emitter sidewall junction charge

QBEj base-emitter charge in the partitioned region j

QBO intrinsic base charge at VBE = 0 V

QQNR charge in the collector quasi-neutral region

QSCR charge in the collector space-charge 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 current-dependent epi-layer 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 base-collector voltage

VBC' base-collector junction voltage

VBCI base-collector voltage at the moving boundary between
the collector quasi-neutral region and the collector
space-charge region

VBCj base-collector charge in the partitioned region j

x









VBCO base-collector voltage at the metallurgical base-
collector region

VBE applied base-emitter voltage

VBEj base-emitter junction voltage in the partitioned region j

VBE' base-emitter junction voltage

Vbi junction built-in voltage

VCB applied collector-base voltage

VCE applied collector-emitter voltage

VDQNR lateral diffusion velocity in the collector quasi-neutral
region

VDSCR lateral diffusion velocity in the collector space-charge
region

VT thermal voltage kT/q

V* effective junction built-in voltage

AV ohmic drops in the emitter and base regions

Vpe even-mode phase velocity of propagated signal in
coupled transmission lines

Vpo odd-mode phase velocity of propagated signal in
coupled transmission lines

vs electron saturation velocity

WE emitter width

WQNR collector quasi-neutral region width

WSCR collector space-charge 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) frequency-dependent effective interconnect width

Z transmission line impedance

ZOe even-mode characteristic impedance of coupled
transmission line

Zo0 odd-mode characteristic impedance of coupled transmission
line

Zoe(f) frequency-dependent even-mode characteristic impedance
of coupled transmission line

Zo0(f) frequency-dependent odd-mode 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 collector-base junction potential

Oe emitter-base junction potential

r effective base doping gradient

rF bipolar transistor forward transit time

rn doping-dependent electron recombination lifetime

Tn0 electron recombination lifetime at low doping

7p doping-dependent hole recombination lifetime

Tp0 hole recombination lifetime at low doping

rQNR injection-level-dependent hole recombination lifetime in
the collector quasi-neutral region

TR bipolar transistor reverse transit time

PnO electron mobility

Pp(xy) position-dependent 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



JIANN-SHIUN YUAN



December 1988



Chairman: William R. Eisenstadt
Major Department: Electrical Engineering

This dissertation discusses the modeling of two-dimensional

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 quasi-saturation 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 physics-based current-dependent 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 current-dependent base

resistance model. Comparisons of the model predictions with

measurements and device simulations show excellent agreement.

Two-dimensional circuit modeling is developed for the nonuniform

current and charge distribution effects at the emitter-base sidewall

and under the emitter during switch-on transients. The charge and

current partitioning implemented in the bipolar transistor model treats

the transient emitter crowding and current-dependent 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 high-frequency small-signal s-parameter 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 three-port or

four-port network characterization and for predicting the high-

frequency small-signal 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 mixed-mode 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 computer-aided device and circuit design.
















CHAPTER ONE
INTRODUCTION

The bipolar transistor (BJT) circuit model implemented in SPICE

(the Gummel-Poon model) is derived based on one-dimensional 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

one-dimensional 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 two-dimensional device simulations, and,

second, to develop a representative two-dimensional circuit model for

circuit simulation. The model developed describes the nonuniform

current and charge distribution in the quasi-neutral 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 quasi-saturation 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 quasi-saturation

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 1-D-

collector and 2-D-collector 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 physics-based current-dependent base

resistance model for all levels of injection. The model includes the 1-

D and 2-D physical mechanisms of base width modulation, base

conductivity modulation, emitter current crowding, and base pushout; it

describes a current and voltage-dependent 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 current-dependent 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 current-dependent base resistance in a unified manner. The model

describes a nonuniform transient current and charge distribution under

the emitter and at the emitter-base sidewall. This current and charge

partitioning accurately represents the charge dynamics of the BJT

during switch-on transient. The model predictions shows good agreement

when compared with measurements and transient device simulations.

