a genetic algorithm for deep-submicron ...mail.ymlab.org/~ckchen/resource/ckchen_thesis.pdfa genetic...

A GENETIC ALGORITHM FOR DEEP-SUBMICRON

MOSFET PARAMETERS EXTRACTION AND

SIMULATION

A THESIS

SUBMITTED TO THE DEPARTMENT OF

COMPUTER AND INFORMATION SCIENCE

AND THE COMMITTEE ON GRADUATE STUDIES OF

CHIAO TUNG UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

MASTER

Cheng-Kai Chen

July 2002

c© Copyright by Cheng-Kai Chen 2002

All Rights Reserved

ii

I certify that I have read this dissertation and that in my opinion it is fully adequate,

in scope and in quality, as a dissertation for the degree of master.

Chuen-Tsai Sun(Principal Advisor)

I certify that I have read this dissertation and that in my opinion it is fully adequate,

in scope and in quality, as a dissertation for the degree of master.

Yiming Li(Associate Advisor)

Approved for the University Committee on Graduate Studies:

iii

Abstract

G enetic algorithm is a stochastic-based optimization strategy with its randomly but

systematically search strategy which is usually applied for solving complex prob-

lem, such as simulated model parameters extraction. To characterize the properties of

MOSFET accurately, various compact models have been proposed for deep-submicron and

nanoscale MOSFET device simulation. Each model consists of diverse governing equa-

tions and parameters. It leads to a multivariable optimization problem to be solved and

extracted efficiently for the device applications. Different approaches, for instance the

direct method and numerical method have been applied to extract and optimize the model

parameters. In this work we present a unified multiobject evolutionary approach for BSIM3

MOSFET model parameter extraction. In contract to conventional time-consuming large-

scale approach, our genetic algorithm includes: (1) a physical-based weight function; (2)

floating-point operators; and (3) dynamic mutation techniques, and solves the problem ef-

ficiently. The proposed method outputs a set of optimal parameters for device simulation;

iv

in our simulation experiences, this method is stable and accurate. Comprehensive compar-

isons among models are reported for the parameters sensitivity test. Simulations and mea-

surements for sub-micron MOSFETs compact models are examined to show the accuracy

and robustness of the method. The developed CAD tool can be further applied to extract

nanoscale MOSFTEs parameters for advanced VLSI circuit design and SOC applications.

v

Acknowledgments

I would like to express my deepest gratitude to my advisors Dr. Chuen-Tsai Sun of

Department of Computer and Information Science, and Dr. Yiming Li of National

Nano Device Laboratories and Microelectronics and Information Systems Research Center

in National Chiao-Tung University, for their patient guidance, encouragement and valuable

discussions during the course of this study. In addition, I would like to express my appre-

ciation to my examination committees Dr. Jyh-Shing Roger Jang, Dr. Yu-Tai Ching, and

Dr. Tien Sheng Chao for taking the time to read this thesis.

I further wish to acknowledge the support from National Nano Device Laboratories, Learn-

ing Laboratory, and Parallel and Scientific Computing Laboratory. I would like to thank

to all my friends especially Pu Chen, Chuan-Sheng Wang, Yen-Yu Cho, Hsiao-Mei Lu,

Shao-Ming Yu, Hao-Yun Hung, Zhau-Wei Huang, and Yan-Liang Lin.

And lastly, I would like to dedicate this thesis to my parents and family for their support

and everlasting love.

vi

Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1 Introduction 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Semiconductor Device Simulation . . . . . . . . . . . . . . . . . . 3

1.2.2 Model Parameters Extraction . . . . . . . . . . . . . . . . . . . . . 4

1.2.3 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.4 Historical Development . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.4 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

viii

CONTENTS ix

2 MOSFET Compact Models and Parameter Extraction Methods 9

2.1 The MOSFET BSIM3 Compact Model . . . . . . . . . . . . . . . . . . . . 10

2.1.1 A Physical-Based Derivation of the Unified I-V Model . . . . . . . 11

2.1.2 A Classification of Extracted Parameters . . . . . . . . . . . . . . 16

2.2 Conventional Parameters Extraction Methods . . . . . . . . . . . . . . . . 17

3 Genetic Algorithm for Deep-Submicron MOSFET Simulation 19

3.1 Problem Definition and Analysis . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 Evolutionary Computation Steps . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.1 Gene Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.2 Competition Procedure . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2.3 Selection Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.4 Recombination Process . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.5 Mutation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.2.6 Termination Criterion . . . . . . . . . . . . . . . . . . . . . . . . . 29

4 Simulation Results and Discussion 30

4.1 Accuracy and Efficiency of the Developed BSIM3v3 Simulator and Optimizer 31

4.2 Effects of Different Weight Functions . . . . . . . . . . . . . . . . . . . . 33

4.3 The Uniqueness of Extracted Parameters . . . . . . . . . . . . . . . . . . . 34

4.4 The Sensitivities of the Extracted Parameters . . . . . . . . . . . . . . . . 35

CONTENTS x

5 Conclusions 37

5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.2 Suggestions and Future Works . . . . . . . . . . . . . . . . . . . . . . . . 38

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

Appendix A

The EKV I-V model in DC simulation. . . . . . . . . . . . . . . . . . . . . . . . 48

Appendix B

The MosM9 I-V model in DC simulation. . . . . . . . . . . . . . . . . . . . . . 52

Appendix C

The BSIM3v3 I-V model in DC simulation. . . . . . . . . . . . . . . . . . . . . 55

Appendix D

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Appendix E

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Appendix F

VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

List of Tables

D.1 The descriptions of each term in Idso(vdseff) in Eq. (2.3). . . . . . . . . . 59

D.2 The descriptions of each term in Vdseff in Eq. (2.4). . . . . . . . . . . . . . 60

D.3 The descriptions of each term in VASCBE in Eq. (2.5). . . . . . . . . . . . . 61

D.4 The descriptions of each term in Rds in Eq. (2.6). . . . . . . . . . . . . . . 62

D.5 The descriptions of each term in Vth in Eq. (2.7). . . . . . . . . . . . . . . 63

D.6 The descriptions of each term in Vth in Eq. (2.7). . . . . . . . . . . . . . . 64

D.7 The descriptions of each term in µeff in Eqs. (2.8-2.10). . . . . . . . . . . 65

D.8 The descriptions of each term in Abulk in Eq. (2.13). . . . . . . . . . . . . . 66

D.9 The descriptions of each term in dW , dW′, and dL in Eqs. (2.17-2.19). . . 67

D.10 A list of extracted parameters in BSIM3v3 DC simulation. . . . . . . . . . 68

D.11 A classification of BSIM3v3 model parameters in DC simulation. . . . . . 69

D.12 Comparisons between GA and traditional methods for solving optimization

problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

xi

LIST OF TABLES xii

D.13 A partial list (1) of parameters for BSIM3v3 model (with its range and

resolution) to be extracted. . . . . . . . . . . . . . . . . . . . . . . . . . . 71

D.14 A partial list (2) of parameters for BSIM3v3 model (with its range and

resolution) to be extracted. . . . . . . . . . . . . . . . . . . . . . . . . . . 72

D.15 The proceed generations and computational time for BSIM3v3 single I-V

curve parameters extraction and optimization. . . . . . . . . . . . . . . . . 73

D.16 The proceed generations and computational time for BSIM3v3 multiple

I-V curves parameters extraction and optimization. . . . . . . . . . . . . . 74

D.17 The comparison of the error norms between different weight functions for

BSIM3v3 I-V curves evolution (with the same random seed for ten best runs). 75

D.18 Number of proceed generations and error norms for each sub-experiment

in sensitivity test (Only one parameters set is allowed to be change). . . . . 76

D.19 Number of proceed generations and error norms for each sub-experiment in

sensitivity test (Two parameters sets are allowed to be change in the same

time). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

List of Figures

E.1 A symbol of MOSFET in VLSI circuit . . . . . . . . . . . . . . . . . . . . 79

E.2 A BSIM3v3 MOSFET equivalent circuit . . . . . . . . . . . . . . . . . . . 80

E.3 The comparison between SPICE results and our simulated results for ter-

minal IDS-VGS characteristics with the same construction parameters for

0.25 µm N-MOSFET device . . . . . . . . . . . . . . . . . . . . . . . . . 81

E.4 The comparison between SPICE results and our simulated results for ter-

minal IDS-VBS characteristics with the same construction parameters for

0.25 µm N-MOSFET device . . . . . . . . . . . . . . . . . . . . . . . . . 82

E.5 A flowchart of the proposed genetic algorithm for deep-submicron MOS-

FETs simulation and optimization . . . . . . . . . . . . . . . . . . . . . . 83

E.6 The shape plot of the relationship between diversity and mutation rate . . . 84

E.7 The comparison between measured curve and simulated evolutionary curve

for 0.25 µm N-MOSFET device . . . . . . . . . . . . . . . . . . . . . . . 85

xiii

LIST OF FIGURES xiv

E.8 A zoom-in view of discrepancies for measured and simulated I-V points

(VDS = 0.2 ∼ 0.6) for single I-V curve evolution . . . . . . . . . . . . . . 86





E.11 The comparison between measured and simulated I-V curves for BSIM3v3

model extracted parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 89


(VDS = 0.2 ∼ 0.6) for multiple I-V curves evolution . . . . . . . . . . . . 90





E.15 BSIM3v3 model simulated results for GA w/ or w/o apply weight function . 93

E.16 Convergent behaviors of evolutionary parameters extraction with different

weight functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

E.17 The extracted values of BSIM3v3 general parameters in optimal 5 runs for

I-V curves optimization. Each parameter is normalized to a limited range . 95

LIST OF FIGURES xv

E.18 The extracted values of BSIM3v3 threshold voltage parameters in optimal

5 runs for I-V curves optimization. Each parameter is normalized to a

limited range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

E.19 The extracted values of BSIM3v3 mobility parameters in optimal 5 runs

for I-V curves optimization. Each parameter is normalized to a limited range 97

E.20 The extracted values of BSIM3v3 subthreshold current parameters in opti-

mal 5 runs for I-V curves optimization. Each parameter is normalized to a

limited range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

E.21 The extracted values of BSIM3v3 Rout parameters in optimal 5 runs for

I-V curves optimization. Each parameter is normalized to a limited range . 99

E.22 A comparison of convergent behaviors between different varying parame-

ters categories (Only one parameters set is allowed to be change) . . . . . . 100

E.23 A comparison of convergent behaviors between different varying parame-

ters categories (Two parameters sets are allowed to be change in the same

time) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Chapter 1

Introduction

I n the design of VLSI circuit, the computer aided design (CAD) tools for device simula-

tion and optimization have been of great interested in recent years. As the dimensions

of devices continue to shrink, the demand of CAD tools for analyzing the semiconduc-

tor device is necessary and urgent. In general speaking, the technology CAD (TCAD)

tools include at least two parts, semiconductor device simulator and device characteristic

optimizer. Both of them play important roles in VLSI circuit design. However, a compre-

hensive TCAD for deep-submicron device simulation and optimization encountered many

difficulties in practical applications. In this work, an evolutionary architecture for MOS-

FET compact model simulation and I-V characteristic optimization will be developed and

presented.

