Next: 1. Introduction Up: Dissertation Stephan Wagner Previous: List of Figures

List of Symbols and Acronyms

$\mathbf{A}$ System matrix of a linear equation system

$\tilde{\ensuremath{\mathbf{A}}}$ System matrix of the complete linear equation system

$\ensuremath{\mathbf{A}}_i$ System matrix of the inner equation system

$\ensuremath{\mathbf{A}}_{\mathrm{b}}$ System matrix of the boundary system

$\ensuremath{\mathbf{A}}_{\mathrm{s}}$ System matrix of the segment system

BV $_{\mathrm{CEO}}$ Collector breakdown voltage

$\beta_n$ Electron kurtosis

$\beta_p$ Hole kurtosis

$\mathbf{b}$ Right-hand-side vector of a linear equation system

$\tilde{\ensuremath{\mathbf{b}}}$ Right-hand-side vector of the complete linear equation system

$\ensuremath{\mathbf{b}}_i$ Right-hand-side vector of the inner equation system

$b_{\mathrm{avg}}$ Average bandwidth

$\underline{\ensuremath{\mathbf{b}}}$ Complex-valued right-hand-side vector of the small-signal system

$\mathbf{b_\mathrm{I}}$ Imaginary part of the complex-valued right hand side vector

$\mathbf{b_\mathrm{R}}$ Real part of the complex-valued right-hand-side vector

$\ensuremath{\mathbf{b}}_{\mathrm{b}}$ Right-hand-side vector of the boundary system

$\ensuremath{\mathbf{b}}_{\mathrm{s}}$ Right-hand-side vector of the segment system

$c_{\mathrm{L}}$ Heat capacity

$C_{ij}$ Capacitance between ports and

Electron diffusion coefficient

$f_\mathrm{max}$ Maximum oscillation frequency

$f_\textrm {T}$ Cut-off or transit frequency

$f_\mathrm{op}$ Operating frequency

$F_{x_{i,j}}$ Flux between points and

$g_\mathrm{m}$ Matched gain

Source term

$i_{\mathrm{B}}$ Base Current

$i_{\mathrm{C}}$ Collector Current

$\mathbf{J}$ Jacobian matrix

$J_\mathrm{C}$ Density of the collector current

$\kappa_{\mathrm{L}}$ Thermal conductivity

$\ensuremath{\kappa_{\mathrm{s}}}$ Spectral condition number

$\mathrm{k_B}$ Boltzmann's constant

$\mathbf{L}$ Lower triangular matrix

$L_\mathrm{g}$ Gate Length

$\lambda_\mathrm{min }$ Smallest eigenvalue

$\lambda_\mathrm{max }$ Largest eigenvalue

$\mu_n$ Electron mobility

$\mu_p$ Hole mobility

$\mathbf{M}$ Preconditioner

Dimension of a linear equation system

Electron concentration

$P_\mathrm{IN}$ Input power

$P_\mathrm{OUT}$ Output power

$\psi$ Electrostatic potential

$\psi_\mathrm{C}$ Contact potential

Hole concentration

$\mathrm{q}$ Elementary charge

$\rho$ Space charge density

$\rho_{\mathrm{L}}$ Mass density

Recombination rate

$\sigma_n$ Electron conductivity

$\sigma_p$ Hole conductivity

$\ensuremath{\mathbf{S}}_{\mathrm{c}}$ Scaling vector (diagonal matrix) for columns

$\ensuremath{\mathbf{S}}_{\mathrm{r}}$ Scaling vector (diagonal matrix) for rows

$\ensuremath{\mathbf{T}}_{\mathrm{b}}$ Transformation matrix of boundary conditions

$\ensuremath{\mathbf{T}}_{\mathrm{v}}$ Transformation matrix of variables

$T_{\mathrm{L}}$ Lattice temperature

Electron temperature

Hole temperature

$\mathbf{U}$ Upper triangular matrix

$\mathbf{v}$ Variable vector

V Velocity

V $_\mathrm{sat}$ Saturation velocity

$V_\mathrm{CE}$ Collector Emitter Voltage

$V_\mathrm{DS}$ Drain Source Voltage

$V_\mathrm{GS}$ Gate Source Voltage

$W_\mathrm{g}$ Gate Width

$\mathbf{x}$ Solution vector of a linear equation system

$\tilde{\ensuremath{\mathbf{x}}}$ Solution vector of the complete linear equation system

$\ensuremath{\mathbf{b}}_i$ Solution of the inner equation system

$\underline{\ensuremath{\mathbf{x}}}$ Complex-valued solution vector of the small-signal system

$\mathbf{x_\mathrm{I}}$ Imaginary part of the complex-valued solution vector

$\mathbf{x_\mathrm{R}}$ Real part of the complex-valued solution vector

$\mathbf{y}$ Forward substitution vector

AC Alternating current

ACML AMD Core Math Library

AlAs Aluminum Arsenide

A-parameter/matrix Chain parameter/matrix (also ABCD)

ADS Advanced Design System

AINV Approximate Inverse (Preconditioner)

AIX Advanced Interactive eXecutive

AMG Algebraic Multi-Grid

AM Amplitude Modulation

AMD Advanced Micro Devices

API Application Programming Interface

ARPACK Arnoldi Package

ASCII American Standard Code for Information Interchange

ATLAS Automatically Tuned Linear Algebra Software

BICG Bi-Conjugate Gradient

BICGSTAB Bi-Conjugate Gradients Stabilized

BICMOS Bipolar Complementary Metal Oxide Semiconductor

BJT Bipolar Junction Transistor

BLAS Basic Linear Algebra Subprograms

BSIM Berkeley Short-Channel IGFET Model

CB Consumer Band

CGS Conjugate Gradient Squared

CG Conjugate Gradient

CMOS Complementary Metal Oxide Semiconductor

CPU Central Processing Unit

CSR Compressed Sparse Row

CVS Concurrent Version System

CV Capacitance (C) - Voltage (V) plot

DC Direct current

DANSYS Distributed ANSYS

DESSIS Device Simulation for Smart Integrated Systems

EAS Equation Assembly System

EISPACK Eigensolver Package

ESSL Engineering and Scientific Subroutine Library

FEDOS Finite Element Diffusion and Oxidation Simulator

FET Field Effect Transistor

FFT Fast Fourier Transformation

FM Frequency Modulation

FORTRAN Formula Translator

GaAs Gallium Arsenide

GaP Gallium Phosphide

Gb Gigabit

GB Gigabyte

GHz Gigahertz

GMRES Generalized Minimal Residual

GNU GNU's not Unix

GUI Graphical User Interface

HBT Heterojunction Bipolar Transistor

HEMT High Electron Mobility Transistor

HF High Frequency

H-parameter/matrix Hybrid parameter/matrix

HPF High Performance Fortran

HSL Harwell Subroutine Library

IGFET Insulated Gate Field Effect Transistor

IBM International Business Machines

IEEE Institute of Electrical and Electronics Engineers

IISS Intelligent Iterative Solver Service

ILU Incomplete LU-factorization

IMSL International Mathematical and Statistical Library

InAs Indium Arsenide

InGaP Indium Gallium Phosphide

InP Indium Phosphide

IPL input-deck programming language

IR Infrared

ISE Integrated Systems Engineering

IV Current (I) - Voltage (V) plot

LF Low Frequency

LINPACK Linear Package

MAG Maximum Available Gain

MCSC Modified Compressed Sparse Column

MCSR Modified Compressed Sparse Row

MDI Multiple Document Interface

MESFET Metal Semiconductor Field Effect Transistor

MF Middle Frequency

MHz Megahertz

MODFET Modulation-Doped Field Effect Transistor

MOS Metal Oxide Semiconductor

MOSFET Metal Oxide Semiconductor Field Effect Transistor

MPI Message Passing Interfaces

MSG Maximum Stable Gain

MUMPS Multifrontal Massively Parallel Sparse Direct Solver

NAG Numerical Algorithms Group

NaN Not a Number

OPENMP Open Multi Processing

PARDISO Parallel Direct Solver

PSBLAS Parallel Sparse Basic Linear Algebra Subroutines

PVM Parallel Virtual Machines

RFIC Radio Frequency Integrated Circuits

RF Radio Frequency

SAMG Algebraic Multi-Grid Methods for Systems

SEILIB Simulation Environment Interaction Library

SIESTA Simulation Environment for Semiconductor Technology Analysis

SiC Silicon Carbide

SiGe Silicon Germanium

SMP Shared Memory Parallelization

SOI Silicon-On-Insulator

SOR Successive Over-Relaxation

SPAI Sparse Approximate Inverse Preconditioner

S-parameter/matrix Scattering parameter

SPICE Simulation Program with Integrated Circuit Emphasis

STL Standard Template Library

SSOR Symmetric Successive Over-Relaxation

${\textrm{S}^3\textrm{A}}$ Sinusoidal Steady-State Analysis

TCAD Technology Computer Aided Design

UHF Ultra High Frequency

UMFPACK Unsymmetric Multi-Frontal Package

VBIC95 Vertical Bipolar Inter-Company Model 1995

VHF Very High Frequency

VTK Visualization Toolkit

WSMP Watson Sparse Matrix Package

Y-parameter/matrix Admittance parameter/matrix