Chapter Five describes the s-parameter 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 y-parameters simulated in PISCES. The

terminal responses are obtained by multiplying the cascaded T-matrix

components representing the intrinsic BJT and extrinsic layout

parasitic effects. Two interconnect cross-sections 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 cross-section 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 mixed-mode

circuit simulation. The utility of the interconnect model is

demonstrated in a five-stage 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
TWO-DIMENSIONAL COLLECTOR CURRENT SPREADING EFFECTS IN QUASI-SATURATION

2.1 Introduction

Advanced self-aligned 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 circuit-simulator models such as the Gummel-Poon model in

SPICE2 [1]. Recently, a novel 3-D BJT circuit model has been developed

by using a 2-D 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 quasi-saturation effects have been investigated by numerous

authors for the past twenty years [3-8]. In general, two distinct

models (one-dimensional and two-dimensional) have been developed. In

the 1-D model, base push-out or quasi-saturation effect occurs when the

current density is high enough that the intrinsic base-collector

metallurgical junction becomes forward biased. Then carriers are

injected into the epitaxial collector [3], [8].

In the two-dimensional model, there is a maximum current density,

called space-charge-limited current flow, and any further increase in

collector current results in a 2-D base spreading [4], [5]. Detailed

explanations for the operating regions of each mechanism are shown in

[6-8].









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 push-out due to high

current in the collector is two-dimensional 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 Gummel-Poon model to

include quasi-saturation, or base push-out 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 current-induced

space-charge region in the epitaxial collector. The modeling in [11]

[12] is based a one-dimensional derivation and does not represent the

two-dimensional currents in the collector. Thus, this modeling can

overestimate quasi-saturation effects [9], [10].

In this chapter, the model in [12] is extended to take into

account the multidimensional collector-current-spreading mechanism that

occurs in quasi-saturation. The extension is facilitated by using the

two-dimensional device simulator PISCES [14) to perform simulations of

the advanced BJT's (Sec. 2.2). The PISCES simulations reveal the

physical mechanism producing 2-D 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 heavy-doping effects (bandgap

narrowing, Auger recombination), doping and field dependent carrier

mobilities, and Shockley-Read-Hall (SRH) recombination. A generic

advanced BJT cross-section was constructed by incorporating common

features of many state-of-the-art transistors reported in the

literature [16], [17].

The advanced bipolar transistor is illustrated in Fig. 2.1, where

only half cross-section and doping profile need to be simulated due to

the cross-section's symmetry. The emitter and base doping profiles and

the emitter-base 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 side-collector 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 cross-section of an advanced bipolar
transistor used for multidimensional current studies.
Dimensions of the cross-section 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 electron-current-density-vector plot, Jn, of

the advanced BJT biased at applied collector-emitter voltage, VCE = 2.0

V and applied base-emitter voltage, VBE = 0.9 V (IC = 0.5 mA/pm). In

the quasi-saturation region depicted in Fig. 2.2, excess carriers are

injected into the epitaxial collector (base push-out). 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 current-density 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 emitter-base junction because of the position-

dependent doping density at these regions. The magnitudes of the

current-density 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 right-side of the BJT. Figure 2.3 shows a

BJT simulation from PISCES of the current-density vectors for a right-

side-collector 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 current-density 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 right-side collector contact

only controls the current flow in the buried-collector region, and that

it does not significantly affect the lateral flow. Thus, there is no

significant drift component in the collector spreading mechanism.

A 1-D-collector transistor was simulated in order to isolate the

effects of collector spreading in the advanced BJT operation. This 1-D-

collector BJT, shown in Fig. 2.4, has the same emitter and base regions

as the 2-D BJT in Fig. 2.1; however, below the extrinsic base region of

the 1-D-collector transistor, the epitaxial and buried-collector

regions are replaced with SiO2. This forces the collector current to

flow solely in the vertical direction below the intrinsic base, hence

the name l-D-collector transistor.