1

1.1 : Motivation 2

This chapter is organized as follows. First of all, the motivation of the study will be in-

troduced, then the basic concepts for semiconductor device simulation and I-V curves

optimization will be studied. Followed by reviews of historical developments for device

characteristics optimization. In the fourth part, the aim of this work will also be given and

discussed. Finally, the descriptions of each chapter in this thesis will be described in detail.

1.1 Motivation

In semiconductor device simulation, the setting for each construction parameter is a com-

plicated problem. For any semiconductor device simulator, it works as well just when the

proper construction parameters are set. In other word, both of an accurate simulator and

suitable parameters set are important issues for VLSI circuit design. There are many re-

searches and publications for model parameters extraction have been proposed in the last

decade. However, most of them are based on conventional optimization methodologies

or numerical methods, and they are not easy to find out the optimal solution with accuracy

and efficiency. Therefore, in this work, genetic algorithm is used to extract parameters form

device models, and finds out the optimal solution with both of accuracy and efficiency.

1.2 : Background 3

1.2 Background

In this section, the basic concepts for semiconductor device simulation, model parameters

extraction, and genetic algorithm will be introduced,

1.2.1 Semiconductor Device Simulation

The main task of a semiconductor device simulator is to analyze the intrinsic and extrinsic

electrical behaviors of the most basic device’s structures. Basically, the semiconductor can

be classified into two categories, technology computer aided design (TCAD) and electronic

computer aided design (ECAD). These two kinds of simulators simulate the device behav-

iors with different points of view, and both of them have its advantages and disadvantages.

The TCAD simulates the electronics and holes transportation in the device through some

basic physical models at a very fundamental physical level. The advantages of the method

are that the basic physical models are without many factitious factors, and the simulated

results may be more accurate. However, the basic physical models, such as Maxwell’s

model, DD model, etc, are always multi-dimensional nonlinear partial differential equa-

tions (PDEs), and difficult to find out the numerical solutions.

On the contrary, the ECAD simulates the physical phenomenon not in the fundamental

ways, but through many approximation equations, so called the device compact model.

1.2 : Background 4

The device compact model is an equivalent circuit model for a typical semiconductor de-

vice. The approximation simulated results for specific device can be gathered by solving

the nodal equations in the equivalent circuit. The advantage of the compact model approach

is the computational time is much less than solving the fundamental physical models di-

rectly, but the compact models need many construction parameters which are not easy to

be determined.

1.2.2 Model Parameters Extraction

In the design of integrated digital or analog circuits, the proper construction parameters for

nonlinear device compact models are difficult to be determined. The conventional device

parameters extraction procedure begins with precisely measurement for device character-

izations from a fabricated device, and it is always comprised of the I-V (current versus

voltage) curves. According to real measured data, the engineers want to know the con-

figurations of the model parameters to fit the simulated results as closely as possible to

the measured data for the corresponding device compact model. The parameters extrac-

tion can be regarded as a minimization problem to minimize the errors between measured

data and simulated results. Unfortunately, the extraction process is not only tiresome and

time-consuming, but also requiring empirical experiences to perform an accurate parameter

extraction.

1.2 : Background 5

1.2.3 Genetic Algorithm

Genetic algorithm (GA) is an evolutionary search strategy based on natural selections and

genetic processes, and it has been thought highly as a robust optimization algorithm to find

the global optimal solution. Unlike some traditional search strategies, GA has its stochas-

tic information and randomized operators to explore and exploit the global optima in the

search domain instead of trapped into local optima. GA is one of the premier approaches

in the field of intelligent computing. It covers a quite wide range in real world applications,

such as optimization problems arising from science and engineering [1], combinatorial and

numerical optimizations [2], automatic machine learning [3][4], N.P. problem [5][6][7],

supervised and unsupervised learning [8][9], evolutionary design and evolvable hardware

[10][11][12], and molecular computing [13][14], etc. Based on the metaphors from bio-

logical evolution, GA was first developed and introduced by Holland in 1975 [15].

GA for problem optimization is realized by evolutionary procedures which include prob-

lem definition, gene encoding, fitness evaluator, selection, recombination and mutation. In

GAs, all unknowns to be optimized are represented as genes on a chromosome in the popu-

lation, and each chromosome received a measure so called the fitness score by applying the

fitness evaluator to judge the survival rate to the surrounding environment. The reproduc-

tion procedure contains three main evolutionary operators, selection, recombination, and

1.2 : Background 6

mutation. Through generations, individuals that survive the natural selection pass their ge-

netic codes to their offspring, while strings poorly fit to the environment evolves to adapt

more favorably to the environment, which brings the optimized values for maximizing the

fitness function. GA has its random, but additional information exchanging for memory

components make it explores the vast solution space intelligently.

1.2.4 Historical Development

In recent years, GA has been extensively used in VLSI circuit design area, such as cell

placement [16][17][18][19] and floor-planning [20][21], channel routing [22][23], digital

signal process [24], and device model parameters extraction [25][26][27][28][29].

R. Menozzi and his research group have proposed the evolutionary schemes for various

devices’ model parameters extraction [25][26][27], such as bipolar junction transistors

(BJTs), high electron mobility transistors (HEMTs), and microwave field effect transis-

tors (FETs). They use simple (standard) GA to extract the S-parameters from small-signal

model (SSM) of microwave and millimeter-wave devices. However, the number of ex-

tracted parameters in small-signal model is less than 20, and the solution scheme may not

have good accuracy and efficiency in the modern compact model parameters extraction

which the number of the extracted parameters is always larger than 60.

1.2 : Background 7

H. Yang, and et al., have proposed a hybrid parameters extraction strategy which combines

the traditional Levenberg-Marquardt (L-M) method and GA to extract DC model parame-

ters of BJT [28]. The idea of the hybrid method is using GA to find out rough solutions

firstly, and the rough solutions can be regarded as initial guesses for L-M method. Although

GA can be always expected to gain a good result after a number of generations, due to the

convergence property of L-M method, the uniqueness of the optimal solution which are

derived from L-M method still can not be guaranteed.

M. Keser and K. Joardar have introduced an enhanced GA which contains two genetic op-

erators in order to address the specific needs of parameter extraction [29]. The first is a

niching operator, which allows GA to maintain a collection of solutions rather than con-

verging to a single one. The second is a nondominated sorting procedure, which enables

GA to simultaneously optimize several objective functions in a single run. The enhanced

GA shows good capabilities for model parameters extraction; however, the analyses of

model parameters, such as uniqueness of extracted solution, efficiency, and accuracy are

not performed in this work.

1.3 : Objectives 8

1.3 Objectives

In this work, the most well-known and well-developed approximation compact model (so

called BSIM3 MOSFET model) for MOSFET device will be implemented, and GA will

be used to perform the parameters extraction from BSIM3 model. The proposed GA with

our developed floating-point operators, dynamic mutation mechanism, and physical based

weight function shows an excellent result with highly accuracy and efficiency for modern

device simulation and parameters extraction. Based on the model nonlinear behaviors, the

uniqueness and sensitivity of extracted solutions are also addressed in this work.

1.4 Outline of the Thesis

This thesis is organized as follows. In Chapter 2, BSIM3v3 compact model for MOSFET

will be introduced, and the conventional parameter extraction methodologies will also be

discussed here. Chapter 3 discusses the proposed GA which is applied in this optimization

problem. In Chapter 4, the computed results for 0.25µm N-MOSFET I-V curves simulation

and optimization will be presented. Finally, we draw some conclusions and suggest the

future works in Chapter 5.

Chapter 2

MOSFET Compact Models and

Parameter Extraction Methods

M OSFET compact models have been widely used in the optimal design and charac-

terization for deep-submicron devices. The approximation model simulates the

physical phenomenons in device through applying multiple physical-based models. How-

ever, the simulated results are concerned with a well-defined construction parameters set.

To find out the optimal parameters set for a specific device characterization is very compli-

cated and tedious. This process, known as parameters extraction, is not only laborious but

also requires extensive expertise to achieve the meaningful parameters set. The conven-

tional parameters extraction strategies, such as gradient-based methods or direct methods

9

2.1 : The MOSFET BSIM3 Compact Model 10

provide a succession of local optima instead of global optimal solutions for device charac-

teristics.

There are many compact models for MOSFET device simulation presently, such as BSIM3,

EKV, MosM9, et al. However, the BSIM3 compact model is the most well-developed, and

widely-used model than others. In this work, we choose the MOSFET BSIM3 model as

simulated kernel, and focus on the BSIM3 model parameters extraction. The brief intro-

duction for EKV, and MosM9 compact models will be described in appendix A-B.

This chapter is organized as follows. First of all, the basic concepts of BSIM3 compact

model, such as the approximation physical models or the relationship of extracted parame-

ters, will be described in the first part, and device simulation equations will also be formu-

lated here. Various conventional parameters extraction techniques will be introduced, and

comparisons will also be included in the second part.

2.1 The MOSFET BSIM3 Compact Model

The BSIM3 (Berkeley Short-Channel IGFET Model) is a physics-based, deep-submicron

MOSFET model for digital and analog circuit designs from the device group at the Univer-

sity of California at Berkeley. It had been widely used by many advanced IC design compa-

nies. From the continuous updating and developing of the model, the latest BSIM3 model is


BSIM3 v3.2 model (commonly abbreviated as BSIM3v3) which is an industry-wide stan-

dard model for circuit simulation. This section covers two major topics, the derivation of

the simulated equations in BSIM3 model, and the classification of the extracted parameters.

2.1.1 A Physical-Based Derivation of the Unified I-V Model

In this work, we implement the BSIM3v3 to perform deep-submicron MOSFET simulation

and I-V curves optimization. Figure E.1 shows a VLSI circuit with a N-MOSFET device.

