Physical Quantities

Symbol		Unit		Description
$\ensuremath{\alpha}$		VK$^{-1}$		Seebeck coefficient
$\ensuremath{\epsilon}$		AsV$^{-1}$ m$^{-1}$		Dielectric permittivity
$\ensuremath{\ensuremath{\epsilon}_\ensuremath{\mathrm{r}}}$		1		Relative dielectric permittivity
$\ensuremath {\ensuremath {\epsilon }_{\ensuremath {\mathrm {s}}}}$		1		Relative low frequency dielectric permittivity
$\ensuremath{\ensuremath{\epsilon}_{\infty}}$		1		Relative high frequency dielectric permittivity
$\ensuremath{\mathcal{E}}$		eV		Energy
$\ensuremath{\ensuremath{\mathcal{E}}_0}$		eV		Reference energy
$\ensuremath{\ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{c}}}}$		eV		Conduction band edge energy
$\ensuremath{\Delta \ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{c}}}}$		eV		Conduction band edge narrowing
$\ensuremath{\ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{f}}}}$		eV		Fermi energy
$\ensuremath{\ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{g}}}}$		eV		Band gap energy
$\ensuremath{\ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{T}}}}$		eV		Trap energy
$\ensuremath{\ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{v}}}}$		eV		Valence band edge energy
$\ensuremath{\Delta \ensuremath{\mathcal{E}}_{\ensuremath{\mathrm{v}}}}$		eV		Valence band edge narrowing
$\kappa$		WK$^{-1}$ m$^{-1}$		Thermal conductivity
$\ensuremath{\kappa_{\ensuremath{\nu}}}$		WK$^{-1}$ m$^{-1}$		Carrier contribution to thermal conductivity
$\ensuremath{\kappa_{\mathrm{L}}}$		WK$^{-1}$ m$^{-1}$		Lattice contribution to thermal conductivity
$\ensuremath{\kappa_{\ensuremath{n}}}$		WK$^{-1}$ m$^{-1}$		Electron contribution to thermal conductivity
$\ensuremath{\kappa_{\ensuremath{p}}}$		WK$^{-1}$ m$^{-1}$		Hole contribution to thermal conductivity
$\ensuremath{\eta}$		1		Conversion efficiency
$\ensuremath{\ensuremath{\mu}_\nu}$		m$^{2}$ V$^{-1}$ s$^{-1}$		Carrier mobility
$\ensuremath{\ensuremath{\mu}_{\ensuremath{n}}}$		m$^{2}$ V$^{-1}$ s$^{-1}$		Electron mobility
$\ensuremath{\ensuremath{\mu}_{\ensuremath{p}}}$		m$^{2}$ V$^{-1}$ s$^{-1}$		Hole mobility
$\ensuremath{\ensuremath{\mu}_\nu^\mathrm{u}}$		m$^{2}$ V$^{-1}$ s$^{-1}$		Energy flux mobility
$\ensuremath{\ensuremath{\mu}_\ensuremath{n}^\mathrm{u}}$		m$^{2}$ V$^{-1}$ s$^{-1}$		Electron energy flux mobility
$\ensuremath{\ensuremath{\mu}_\ensuremath{p}^\mathrm{u}}$		m$^{2}$ V$^{-1}$ s$^{-1}$		Hole energy flux mobility
$\ensuremath{\nu}$		m$^{-3}$		Carrier concentration
$\pi$		V		Peltier coefficient
$\rho$		kg m$^{-3}$		Mass density
$\ensuremath{\sigma}$		AV$^{-1}$ m$^{-1}$		Electric conductivity
$\ensuremath{\tau_0}$		s		Relaxation time constant in power law approximation
$\ensuremath{{\tau_{\!\ensuremath{\mathcal{E}}}}}$		s		Energy dependent microscopic relaxation time
$\ensuremath{{\tau_\ensuremath{\ensuremath{\mathitbf{j}}}}}$		s		Macroscopic particle flux relaxation time