Comparing the current gain, f and cut-off frequency, fT of the 2-D

BJT to those of the 1-D-collector BJT at high currents is one of the

keys to understanding the role of collector current-spreading. The 2-D

BJT exhibits a larger p (see Fig. 2.5) and fT than the 1-D-collector

BJT as both transistors are driven further into saturation [10].

Figure 2.6 indicates how quasi-saturation 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 2-D BJT and l-D-collector 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 1-D BJT displays significantly more base widening than

the 2-D-collector BJT, which results in an enhanced 2-D-BJT 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 cross-section designed
with a 1-D-collector. This transistor is used to isolate
the 2-D 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 2-D BJT and the dashed line represents
the 1-D-collector 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 2-D BJT and the dashed line
represents the l-D-collector BJT.












at high currents. The reduced quasi-saturation effects in 2-D-BJT 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 semi-empirical 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 charge-based 1-D BJT model [12] to yield

a quasi-2-D model. The 1-D BJT model accounts for quasi-saturation

ohmicc and non-ohmic) by describing the collector current in terms of

the quasi-Fermi potentials at the boundaries of the epitaxial collector

which, in conjunction with the base transport, characterizes

IC(VBE,VBC). Since this charge-based 1-D model correctly accounts for

the 1-D BJT physics [12] it can be modified to incorporate the

multidimensional current effects in the advanced BJT.

In the formulation of the 2-D model, we estimate the lateral

diffusion currents in the collector quasi-neutral region and the

collector space-charge region (ILQNR and ILSCR) as a function of the

normalized 1-D-collector quasi-neutral region charge and space-charge

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 quasi-neutral base, collector

transport currents, ICQNB and ILQNB in the collector quasi-neutral

region, and ICSCR and ILSCR in the collector space-charge region. In

Fig. 2.7 a moving boundary between collector quasi-neutral region and

collector space-charge region defines the collector quasi-neutral

region width, WQNR and the collector space-charge region width, WSCR

(WSCR WEPI-WQNR, and WEPI is the epitaxial collector width).

The following equations incorporate the collector-spreading

mechanism into the 1-D model and make it a 2-D 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) VBCO-VBCI
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 quasi-Fermi level, EFP is the hole quasi-

Fermi level, VBE' is the base-emitter junction voltage, and IS, qb, C2,

and ne retain their meanings given in the Gummel-Poon model [1].

Figure 2.8 displays the overall SPICE model topology of the 2-D

model for collector spreading. Two new current sources which are

highlighted in the figure have been added to the 1-D-BJT model [12] to

account for the lateral diffusion currents in the epitaxial collector.

Note that, since the 2-D model modifies the 1-D BJT quasi-static charge

in the collector region, the transient currents dQQNR/dt and dQSCR/dt

are effectively refined in terms of this new quasi-static charge

distribution as Eqs. (2.1)-(2.7) are solved simultaneously. A l-D BJT

model can not represent this collector charge redistribution [12] and

gives erroneous estimates of the BJT transient performance [10]. In

contrast, the 2-D BJT circuit model correctly accounts for the charge










21

dynamics in the collector and the moving boundary between the quasi-

neutral region and the space-charge 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 quasi-neutral collector width,

WQNR(IC,VCE). A component of base recombination current, QQNR/rQNR due

to a finite recombination lifetime, rQNR in the collector quasi-neutral

region [20] is also included in the base current, IB. The injection-

level-dependent 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 user-defined controlled-sources (UDCS's) available

in SLICE, the Harris Corporation enhanced version of SPICE. In the

SPICE circuit analysis, UDCS's are user-defined 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 quasi-static stored charges

thus properly represent the distributed charging currents. Also the

inherent nonreciprocal transcapacitance of the BJT are simulated

directly, without the use of equivalent-circuit capacitors [23].