The typical MOSFET has four control sources- drain (VD), gate (VG), source (VS), and

bulk (VB). As shown in Figure E.2 is a equivalent BSIM3v3 MOSFET circuit model. The

development of BSIM3v3 is based upon finding solutions to Poisson’s equation which is

given here:

∆φ =q

εs

(n − p + D). (2.1)

The unknown φ in (2.1) to be solved is the electrostatic potential for each simulated node.

The unknowns n and p are electrons and holes concentrations, and the function D =

−(N+D −N−

A ) is the specified ionized net doping profile and is a spatially-dependent given

function. Because of the nonlinear relationship for φ, n, and p, to find solutions for Pois-

son’s equation is a difficult task [31][32]. The BSIM3v3 model solves Poisson’s equation


by using the gradual channel approximation and quasi-two dimensional approximation

approaches. It includes compact, analytical expressions for the following physical phe-

nomenon observed in present day MOSFET devices [30]: short and narrow channel effects

on threshold voltage, non-uniform doping effect, mobility reduction due to vertical field,

carrier velocity saturation, bulk charge effect, drain-induced barrier lowering (DIBL), chan-

nel length modulation (CLM), substrate current induced body effect (SCBE), subthreshold

conduction, and source/drain parasitic resistances.

The unified I-V model in (A.1) is used for DC I-V curves simulation and optimization.

IDS =Idso(Vdseff )

1 +RdsIdso(Vdseff )

Vdseff

(1 +Vds − Vdseff

VA

)(1 +Vds − Vdseff

VASCBE

), (2.2)

where the Idso is the complete current expression in the saturation region, Vdseff is the

effective voltage from drain to source, Vds is the difference between drain to source voltage,

VASCBE is called as the Early voltage due to the substrate current induced body effect, and

Rds is the parasitic resistance model in BSIM3v3.

Idso(V dseff) =WeffµeffCoxVgsteff (1 − Abulk

Vdseff

2(Vgsteff+2VT ))Vdseff

Leff [1 + Vdseff/(EsatLeff )], (2.3)

Vdseff = Vdsat − 1

2(Vdsat − Vds − δ +

√(Vdsat − Vds − δ)2 + 4δVdsat), (2.4)

1

VASCBE

=Pscbe2

Leff

exp(−Pscbe1litl

Vds − Vdseff

), (2.5)

Rds =Rdsw[1 + PrwgVgsteff + Prwb(

√φs − Vbseff −

√φs)]

(106W′eff )

Wr. (2.6)


The descriptions of each term in above expressions are listed in Tables D.1-D.2.

To formulate the accurate drain-to-source I-V model (IDS), each observed physical phe-

nomenon should be modeled. In the following, various physical models which include

threshold voltage model, mobility model, carrier drift velocity model, bulk charge effect

model, subthreshold drain current model, and effective channel length and width model

will be introduced and formulated.

For the precise description of a device’s electrical characteristics, the accurate modeling of

threshold voltage Vth is required. It serves as an useful reference point for evaluations of

device operation regimes. In BSIM3v3, the considerations for non-uniform doping profile,

short and narrow channel effects on threshold voltage are considered, and the complete

formulation for threshold voltage Vth is given here:

Vth = Vtho + K1(√

φs − Vbseff −√

φs) − K2Vbseff

+K1(

√1 +

NLX

Leff

− 1)√

φs + (K3 + K3bVbseff )Tox

W′eff + Wo

φs

−DV TOw[e(−DV T1w

W′eff Leff

2ltw)+ 2e

(−DV T1w

W′eff Leff

ltw)](Vbi − Φs)

−DV TO[e(−DV T1

Leff2lt

)+ 2e

(−DV T1Leff

lt)](Vbi − Φs)

−[e(−Dsub

Leff2lto

)+ 2e

(−DsubLeff

lto)](Etao + EtabVbseff )Vds. (2.7)


In the expression of threshold voltage Vth, the extracted parameters are Vth0, K1, K2, K3,

Dvt0, Dvt1, Dvt2, Dvt0w, Dvt1w, Dvt2w, Nlx, W0, K3b, Dsub, Eta0, Etab, and Tox. Table

D.5-D.6 list the descriptions of each parameter and physical function in Vth.

A good model for surface carrier mobility is very critical to the accuracy of a MOS-

FET model. The scattering mechanisms responsible for surface mobility basically include

phonons, columbic scattering sites, and surface roughness. For good quality interfaces,

phonon scattering is generally the dominant scattering mechanism at room temperature. In

general, mobility depends on many process parameters and bias conditions, such as gate ox-

ide thickness, doping concentration, threshold voltage, gate voltage and substrate voltage,

etc. In BSIM3v3 model, the unified mobility model µeff has three different formulations

which are listed below:

µ1eff =

µ0

(1 + (Ua + UcVbseff )(Vgsteff+2Vth

Tox) + Ub(

Vgsteff+2Vth

Tox)2)

, (2.8)

µ2eff =

µ0

(1 + (Ua + UcVbseff )(Vgsteff

Tox) + Ub(

Vgsteff

Tox)2)

, (2.9)

µ3eff =

µ0

(1 + [Ua(Vgsteff+2Vth

Tox) + Ub(

Vgsteff+2Vth

Tox)2](1 + UcVbseff ))

. (2.10)

The dedicated mobility model which is used in the device simulation is determined by the

mobility selection parameter Mobmod. The unknowns in µeff are µ0, Ua, Ub, Uc, and Tox,

and Table D.7 shows the definitions of the parameters in µeff .


The carrier drift velocity is one of the most important parameters that affects device per-

formance characteristics. The semi-empirical saturation velocity model used in BSIM3v3

is given by:

v =

µeff E

1+(E/Esat), if E < Esat

vsat, if E > Esat

, (2.11)

Esat =2vsat

µeff

. (2.12)

The parameter Esat corresponds to the critical electrical field at which the carrier velocity

becomes saturated, and vsat is the saturation velocity in above model.

The bulk charge effect is caused by large drain voltage and/or channel length is long. In

BSIM3v3, the parameter Abulk is used to take into account the bulk charge effect. Several

extracted parameters such as A0, B0, B1 are introduced to account for the channel length

and width dependence of the bulk charge effect, and the parameter Keta is introduced to

model the charge in bilk charge effect under high back or substrate bias conditions. The

Abulk expression used in BSIM3v3 is given in Eq. 2.13, and the extracted parameters A0,

Ags, K1, B0, B1, and Keta are determined by experimental data; Table D.8 gives the

descriptions of each parameter in Abulk formulation.

Abulk = (1 +K1

2√

φs − Vbseff

A0Leff

Leff + 2√

XjXdep

[1 − AgsVgsteff

(Leff

Leff + 2√

XjXdep

)2] +B0

W′eff + B1

) 1

1 + KETAVbseff

. (2.13)


The effective channel length and width used in all model expressions is given below:

Weff = Wdrawn − 2dW, (2.14)

W′eff = Wdrawn − 2dW

′, (2.15)

L′eff = Ldrawn − 2dL. (2.16)

The parameters dW and dL are modeled by the following:

dW = dW′+ dWgVgsteff + dWb(

√φs − Vbseff −

√φs), (2.17)

dW′= Wint +

wl

Lwln+

ww

Wwwn+

wwl

LwlnWwwn, (2.18)

dL = Lint +ll

Llln+

lw

W lwn+

lwl

LllnW lwn. (2.19)

All extracted terms from above expressions are listed in Table D.9.

The complete equations for BSIM3v3 I-V model in DC simulation are listed in appendix C.

2.1.2 A Classification of Extracted Parameters

In BSIM3v3 model, there are about 400 parameters for a complete AC and DC simulation.

For DC curves simulation, there are at least 62 parameters have to be extracted. Table D.10

shows the notation and unit for 62 parameters in BSIM3v3 model. Each parameter can be

grouped into five categories which include general parameters, threshold voltage param-

eters, mobility parameters, subthreshold current parameters, and rout parameters. Table

2.2 : Conventional Parameters Extraction Methods 17

D.11 lists the classification of all extracted parameters in BSIM3v3 model for I-V curves

DC simulation.

2.2 Conventional Parameters Extraction Methods

The device model parameters extraction is an important issue for VLSI circuit design,

and the conventional extraction approach is typically accomplished in either of two fun-

damental ways: gradient-based methods [33][34][35][36][37], and direct search methods

[38][39][40].

Gradient-based methods extract model parameters based on mathematical and physical

phenomenons of specific model. However, the drawbacks of gradient-based methods are

tendency of numerical optimization techniques which are blocked into local minima of the

object function easily.

The most popular gradient-based method is Levenberg-Marquardt (L-M) [41] minimization

method which is one of the most used nonlinear curve fitting method. It can be thought of

a trust-region modification of the Guass-Newton algorithm. Although L-M method has

proved to be an effective and popular way to solve the nonlinear square problem, it has

several known deficiencies, such as poor convergence behaviors which can be trapped into

local minima easily, and difficulty with multiobjective optimizations.

2.2 : Conventional Parameters Extraction Methods 18

On the other hand, the ideas of direct search methods are straightforward, but when the

complexity of the problem is huge, the direct method will spend a lot of time.

Direct search methods such as calculus-based methods, enumerative schemes, and ran-

dom search algorithms are also widely used for parameters extraction. The calculus-based

method use derivatives to determine the optimal solution. However, it is difficult to find the

global solutions due to the limitation of the local search scope. The enumerative schemes

look for all possible combinations in the problem domain, and straightforwardly it take lots

of time if the dedicated problem is quite complex. Unlike the enumerative schemes, the

random search algorithms explore the problem domain randomly, and its performance is

between the former two methods.

