symbol description

symbol
description

Physical constants

$\ensuremath{k}$ Boltzmann's constant

$\ensuremath{h}$ Plank's constant

$\ensuremath{q}$ electron charge

$\ensuremath{v_{\mathit{c}}}$ speed of light

$\ensuremath{\epsilon _0}$ vacuum permittivity

$\ensuremath{\mu _0}$ vacuum permeability

Environmental quantities

$\ensuremath{T}$ temperature

$\ensuremath{U_{\mathit{T}}}$ thermal voltage

$\ensuremath{n_{\mathit{i}}}$ intrinsic carrier density

Material parameters

$\ensuremath{E_{\mathit{g}}}$ band gap energy

$\ensuremath{v_{\mathit{sat}}}$ saturation velocity

$\ensuremath{\mu }$ carrier mobility

$\ensuremath{\epsilon _{\mathit{r}}}$ relative permittivity

$\ensuremath{\epsilon _{\mathit{i}}}$ insulator permittivity

$\ensuremath{\epsilon _{\mathit{s}}}$ semiconductor permittivity

$\ensuremath{\epsilon _{\mathit{M}}}$ interconnect insulator permittivity

$\ensuremath{\rho _{\mathit{M}}}$ interconnect conductor resistivity

Technology parameters and structural device data

$\ensuremath{V_{\mathit{DD,nom}}}$ nominal supply voltage

$\ensuremath{V_{\mathit{DD,min}}}$ minimum supply voltage

$\ensuremath{V_{\mathit{DD,max}}}$ maximum supply voltage

$\ensuremath{V_{\mathit{T,nom}}}$ nominal threshold voltage

$\ensuremath{I_{\mathit{off,nom}}}$ nominal off-state current

$\ensuremath{f_{\mathit{c,nom}}}$ nominal clock frequency

$\ensuremath{T_{\mathit{nom}}}$ nominal operating temperature

$\ensuremath{W}$ transistor width

$\ensuremath{W_{\mathit{nom}}}$ nominal transistor width

$\ensuremath {L}$ gate length

$\ensuremath{L_{\mathit{nom}}}$ nominal gate length

$\ensuremath{L_{\mathit{min}}}$ minimum gate length

$\ensuremath{t_{\mathit{ox}}}$ gate oxide thickness

$\ensuremath{t_{\mathit{ox,nom}}}$ nominal gate oxide thickness

$\ensuremath{C_{\mathit{ox}}}$ gate capacitance per area

$\ensuremath{X_{\mathit{j}}}$ junction depth

$\ensuremath{X_{\mathit{j,nom}}}$ nominal junction depth

$\ensuremath{N_{\mathit{ch}}}$ channel doping level

$\ensuremath{c_{\mathit{M}}}$ interconnect capacitance per length

$\ensuremath{r_{\mathit{M}}}$ interconnect resistance per length

$\ensuremath{t_{\mathit{ox,M}}}$ interconnect insulator thickness

$\ensuremath{H_{\mathit{M}}}$ interconnect metal thickness

$\ensuremath{W_{\mathit{M}}}$ interconnect width

$\ensuremath{S_{\mathit{M}}}$ interconnect spacing

Device physical quantities

$\ensuremath{N_{\mathit{D}}}$ donor concentration

$\ensuremath{N_{\mathit{A}}}$ acceptor concentration

$\ensuremath{\psi _{\mathit{s}}}$ surface potential displacement

$\ensuremath{\Phi _{\mathit{B}}}$ bulk built-in potential

$\ensuremath{\Phi _{\mathit{G}}}$ gate built-in potential

$\ensuremath{\Phi _{\mathit{MS}}}$ work function difference

$\ensuremath{V_{\mathit{FB}}}$ flat band voltage

$\ensuremath{X_{\mathit{d}}}$ depletion depth

$\ensuremath{C_{\mathit{d}}}$ depletion capacitance per area

$\ensuremath{C_{\mathit{i}}}$ insulator capacitance per area

$\ensuremath{\beta }$ MOSFET conductivity parameter

$\ensuremath{\gamma }$ MOSFET body factor

$\ensuremath{Q_{\mathit{ss}}}$ fixed interface charge per area

$\ensuremath{I_{\mathit{s}}}$ reverse saturation current

$\ensuremath{\kappa }$ scaling factor

Terminal quantities

$\ensuremath{V_{\mathit{D}}}$ drain voltage

$\ensuremath{V_{\mathit{G}}}$ gate voltage

$\ensuremath{V_{\mathit{B}}}$ bulk voltage

$\ensuremath{V_{\mathit{S}}}$ source voltage

$\ensuremath{V_{\mathit{DS}}}$ drain-source voltage