Test devices representative of the advanced BJT were used to

verify the model and to define a parameter-extraction 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 2-D simulation (WE

SLE) are:



AWE [Jn(x,y=O) + Jn(x,y-WE)] 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,y-WE)] dx
JWQNR

[WE WEPI
2 JE q[n(x,y) NEPI] dxdy
J0 JWQNR


(2.11)









24

where n is the position-dependent electron carrier concentration, the x

axis is in the vertical direction, the y axis is in the horizontal

direction, y 0 stands for the left-side emitter edge, and y WE

stands for the right-side 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 tune-up 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 1-D [12] and 2-D models are compared with

measurements in Fig. 2.9. In this figure, the solid line represents

measurements, the symbol x's represent 2-D model simulations, and the

circles represent l-D model simulations. It is clear that 1-D model

overestimates quasi-saturation effects. This is seen in Fig. 2.9 at

high IC and low VCE, where non-ohmic quasi-saturation 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 "boot-shaped" 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 1-D 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 2-D model
simulations, and "0" represents 1-D 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 2-D model
simulations, and "0" represents l-D model simulations.


Figure 2.10












significantly from measurements in quasi-saturation, especially with

the small emitter size BJT.

The 2-D and 1-D 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 2-D and 1-D 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 2-D 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 2-D model simulations of an inverter show good

agreement with PISCES numerical results (circles in Fig. 2.10) in

transient operation which indicates that 2-D 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 quasi-saturation 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 10-9s)





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 2-D model (solid line), 1-D model (dashed line), and
PISCES simulation (circles).












equations describing base and collector transport. Two lateral

diffusion current sources were added to the l-D 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 quasi-saturation 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
PHYSICS-BASED CURRENT-DEPENDENT 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 Gummel-Poon 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 [30-34] 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 base-emitter

voltages, the current-dependent 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 physics-based 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 2-D device simulations (Sec. 3.4).

In order to illustrate its usefulness, the RB model is also implemented

in the user-defined 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 (1-D and 2-D)

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 [33-36]. 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+-p-n-n+ bipolar

transistor. Using conventional terminology, the base width, Xg is the

vertical dimension between the emitter-base space-charge region (SCR)

and the collector-base space-charge region. The emitter length, LE is

defined as the dimension pointing into the figure. The cross-sectional

area of the base (perpendicular to the base current path) is determined

by the product of the quasi-neutral base width, XB and LE.

Since RBI is inversely proportional to the cross-sectional area

of the base, the modulation of the emitter-base or the collector-base

space-charge region will change the magnitude of RgB. For example,

assume that the emitter-base junction is forward-biased and there is a

constant collector-base applied voltage, VCB. Then XB is modulated by

the moving edge of the emitter-base space-charge region when VBE

changes. As VBE increases, the emitter-base space-charge 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 quasi-neutral base charge can be modeled as

QBO/(QBO+AQB) where QBO is the zero-biased 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 space-charge
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 base-emitter junction voltage (VBE'= the

quasi-Fermi level separation between the edges of the emitter-base

space-charge region).

To find AQB, a recently reported comprehensive l-D model for the

emitter-base 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

emitter-base junction impurity gradient, Vbi is the built-in 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 built-in voltage.

For a linearly-graded 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) [1-2(VBE'-Vl)/(Vl-V2)] [(VBE'-V2)/(Vl-V2)12

+ CJE(V2) [1-2(VBE'-V2)/(V2-Vl)] [(VBE'-Vl)/(V2-Vl)]2

+ C'JE(V1) (VBE'-Vl) [(VBE'-V2)/(Vl-V2)]2

+ C'JE(V2) (VBE'-V2) [(VBE'-Vl)/(V2-Vl)12

for Vbi 0.3 VI < VBE' < Vbi 7VT = V2 (3.5)


Figure 3.2 shows a plot of a base-width modulation QBO/(QBO+AQB)

versus VBE'. We define a base-width 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 quasi-neutral region [38]. The

monotonic decrease of fBWM at low VBE' is due to the contraction of the

emitter-base SCR width shrinking. For VBE' above 0.8 V, the fBWM slope

is zero because the emitter-base SCR width can not contract further.