$\ensuremath{{\tau_\ensuremath{\ensuremath{\mathitbf{u}}}}}$		s		Macroscopic energy flux relaxation time
$\ensuremath{{\tau_\ensuremath{x}}}$		s		Relaxation time of quantity $\ensuremath{x}$
$\ensuremath{\varphi}$		V		Electrostatic potential
$\ensuremath{\tilde{\varphi}}$		V		Effective electrostatic potential
$\ensuremath{\ensuremath{\Phi}_{\ensuremath{\nu}}}$		V		Electrochemical potential
$\ensuremath{\ensuremath{\Phi}_{\ensuremath{n}}}$		V		Electrochemical potential of electrons
$\ensuremath{\ensuremath{\Phi}_{\ensuremath{p}}}$		V		Electrochemical potential of holes
$\ensuremath{\ensuremath{\Phi}_{\ensuremath{\nu}}^\mathrm{c}}$		V		Chemical potential
$\ensuremath{c_{\mathrm{L}}}$		JK$^{-1}$ m$^{-3}$		Lattice heat capacity
$\ensuremath{c_{\ensuremath{n}}}$		JK$^{-1}$ m$^{-3}$		Heat capacity of the electron subsystem
$\ensuremath{c_{\ensuremath{p}}}$		JK$^{-1}$ m$^{-3}$		Heat capacity of the hole subsystem
$\ensuremath{c_{\mathrm{tot}}}$		JK$^{-1}$ m$^{-3}$		Total heat capacity
$\ensuremath{\ensuremath{\mathitbf{F}}}$		N		Force vector
$G$		s$^{-1}$		Net carrier generation rate
$\ensuremath{H}$		Wm$^{-3}$		Heat source density
$\ensuremath{\ensuremath{\mathitbf{J}}}$		s$^{-1}$		Particle flux vector
$\ensuremath{\ensuremath{\mathitbf{J}}^\mathrm{q}}$		Js$^{-1}$		Heat flux vector
$\ensuremath{\ensuremath{\mathitbf{j}}}$		m$^{-2}$ s$^{-1}$		Flux density vector
$\ensuremath{\ensuremath{\mathitbf{j}}_\nu}$		m$^{-2}$ s$^{-1}$		Particle flux density vector
$\ensuremath{\ensuremath{\mathitbf{j}}_{n}}$		m$^{-2}$ s$^{-1}$		Electron flux density vector
$\ensuremath{\ensuremath{\mathitbf{j}}_{p}}$		m$^{-2}$ s$^{-1}$		Hole flux density vector
$\ensuremath{\ensuremath{\mathitbf{j}}_\nu^\mathrm{q}}$		Jm$^{-2}$ s$^{-1}$		Heat flux density vector
$\ensuremath{\ensuremath{\mathitbf{j}}_{n}^\mathrm{q}}$		Jm$^{-2}$ s$^{-1}$		Heat flux density vector of the electron subsystem
$\ensuremath{\ensuremath{\mathitbf{j}}_{p}^\mathrm{q}}$		Jm$^{-2}$ s$^{-1}$		Heat flux density vector of the hole subsystem
$\ensuremath{\ensuremath{\mathitbf{j}}_\nu^\mathrm{u}}$		Jm$^{-2}$ s$^{-1}$		Energy flux density vector
$\ensuremath{\ensuremath{\mathitbf{j}}_{n}^\mathrm{u}}$		Jm$^{-2}$ s$^{-1}$		Electron energy flux density vector
$\ensuremath{\ensuremath{\mathitbf{j}}_{p}^\mathrm{u}}$		Jm$^{-2}$ s$^{-1}$		Hole energy flux density vector
$\ensuremath{\ensuremath{\mathitbf{J}}^\mathrm{q}}$		Js$^{-1}$		Heat flux vector
$\ensuremath{\ensuremath{\mathitbf{k}}}$		m$^{-1}$		Wave number vector
$m^*$		kg		Density of states effective mass
$\ensuremath{m^*_\ensuremath{\mathrm{t}}}$		kg		Transversal effective mass
$\ensuremath{m^*_\ensuremath{\mathrm{l}}}$		kg		Longitudinal effective mass
$\ensuremath{m^*_\ensuremath{\mathrm{c}}}$		kg		Density of states effective mass of the conduction band
$\ensuremath{m^*_\ensuremath{\mathrm{v}}}$		kg		Density of states effective mass of the valence band