$\ensuremath{V_{\mathit{GS}}}$ gate-source voltage

$\ensuremath{V_{\mathit{BS}}}$ bulk-source voltage

$\ensuremath{I_{\mathit{D}}}$ drain current

$\ensuremath{I_{\mathit{G}}}$ gate current

$\ensuremath{I_{\mathit{B}}}$ bulk current

$\ensuremath{g_{\mathit{m}}}$ transfer conductance

$\ensuremath{g_{\mathit{o}}}$ output conductance

$\ensuremath{Q_{\mathit{D}}}$ drain charge

$\ensuremath{Q_{\mathit{G}}}$ gate charge

$\ensuremath{C_{\mathit{G}}}$ gate capacitance

$\ensuremath{C_{\mathit{GD}}}$ gate-drain capacitance

$\ensuremath{C_{\mathit{SB}}}$ source-bulk capacitance

$\ensuremath{C_{\mathit{DB}}}$ drain-bulk capacitance

$\ensuremath{V_{\mathit{BE}}}$ base-emitter voltage

$\ensuremath{V_{\mathit{A}}}$ Early voltage

Electrical device data

$\ensuremath{I_{\mathit{on}}}$ on-state current

$\ensuremath{I_{\mathit{on,eff}}}$ effective turn-on current

$\ensuremath{I_{\mathit{off}}}$ off-state current

$\ensuremath{Q_{\mathit{sw}}}$ switching charge

$\ensuremath{V_{\mathit{T}}}$ threshold voltage

$\ensuremath{V_{\mathit{T,inv}}}$ strong-inversion threshold voltage

$\ensuremath{V_{\mathit{T,fit}}}$ fitted threshold voltage

$\ensuremath{V_{\mathit{T,lin}}}$ linear threshold voltage

$\ensuremath{V_{\mathit{T,sat}}}$ saturation threshold voltage

$\ensuremath{I_{\mathit{T}}}$ threshold current

$\ensuremath{S}$ gate swing

$\ensuremath{D}$ surface DIBL parameter

$\ensuremath{R_{\mathit{dibl}}}$ surface DIBL rate

$\ensuremath{R_{\mathit{punch}}}$ sub-surface DIBL rate

$\ensuremath{R_{\mathit{on}}}$ on-state resistance

$\ensuremath{R_{\mathit{off}}}$ off-state resistance

$\ensuremath{C_{\mathit{sw}}}$ switching capacitance

VLSI System parameters

$\ensuremath{V_{\mathit{DD}}}$ supply voltage

$\ensuremath{f_{\mathit{c}}}$ clock frequency

$\ensuremath{D_{\mathit{chip}}}$ chip diameter

$\ensuremath{N_{\mathit{t}}}$ number of transistors

$\ensuremath{N_{\mathit{g}}}$ number of gates

$\ensuremath{{\mathit{ld}}}$ logic depth

$\ensuremath{{\mathit{ar}}}$ activity ratio

$\ensuremath{{\mathit{sr}}}$ standby ratio

$\ensuremath{F_{\mathit{in}}}$ fan-in

$\ensuremath{F_{\mathit{out}}}$ fan-out

$\ensuremath{F_{\mathit{io}}}$ average fan-in/fan-out

$\ensuremath{L_{\mathit{M}}}$ average interconnect length

$\ensuremath{C_{\mathit{L}}}$ average load capacitance

System performance and qualification parameters

$\ensuremath{t_{\mathit{d}}}$ delay time

$\ensuremath{t_{\mathit{i}}}$ inverter delay

$\ensuremath{t_{\mathit{i,0}}}$ unloaded-inverter delay

$\ensuremath{t_{\mathit{g}}}$ gate delay

$\ensuremath{t_{\mathit{CVI}}}$ CV/I delay metric

$\ensuremath{t_{\mathit{RC}}}$ RC delay metric

$\ensuremath{t_{\mathit{M}}}$ interconnect delay time

$\ensuremath{f_{\mathit{c,max}}}$ maximum clock frequency

$\ensuremath{P}$ power consumption

$\ensuremath{P_{\mathit{stat}}}$ static power consumption

$\ensuremath{P_{\mathit{dyn}}}$ dynamic power consumption

$\ensuremath{P_{\mathit{sc}}}$ short-circuit power consumption

$\ensuremath{P_{\mathit{tot}}}$ total power consumption

$\ensuremath{P_{\mathit{act}}}$ active-mode power consumption

$\ensuremath{P_{\mathit{stb}}}$ standby-mode power consumption

$\ensuremath{E_{\mathit{s}}}$ switching energy

$\ensuremath{P t_{\mathit{d}}}$ power-delay product

$\ensuremath{E_{\mathit{CV2}}}$ CV² energy metric

$\ensuremath{A_{\mathit{inv}}}$ inverter gain

$\ensuremath{A_{\mathit{max}}}$ maximum gain

$\ensuremath{{\mathit{NM}}}$ normalized noise margins

$\ensuremath{{\mathit{NM}}_{\mathit{H}}}$ high noise margin