The base width modulation due to the base-collector SCR edge variation

in the base is neglected because modern BJT's have base doping density

much higher than their epi-layer 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 (n-p-n) 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 base-width-modulation factor, fBWM versus the
base-emitter junction voltage, VBE'.










(2+Al+no)A2n0
6QB QBO (3.6)
(2+AI)A2/A3+n0


where A1=2[exp(r)-l]/[rexp(r)], A2-1/A1, A3-exp[(r-l)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 emitter-base space-charge region. Note that no is

determined by no(l+no)-ni2/N2(0)exp(VBE'/VT)

The simulated result of base-conductivity modulation versus VBE'

is shown in Fig. 3.3. We define a base-conductivity-modulation 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 quasi-neutral 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 emitter-base 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 two-dimensional 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 epi-layer depth, XEpI.










































0.2 0.4 0.6 0.8


VBE (v)


Figure 3.3 Plot of the base-conductivity-modulation factor, fCM
versus the base-emitter 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 emitter-base 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 epi-layer. The peak dopings are 2 x 1020

cm-3, 8 x 1017 cm-3, and 2 x 1016 cm-3 in the emitter, intrinsic base,

and epi-layer, respectively. The non-uniform 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 non-uniform emitter

current caused by lateral ohmic drops, can not be solved analytically

[40-42], [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 emitter-current density

at the different emitter sections including the ohmic drops in the

quasi-neutral 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
quasi-neutral base and emitter regions.








42

IEO ISE/5 exp[(VBE-IBORBO-IEOREO)/VT] (3.8)


IE1 ISE/5 exp[(VBE-IBBORBO-IBRBl-IElREl)/VT] (3.9)


IE2 = ISE/5 exp[(VBE-IBORBO-IBlRB1-IB2RB2-IE2RE2)/VT] (3.10)


IE3 ISE/5 exp[(VBE-IBORB0-1BIRBl-IB2RB2-IB3RB3-1E3RE3)/VT]
(3.11)

IE4 ISE/5 exp[(VBE-IBORBO-IBIRB1-IB2RB2-IB3RB3-IB4RB4

-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(j-1,2,3,4) = RBI/4,

REj(j-0,1,2,3,4) 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 single-base-

contact BJT. The method also applies to a double-base-contact 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 trade-off 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
base-emitter applied voltage, VBE with RRI 480 0, RE -
20 0, ISE 10 x 10-18 A, ISB 6 x 10-22 A for a single-
base-contact BJT. The solid line represents the emitter
crowding without base-conductivity 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+-p-n-n+ BJT at the emitter-collector 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 current-induced 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 epitaxial-collector width between the base-collector

junction and collector high-low 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 base-widening is shown in

the plot in Fig. 3.8. We define a base-pushout 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 -I-T- I I I I I --!-1-1-

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 epi-layer doping density, Nepi 2 x 1016
cm, the epitaxial collector thickness, Wepi 0.5 pm,
and the collector-base 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 --/2-1 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

cm-3, WEPI 0.5 pm, and VCB 2.0 V, the dashed line represents BJT

base pushout with NEPI 0.8 x 1016 cm-3, WEPI 0.5 pm, and VCB = 2.0

V, and the dotted and dashed line represents BJT base pushout with NEPI

- 2 x 1016 cm-3, WEPI = 0.5 pm, and VCB = 3.0 V. The base widening is

more significant when the epi-layer doping density is low, the width of

the epitaxial collector is large, or the collector-base applied voltage

is small. The base-widening increases dramatically for BJT operated at

high current densities and results in a very low fPUSHOUT-



3.2.4 The Coupling Effects

The emitter-crowding 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 emitter-crowding 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[(VBE-IBORBO-IEOREO)/VT] (3.15)