Chapter 3

Genetic Algorithm for Deep-Submicron

MOSFET Simulation

G A is a search algorithm based on mechanics of natural genetics, and it combines

Darwinian survival of the fittest approach with a structured, yet randomized, in-

formation exchange. It has proved to be a robust [42], domain independent [43][44][45],

and efficient search method for a large space using probabilistic operations [46]. The ad-

vantages of GA are that it can search the optimal solutions in complex and large amount of

spaces efficiently and rapidly. The GA based optimization strategy is realized by genetic

operators which include gene encoding, competition procedure, selection method, recom-

bination process, and mutation scheme. After performing gene encoding operations, the

19

20

model parameters set is transformed into genes, and competition procedure is implemented

by evaluator functions which evaluates the survival rates for each individual. Selection,

recombination, and mutation operators are the so called “breeding operations” which keep

the better chromosomes, phase out the poor ones, regenerate the offspring from better chro-

mosomes, and finally perform the mutation scheme on randomly selected genes. Through

proper encoding method, fitness evaluators and reproduction strategies, the transformed

chromosomes will fit to the environment and adapt themselves more favorably to the sur-

rounding environment [47]. The design of gene encoding and fitness evaluator are usually

problem dependent [48][49]. As shown in Figure E.5 is a basic flowchart for the proposed

GA, and Table D.12 demonstrates the short comparisons between GA and other traditional

search methods. In this chapter, we give a brief descriptions for the proposed GA for MOS-

FET compact model parameters extraction and I-V curves optimization.

This chapter is organized as follows. First, the definition of the presented problem will be

described and analyzed. Then, series genetic operators include gene encoding, fitness eval-

uator, reproduction procedure, floating-point operator, dynamic mutation technique, and

termination criterion will be introduced in the second part.

3.1 : Problem Definition and Analysis 21

3.1 Problem Definition and Analysis

The goal in the design of optimal I-V curves is to find the configurations of model pa-

rameters for device compact model that satisfies the features of the measured I-V curves.

In MOSFET device simulation, the relationship between modeling input parameters and

computed results can be written as follows:

f(VDS, VGS, VBS, C) = IDS, (3.1)

where VDS , VGS , and VBS are input bias voltage in MOSFET operating regions, and vector

C is the construction parameters vector for compact model. The function f can be regarded

as a unified I-V model in BSIM3v3 model. The bias voltage VDS , VGS , and VBS represent

as the drain-to-source voltage, gate-to-source voltage, and bulk-to-source voltage, respec-

tively. The vector C contains all extracted parameters which are listed in Table D.10. The

simulated results IDS represent a single I-V curve. For a specific bias voltage VGS , VBS and

C, the vector CV DS is a result set for device simulation by changing the bias voltage VDS .

The vector CV DS can be written as follows:

CV DS = f(VDS(1), VGS, VBS, C),

f(VDS(2), VGS, VBS, C),

. . . ,

f(VDS(n), VGS, VBS, C) , (3.2)

3.1 : Problem Definition and Analysis 22

Similarly, for a given control voltage VDS , VBS and C, the below shows a representation of

output set CV GS by changing the bias voltage VGS:

CV GS = f(VDS, VGS(1), VBS, C),

f(VDS, VGS(2), VBS, C),

. . . ,

f(VDS, VGS(n), VBS, C) . (3.3)

The vector CV DS corresponds to a specific I-V curve, and vector CV GS represents the

collections of simulated results for implied bias voltages, VDS and VBS . The number of

elements in CV GS is the total number of I-V curves in model simulation. Therefore an union

set Ctarget can be obtained from CV DS and CV GS . For the circuit design procedure, the

Ctarget represents as the measured I-V curves, and C indicates the construction parameters

to be extracted. The presented problem can be regarded as a function and inverse function

problem as shown as follows:

f(VDS, VGS, VBS, C) = Ctarget, (3.4)

f−1(Ctarget) = VDS, VGS, VBS, C. (3.5)

For given sets of input voltages VDS , VGS , VBS , and measured data Ctarget, the proposed

GA approach will find out the optimal solution C to fit the measured I-V curves.

3.2 : Evolutionary Computation Steps 23

3.2 Evolutionary Computation Steps

The proposed evolutionary algorithm for finding the optimal fitting curves to the measured

data contains the following steps: gene encoding, competition procedure, selection method,

recombination process, and mutation scheme. The optimization procedure stops the evolu-

tionary computation steps until the termination criterion is satisfied. Each step is described

in the following sub-sections, respectively.

3.2.1 Gene Encoding

The design of gene encoding strategy depends on the properties of the problem. In MOS-

FET device compact model simulation, at least 62 parameters have to be extracted in the

DC simulation. Some of them are intrinsic parameters with physical meanings, and oth-

ers are numerical fitting terms. Table D.11 shows the categories for each parameter in

BSIM3v3 DC simulation. All parameters are floating-point number with its value ranges

and defined resolutions. Table D.13 and D.14 show value ranges, and resolutions of each

parameter in BSIM3v3 model. Intuitively, parameters with limited value ranges and dis-

crete resolutions reduce the search spaces for finding the optimal solution. In this work, we

encode floating-point number as bit string into genes instead of real number, and we find

that the bit string has strongly combinatorial ability for performing the genetic operators.


A mapping from bit string to floating-point number is given as follows:

real number = πmin + P ∗ resoultion, 0 ≤ P ≤ πmax − πmin

resolution, (3.6)

where P is an integer which is larger than zero, but less than the total number of slices

between πmin and πmax for a specific resolution. According to the transformation, only

integer P can be encoded into bit string on genes, and hence the memory usage can be

reduced.

3.2.2 Competition Procedure

The survival rate for each individual will be obtained through performing the competition

procedure. The competition procedure is realized by applying fitness function or payoff

function, so called the fitness evaluator for each chromosome in the population. The evalu-

ation function calculates the misfits between measure data and simulated results, and each

individual receives a fitness score after applying the fitness function. Eq. 3.7 shows the

definition of fitness function:

fitness =m∑

i=1

n∑j=1

W (i, j)∣∣Ict

i,j − Icsi,j

∣∣ , (3.7)

where W is the weight function. The weight function is a scalar function which turns the

multiobjective problems into a single attribute problem [50][51]. Different shapes of scalar


functions lead to different evolutionary trends. Because the linear region of the I-V curve is

rather sensitive in MOSFET compact model, the weight function is used to emphasize the

relative importance for every I-V point in the linear region. In this work, we take the power

law scaling scheme as the weight function, and we find it has better simulated results in

linear region of I-V curves. Equation (3.8) shows the formulation of the power law scaling

function which is used in this work, and the coefficient K is a positive constant which is

always larger than Icti,j for any giving i and j to keep the exponential term positive. In

next chapter we will give the comparisons to three different types of scalar schemes, and

demonstrate the benefits of the power law scaling scheme for this problem.

W (i, j) = eK−Icti,j . (3.8)

The differences between measured and simulated data, so called the error norm, is used

to evaluate the discrepancies for measured I-V curves Icti,j and simulated I-V curves Ics

i,j .

The expression of error norm is given as follows.

ErrorNorm =m∑

i=1

n∑j=1

∣∣∣∣Icti,j − Ics

i,j

Icti,j

∣∣∣∣ , (3.9)

For this parameters optimization problem, there are total m measured I-V curves, and n

I-V simulated points on a curve. Hence there are m∗n measured I-V nodes to be fitted and

to be optimized totally.


3.2.3 Selection Method

After applying competition procedure, each chromosome has its fitness score. GA applies

selection strategies to select individuals with higher fitness score and eliminates the poorly

fit ones. The conventional selection methods, such as tournament selection or roulette

wheel selection are the “fitness proportional” method [52][53] which select chromosomes

with better fitness score. But it may cause the premature convergence. In the multidimen-

sional optimization problem, the loss of diversity leads the extracted solution to be trapped

into local optima easily. The conventional selection operators speed up the convergence

behaviors with high selection rate, but loss of population diversity. Conversely, the lower

selection rate will decrease the convergence but more variation of population. In this work,

we adopt the tournament selection with floating-point operators as our selection strategy.

The hybrid operator avoids complete loss of characteristics, and improves the evolution-

ary trend effectively. In conventional tournament selection method, a pair of strings in

this population are selected randomly, and one with higher fitness score is kept. Repeat

the competitions until the sufficient number of chromosomes are obtained. After applying

tournament selection, we introduce the floating-point operator to keep the population di-

versity from generations to generations. The main idea of floating-point operator is that the

worse solutions may also contain useful information for biasing the search, and this may


advance some characteristics in the worse chromosomes and the variation of the popula-

tion can be kept. The floating-point operator selects worse chromosomes from rest group

of weak ones, and forces them to perform crossover scheme with better ones.

3.2.4 Recombination Process

As for crossover scheme, in MOSFET compact device model, all parameters to be opti-

mized can be classified into different categories which consist of different numerical con-

straints. We use the uniform crossover to perform the crossover operation in this work

[54], and based on our simulation experiences, it is more effective than other conventional

crossover schemes in this problem.

3.2.5 Mutation Scheme

For a chromosome chosen randomly from the population of the new generation, random

mutates to the genes in the dedicated chromosome with dynamic mutation rate. The dy-

namic mutation techniques are introduced here and applied to keep and increase population

diversity in the population. The variation of mutation rate depends on the diversity variable

D. The expression of dynamic mutation rate Mr is given as follows:


Mr(D) =

Mhigh Dlow > D

Mlow−Mhigh

Dhigh−DlowD +

DhighMhigh−DlowMlow

Dhigh−DlowDhigh ≥ D ≥ Dlow

Mlow D > Dhigh,

(3.10)

where D is the diversity function to detect the variation of the population. Dhigh is a given

lower bound for high diversity area, and Dlow is a upper bound for low diversity area.

Figure E.6 shows the shape plot of the relationship between diversity and mutation rate.

The expression of diversity function is given here:

D =

∣∣∣∣FW (scope) − FB(scope)

FC

∣∣∣∣ , (3.11)

where FW and FB return the worst and best fitness scores in recent generations, and FC

returns the best fitness score in current generation. The scope is a given constant which

is used to examine the variation of the population diversity in recent generations, and ad-

justs the mutation rate according to the variation of the population. The dynamic mutation

techniques decrease the mutation rate when the population achieve to high diversity, and

raise up the mutation rate when the evolutionary behavior tends to a saturation situation.

The mutation strategy randomly generates floating-point values with proper resolution in

limited value boundaries for genes.


3.2.6 Termination Criterion

The evolutionary procedure stops the processes if the extracted results are satisfied with ter-

mination criterion. In BSIM3v3 model parameters extraction and optimization, we adopt

absolute stopping criterion which stops the evolution as long as the error norm of the best

chromosome tends to a fixed tolerance error ε, i.e. ε = 0.05. To make up the value bound-

ary of tolerance error is considerable because the large coefficient will lead to premature

saturation, but the small constant may take long time to reach to the saturation region or

achieve to the specified error.