$\ensuremath{{\mathit{NM}}_{\mathit{L}}}$ low noise margin

$\ensuremath{V_{\mathit{os}}}$ output voltage swing

$\ensuremath{{\mathit{OS}}}$ normalized output voltage swing

$\ensuremath{t_{\mathit{l}}}$ leakage time

$\ensuremath{f_{\mathit{c,min}}}$ minimum clock frequency

$\ensuremath{P_{\mathit{E}}}$ error probability

$\ensuremath{R_{\mathit{E}}}$ bit error rate

Circuit specific quantities

$\ensuremath{V_{\mathit{in}}}$ input voltage

$\ensuremath{V_{\mathit{out}}}$ output voltage

$\ensuremath{I_{\mathit{sc}}}$ inverter crow bar current

$\ensuremath{X}$ supply voltage usage ratio

$\ensuremath{X_{\mathit{eff}}}$ effective supply voltage usage ratio

$\ensuremath{X_{\mathit{crit}}}$ critical supply voltage usage ratio

$\ensuremath{F_{\mathit{U}}}$ unsymmetry factor

$\ensuremath{V_{\mathit{IH}}}$ input high voltage

$\ensuremath{V_{\mathit{IL}}}$ input low voltage

$\ensuremath{V_{\mathit{OH}}}$ output high voltage

$\ensuremath{V_{\mathit{OL}}}$ output low voltage

Signal processing quantities

$\ensuremath{s}$ complex frequency

$\ensuremath{f_{\mathit{s}}}$ sampling frequency

$\ensuremath{f_{\mathit{os}}}$ oversampling frequency

symbol	description
symbol	description


Physical constants
$\ensuremath{k}$	Boltzmann's constant
$\ensuremath{h}$	Plank's constant
$\ensuremath{q}$	electron charge
$\ensuremath{v_{\mathit{c}}}$	speed of light
$\ensuremath{\epsilon _0}$	vacuum permittivity
$\ensuremath{\mu _0}$	vacuum permeability

Environmental quantities
$\ensuremath{T}$	temperature
$\ensuremath{U_{\mathit{T}}}$	thermal voltage
$\ensuremath{n_{\mathit{i}}}$	intrinsic carrier density

Material parameters
$\ensuremath{E_{\mathit{g}}}$	band gap energy
$\ensuremath{v_{\mathit{sat}}}$	saturation velocity
$\ensuremath{\mu }$	carrier mobility
$\ensuremath{\epsilon _{\mathit{r}}}$	relative permittivity
$\ensuremath{\epsilon _{\mathit{i}}}$	insulator permittivity
$\ensuremath{\epsilon _{\mathit{s}}}$	semiconductor permittivity
$\ensuremath{\epsilon _{\mathit{M}}}$	interconnect insulator permittivity
$\ensuremath{\rho _{\mathit{M}}}$	interconnect conductor resistivity

Technology parameters and structural device data
$\ensuremath{V_{\mathit{DD,nom}}}$	nominal supply voltage
$\ensuremath{V_{\mathit{DD,min}}}$	minimum supply voltage
$\ensuremath{V_{\mathit{DD,max}}}$	maximum supply voltage
$\ensuremath{V_{\mathit{T,nom}}}$	nominal threshold voltage
$\ensuremath{I_{\mathit{off,nom}}}$	nominal off-state current
$\ensuremath{f_{\mathit{c,nom}}}$	nominal clock frequency
$\ensuremath{T_{\mathit{nom}}}$	nominal operating temperature
$\ensuremath{W}$	transistor width
$\ensuremath{W_{\mathit{nom}}}$	nominal transistor width
$\ensuremath {L}$	gate length
$\ensuremath{L_{\mathit{nom}}}$	nominal gate length
$\ensuremath{L_{\mathit{min}}}$	minimum gate length
$\ensuremath{t_{\mathit{ox}}}$	gate oxide thickness
$\ensuremath{t_{\mathit{ox,nom}}}$	nominal gate oxide thickness
$\ensuremath{C_{\mathit{ox}}}$	gate capacitance per area
$\ensuremath{X_{\mathit{j}}}$	junction depth
$\ensuremath{X_{\mathit{j,nom}}}$	nominal junction depth
$\ensuremath{N_{\mathit{ch}}}$	channel doping level
$\ensuremath{c_{\mathit{M}}}$	interconnect capacitance per length
$\ensuremath{r_{\mathit{M}}}$	interconnect resistance per length
$\ensuremath{t_{\mathit{ox,M}}}$	interconnect insulator thickness
$\ensuremath{H_{\mathit{M}}}$	interconnect metal thickness
$\ensuremath{W_{\mathit{M}}}$	interconnect width
$\ensuremath{S_{\mathit{M}}}$	interconnect spacing

Device physical quantities
$\ensuremath{N_{\mathit{D}}}$	donor concentration
$\ensuremath{N_{\mathit{A}}}$	acceptor concentration
$\ensuremath{\psi _{\mathit{s}}}$	surface potential displacement
$\ensuremath{\Phi _{\mathit{B}}}$	bulk built-in potential
$\ensuremath{\Phi _{\mathit{G}}}$	gate built-in potential
$\ensuremath{\Phi _{\mathit{MS}}}$	work function difference
$\ensuremath{V_{\mathit{FB}}}$	flat band voltage
$\ensuremath{X_{\mathit{d}}}$	depletion depth
$\ensuremath{C_{\mathit{d}}}$	depletion capacitance per area
$\ensuremath{C_{\mathit{i}}}$	insulator capacitance per area
$\ensuremath{\beta }$	MOSFET conductivity parameter
$\ensuremath{\gamma }$	MOSFET body factor
$\ensuremath{Q_{\mathit{ss}}}$	fixed interface charge per area
$\ensuremath{I_{\mathit{s}}}$	reverse saturation current
$\ensuremath{\kappa }$	scaling factor

Terminal quantities
$\ensuremath{V_{\mathit{D}}}$	drain voltage
$\ensuremath{V_{\mathit{G}}}$	gate voltage
$\ensuremath{V_{\mathit{B}}}$	bulk voltage
$\ensuremath{V_{\mathit{S}}}$	source voltage
$\ensuremath{V_{\mathit{DS}}}$	drain-source voltage
$\ensuremath{V_{\mathit{GS}}}$	gate-source voltage
$\ensuremath{V_{\mathit{BS}}}$	bulk-source voltage
$\ensuremath{I_{\mathit{D}}}$	drain current
$\ensuremath{I_{\mathit{G}}}$	gate current
$\ensuremath{I_{\mathit{B}}}$	bulk current
$\ensuremath{g_{\mathit{m}}}$	transfer conductance
$\ensuremath{g_{\mathit{o}}}$	output conductance
$\ensuremath{Q_{\mathit{D}}}$	drain charge
$\ensuremath{Q_{\mathit{G}}}$	gate charge
$\ensuremath{C_{\mathit{G}}}$	gate capacitance
$\ensuremath{C_{\mathit{GD}}}$	gate-drain capacitance
$\ensuremath{C_{\mathit{SB}}}$	source-bulk capacitance
$\ensuremath{C_{\mathit{DB}}}$	drain-bulk capacitance
$\ensuremath{V_{\mathit{BE}}}$	base-emitter voltage
$\ensuremath{V_{\mathit{A}}}$	Early voltage

Electrical device data
$\ensuremath{I_{\mathit{on}}}$	on-state current
$\ensuremath{I_{\mathit{on,eff}}}$	effective turn-on current
$\ensuremath{I_{\mathit{off}}}$	off-state current
$\ensuremath{Q_{\mathit{sw}}}$	switching charge
$\ensuremath{V_{\mathit{T}}}$	threshold voltage
$\ensuremath{V_{\mathit{T,inv}}}$	strong-inversion threshold voltage
$\ensuremath{V_{\mathit{T,fit}}}$	fitted threshold voltage
$\ensuremath{V_{\mathit{T,lin}}}$	linear threshold voltage
$\ensuremath{V_{\mathit{T,sat}}}$	saturation threshold voltage
$\ensuremath{I_{\mathit{T}}}$	threshold current
$\ensuremath{S}$	gate swing
$\ensuremath{D}$	surface DIBL parameter
$\ensuremath{R_{\mathit{dibl}}}$	surface DIBL rate
$\ensuremath{R_{\mathit{punch}}}$	sub-surface DIBL rate
$\ensuremath{R_{\mathit{on}}}$	on-state resistance
$\ensuremath{R_{\mathit{off}}}$	off-state resistance
$\ensuremath{C_{\mathit{sw}}}$	switching capacitance

VLSI System parameters
$\ensuremath{V_{\mathit{DD}}}$	supply voltage
$\ensuremath{f_{\mathit{c}}}$	clock frequency
$\ensuremath{D_{\mathit{chip}}}$	chip diameter
$\ensuremath{N_{\mathit{t}}}$	number of transistors
$\ensuremath{N_{\mathit{g}}}$	number of gates
$\ensuremath{{\mathit{ld}}}$	logic depth
$\ensuremath{{\mathit{ar}}}$	activity ratio
$\ensuremath{{\mathit{sr}}}$	standby ratio
$\ensuremath{F_{\mathit{in}}}$	fan-in
$\ensuremath{F_{\mathit{out}}}$	fan-out
$\ensuremath{F_{\mathit{io}}}$	average fan-in/fan-out
$\ensuremath{L_{\mathit{M}}}$	average interconnect length
$\ensuremath{C_{\mathit{L}}}$	average load capacitance

System performance and qualification parameters
$\ensuremath{t_{\mathit{d}}}$	delay time
$\ensuremath{t_{\mathit{i}}}$	inverter delay
$\ensuremath{t_{\mathit{i,0}}}$	unloaded-inverter delay
$\ensuremath{t_{\mathit{g}}}$	gate delay
$\ensuremath{t_{\mathit{CVI}}}$	CV/I delay metric
$\ensuremath{t_{\mathit{RC}}}$	RC delay metric
$\ensuremath{t_{\mathit{M}}}$	interconnect delay time
$\ensuremath{f_{\mathit{c,max}}}$	maximum clock frequency
$\ensuremath{P}$	power consumption
$\ensuremath{P_{\mathit{stat}}}$	static power consumption
$\ensuremath{P_{\mathit{dyn}}}$	dynamic power consumption
$\ensuremath{P_{\mathit{sc}}}$	short-circuit power consumption
$\ensuremath{P_{\mathit{tot}}}$	total power consumption
$\ensuremath{P_{\mathit{act}}}$	active-mode power consumption
$\ensuremath{P_{\mathit{stb}}}$	standby-mode power consumption
$\ensuremath{E_{\mathit{s}}}$	switching energy
$\ensuremath{P t_{\mathit{d}}}$	power-delay product
$\ensuremath{E_{\mathit{CV2}}}$	CV² energy metric
$\ensuremath{A_{\mathit{inv}}}$	inverter gain
$\ensuremath{A_{\mathit{max}}}$	maximum gain
$\ensuremath{{\mathit{NM}}}$	normalized noise margins
$\ensuremath{{\mathit{NM}}_{\mathit{H}}}$	high noise margin
$\ensuremath{{\mathit{NM}}_{\mathit{L}}}$	low noise margin
$\ensuremath{V_{\mathit{os}}}$	output voltage swing
$\ensuremath{{\mathit{OS}}}$	normalized output voltage swing
$\ensuremath{t_{\mathit{l}}}$	leakage time
$\ensuremath{f_{\mathit{c,min}}}$	minimum clock frequency
$\ensuremath{P_{\mathit{E}}}$	error probability
$\ensuremath{R_{\mathit{E}}}$	bit error rate

Circuit specific quantities
$\ensuremath{V_{\mathit{in}}}$	input voltage
$\ensuremath{V_{\mathit{out}}}$	output voltage
$\ensuremath{I_{\mathit{sc}}}$	inverter crow bar current
$\ensuremath{X}$	supply voltage usage ratio
$\ensuremath{X_{\mathit{eff}}}$	effective supply voltage usage ratio
$\ensuremath{X_{\mathit{crit}}}$	critical supply voltage usage ratio
$\ensuremath{F_{\mathit{U}}}$	unsymmetry factor
$\ensuremath{V_{\mathit{IH}}}$	input high voltage
$\ensuremath{V_{\mathit{IL}}}$	input low voltage
$\ensuremath{V_{\mathit{OH}}}$	output high voltage
$\ensuremath{V_{\mathit{OL}}}$	output low voltage

Signal processing quantities
$\ensuremath{s}$	complex frequency
$\ensuremath{f_{\mathit{s}}}$	sampling frequency
$\ensuremath{f_{\mathit{os}}}$	oversampling frequency

Next: 1. Introduction Up: No Title Previous: Acknowledgment

G. Schrom

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