IEl ISE/5 exp[(VBE-IBORBO-IBlRBlfc-IE1RE1)/VT] (3.16)


IE2 ISE/5 exp[(VBE-IBORBO-BIlRBlfc-IB2RB2fc-IE2RE2)/VT] (3.17)


IE3 ISE/5 exp[(VBE-IBORBO^BlRBfc^-B2RB2fc-B3RB3fc

-IE3RE3)/VT] (3.18)


IE4 = ISE/5 exp[(VBE-IBORBO-1BlRBlfc-IB2RB2fc-B3RB3f

-IB4RB4fc-IE4RE4)/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 current-dependent 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 current-dependent 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

emitter-base space-charge 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

quasi-neutral base and emitter regions can be defined


IBideal ISB exp(qVBE/nkT) (3.21)


where ISB is the pre-exponential 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(VBE-AV)/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 base-emitter
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

excitation-dependent 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 position-dependent

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 space-charge-region edges in the PISCES

simulations.



3.5 Application

In order to demonstrate the utility of the current-dependent base

resistance model, the present model was implemented in SLICE using

user-defined subroutines [10]. Transient simulations from Gummel-Poon

model with current-dependent 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 large-signal

transition. These simulations indicate that the existing constant RB

model is inadequate for predicting the transient performance of

advanced bipolar technologies and the current-dependent 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 10-s)


Figure 3.10


Transient responses from Gummel-Poon model with constant
base resistance model (dashed line) and current-depend-
ent base resistance model (solid line) for an emitter-
coupled logic inverter with an emitter follower.









54

3.6 Summary and Discussion

A physics-based current-dependent 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 two-dimensional

device simulator PISCES, and from measurement data show excellent

agreement.

We have implemented this physics-based base resistance model in

SLICE/SPICE using user-defined subroutines. For an emitter-coupled

logic circuit, the Gummel-Poon 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 integrated-circuit simulation in

advanced IC technologies.















CHAPTER FOUR
CIRCUIT MODELING FOR TRANSIENT EMITTER CROWDING AND
TWO-DIMENSIONAL CURRENT AND CHARGE DISTRIBUTION EFFECTS

4.1 Introduction

Today's advanced bipolar transistors, resulting from double

polysilicon self-aligned 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 quasi-2-D model,

useful for quasi-saturation, to account for the two-dimensional

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 switch-on transient.

The emitter current crowding and sidewall injection effects have

been investigated by numerous authors [40-45], [47-55]. 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 non-negligible compared to the base ohmic

drop, IBRB. It is the author's experience that neither the distributed

model [42] nor the two-lump empirical models [48] [49] are optimal for

parameter extraction and circuit simulation in terms of CPU time. In

addition, emitter-base sidewall injection and its junction charge









56

storage effects, usually neglected in the lumped circuit models, can be

quite significant in small emitter-width 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 emitter-base

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 emitter-base 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

switch-on 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

time-dependent 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 time-dependent emitter current density, x

is the horizontal direction (x 0 is the emitter edge), t is time, and

V is the position and time-dependent 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/2-1
--JE(0,t)+JE(WE,t)+4 X JE[(2j-l)WE/n,t]+2 X JE(2jWE/n,t))
3n j-1 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 three-dimensional bipolar structure

shown in Fig. 3.1. The concept of charge-based model was developed by

Jeong and Fossum [12]. This work extends the development of Chapter 3

using this charge-based concept for regional BJT partitioning. The

time-dependent 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(k-1)(t)RBk (4.4)
k=l



VBCj(t) VBC(t) IB(t)RBX IC(t)RC IBI(k-1)(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 Gummel-Poon model.

The regional base-emitter 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 voltage-dependent emitter-base junction capacitance,

AE is the emitter area, and TF is the forward transit time. Similarly,

the regional base-collector 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

collector-base junction capacitance, in which the collector-base









59

junction is reverse-biased when the BJT is at the forward active mode.