Z-parameter/matrix Impedance parameter/matrix

Next: 1. Introduction Up: Dissertation Stephan Wagner Previous: List of Figures

S. Wagner: Small-Signal Device and Circuit Simulation

$\mathbf{A}$	System matrix of a linear equation system
$\tilde{\ensuremath{\mathbf{A}}}$	System matrix of the complete linear equation system
$\ensuremath{\mathbf{A}}_i$	System matrix of the inner equation system
$\ensuremath{\mathbf{A}}_{\mathrm{b}}$	System matrix of the boundary system
$\ensuremath{\mathbf{A}}_{\mathrm{s}}$	System matrix of the segment system
BV $_{\mathrm{CEO}}$	Collector breakdown voltage
$\beta_n$	Electron kurtosis
$\beta_p$	Hole kurtosis
$\mathbf{b}$	Right-hand-side vector of a linear equation system
$\tilde{\ensuremath{\mathbf{b}}}$	Right-hand-side vector of the complete linear equation system
$\ensuremath{\mathbf{b}}_i$	Right-hand-side vector of the inner equation system
$b_{\mathrm{avg}}$	Average bandwidth
$\underline{\ensuremath{\mathbf{b}}}$	Complex-valued right-hand-side vector of the small-signal system
$\mathbf{b_\mathrm{I}}$	Imaginary part of the complex-valued right hand side vector
$\mathbf{b_\mathrm{R}}$	Real part of the complex-valued right-hand-side vector
$\ensuremath{\mathbf{b}}_{\mathrm{b}}$	Right-hand-side vector of the boundary system
$\ensuremath{\mathbf{b}}_{\mathrm{s}}$	Right-hand-side vector of the segment system
$c_{\mathrm{L}}$	Heat capacity
$C_{ij}$	Capacitance between ports and
	Electron diffusion coefficient
$f_\mathrm{max}$	Maximum oscillation frequency
$f_\textrm {T}$	Cut-off or transit frequency
$f_\mathrm{op}$	Operating frequency
$F_{x_{i,j}}$	Flux between points and
$g_\mathrm{m}$	Matched gain
	Source term
$i_{\mathrm{B}}$	Base Current
$i_{\mathrm{C}}$	Collector Current
$\mathbf{J}$	Jacobian matrix
$J_\mathrm{C}$	Density of the collector current
$\kappa_{\mathrm{L}}$	Thermal conductivity
$\ensuremath{\kappa_{\mathrm{s}}}$	Spectral condition number
$\mathrm{k_B}$	Boltzmann's constant
$\mathbf{L}$	Lower triangular matrix
$L_\mathrm{g}$	Gate Length
$\lambda_\mathrm{min }$	Smallest eigenvalue
$\lambda_\mathrm{max }$	Largest eigenvalue
$\mu_n$	Electron mobility
$\mu_p$	Hole mobility
$\mathbf{M}$	Preconditioner
	Dimension of a linear equation system
	Electron concentration
$P_\mathrm{IN}$	Input power
$P_\mathrm{OUT}$	Output power
$\psi$	Electrostatic potential
$\psi_\mathrm{C}$	Contact potential
	Hole concentration
$\mathrm{q}$	Elementary charge
$\rho$	Space charge density
$\rho_{\mathrm{L}}$	Mass density
	Recombination rate
$\sigma_n$	Electron conductivity
$\sigma_p$	Hole conductivity
$\ensuremath{\mathbf{S}}_{\mathrm{c}}$	Scaling vector (diagonal matrix) for columns
$\ensuremath{\mathbf{S}}_{\mathrm{r}}$	Scaling vector (diagonal matrix) for rows
$\ensuremath{\mathbf{T}}_{\mathrm{b}}$	Transformation matrix of boundary conditions
$\ensuremath{\mathbf{T}}_{\mathrm{v}}$	Transformation matrix of variables
$T_{\mathrm{L}}$	Lattice temperature
	Electron temperature
	Hole temperature
$\mathbf{U}$	Upper triangular matrix
$\mathbf{v}$	Variable vector
V	Velocity
V $_\mathrm{sat}$	Saturation velocity
$V_\mathrm{CE}$	Collector Emitter Voltage
$V_\mathrm{DS}$	Drain Source Voltage
$V_\mathrm{GS}$	Gate Source Voltage
$W_\mathrm{g}$	Gate Width
$\mathbf{x}$	Solution vector of a linear equation system
$\tilde{\ensuremath{\mathbf{x}}}$	Solution vector of the complete linear equation system
$\ensuremath{\mathbf{b}}_i$	Solution of the inner equation system
$\underline{\ensuremath{\mathbf{x}}}$	Complex-valued solution vector of the small-signal system
$\mathbf{x_\mathrm{I}}$	Imaginary part of the complex-valued solution vector
$\mathbf{x_\mathrm{R}}$	Real part of the complex-valued solution vector
$\mathbf{y}$	Forward substitution vector
AC	Alternating current
ACML	AMD Core Math Library
AlAs	Aluminum Arsenide
A-parameter/matrix	Chain parameter/matrix (also ABCD)
ADS	Advanced Design System
AINV	Approximate Inverse (Preconditioner)
AIX	Advanced Interactive eXecutive
AMG	Algebraic Multi-Grid
AM	Amplitude Modulation
AMD	Advanced Micro Devices
API	Application Programming Interface
ARPACK	Arnoldi Package
ASCII	American Standard Code for Information Interchange
ATLAS	Automatically Tuned Linear Algebra Software
BICG	Bi-Conjugate Gradient
BICGSTAB	Bi-Conjugate Gradients Stabilized
BICMOS	Bipolar Complementary Metal Oxide Semiconductor
BJT	Bipolar Junction Transistor
BLAS	Basic Linear Algebra Subprograms
BSIM	Berkeley Short-Channel IGFET Model
CB	Consumer Band
CGS	Conjugate Gradient Squared
CG	Conjugate Gradient
CMOS	Complementary Metal Oxide Semiconductor
CPU	Central Processing Unit
CSR	Compressed Sparse Row
CVS	Concurrent Version System
CV	Capacitance (C) - Voltage (V) plot
DC	Direct current
DANSYS	Distributed ANSYS
DESSIS	Device Simulation for Smart Integrated Systems
EAS	Equation Assembly System
EISPACK	Eigensolver Package
ESSL	Engineering and Scientific Subroutine Library
FEDOS	Finite Element Diffusion and Oxidation Simulator
FET	Field Effect Transistor
FFT	Fast Fourier Transformation
FM	Frequency Modulation
FORTRAN	Formula Translator
GaAs	Gallium Arsenide
GaP	Gallium Phosphide
Gb	Gigabit
GB	Gigabyte
GHz	Gigahertz
GMRES	Generalized Minimal Residual
GNU	GNU's not Unix
GUI	Graphical User Interface
HBT	Heterojunction Bipolar Transistor
HEMT	High Electron Mobility Transistor
HF	High Frequency
H-parameter/matrix	Hybrid parameter/matrix
HPF	High Performance Fortran
HSL	Harwell Subroutine Library
IGFET	Insulated Gate Field Effect Transistor
IBM	International Business Machines
IEEE	Institute of Electrical and Electronics Engineers
IISS	Intelligent Iterative Solver Service
ILU	Incomplete LU-factorization
IMSL	International Mathematical and Statistical Library
InAs	Indium Arsenide
InGaP	Indium Gallium Phosphide
InP	Indium Phosphide
IPL	input-deck programming language
IR	Infrared
ISE	Integrated Systems Engineering
IV	Current (I) - Voltage (V) plot
LF	Low Frequency
LINPACK	Linear Package
MAG	Maximum Available Gain
MCSC	Modified Compressed Sparse Column
MCSR	Modified Compressed Sparse Row
MDI	Multiple Document Interface
MESFET	Metal Semiconductor Field Effect Transistor
MF	Middle Frequency
MHz	Megahertz
MODFET	Modulation-Doped Field Effect Transistor
MOS	Metal Oxide Semiconductor
MOSFET	Metal Oxide Semiconductor Field Effect Transistor
MPI	Message Passing Interfaces
MSG	Maximum Stable Gain
MUMPS	Multifrontal Massively Parallel Sparse Direct Solver
NAG	Numerical Algorithms Group
NaN	Not a Number
OPENMP	Open Multi Processing
PARDISO	Parallel Direct Solver
PSBLAS	Parallel Sparse Basic Linear Algebra Subroutines
PVM	Parallel Virtual Machines
RFIC	Radio Frequency Integrated Circuits
RF	Radio Frequency
SAMG	Algebraic Multi-Grid Methods for Systems
SEILIB	Simulation Environment Interaction Library
SIESTA	Simulation Environment for Semiconductor Technology Analysis
SiC	Silicon Carbide
SiGe	Silicon Germanium
SMP	Shared Memory Parallelization
SOI	Silicon-On-Insulator
SOR	Successive Over-Relaxation
SPAI	Sparse Approximate Inverse Preconditioner
S-parameter/matrix	Scattering parameter
SPICE	Simulation Program with Integrated Circuit Emphasis
STL	Standard Template Library
SSOR	Symmetric Successive Over-Relaxation
${\textrm{S}^3\textrm{A}}$	Sinusoidal Steady-State Analysis
TCAD	Technology Computer Aided Design
UHF	Ultra High Frequency
UMFPACK	Unsymmetric Multi-Frontal Package
VBIC95	Vertical Bipolar Inter-Company Model 1995
VHF	Very High Frequency
VTK	Visualization Toolkit
WSMP	Watson Sparse Matrix Package
Y-parameter/matrix	Admittance parameter/matrix
Z-parameter/matrix	Impedance parameter/matrix