Chapter 4

Simulation Results and Discussion

I n this chapter, five optimization experiments will be presented and discussed. The

former two experiments show accuracy and efficiency for our developed BSIM3v3

MOSFET model simulator, and proposed GA for model parameters extraction. The third

experiment demonstrates the effects for applying different weight function in the fitness

function. A simple experiment for fitting the synthetic multiple I-V curves will be executed

to observe the uniqueness of the extracted solution in the fourth part. Finally, some tests

will be performed to examine the sensitivities of the extracted parameters for BSIM3v3

model in the fifth part.

30

4.1 : Accuracy and Efficiency of the Developed BSIM3v3 Simulator and Optimizer 31

Because of the stochastic property of GA, it may have different evolution results from dif-

ferent initial conditions. However, our GA still shows the good global convergence behav-

iors which achieves to good results within reasonable time in fitting synthetic I-V curves

or measured I-V curves. We perform 10 optimization runs for each experiment to show

accuracy and reliability of the method.

4.1 Accuracy and Efficiency of the Developed BSIM3v3

Simulator and Optimizer

Accuracy for our developed BSIM3v3 simulator is the basic requirement in this work. In

the beginning, we demonstrate the accuracy for the BSIM3v3 simulator firstly. Figure E.3

and E.4 show the comparison between simulated results by feeding benchmark parameters

into our BSIM3v3 simulator and SPICE simulated results. Similarities for SPICE and our

simulation results indicate the accuracy of the simulator.

In the first part, we extract model parameters for single I-V curve from BSIM3v3 model.

The range of applied voltage VDS is between 0.2 V and 3.4 V, and each step is 0.2 V. The

bias voltage is VGS = 2.0 V for only one I-V curve. There are totally 17 I-V points in this

I-V curve. Table D.15 shows the requirements of the proceed generations and computation

4.1 : Accuracy and Efficiency of the Developed BSIM3v3 Simulator and Optimizer 32

time for best 10 runs. The absolute stopping coefficient is ε = 0.05, and the computational

time is rather acceptable which suggests our proposed GA is quite efficient. Figure E.7

shows the comparison between measured and simulated I-V curve, and the coincides of

two similar I-V curves demonstrate accuracy of the method. Figures E.8-E.10 demonstrate

a zoom-in view for measured and simulated curves to examine discrepancies for these two

curves. The detail plots for simulated I-V points (VDS = 0.2V, 0.4V, 0.6V ) in Figure E.8

indicate that the error norms of the first three I-V nodes in linear region converge to a very

small interval. The differences between measured and simulated I-V curves for the first

three points are 7.07e−8, 2.069e−6, and 2.07e−6, respectively, and the average error norm

of three nodes is E1=1.403e−6. Figure E.9 demonstrates the error norms for three simulated

nodes, such as VDS = 1.2 V, 1.4 V, 1.6 V . The error norms achieve to 2.07e−6 ,2.01e−6

,1.47e−6, and the average error norm in this region is E2=1.85e−6. Finally, in the saturation

region of the simulated curve, Figure E.10 show the tiny differences between two set of

curves, the error norms for each node (VDS = 3.0V, 3.2V, 3.4V ) are 2.0664e−6, 2.09e−6,

1.83e−6, and the average of the three error norms in this region is E3 = 1.9954e−6. By

performing numerical comparison of three average error norms, the error norm E1 < E2 <

E3, and it suggests the weight function emphasizes on the simulated nodes in linear region,

and redirects the evolutionary trend. Furthermore, applying proper weight function is an

important issue in multiple objects evolution.

4.2 : Effects of Different Weight Functions 33

In the second evolutionary experiment, we extend the problem complexity. The goal of the

evolution problem is set to fit three I-V curves with applied voltages VDS is start from 0.2

V to 3.4 V with 0.2 V steps, and bias voltages VGS are 2.0 V, 2.5 V, and 3.0 V. Similarly,

Table D.16 summarizes 10 optimization runs as have shown in the previous experiment.

The error norm finally converges to the specified tolerance error in time while the error

coefficient ε = 0.05. It suggests that the robustness of our GA reveals in both of easier and

heavier experimental cases. Figure E.11 demonstrates the similarities for three measured I-

V curves and BSIM3v3 evolutionary curves. Figures E.12-E.14 show the similarities of two

curves set. In this experiment, the slight differences for evolutionary and measured curves

suggest that accuracy for multiple I-V curves evolution can also be obtained by proposed

method; The average error norms of two sets of I-V curves in three distinct regions are

1.3764e−7, 1.919e−6, 2.128e−6, and they indicate the weight function has successfully put

more stresses on the sensitive region of the curves.

4.2 Effects of Different Weight Functions

The weight function plays an important role for GA to solve the multiobjective problem. In

this section, we execute a simple test to examine the simulated results for different weight

functions. As shown in Figure E.15 is the measured and evolutionary curves for 0.25µ

4.3 : The Uniqueness of Extracted Parameters 34

N-MOSFET. The contract between the BSIM3v3 simulated results for GA with and with-

out applying weight function for the same proceed generations show the essentiality of

the weight function of this genetic optimization work. Table D.17 and Figure E.16 show

convergent behavior of error norm for BSIM3v3 compact model with different weight func-

tions. We find that the power law scaling function has better evolutionary trend, because it

put more emphases on linear regions of goal curves.

4.3 The Uniqueness of Extracted Parameters

As long as parameters extraction of the model is concerned, the proposed evolutionary al-

gorithm has to face an interested problem of uniqueness of extracted solutions. To observe

the uniqueness of the extracted solutions, a simple experiment will be executed. First, we

need to generate a synthetic parameters set as an optimal solution, and the corresponding

multiple I-V curves can be regarded as target curves in the evolutionary process. Figures

E.17-E.21 plot values of extracted parameters for 5 optimal runs in multiple I-V curves

optimization, and the error coefficient is ε = 0.01. Those figures show that many modeled

parameters are normalized in very small value ranges, and only few extrinsic variables can

not be extracted accurately. It indicates the uniqueness of the extracted parameters.

4.4 : The Sensitivities of the Extracted Parameters 35

4.4 The Sensitivities of the Extracted Parameters

The sensitivity of extracted parameters is also an important issue in model parameters anal-

ysis. In this section, we try to examine the sensitivities of each parameter in the aspect of

GA. To measure the sensitivities of parameters, we first define two sets of synthetic bench-

mark parameters to generate two I-V curves which are named as initial and target curves;

the configurations of parameters for all individuals in the initial generation are set to be

equal to the extracted parameters of initial curves. Evolutionary procedures are performed

to find the target curves from initial curves. Unlike the conventional genetic approach, the

proposed experiments fixed most of extracted parameters, and only partial of parameters

in simulated model are allowed to be extracted. The sensitivities can be figured out by

examining the convergence behaviors for different cases.

In BSIM3v3 model, because all parameters can be grouped into 5 categories, we perform

series of experiments to measure, and analyze the sensitivities for each category. In the

first case, four parameters groups are fixed, and GA is allowed to find the optimal solution

in rest one of parameters class. There are 5 different sub-experiments in this case. Table

D.18 shows the number of proceed generations and the convergence of the error norm for

each sub-experiment. Figure E.22 demonstrates the comparison of convergence behavior

between different varying parameters categories. As shown in this figure, the evolution

with varying general parameters class has better convergence behavior from initial curve

4.4 : The Sensitivities of the Extracted Parameters 36

to target curve, and has superior results than other four evolutionary cases. However, the

mobility model parameters have great changes from initial to final curves. This may induce

that the mobility model parameters also have strong effects on evolutionary process. Both

of general and mobility model parameters have strong sensitivities, and genetic process

can find better configurations of parameters within limited solution space. Contrarily, the

rest of three categories, such as threshold voltage, subthreshold current and rout parame-

ters have weak sensitivities because of the slow convergence from initial curves to target

curves.

In the second experimental case, we extend the solution spaces to two parameters classes to

perform the cross analysis for each two parameters categories. There are ten kinds of com-

binations for each two parameters sets. Similarly, Table D.19 and Figure E.23 summarize

the evolution results as have shown in the previous experiment. According to the simulated

results, it suggests that the mobility model and rout parameter sets have stronger sensitiv-

ities than any other combinations, and the poor evolution trend of threshold voltage and

rout sets demonstrate the weak sensitivities. To evaluate the sensitivities of compact model

parameters is quite meaningful and useful. At the beginning of the parameters extrac-

tion procedure, the calibration of the sensitive parameters causes the fitted curve changes

acutely. Once the fitted curves are similar to key features of target curves, the parameters

with low sensitivities can be used for advanced fine tuning.

Chapter 5

Conclusions

I n this thesis, a deep-submicron MOSFET device simulator based on BSIM3v3 com-

pact model, and a model parameters extractor have been implemented and proposed

successfully. Accuracy and efficiency are also presented in both of device simulator and

parameters extractor. In this chapter, the contributions of the thesis will be addressed firstly,

and followed by suggestions and future works.

5.1 Summary

In this work, a comprehensive architecture for semiconductor device simulation and I-

V curves optimization is developed. The BSIM3v3 based MOSFET device simulator

shows high accuracy and efficiency for deep-submicron MOSFET simulation; moreover,

37

5.2 : Suggestions and Future Works 38

a GA based I-V curves optimizer also demonstrates high reliability and excellent flexi-

bility for MOSFET BSIM3v3 model parameters extraction. The novel GA with physical

based weight function, floating-point operator, and dynamic mutation techniques, extracts

BSIM3v3 model parameters with high efficiency and accuracy.

5.2 Suggestions and Future Works

Our well-developed evolutionary architecture has strong expansibility for both of device

simulation and optimization. In future, multiple compact models for various devices can

be implemented in the simulator. They include BSIM4 model, EKV3.0 model, MosM11

model, HiSIM model, SP2001 model, et al., for nano-scale MOSFET AC and DC simula-

tions, and Ebers-Moll model, Gummel-Poon model, MAXTERM model, et al., for bipolar

junction transistor (BJT) AC and DC simulations. All the models are available or soon to be

available. As for evolutionary algorithms, multiple stages evolution can be implemented by

performing the model parameters sensitivity analysis first. Because in any given compact

models, each parameter has different impact factors to the simulated results. Therefore, it

would be more effective to perform the extraction of parameters which have heavy impact

factors in the early evolved stage.

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Appendix A

The EKV I-V model in DC simulation.