When emitter crowding occurs, however, the junction voltage across the

emitter-base space-charge region is usually high enough to invalidate

the depletion approximation for finding the emitter-base junction

capacitance. A recently developed junction capacitance model [37] which

takes into account the free carrier charges in the space-charge region

in high forward bias is therefore used in this circuit model to

determine emitter-base charging currents. The biased-dependent CJE

model can be found in Section 3.2.1.

Through the regional voltage drops which define the position and

time-dependent 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

time-dependent 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 charge-based 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)RBX-IE(t)RE
IC = fCR {ISexp[]
VT

VBE(t)-IB(t)RBX-IE(t)RE
+ C21Sexp[ ]) (4.7)
neVT































dOBC2 V = VBO- V
di VBE1 = VB;. VE
RB RB 81 RB2 B VBE2=VB2-VE


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 charge-based 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 time-dependent 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 two-dimensional 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 emitter-base 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 emitter-base 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 epi-layer depth. The doping profiles are

assumed Gaussian for the emitter, Gaussian for the base, and uniform

for the epi-layer. 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 cm-3, 8 x 1017 cm-3, and 2 x 1016

cm-3 in the emitter, intrinsic base, and epi-layer, respectively. The

physical mechanisms used in PISCES simulations include Shockley-Read-

Hall recombination, Auger recombination, bandgap narrowing, and doping

and field-dependent mobility.

PISCES 2-D simulation readily shows the multidimensional current

paths as illustrated in Fig. 4.2. The figure displays the electron-

current-density and hole-current-density 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 emitter-base junction sidewall. Simulation of the current

gain versus emitter width also indicates the significance of the

sidewall injection current and the emitter-width 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 2-D-BJT simulations

indicate the peak-current 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 emitter-base

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 electron-current-density 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 hole-current-density 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 base-width modulation at the emitter-base junction; this effect is

significant in narrow-base BJT's [56].

Based on device simulation and analytical approximation [52]

[53], the emitter-base 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 = IB-IBI) is significant.

As a first-order approximation, the collector current flow out of

the emitter-base sidewall can be neglected [52]. Thus the charge stored

at the emitter-base 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 built-in voltage V*.

Similarly, the extrinsic base-collector junction charge, QBCX

associated with the collector-base junction outside the intrinsic

emitter region is (AC-AE)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-

defined-controlled-sources in SLICE. In SLICE/SPICE circuit analysis,

UDCS's are user-defined 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 quasi-static 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 parameter-extraction 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 Gummel-Poon 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 quasi-saturation. The simulated results

from the present model and the Gummel-Poon model show excellent

agreement with the experimental data at low currents; however, the

simulated results from the Gummel-Poon 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 emitter-base junction at various times in the PISCES

transient simulation. In Fig. 4.5 emitter crowding is very significant

during the initial turn-on 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















10-2


10"3 IC


10-4


10-5


10-6


10- 6


10.8


108
10-9 I \ -I \ I I
0.6 0.7 0.8 0.9 1.
VBE (V)




Figure 4.4 Log I versus base-emitter applied voltage, VBE. The solid
line represents the present model simulation, the dashed
line represents the Gummel-Poon 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 emitter-base 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 Gummel-Poon model and

the present model) and PISCES. The predictions of the present model are

in good agreement with PISCES results; however, the Gummel-Poon model

shows a slower turn-on transient and a large propagation delay. The

discrepancy between the Gummel-Poon 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 steady-state

in the Gummel-Poon 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, emitter-base 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 emitter-base sidewall and under the

emitter in a unified manner. Furthermore, second order effects such as

base-width 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 single-transistor
inverter. The solid line represents the present model
simulation, the dashed line represents the Gummel-Poon
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 computer-aided

circuit design and process sensitivity diagnosis.















CHAPTER FIVE
S-PARAMETER 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 s-parameter

equipment. State of the art probes, and proper calibration technique

have proven essential in the measurement of s-parameters of single BJT

test structure [57]. However, s-parameter measurements cannot predict

the test-structure response of new BJT technologies in the "on paper"

development stage.

