List of Symbols

Notation

$x$		Scalar
$\ensuremath{\mathitbf{x}}$		Vector
$\ensuremath{{\mathbf{A}}}$		Matrix
$A_{ij}$		Elements of the matrix ${\mathbf{A}}$
$\partial_t(\cdot)$		Partial derivative with respect to $t$
$\ensuremath{\ensuremath{\mathitbf{\nabla}}}$		Nabla operator
$\ensuremath{\ensuremath{\ensuremath{\mathitbf{\nabla}}}}x$		Gradient of $x$
$\ensuremath{\ensuremath{\ensuremath{\mathitbf{\nabla}}}\ensuremath{\cdot}}\ensuremath{\mathitbf{x}}$		Divergence of $\ensuremath{\mathitbf{x}}$

Physical Quantities

Symbol		Description
$\ensuremath{\epsilon}$		Dielectric permittivity
$\ensuremath{\ensuremath{\epsilon}_{\ensuremath{\mathrm{s}}}}$		Relative low frequency dielectric permittivity
$\ensuremath{\ensuremath{\epsilon}_{\infty}}$		Relative high frequency dielectric permittivity
$\ensuremath{\mathcal{E}}$		Energy
$\ensuremath{\ensuremath{\mathcal{E}}_0}$		Reference energy
$\ensuremath{\ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{c}}}}$		Conduction band edge energy
$\ensuremath{\Delta \ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{c}}}}$		Conduction band edge energy difference
$\ensuremath{\ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{f}}}}$		Fermi energy
$\ensuremath{\ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{g}}}}$		Band gap energy
$\ensuremath{\ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{v}}}}$		Valence band edge energy
$\ensuremath{\Delta \ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{v}}}}$		Valence band edge energy difference
$\kappa$		Thermal conductivity
$\ensuremath{\kappa_{\mathrm{L}}}$		Lattice contribution to thermal conductivity
$\ensuremath{\kappa_{\ensuremath{n}}}$		Electron contribution to thermal conductivity
$\ensuremath{\kappa_{\ensuremath{p}}}$		Hole contribution to thermal conductivity
$\mu_\nu$		Mobility of carrier type $\nu$
$\ensuremath{\ensuremath{\mu}_{\ensuremath{n}}}$		Electron mobility
$\ensuremath{\ensuremath{\mu}_{\ensuremath{p}}}$		Hole mobility
$\ensuremath{\ensuremath{\mu}_\nu}^\ensuremath{\mathrm{L}}$		mobility due to lattice scattering
$\ensuremath{\ensuremath{\mu}_\nu}^\ensuremath{\mathrm{LI}}$		mobility due to lattice and impurity scattering
$\ensuremath{\ensuremath{\mu}_\nu}^\ensuremath{\mathrm{LIF}}$		mobility including lattice, impurity, and high field reduction
$\ensuremath{\ensuremath{\mu}_\nu}^\ensuremath{\mathrm{LIT}}$		mobility including lattice, impurity, and high temperature reduction
$C_\ensuremath{\mathrm{net}}$		Net concentration
$\ensuremath{\sigma}$		Electric conductivity
$\tau_{\epsilon,n}$		Electron energy relaxation time
$\tau_{\epsilon,p}$		Hole energy relaxation time
$\ensuremath{\varphi}$		Electrostatic potential
$\ensuremath{\ensuremath{\mathitbf{B}}}$		Magnetic field vector
$\ensuremath{c_{\mathrm{L}}}$		Lattice heat capacity
$\ensuremath{c_{\ensuremath{n}}}$		Heat capacity of the electron subsystem
$\ensuremath{c_{\ensuremath{p}}}$		Heat capacity of the hole subsystem
$\ensuremath{\ensuremath{\mathitbf{F}}}$		Force vector
$G$		Carrier generation rate
$\ensuremath{H}$		Heat generation term
$\ensuremath{\ensuremath{\mathitbf{J}}}$		Current density

$m^*$		Density of states effective mass
$\ensuremath{M_\mathrm{c,v}}$		Valley multiplicity
$\ensuremath{n}$		Electron concentration
$\ensuremath{n_\mathrm{i}}$		Intrinsic carrier concentration
$\ensuremath{N_A}$		Concentration of acceptors
$\ensuremath{N_\mathrm{c}}$		Effecive density of states in the conduction band
$\ensuremath{N_D}$		Concentration of donors
$\ensuremath{N_\ensuremath{\mathrm{tot}}}$		Total dopant concentration
$\ensuremath{N_\mathrm{v}}$		Effecive density of states in the valence band
$\ensuremath{p}$		Hole concentration
$\ensuremath{Q}$		Heat flow
$R$		Carrier recombination rate
$\ensuremath{R_\ensuremath{\mathrm{th}}}$		Thermal resistance
$\ensuremath{t}$		Time
$\ensuremath{T_\ensuremath{\nu}}$		Carrier temperature
$\ensuremath{T_{\mathrm{L}}}$		Lattice temperature
$\ensuremath{T_\ensuremath{n}}$		Electron temperature
$\ensuremath{T_\ensuremath{p}}$		Hole temperature
$I$		Current
$V$		Voltage
$V_\ensuremath{\mathrm{C}}$		Contact voltage
$v$		Velocity
$\ensuremath{v_{\rm {s}}}$		Average sound velocity
$\ensuremath{v_{\rm {st}}}$		Transversal sound velocity
$\ensuremath{v_{\rm {sl}}}$		Longitudinal sound velocity

Fundamental Constants

$\mathrm{h}$		Planck's constant	$6.6260755 \times 10^{-34} \mathrm{J} \mathrm{s}$
$\hbar$		Reduced Planck's constant	$\mathrm{h} / (2 \pi)$
$\ensuremath{\mathrm{k}}_\ensuremath{\mathrm{B}}$		Boltzmann's constant	$1.3806503 \times 10^{-23} \mathrm{JK^{-1}}$
$\mathrm{q}$		Elementary charge	$1.6021892 \times 10^{-19} \mathrm{C}$
$m_0^*$		Electron rest mass	$9.1093897 \times 10^{-31} \mathrm{kg}$
$\ensuremath{\epsilon}_0$		Vacuum permittivity	$8.8541878 \times 10^{-12} \mathrm{Fm^{-1}}$