Physical Quantities

symbol description unit

$\alpha$ Temperature coefficient of $\tau _{n,p}$ 1

$\alpha _{n,p}$ Electron, hole impact ionization coefficient cm $^{-1}$

$\alpha _\mathrm{eff}$ Effective impact ionization coefficient cm $^{-1}$

$BV_\mathrm{ld}$ Lateral diode breakdown voltage V

$C_\mathrm{sub}$ Substrate doping concentration $cm^{-3}$

$C_{n,p}$ Auger coefficient cm $^{6}\cdot$ s $^{-1}$

, $D_{n,p}$ Diffusion coefficient cm $^{2}\cdot$ s $^{-1}$

$d_\mathrm{nepi}$ , $d_\mathrm{n1}$ , $d_\mathrm{n2}$ , $d_\mathrm{ptop}$ Depletion extensions $\mu$ m

, $\mathbf{E}$ Electric field V $\cdot$ cm $^{-1}$

$E_\mathrm{c}$ Critical electric field V $\cdot$ cm $^{-1}$

$E_\mathrm{MAX}$ Maximum electric field V $\cdot$ cm $^{-1}$

Electron energy eV

$E_{n(ox)}$ Electric field of side at the interface V $\cdot$ cm $^{-1}$

$E_{n(si)}$ Electric field of silicon side at the interface V $\cdot$ cm $^{-1}$

$E_\mathrm{i}$ Intrinsic energy level eV

$E_\mathrm{r}$ Recombination energy level eV

$E_\mathrm{t}$ Trap energy level eV

$\varepsilon$ Bands structure oo silicon for parabolic bands 1

( ${\mathbf{x}, \mathbf{k}, t}$ ) Carrier distribution function 1

Slope of the graded junction 1

$G_{ii}$ Generation due to impact ionization cm $^{-3}\cdot$ s $^{-1}$

$G_{n,p}$ Generation rates cm $^{-3}\cdot$ s $^{-1}$

$\mathbf{J}$ , $\mathbf{J}_{n,p}$ Current densities A $\cdot$ cm $^{-2}$

, $\mathbf{k}$ Momentum 1

$L_\mathrm{d}$ Drift length $\mu$ m

$L_\mathrm{g}$ Gate length cm

$L_\mathrm{FP}$ Field plate length $\mu$ m

$L_\mathrm{min}$ Minimum channel length $\mu$ m

Multiplication coefficient 1

$\mu$ , $\mu_{n,p}$ Carrier mobilities cm $^{2}\cdot$ V $^{-1}\cdot$ s $^{-1}$

Mass

symbol description unit

Effective mass

Electron concentration cm $^{-3}$

$n_\mathrm{i}$ Intrinsic density cm $^{-3}$

$n_\mathrm{0}$ Equilibrium electron concentration cm $^{-3}$

$\delta n$ Excess electron concentration cm $^{-3}$

$N_\mathrm{drift}$ -drift layer doping concentration $cm^{-3}$

$N_\mathrm{epi}$ -epi layer doping concentration $cm^{-3}$

$N_\mathrm{D,A}$ Donor, acceptor doping concentration $cm^{-3}$

$N_\mathrm{ch(source)}$ Doping concentration at the source end $cm^{-3}$

$N_\mathrm{ch(drift)}$ Doping concentration at the drift end $cm^{-3}$

$N^+_\mathrm{D}$ , $N^-_\mathrm{A}$ Ionized donor, acceptor concentration cm $^{-3}$

$N_n^\mathrm{ref}$ , $N_p^\mathrm{ref}$ , $\gamma_n$ , $\gamma_p$ Lifetime fitting parameters 1

$P_\mathrm{top}$ Doping concentration of the -top region cm $^{-3}$

Hole concentration cm $^{-3}$

$Q_{n}$ -epi layer net charge $cm^{-3}$

$Q_{n,max}$ Maximum $Q_{n}$ $cm^{-3}$

$Q_\mathrm{nd}$ -drift integrated charge $cm^{-3}$

$Q_\mathrm{pd}$ -drift integrated charge $cm^{-3}$

$Q_\mathrm{nd,max}$ Maximum -drift integrated charge $cm^{-3}$

$Q_\mathrm{pd,max}$ Maximum -drift integrated charge $cm^{-3}$

$Q_\mathrm{N}$ -column charge C

$Q_\mathrm{P}$ -column charge C

$Q_\mathrm{DB}$ Charge of the depletion region C

, $R_{n,p}$ Recombination rate cm $^{-3}\cdot$ s $^{-1}$

$R_\mathrm{A}$ Accumulation region resistance $\Omega$

$R_\mathrm{Auger}$ Auger recombination rate cm $^{-3}\cdot$ s $^{-1}$

$R_\mathrm{D}$ Drift region resistance $\Omega$

$R_\mathrm{CH}$ Channel region resistance $\Omega$

$R_\mathrm{J}$ JFET region resistance $\Omega$

$R_\mathrm{SRH}$ Shockley, Read, and Hall recombination rate cm $^{-3}\cdot$ s $^{-1}$

$R_\mathrm{on}$ On-resistance $\Omega$

$R_\mathrm{sp}$ Specific on-resistance m $\Omega$ $cm^{-3}$

Temperature K

Time s

$t_\mathrm{N}$ -column length $\mu$ m

$t_\mathrm{P}$ -column length $\mu$ m

$t_\mathrm{N,P}$ -column length $\mu$ m

$T_{n,p,\mathrm{L}}$ Electron, hole, and lattice temperature K

Room temperature (300 K) K

$\tau_\mathrm{HL}$ High level carrier lifetime s

$\tau _\mathrm{LL}$ Low level carrier lifetime s

$\tau _{n,p}$ Electron, hole minority carrier lifetime s

$\tau _{n0,p0}$ Minority carrier lifetimes at low doping level s

$\tau_\mathrm{sc}$ Space charge generation lifetime s

$t_\mathrm{epi}$ Epitaxial layer thickness $\mu$ m

symbol description unit

$t_\mathrm{nepi}$ -epi layer thickness $\mu$ m

$t_\mathrm{ndrift}$ -drift layer thickness $\mu$ m

$t_\mathrm{ptop}$ -top layer thickness $\mu$ m

$t_\mathrm{soi}$ SOI thickness $\mu$ m

$t_\mathrm{ox}$ Buried oxide thickness $\mu$ m

Drift velocity cm $\cdot$ s $^{-1}$

( $\mathbf{k}$ ) Electron group velocity cm $\cdot$ s $^{-1}$

$V_\mathrm{A}$ Anode voltage V

$V_\mathrm{BR}$ Breakdown voltage V

$V_\mathrm{DS,GS,BS}$ Drain to source, gate to source, bulk to source voltage V

$V_\mathrm{PT}$ Punchthrough voltage V

$V_\mathrm{R}$ Reverse voltage V

Depletion region width $\mu$ m

$W_\mathrm{N}$ -column width $\mu$ m

$W_\mathrm{P}$ -column width $\mu$ m

$W_\mathrm{PT(ch)}$ Depletion layer width in the channel $\mu$ m

$\zeta$ capture cross section ratio 1

Jong-Mun Park 2004-10-28

symbol	description	unit

$\alpha$	Temperature coefficient of $\tau _{n,p}$	1
$\alpha _{n,p}$	Electron, hole impact ionization coefficient	cm $^{-1}$
$\alpha _\mathrm{eff}$	Effective impact ionization coefficient	cm $^{-1}$
$BV_\mathrm{ld}$	Lateral diode breakdown voltage	V
$C_\mathrm{sub}$	Substrate doping concentration	$cm^{-3}$
$C_{n,p}$	Auger coefficient	cm $^{6}\cdot$ s $^{-1}$
, $D_{n,p}$	Diffusion coefficient	cm $^{2}\cdot$ s $^{-1}$
$d_\mathrm{nepi}$ , $d_\mathrm{n1}$ , $d_\mathrm{n2}$ , $d_\mathrm{ptop}$	Depletion extensions	$\mu$ m
, $\mathbf{E}$	Electric field	V $\cdot$ cm $^{-1}$
$E_\mathrm{c}$	Critical electric field	V $\cdot$ cm $^{-1}$
$E_\mathrm{MAX}$	Maximum electric field	V $\cdot$ cm $^{-1}$
	Electron energy	eV
$E_{n(ox)}$	Electric field of side at the interface	V $\cdot$ cm $^{-1}$
$E_{n(si)}$	Electric field of silicon side at the interface	V $\cdot$ cm $^{-1}$
$E_\mathrm{i}$	Intrinsic energy level	eV
$E_\mathrm{r}$	Recombination energy level	eV
$E_\mathrm{t}$	Trap energy level	eV
$\varepsilon$	Bands structure oo silicon for parabolic bands	1
( ${\mathbf{x}, \mathbf{k}, t}$ )	Carrier distribution function	1
	Slope of the graded junction	1
$G_{ii}$	Generation due to impact ionization	cm $^{-3}\cdot$ s $^{-1}$
$G_{n,p}$	Generation rates	cm $^{-3}\cdot$ s $^{-1}$
$\mathbf{J}$ , $\mathbf{J}_{n,p}$	Current densities	A $\cdot$ cm $^{-2}$
, $\mathbf{k}$	Momentum	1
$L_\mathrm{d}$	Drift length	$\mu$ m
$L_\mathrm{g}$	Gate length	cm
$L_\mathrm{FP}$	Field plate length	$\mu$ m
$L_\mathrm{min}$	Minimum channel length	$\mu$ m
	Multiplication coefficient	1
$\mu$ , $\mu_{n,p}$	Carrier mobilities	cm $^{2}\cdot$ V $^{-1}\cdot$ s $^{-1}$
	Mass