$\ensuremath{\ensuremath{m^*_\ensuremath{\mathrm{c,l}}}}$		kg		Longitudinal effective mass of the conduction band
$\ensuremath{\ensuremath{m^*_\ensuremath{\mathrm{v,l}}}}$		kg		Longitudinal effective mass of the valence band
$\ensuremath{\ensuremath{m^*_\ensuremath{\mathrm{c,t}}}}$		kg		Transversal effective mass of the conduction band
$\ensuremath{\ensuremath{m^*_\ensuremath{\mathrm{v,t}}}}$		kg		Transversal effective mass of the valence band
$\ensuremath{M_\mathrm{c,v}}$		1		Valley multiplicity
$\ensuremath{n}$		m$^{-3}$		Electron density
$\ensuremath{n_\mathrm{i}}$		m$^{-3}$		Intrinsic carrier concentration
$\ensuremath{N_A}$		m$^{-3}$		Concentration of acceptors
$\ensuremath{N_\mathrm{c}}$		m$^{-3}$		Effective density of states in the conduction band
$\ensuremath{N_D}$		m$^{-3}$		Concentration of donors
$\ensuremath{N_\mathrm{T}}$		m$^{-3}$		Trap density
$\ensuremath{N_\ensuremath{\mathrm{tot}}}$		m$^{-3}$		Total dopant concentration
$\ensuremath{N_\mathrm{v}}$		m$^{-3}$		Effective density of states in the valence band
$\ensuremath{p}$		m$^{-3}$		Hole density
$\ensuremath {\ensuremath {\mathitbf {p}}}$		kg ms$^{-1}$		Pulse vector
$\ensuremath{P_\ensuremath{\mathrm{el}}}$		W		Electric power
$\ensuremath{Q}$		J		Heat
$\ensuremath {\ensuremath {\mathitbf {r}}}$		m		Space vector
${\ensuremath{r_\nu}}$		1		Scattering parameter
$\ensuremath{r_n}$		1		Scattering parameter for electrons
$\ensuremath{r_p}$		1		Scattering parameter for holes
$R$		s$^{-1}$		Net carrier recombination rate
$\ensuremath{R_\ensuremath{\mathrm{l}}}$		VA$^{-1}$		Load resistance
$\ensuremath{R_\ensuremath{\mathrm{i}}}$		VA$^{-1}$		Inner resistance
$\ensuremath{R_\ensuremath{\mathrm{th}}}$		KW$^{-1}$		Thermal resistance
$\ensuremath{S}$		JK$^{-1}$		Entropy
$\ensuremath{t}$		s		Time
$\ensuremath{T}$		K		Temperature
$\ensuremath{T_\ensuremath{\nu}}$		K		Carrier temperature
$\ensuremath{T_{\mathrm{C}}}$		K		Temperature at the cooled end of a thermoelectric device
$\ensuremath{T_{\mathrm{H}}}$		K		Temperature at the heated end of a thermoelectric device
$\ensuremath{T_{\mathrm{L}}}$		K		Lattice temperature
$\ensuremath{T_\ensuremath{n}}$		K		Electron temperature
$\ensuremath{T_\ensuremath{p}}$		K		Hole temperature
$\ensuremath{U}$		V		Voltage
$\ensuremath{U_\ensuremath{\mathrm{c}}}$		V		Contact voltage
$v$		ms$^{-1}$		Velocity
$\ensuremath{\ensuremath{\mathitbf{v}}}$		ms$^{-1}$		Velocity vector
$\ensuremath{v_{\rm {s}}}$		ms$^{-1}$		Average sound velocity
$\ensuremath{v_{\rm {st}}}$		ms$^{-1}$		Transversal sound velocity
$\ensuremath{v_{\rm {sl}}}$		ms$^{-1}$		Longitudinal sound velocity
$\ensuremath{w}$		Jm$^{-3}$		Energy density
$\ensuremath{X}$		1		Microscopic density
$\ensuremath{X}_0$		1		Microscopic density in equilibrium
$\ensuremath{x}$		m$^{-3}$		Macroscopic density
$Z$		K$^{-1}$		Thermoelectric figure of merit

M. Wagner: Simulation of Thermoelectric Devices