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$^{-1}$
$D$, $D_{n,p}$	Diffusion coefficient	cm$^{2}\cdot$s$^{-1}$
$d_\mathrm{nepi}$, $d_\mathrm{n1}$, $d_\mathrm{n2}$, $d_\mathrm{ptop}$	Depletion extensions	$\mu$m
$E$, $\mathbf{E}$	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$^{-1}$
$E_n$	Electron energy	eV
$E_{n(ox)}$	Electric field of $SiO_2$ 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
$f$ ( ${\mathbf{x}, \mathbf{k}, t}$)	Carrier distribution function	1
$S$	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$^{-2}$
$k$, $\mathbf{k}$	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
$M(x)$	Multiplication coefficient	1
$\mu$, $\mu_{n,p}$	Carrier mobilities	cm$^{2}\cdot$V $^{-1}\cdot$s$^{-1}$
$m$	Mass	$kg$

symbol	description	unit
$m^*$	Effective mass	$kg$
$n$	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$^{-3}$
$N_\mathrm{drift}$	$n$-drift layer doping concentration	$cm^{-3}$
$N_\mathrm{epi}$	$n$-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 $p$-top region	cm$^{-3}$
$p$	Hole concentration	cm$^{-3}$
$Q_{n}$	$n$-epi layer net charge	$cm^{-3}$
$Q_{n,max}$	Maximum $Q_{n}$	$cm^{-3}$
$Q_\mathrm{nd}$	$n$-drift integrated charge	$cm^{-3}$
$Q_\mathrm{pd}$	$p$-drift integrated charge	$cm^{-3}$
$Q_\mathrm{nd,max}$	Maximum $n$-drift integrated charge	$cm^{-3}$
$Q_\mathrm{pd,max}$	Maximum $p$-drift integrated charge	$cm^{-3}$
$Q_\mathrm{N}$	$n$-column charge	C
$Q_\mathrm{P}$	$p$-column charge	C
$Q_\mathrm{DB}$	Charge of the depletion region	C
$R$, $R_{n,p}$	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$\Omega$ $cm^{-3}$
$T$	Temperature	K
$t$	Time	s
$t_\mathrm{N}$	$n$-column length	$\mu$m
$t_\mathrm{P}$	$p$-column length	$\mu$m
$t_\mathrm{N,P}$	$n,p$-column length	$\mu$m
$T_{n,p,\mathrm{L}}$	Electron, hole, and lattice temperature	K
$T_0$	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
$t_\mathrm{nepi}$	$n$-epi layer thickness	$\mu$m
$t_\mathrm{ndrift}$	$n$-drift layer thickness	$\mu$m
$t_\mathrm{ptop}$	$p$-top layer thickness	$\mu$m
$t_\mathrm{soi}$	SOI thickness	$\mu$m
$t_\mathrm{ox}$	Buried oxide thickness	$\mu$m
$v$	Drift velocity	cm$\cdot$s$^{-1}$
$v_n$( $\mathbf{k}$)	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
$W$	Depletion region width	$\mu$m
$W_\mathrm{N}$	$n$-column width	$\mu$m
$W_\mathrm{P}$	$p$-column width	$\mu$m
$W_\mathrm{PT(ch)}$	Depletion layer width in the channel	$\mu$m
$\zeta$	capture cross section ratio	1