A new method of predicting s-parameter test structure response

from physical device simulator output has been developed. This

predicted s-parameter response is particularly useful for examining the

performance of conceptual designs of submicron BJT technologies.

Submicrometer BJT's have significant dc, transient and small-signal

multidimensional effects which include collector current spreading,

emitter crowding, and emitter-base sidewall injection; these effects

have been evaluated by a 2-D physical device simulator previously [58]

[59] and are discussed in Chapters 2, 3, and 4. The new method of

predicting s-parameter response provides a direct comparison between 2-

D BJT simulations and measurement data from BJT test structures.

Important uses of this simulated s-parameter response also

include verifying BJT test structure s-parameter 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 3-port BJT,

three sets of 2-port measurements must be taken, generally requiring 3

separate test structures. Since the 3-port measurement is time

consuming and IC layout area intensive, often only a single 2-port BJT

measurement is made. The s-parameter prediction technique can

supplement an existing 2-port test structure measurement so that a

complete 3-port BJT characterization is possible. The simulated s-

parameter response also can be extended beyond s-parameter

instrumentation frequency ranges.

This modeling technique is demonstrated using submicrometer BJT

simulations from the PISCES 2-D physical device simulator [60]. Other

small-signal device simulations or characterizations [61) could be

substituted for the PISCES data. Simulated small-signal BJT y-parameter

measurements are converted (via software) to s-parameters. S-parameter

measurements are preferred for high-frequency characterizations and

have been demonstrated on-chip at frequencies up to 50 GHz [62]. In

addition, s-parameter best represent a distributed circuit with high

frequency discontinuities [63], such as a BJT IC test structure

measured at microwave frequencies. The BJT s-parameter 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 2-D device simulation output

in order to predict test structure s-parameter response. In addition, a

novel two-layer metal-based 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 s-parameter measurements or evaluate the accuracy

of s-parameter calibration algorithms.



5.2 Bipolar Test Structure Modeling

In order to demonstrate the utility of the bipolar test structure

modeling, an n-p-n BJT small-signal 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 emitter-depth, a 0.2 pm base-depth, and a

0.8 pm epitaxial collector-depth shown in Fig. 2.1.1. The doping

profiles are shown in Fig. 2.1.2. Small-signal parameters from l-D, 2-

D, or 3-D simulator may be used for input in this test structure

modeling technique.

A 2-D simulation typically provides BJT y-parameter 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 y-parameters are

normalized by the distributed circuit admittance (frequency dependent









78

interconnect admittance) and then converted to s-parameters. The y-

parameter to s-parameter conversion equations are [64]:


(1-yll)(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)(1-y22) + Y12Y21
s22 = (5.4)
(1+yll)(l+y22) Y12Y21


In order to predict the s-parameter 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 s-parameter 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 y-parameters. These y-parameters are converted to s-parameters




























































Figure 5.1 BJT test structure layout typically used for s-parameter
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 on-chip interconnect admittance. Then the

BJT s-parameters are cascaded with the s-parameter 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 s-parameter data in each component matrix are converted

to readily cascaded high frequency T-parameters which are similar to

low frequency ABCD parameters [63]. The cascaded T-parameter matrices

are multiplied in order to model the BJT test structure response at the

bond pads and the result is converted back to s-parameters.

The s-parameters at the bond pads, which are normalized by the

on-chip interconnect admittance, are converted to a 50 0 system

impedance that is common to s-parameter 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 s-parameter 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 cross-section with microstrip metal over Si02

over the Si substrate is used for the BJT test structure layout. Then a

novel two-layer-metal IC interconnect is examined as a superior

interconnect alternate. Fig. 5.4 displays a cross-section of a metal-

SiO2-Si microstrip interconnect cross-section. 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 0-cm.

The transmission-line 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 interconnect-line resistance plus L, the interconnect-line

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)




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs