Physical Quantities

SYMBOL	DESCRIPTION	UNIT
$a$	channel thickness	cm
$A^*$	effective Richardson constant	A$\cdot$cm $^{-2}\cdot$K$^{-2}$
$c$	heat capacity	J$\cdot$ kg$\cdot$K
$C_{\nu}^{\mathrm{AU}}$	electron, hole Auger coefficient	cm$^{6}\cdot$s$^{-1}$
$D_\nu$	electron, hole diffusivity	cm$^{2}\cdot$s$^{-1}$
$E$	electric field	V$\cdot$cm$^{-1}$
$E_\mathrm{B}$	breakdown/critical electric field	V$\cdot$cm$^{-1}$
$E_\mathrm{a,d}$	acceptor, donor energy	eV
$E_{\mathrm{g}}$	indirect bandgap	eV
$E_\mathrm{gx}$	exciton energy gap	eV
$E_\mathrm{c,v}$	conduction, valence band energy	eV
$E_\mathrm{F}$	Fermi energy	eV
$E_\mathrm{\nu,T}$	electron, hole, trap energy	eV
$E_{i}$	intrinsic Fermi energy	eV
$E_\mathrm{x}$	exciton binding energy	eV
$\Delta E_\mathrm{a,d}$	acceptor, donor ionization energy	eV
$f$	frequency	Hz
$f_\mathrm{t}$	cutoff frequency	Hz
$f_\mathrm{max}$	maximum frequency	Hz
$f_{tp}$	occupation probability of traps	1
$G$	generation rate	cm $^{-3}\cdot$s$^{-1}$
$\alpha _{\nu}$	electron, hole impact ionization coefficients	cm$^{-1}$
$g_\mathrm{m}$	conductance	A$\cdot$V$^{-1}$
$g_\mathrm{A,D}$	acceptor, donor degeneracy factor	1

SYMBOL	DESCRIPTION	UNIT
${\mathbf{J}}$	electric current density	A$\cdot$cm$^{-2}$
$j$	particle current density	cm$^{-2}$
$\kappa$	thermal conductivity	W$\cdot$cm $^{-1}\cdot$K$^{-1}$
$L_\mathrm{g}$	gate length	cm
$L_{\nu}$	electron, hole diffusion length	cm
$m_{\nu}^{\ast }$	electron, hole effective mass	kg
$\mu_\nu$	carrier mobility	cm$^{2}\cdot$V $^{-1}\cdot$s$^{-1}$
$\mu^{\mathrm{low}}_\nu$	low field carrier mobility	cm$^{2}\cdot$V $^{-1}\cdot$s$^{-1}$
$\mu^{\mathrm{high}}_\nu$	high field carrier mobility	cm$^{2}\cdot$V $^{-1}\cdot$s$^{-1}$
$\mu^{\mathrm{max}}_\nu$	undoped material carrier mobility	cm$^{2}\cdot$V $^{-1}\cdot$s$^{-1}$
$\mu^{\mathrm{min}}_\nu$	highly doped material carrier mobility	cm$^{2}\cdot$V $^{-1}\cdot$s$^{-1}$
$_{M_\mathrm{C,V}}$	number of minima in the conduction and valence band	1
$n$	electron density	cm$^{-3}$
$n_{i}$	intrinsic density	cm$^{-3}$
$n_{1}$	Shockley-Read-Hall parameter	cm$^{-3}$
$N_\mathrm{B}$	blocking layer doping concentration	cm$^{-3}$
$N_\mathrm{A,D}$	acceptor, donor doping concentration	cm$^{-3}$
$N_\mathrm{c,v}$	effective density of states	cm$^{-3}$
$N^+_\mathrm{D}$	ionized donor concentration	cm$^{-3}$
$N^-_\mathrm{A}$	ionized acceptor concentration	cm$^{-3}$
$N_{tp}$	density of occupied traps	cm$^{-3}$
$N_{tp}^{emp}$	density of empty traps	cm$^{-3}$
$N^{\mathrm{ref}}_\nu$	doping concentrartion at ( $\mu_{\nu}^{\min}+\mu_{\nu}^\mathrm{max})$/2	cm$^{-3}$
$p$	hole density	cm$^{-3}$
$p_{1}$	Shockley-Read-Hall parameter	cm$^{-3}$
${\mathrm{q}}$	elementary electric charge	A$\cdot$s
$\phi_{\nu}$	electron, hole quasi-Fermi potential	V
$\phi_{\mathrm{B}}$	barrier height	V
$\phi_{\mathrm{m}}$	metal work function	V
$\phi_{\mathrm{s}}$	semiconductor work function	V
$\phi_{\mathrm{wf}}$	work function difference	V
$\psi$	electrostatic potential	eV
$\psi_{\mathrm{bi}}$	built-in potential	eV
$\varepsilon$	relative dielectric constant	1
$R$	recombination rate	cm $^{-3}\cdot$s$^{-1}$
$R_\mathrm{on,sp}$	specific on-resistance	V$\cdot$cm$^{2}\cdot$A$^{-1}$
$\sigma$	electrical conductivity	A$\cdot$V $^{-1}\cdot$cm$^{-1}$
$\varrho$	resistivity	V$\cdot$cm$\cdot$A$^{-1}$
$\rho$	charge density	A$\cdot$s$\cdot$cm$^{-3}$
$s$	entropy density	eV$\cdot$K $^{-1}\cdot$cm$^{-3}$
${\mathbf{S}}_\nu$	electron, hole energy flux density	J$\cdot$cm$^{-2}$ $\cdot$ s$^{-1}$
$T$	temperature	K

SYMBOL	DESCRIPTION	UNIT
$T_\mathrm{n,p,L}$	electron, hole, and lattice temperature	K
$T_{0}$	reference temperature (300 K)	K
$\tau_{\epsilon,\nu}$	elctron, hole energy relaxation times	s
$\tau _{R-G}$	effective lifetime of recombination or generation process	s
$\tau _{\nu}$	effective electron, hole minority carrier lifetime	s
$\tau _{\nu}^{tp}$	electron, hole minority carrier lifetime of impurity t$_{p}$	s
$\tau _{tp,A,D}$	trap, acceptor, donor time constant	s
$\tau_\mathrm{sc}$	space charge generation lifetime	s
$u$	total energy density	eV$\cdot$cm$^{-3}$
$\nu$	substitute for electron or hole density	cm$^{-3}$
$v_{\nu}$	carrier velocity	cm$\cdot$s$^{-1}$
$v_{\nu{\perp, \parallel}}^\mathrm{sat}$	electrons, holes, saturation velocity	cm$\cdot$s$^{-1}$
$\alpha _{\nu}^\mathrm{sat}$	constant specifying how velocity goes into saturation	1
$V_\mathrm{B}$	breakdown voltage	V
$V_{bi}$	built-in voltage	V
$V_\mathrm{D,G,S}$	drain, gate, source voltage	V
$V_\mathrm{T}$	threshold voltage	V
$W$	depletion region width	cm
$W_\mathrm{g}$	gate width	cm
$\omega$	angular frequency	Hz
$\chi$	electron affinity	V
$\xi_\mathrm{A,D}$	acceptor, donor ionization degree	1
$\alpha_{\nu}^{\mu}$	constant measure how mobility changes from $\mu_{\nu}^\mathrm{\min}$ to $\mu_{\nu}^\mathrm{max}$	1
$\beta_{\nu}^{\mu}$	constant temperature coefficient for $\mu_{\nu}^\mathrm{\min}$	1
$\gamma_{\nu}^{\mu}$	constant temperature coefficient for $\mu_{\nu}^\mathrm{max}$	1
$\hbar \omega_{op}$	phonon energy	eV

T. Ayalew: SiC Semiconductor Devices Technology, Modeling, and Simulation