The EKV model is a physics-based compact model for MOSFET device. It was dedicated

to the design and simulation of low-voltage, low-current analog, and mixed analog-digital

circuits using submicron CMOS technologies. The EKV model includes many physical

models such as weak-moderate-strong inversion modelling, doping and mobility effects,

short-channel effects, and geometry- or bias-dependent matching. Figure ?? demonstrates

the equivalent circuit model, and the basic I-V model for DC analysis is given as follows:

IDS = IS(if − i′r) (A.1)

IS = 2nβV 2t (A.2)

if = F [Vp − Vs

Vt

] (A.3)

i′r = F [

Vp − Vds − Vs −√

(V′DSS)2 + ∆V 2 +

√(Vds − V

′DSS)2 + ∆V 2

Vt

] (A.4)

48

49

n = 1 +GAMMAa

2√

Vp + PHI + 4Vt

(A.5)

β =β0

1 + THETA ∗ V ′p

(A.6)

Vp = V′G − PHI − γ

′(

√V

′G + (

γ′

2)2 − γ

′

2) for V

′G > 0

= −PHI for V′G ≤ 0 (A.7)

Vs = VSB = −VBS (A.8)

Vds =VD − Vs

2(A.9)

V′DSS = Vc[

√1

4+

Vt

Vc

(√

if − 3

4ln(if )) − 0.5] + Vt[ln(

Vc

2Vt

) − 0.6] (A.10)

∆V = 4Vt

√LAMBDA(

√if − VDSS

Vt

) +1

64(A.11)

GAMMAa = GAMMA +AGAMMA√

NP ∗ Weff ∗ NS ∗ Leff

(A.12)

β0 = KPaNP ∗ Weff

Leq

(A.13)

V′P =

1

2(Vp +

√V 2

p + 2V 2t ) (A.14)

V′G = VG − V TOa − ∆VRSCE + PHI + GAMMAa

√PHI (A.15)

γ′=

1

2(γo +

√γo2 + 0.1Vt) (A.16)

VD = VDB = VDS − VBS (A.17)

Vc = UCRIT ∗ NS ∗ Leff (A.18)

50

VDSS = Vc[

√1

4+

Vt

Vc

√if − 0.5] (A.19)

Weff = W + DW (A.20)

Leff = L + DL (A.21)

KPa = KP (1 +AKP√


) (A.22)

Leq =1

2(L

′+

√L′2 + L2

min) (A.23)

VG = VGB = VGS − VBS (A.24)

V TOa = V TO +AV TO√


(A.25)

∆VRSCE =2Qo

Cox

∗ 1

[1 + 12(ζ +

√ζ2 + Cε)]2

(A.26)

γo = GAMMAa − ε

Cox

[LETA

Leff

(√

V ′s +

√V

′D) − 3WETA

Weff

√Vpo + PHI] (A.27)

L′= NS ∗ Leff − ∆L +

Vds + Vip

V CRIT(A.28)

Lmin = NS ∗ Leff

10(A.29)

ζ = CA(10Leff

LK− 1) (A.30)

Cε = 4(22 ∗ 10−3)2 (A.31)

V′S =

1

2[Vs + PHI +

√(Vs + PHI)2 + (4Vt)2] (A.32)

V′D =

1

2[VD + PHI +

√(VD + PHI)2 + (4Vt)2] (A.33)

51

Vp0 = V′G − PHI − GAMMAa(

√V

′G +

GAMMAa

4

2

− GAMMAa

2) for V

′G > 0

= −PHI for VG ≤ 0 (A.34)

∆L = LAMBDA ∗ Lc ∗ ln(1 +Vds − Vip

Lc ∗ UCRIT) (A.35)

Vip =√

V 2DSS + ∆V 2 −

√(Vds − VDSS)2 + ∆V 2 (A.36)

CA = 0.028 (A.37)

Lc =

√εsi

Cox

XJ (A.38)

Appendix B

The MosM9 I-V model in DC simulation.

The basic unified I-V model of MosM9 Model equations are given here:

IDS = βG3

VGT3VDS1 − 1+δ12

V 2DS1

[1 + θ1VGT1 + θ2(us − uso)](1 + θ3VDS1)(B.1)

G1 = exp(VGT2

2mφT

) (B.2)

G2 = 1 + α ln(1 +VDS − VDS1

Vp

) (B.3)

G3 =S1[1 − exp(−VDS

φT)] + G1G2

1/S1 + G1

(B.4)

VGT2 = VGS − VT2 (B.5)

VT2 = VT1 + ∆VT1 (B.6)

VT1 = VT0 + ∆VT0 (B.7)

52

53

∆VT0 = [1 − (K

K0

)2]K0usx − K0uso + K

√u2

s − (1 − (K

K0

)2)u2sx (B.8)

VDS1 = VDSS1 − 1

2[(VDSS1 −VDS − ε2

3

VDSS1

)+

√(VDSS1 − VDS − ε2

3

VDSS1

)2 + 4ε23] (B.9)

ε3 = λ3VDSS1

VDSSX + VDSS1

(B.10)

VDSS1 =VGT3

1 + δ1

2

1 +√

1 + 2θ3VGT3

1+δ1

(B.11)

VGT3 = 3mφT ln(1 + G1) (B.12)

m = 1 + m0(uso

us1

)ηm (B.13)

us =√

VSB + φB (B.14)

uso =√

φB (B.15)

VGT1 = VGS − VT1 (B.16)

us1 = ust (B.17)

ust =√

VSBT − φB (B.18)

δ1 =λ1

us

[K +(K0 − K)V 2

SBX

V 2SBX + (λ2VGT1 + VSB)2

] (B.19)

λ1 = 0.3 (B.20)

λ2 = 0.1 (B.21)

∆VT1 = −γ0V 2

GTX

V 2GTX + V 2

GT1

VDS − γ1V 2

GT1

V 2GTX + V 2

GT1

V ηDSDS (B.22)

γ0 = γ00(us1

uso

)ηr (B.23)

54

VGT1 = VGS − VT1 (B.24)

VGTX =

√2

2(B.25)

usx =√

VSBX + φB (B.26)

Appendix C

The BSIM3v3 I-V model in DC

simulation.

VA = VAsat + (1 +PvagVgsteff

EsatLeff

)(1

VACLM

+1

VADIBLC

)−1 (C.1)

VAsat =EsatLeff + Vdsat + 2RDSνsatCoxWeffVgsteff [1 − AbulkVdsat

2(Vgsteff+2VT )]

2λ− 1 + RDSνsatCoxWeffAbulk

(C.2)

VACLM =AbulkEsatLeff + Vgsteff

PCLMAbulkEsatlitl(Vds − Vdseff ) (C.3)

litl =

√εsiToxXj

εox

(C.4)

Vdseff = Vdsat − 1

2(Vdsat − Vds − δ +

√(Vdsat − Vds − δ)2 + 4δVdsat) (C.5)

VADIBLC =Vgsteff + 2VT

θrout(1 + PDIBLCBVbseff )(1 − AbulkVdsat

AbulkVdsat + Vgsteff + 2VT

) (C.6)

55

56

θrout = PDIBLC1[exp(−DROUTLeff

2lto) + 2exp(−DROUT

Leff

lto)] + PDIBLC2 (C.7)

Esat =2νsat

µeff

(C.8)

Abulk = (1 +K1

2√

φs − Vbseff

A0Leff

Leff + 2√

XjXdep

[1 − AgsVgsteff

(Leff

Leff + 2√

XjXdep

)2] +B0

W′eff + B1

) 1

1 + KETAVbseff

(C.9)

(C.10)

Vbseff = Vbc + 0.5[Vbs − Vbc − 0.001 +√

(Vbs − Vbc − 0.001)2 − 0.004Vbc] (C.11)

Vbc = 0.9(φs − K21

4K22

) (C.12)

Vgsteff =2nVT ln[1 + exp(Vgs−Vth

2nVT)]

1 + 2nCox

√2φs

qεsiNchexp(−Vgs−Vth−2Voff

2nVT)

(C.13)

n = 1 + NfactorCd

Cox

+(Cdsc + CdscdVds + CdscbVbseff )

Cox

∗[exp(−DV T1

Leff

2lt) + 2exp(−DV T1

Leff

2lt)] + Cit

Cox

(C.14)

Cd =εsi

Xdep

(C.15)

lt =√

εsiXdep/Cox(1 + Dvt2Vbseff ) (C.16)

ltw =√

εsiXdep/Cox(1 + Dvt2wVbseff ) (C.17)

lt0 =√

εsiXdep0/Cox (C.18)

Xdep =

√2εsi(φs − Vbseff )

qNch

(C.19)

57

Xdep0 =

√2εsiφs

qNch

(C.20)

Vbi = VT lnNchNDS

n2i

(C.21)

Φs = 2KBT

qln

Na

ni

(C.22)

Appendix D

List of Tables

58

59

Table D.1: The descriptions of each term in Idso(vdseff) in Eq. (2.3).

Term name Description TypeWeff Effective channel width functionµeff Mobility model functionVgsteff Channel charge characteristics from subthreshold to strong inversion functionAbulk Bulk charge effect functionVdseff Effective drain-to-source voltage functionLeff Effective channel length functionEsat Saturated carrier velocity functionCox Capacitance of oxide parameter

60

Table D.2: The descriptions of each term in Vdseff in Eq. (2.4).

Term name Description TypeVdsat Saturation voltage functionVds Source-to-drain voltage parameter

61

Table D.3: The descriptions of each term in VASCBE in Eq. (2.5).

Term name Description TypeLeff Effective channel length functionVdseff Effective drain-to-source voltage functionPscbe1 First substrate current induced body-effect parameter parameterPscbe2 Second substrate current induced body-effect parameter parameterVds Source-to-drain voltage parameter

62

Table D.4: The descriptions of each term in Rds in Eq. (2.6).

Term name Description TypeVgsteff Channel charge characteristics from subthreshold to strong inversion functionΦs Surface potential functionVbseff Effective bulk-to-source voltage functionW

′eff Effective channel width function

Rdsw Zero bias LDD resistance per unit width for RDSMOD=0 parameterPrwg Gate-bias dependence of LDD resistance parameterPrwb Body-bias dependence of LDD resistance parameterWr Channel-width dependence parameter of LDD resistance parameter

63

Table D.5: The descriptions of each term in Vth in Eq. (2.7).

