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
	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
	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
	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
	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
	K $^{-1}$	Thermoelectric figure of merit

M. Wagner: Simulation of Thermoelectric Devices

			Dissertation Martin Wagner
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