Term name Description TypeVbseff Effective bulk-to-source voltage functionΦs Surface potential functionLeff Effective channel length functionW


lt Characteristic length functionVbi Build-in voltage between the substrate and the source functionlt0 Characteristic length at zero body-bias functionVth0 Long-channel threshold voltage at Vbs = 0 parameterK1 First-order body bias coefficient parameterK2 Second-order body bias coefficient parameterK3 Narrow width coefficient parameterDvt0 First coefficient of short-channel effect on Vth parameterDvt1 Second coefficient of short-channel effect on Vth parameterDvt2 Body-bias coefficient of short-channel effect on Vth parameter

64

Table D.6: The descriptions of each term in Vth in Eq. (2.7).

Term name Description TypeDvt0w First coef. of narrow width effect on Vth for small channel length parameterDvt1w Second coef. of narrow width effect on Vth for small channel length parameterDvt2w Body-bias coef. of narrow width effect on Vth for small channel length parameterNlx Lateral non-uniform doping parameter parameterW0 Narrow width parameter parameterK3b Body effect coefficient of K3 parameterDsub DIBL coefficient exponent in subthreshold region parameterEta0 DIBL coefficient in subthreshold region parameterEtab Body-bias coefficient for the subthreshold DIBL effect parameterTox Oxide thickness parameterVds Source-to-drain voltage parameter

65

Table D.7: The descriptions of each term in µeff in Eqs. (2.8-2.10).

Term name Description TypeVbseff Effective bulk-to-source voltage functionVgsteff Channel charge characteristics from subthreshold to strong inversion functionVth Threshold voltage functionµ0 Low-field mobility parameterUa Coefficient of first-order mobility degradation due to vertical field parameterUb Coefficient of second-order mobility degradation due to vertical field parameterUc Coefficient of mobility degradation due to body-bias effect parameterTox Oxide thickness parameter

66

Table D.8: The descriptions of each term in Abulk in Eq. (2.13).

Term name Description TypeVbseff Effective bulk-to-source voltage functionVgsteff Channel charge characteristics from subthreshold to strong inversion functionΦs Surface potential functionLeff Effective channel length functionXdep Depletion width functionW


K1 First-order body bias coefficient parameterA0 Coefficient of channel-length dependence of bulk charge effect parameterB0 Bulk charge effect coefficient for channel width parameterB1 Bulk charge effect width offset parameterXj Source/drain junction depth parameterKeta Body-bias coefficient of bulk charge effect parameter

67

Table D.9: The descriptions of each term in dW , dW′, and dL in Eqs. (2.17-2.19).

Term name Description TypeVbseff Effective bulk-to-source voltage functionVgsteff Channel charge characteristics from subthreshold to strong inversion functionΦs Surface potential functiondWg Coefficient of gate bias dependence of Weff parameterdWb Coefficient of body bias dependence of Weff bias dependence parameterWint Channel-width offset parameter parameterLint Channel-length offset parameter parameterwl Coefficient of length dependence for width offset parameterww Coefficient of width dependence for width offset parameterwwl Coefficient of length and width cross term dependence for width offset parameterwlw Power of length dependence of width offset parameterwwn Power of width dependence of width offset parameterll Coefficient of length dependence for length offset parameterlw Coefficient of width dependence for length offset parameterlwl Power of width dependence of length offset parameterlln Power of length dependence for length offset parameterwln Power of length dependence of width offset parameter

68

Table D.10: A list of extracted parameters in BSIM3v3 DC simulation.

Notation Unit Notation Unit Notation Unit Notation UnitVth0 V K1 V

12 K2 — K3 —

Dvt0 — Dvt1 — Dvt2 1/V Dvt0w 1/mDvt1w 1/m Dvt2w 1/V Nlx m W0 mK3b 1/V Vsat m/sec Ua m/V Ub (m/V )2

Uc m/V 2 Rdsw Ω − µmWr Prwb V −1/2 Prwg 1/VWr — µ0

cm2

V/secA0 — A1 1/V

A2 — Keta 1/V Ags 1/V B0 mB1 m Voff V Nfactor — Cit F/m2

Cdsc F/m2 Cdscb F/V m2 Cdscd F/V m2 Eta0 —Etab 1/V Dsub — Pclm — Pdiblc1 —Pdiblc2 — Pdiblcb 1/V Drout — Pscbe1 V/mPscbe2 m/V Pvag — δ V Tox mXj m Nch 1/cm3 lln — lwn —wln — wwn — Lint m ll mlln

lw mlwn lwl mlwn+lln Wint m wl mwln

ww mwwn wwl mwwn+wln Mobmod — Dwg m/VDwb

√m/V

69

Table D.11: A classification of BSIM3v3 model parameters in DC simulation.

General parametersTox, Xj , Nch, lln, lwn, wln, wwn, lint, ll, lw,lwl, wint, wl, ww, wwl, Mobmod, dWg, dWb.Threshold voltage parametersVth0, K1, K2, K3, K3b, W0, Dvt0, Dvt1, Dvt2, Dvt0w, Dvt1w, Dvt2w, Nlx, W0.Mobility parametersVsat, µ0, Ua, Ub, Uc, Rdsw, Prwb, Prwg, Wr, A0, Ags, B0, B1, Keta, A1.Subthreshold current parametersVoff , Nfactor, Cit, Cdsc, Cdscb, Cdscd, Eta0, Etab, Dsub.Rout parametersPclm, Pdiblc1, Pdiblc2, Pdiblcb, Drout, Pscbe1, Pscbe2, Pvag, Delta.

70

Table D.12: Comparisons between GA and traditional methods for solving optimizationproblems.

Genetic Enumerative Random walk Gradient-basedComputational time Rational Time-consuming Time-consuming Problem DependentConvergent behavior Global Sensitive Global LocalMultiple objectives Capable Poor Capable PoorRobustness Yes Moderate Moderate ModerateMultimodel problem Capable Poor Capable PoorImplementation Easy Moderate Easy DifficultAdaptivity Yes Poor Fail PoorAdditional Knowledge Not require Require Not require RequireParallelization Easy Easy Easy DifficultProblem solving scheme Probabilistic Deterministic Probabilistic Deterministic

71

Table D.13: A partial list (1) of parameters for BSIM3v3 model (withits range and resolution) to be extracted.

Variable Range ResolutionVth0 0.0 ∼ 1.5 0.001K1 0.0 ∼ 1.5 0.001K2 0.0 ∼ 0.1 0.0001K3 −5.0 ∼ 0.0 0.001Dvt0 0.0 ∼ 2.0 0.001Dvt1 0.0 ∼ 1.5 0.001Dvt2 −0.15 ∼ 0.0 0.0001Dvt0w −0.03 ∼ 0.0 0.00001Dvt1w −0.2 ∼ 0.2 0.001Dvt2w 0.0 ∼ 0.4 0.001Nlx −0.2 ∼ 0.2 0.001W0 −1.2e−7 ∼ 0.0 1e−9

K3b 0.0 ∼ 0.4 0.0001Vsat 0.0 ∼ 2e5 1000Ua −4e−10 ∼ 0.0 1e−12

Ub 0.0 ∼ 3e−18 1e−20

Uc 0.0 ∼ 5e−11 1e−13

Rdsw 0.0 ∼ 2000 10Prwb 0.0 ∼ 0.5 0.0001Prwg −3e−2 ∼ 0.0 0.0001Wr 0.0 ∼ 2.0 0.001U0 0.0 ∼ 0.1 0.0001A0 0.0 ∼ 1.5 0.001A1 −0.2 ∼ 0.2 0.001A2 0.0 ∼ 2.0 0.001Keta 0.0 ∼ 2e−4 1e−6

Ags −2e−2 ∼ 0.0 1e−5

72

Table D.14: A partial list (2) of parameters for BSIM3v3 model (withits range and resolution) to be extracted.

Variable Range ResolutionB0 −5e−7 ∼ 0.0 1e−9

B1 0.0 ∼ 8e−5 1e−7

Voff −0.2 ∼ 0.0 0.0001Nfactor 0.0 ∼ 2.0 0.001Cit 0.0 ∼ 2e−4 1e−6

Cdsc 0.0 ∼ 5e−4 1e−6

Cdscb −2e−4 ∼ 0.0 1e−7

Cdscd 0.0 ∼ 5e−5 1e−7

Eta0 0.0 ∼ 0.3 0.0001Etab −0.2 ∼ 0.0 0.0001Dsub 0.0 ∼ 1.5 0.001Pclm 0.0 ∼ 2.0 0.001Pdiblc1 0.0 ∼ 3e−3 1e−5

Pdiblc2 0.0 ∼ 3e−3 1e−5

Pdiblcb 0.0 ∼ 0.1 0.0001Drout 0.0 ∼ 1.0 0.001Pscb1 0.0 ∼ 5e8 1e6

Pscb2 0.0 ∼ 1e−6 1e−9

Pvag 0.0 ∼ 1.0 0.001δ 0.0 ∼ 2e−2 1e−4

lln 0.0 ∼ 0.4 0.001lwn 0.0 ∼ 2.0 0.01wln 0.0 ∼ 2.5 0.01wwn 0.0 ∼ 4.0 0.01Lint 1.0 ∼ 1.1 0.001ll −6e−1 ∼ 0.0 1e−10

lw 0.0 ∼ 4e−9 1e−11

lwl −0.2 ∼ 0.2 0.001Wint 0.0 ∼ 1.2e−7 1e−9

wl −4e−15 ∼ 0.0 1e−17

ww −3e−20 ∼ 0.0 1e−22

wwl −0.2 ∼ 0.2 0.001Mobmod 0.0 ∼ 2 1Dwg −1e−8 ∼ 0.0 1e−10

Dwb 0.0 ∼ 2e−8 1e−10

73

Table D.15: The proceed generations and computational time forBSIM3v3 single I-V curve parameters extraction andoptimization.

Runs Proceed generations Computational time Final error1 4352 1506′′ 0.042862 4097 1406′′ 0.048813 1170 405′′ 0.049684 1126 398′′ 0.049945 761 257′′ 0.041826 2834 976′′ 0.049247 1007 384′′ 0.049918 1283 445′′ 0.048999 4293 1478′′ 0.0416610 880 296′′ 0.04946

74

Table D.16: The proceed generations and computational time forBSIM3v3 multiple I-V curves parameters extraction andoptimization.

Runs Proceed generations Computational time Final error1 8821 3406′′ 0.049922 4097 1406′′ 0.040213 3170 1045′′ 0.049824 1926 893′′ 0.049945 6862 2251′′ 0.041326 3384 1176′′ 0.042247 7305 2381′′ 0.049318 2287 984′′ 0.043249 5329 2018′′ 0.0414810 4880 1562′′ 0.04228

75

Table D.17: The comparison of the error norms between differentweight functions for BSIM3v3 I-V curves evolution (withthe same random seed for ten best runs).

Generation Constant Linear Power law20 69.814 51.5758 35.111540 28.0412 40.0487 14.736760 20.8392 18.1099 9.0873180 12.507 13.00649 8.206100 10.2639 11.00222 7.92674120 9.8391 10.98492 6.52684140 9.80239 10.55774 6.15121160 9.42851 10.20099 5.65315180 9.28894 10.02429 5.33504200 9.28427 9.88222 5.24839220 9.28417 9.27141 4.81587240 9.26113 8.86964 4.74585260 9.16339 8.66859 4.70573280 9.03131 7.85095 4.34517300 9.01212 7.63121 4.02546

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Table D.18: Number of proceed generations and error norms for each sub-experiment insensitivity test (Only one parameters set is allowed to be change).

5 50 100 150 200 250 300General 29.821 10.914 7.9009 5.4501 5.1082 4.9043 4.5100Threshold voltage 57.5223 56.0561 55.8519 55.7870 55.7293 55.7165 55.7164Mobility model 99.5448 96.4093 59.4607 46.5081 45.1440 45.0571 44.8646Subthreshold current 21.7025 21.6143 21.6107 21.5865 21.5865 21.5865 21.5865Rout 33.3965 30.8802 30.8758 30.2487 30.2348 30.2348 30.2209

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Table D.19: Number of proceed generations and error norms for eachsub-experiment in sensitivity test (Two parameters sets areallowed to be change in the same time).

5 50 100 150 200 250 300G+T 74.1230 47.1230 40.3400 39.3100 39.3100 38.3200 35.3000G+M 80.2120 13.0215 6.2806 5.2478 4.1426 4.1387 4.1053G+S 80.2130 61.5430 59.5430 53.5600 48.4300 46.3400 46.3400G+R 89.8120 48.1000 39.4330 38.3423 38.3423 38.3423 38.3423T+M 60.5670 48.0320 46.3560 40.0352 38.0129 38.0129 38.0129T+S 29.821 10.914 7.9009 5.4501 5.1082 4.9043 4.5100T+R 90.0896 74.4210 74.3910 74.3120 73.4560 72.3420 72.0100M+S 88.1200 35.6200 32.2120 28.1200 28.1200 27.6200 26.1250M+R 77.1200 6.7800 6.0120 4.3200 3.6630 2.6960 2.6755S+R 75.1230 60.1110 59.1310 58.0129 57.5129 56.0129 56.0000

Appendix E

List of Figures

78

79

VB

VG

VD

VS

Figure E.1: A symbol of device in VLSI circuit.

80

BulkGate

Drain

Source

Cgd Cbd

Qd Ibd

Qb

Ids

Cgb

Ibs

QbsCgs

Qs

Rds

- +

- +

- +

- +

- +

VG

VD

VB

VS

Figure E.2: A BSIM3v3 MOSFET equivalent circuit.

81

Figure E.3: The comparison between SPICE results and our simulatedresults for terminal IDS-VGS characteristics with the sameconstruction parameters for 0.25 µm N-MOSFET device.

82

Figure E.4: The comparison between SPICE results and our simulatedresults for terminal IDS-VBS characteristics with the sameconstruction parameters for 0.25 µm N-MOSFET device.

83

The best solution satisfythe goal conditions

Output the bestsolution.

No

Yes

Decode the bits stringand get the parameters

Apply I-V model(IDS) to obtain thesimulated results

Select nextchromosome

Initialize evolutionary population P

Apply fitness evaluator , and eachindividual fitness score can be obtain.

Apply selection schemes with floatingpoint operator to select the chromosomes

from P in current generation.

Breed new offspring from selectedchromosome with uniform crossover.

After generating the sub-population, thereplacement scheme should be performed.

Apply mutation mechanics to allindividuals in next population.

Figure E.5: A flowchart of the proposed genetic algorithm fordeep-submicron MOSFETs simulation and optimization.

84

Figure E.6: The shape plot of the relationship between diversity andmutation rate.

85

Figure E.7: The comparison between measured curve and simulatedevolutionary curve for 0.25 µm N-MOSFETdevice.(ε=5e−2).

86

Figure E.8: A zoom-in view of discrepancies for measured andsimulated I-V points (VDS = 0.2 ∼ 0.6) for single I-Vcurve evolution.

87


88


89

Figure E.11: The comparison between measured and simulated I-Vcurves for BSIM3v3 model extracted parameters.

90

Figure E.12: A zoom-in view of discrepancies for measured andsimulated I-V points (VDS = 0.2 ∼ 0.6) for multiple I-Vcurves evolution.

91


92


93

Figure E.15: BSIM3v3 model simulated results for GA w/ or w/o applyweight function.

94

Figure E.16: Convergent behaviors of evolutionary parametersextraction with different weight functions.

95

Figure E.17: The extracted values of BSIM3v3 general parameters inoptimal 5 runs for I-V curves optimization. Eachparameter is normalized to a limited range.

96

Figure E.18: The extracted values of BSIM3v3 threshold voltageparameters in optimal 5 runs for I-V curves optimization.Each parameter is normalized to a limited range.

97

Figure E.19: The extracted values of BSIM3v3 mobility parameters inoptimal 5 runs for I-V curves optimization. Eachparameter is normalized to a limited range.

98

Figure E.20: The extracted values of BSIM3v3 subthreshold currentparameters in optimal 5 runs for I-V curves optimization.Each parameter is normalized to a limited range.

99

Figure E.21: The extracted values of BSIM3v3 Rout parameters inoptimal 5 runs for I-V curves optimization. Eachparameter is normalized to a limited range.

100

Figure E.22: A comparison of convergent behaviors between differentvarying parameters categories (Only one parameters set isallowed to be change).

101

Figure E.23: A comparison of convergent behaviors between differentvarying parameters categories (Two parameters sets areallowed to be change in the same time).

Appendix F

VITA

102

103

VITA

Name: Cheng-Kai Chen, 陳正凱

Permanent address: No. 11, Alley 1, Lane 74,

Jungming Rd., Shi Chiu,

Taichung, Taiwan 403, R.O.C.

Degree and date to be conferred: Master's degree,

July, 2002.

Date of birth: October 11, 1978.

Place of birth: Madou Jen, Tainan, Taiwan, R.O.C.

Secondary education: Viator Senior High School, 1997.

Collegiate institutions attended Degree Date of Degree

National Chiao Tung Univeresity, Hsinchu, Taiwan, R.O.C.

BSEE February, 2001

National Chiao Tung Univeresity, Hsinchu, Taiwan, R.O.C.

MSEE July, 2002

Major: Computer and Information Science.

Master thesis title: A genetic algorithm for deep-submicron MOSFET

parameters extraction and simulation.

Professional Talks and Publications: Journal papers: [1]: Yiming Li, Cheng-Kai Chen, and C.-T. Sun, ì Optimal Model Parameters Extraction

for Semiconductor Device Simulation with a Genetic Algorithm,î WSEAS Transactions on Systems, Vol. 1, No. 2, April 2002, pp. 303-308.

Book papers: [1]: Yiming Li, C.-T. Sun, and, Cheng-Kai Chen, ì A Floating-Point Based Evolutionary

Algorithm for Model Parameters Extraction and Optimization in HBT Device Simulation,î to appear in ì Advances in Soft Computing,î Springer-Verlag, 2002.

104

[2]: Yiming Li, Cheng-Kai Chen, and P. Chen, ìMonotone Iterative Method and Adaptive Finite Volume Method for Parallel Numerical Simulation of Submicron MOSFET Devices,î in ì Topics in Applied and Theoretical Mathematics and Computer Scienceî Edited by V. V. Kluev and N. E. Mastorakis, WSEAS Press, ISBN: 960-8052-47-6, Dec. 2001, pp. 25-30.

International Conference papers: [1]: Yiming Li, C.-T. Sun, and, Cheng-Kai Chen, ì A Floating-Point Based Evolutionary

Algorithm for Model Parameters Extraction and Optimization in HBT Device Simulation,î accepted by IEEE The Sixth International Conference on Neural Networks and Soft Computing (IEEE ICNNSC 2002), Zakopane, Poland, 11-15 June, 2002.

[2]: Yiming Li, Kuen-Yu Huang, Cheng-Kai Chen, C. P. Lee, ì A Parallel Computational Technique for High Frequency HBT Circuit Simulation,î Technical Proceedings of 5th ACR/IEEE/SIAM International Conference on Modeling and Simulation of Microsystems (MSM 2002), Puerto Rico, 22-25 April, 2002, pp. 376-379

[3]: Yiming Li, Cheng-Kai Chen, and P. Chen, ìMonotone Iterative Method and

Adaptive Finite Volume Method for Parallel Numerical Simulation of Submicron MOSFET Devices,î Proceedings of 2001 WSEAS International Conference on Applied and Theoretical Mathematics, Cairns, 17-21 Dec., 2001, pp. 6201-6206.

[4]: Yiming Li, Cheng-Kai Chen, S.-S. Lin, Tien-Sheng Chao, J.-L. Liu, and S. M. Sze,

ì An Implementation of Parallel Dynamic Load Balancing for Adaptive Computing in VLSI Device Simulation,î Proceedings of 15th IEEE International Parallel and Distributed Processing Symposium, (IEEE IPDPS 2001), San Francisco, April 2001, pp. 17.3.1-17.3.6.

Presentations in International Conferences: [1]: ì A Floating-Point Based Evolutionary Algorithm for Model Parameters Extraction

and Optimization in HBT Device Simulation, î The Sixth International Conference on Neural Networks and Soft Computing (IEEE ICNNSC 2002), Zakopane, Poland, 11-15 June, 2002.

[2]: ìMonotone Iterative Method and Adaptive Finite Volume Method for Parallel

Numerical Simulation of Submicron MOSFET Devices,î WSEAS International Conference on Applied and Theoretical Mathematics, Cairns, 17-21 Dec., 2001.

[3]: ì An Implementation of Parallel Dynamic Load Balancing for Adaptive Computing in

VLSI Device Simulation,î 15th IEEE International Parallel and Distributed Processing Symposium, (IEEE IPDPS 2001), San Francisco, April 2001.

a genetic algorithm for deep-submicron ...mail.ymlab.org/~ckchen/resource/ckchen_thesis.pdfa genetic...

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