Physical Constants

Name	Symbol	Value	Significance
Elementary charge	$q$	$1.602176634\times 10^{-19}\mathrm{C}$	The magnitude of charge carried by a single electron or hole. Appears in every current density, carrier concentration, and Poisson equation in semiconductor transport theory.
Electron rest mass	$m_0$	$9.1093837015\times 10^{-31}\mathrm{kg}$	Free-electron mass; the reference against which the effective mass $m^{\ast }$ of carriers in a given semiconductor’s band structure is normalized.
Planck’s constant	$h$	$6.62607015\times 10^{-34}\mathrm{J}\cdot \mathrm{s}$	Relates a particle’s energy to the frequency of its associated wave; sets the scale of quantization in density-of-states and subband energy calculations.
Reduced Planck’s constant	$\hslash =h/2\pi$	$1.054571817\times 10^{-34}\mathrm{J}\cdot \mathrm{s}$	The natural unit of angular momentum in quantum mechanics; appears throughout effective-mass Schrodinger-equation treatments (e.g. 2DEG subband energies).
Boltzmann constant	$k_B$	$1.380649\times 10^{-23}J/K$	Relates temperature to average thermal energy per degree of freedom; sets the scale of the Boltzmann (exponential) carrier statistics used throughout equilibrium semiconductor physics.
Permittivity of free space	${\epsilon }_0$	$8.8541878128\times 10^{-12}F/m$	The electric permittivity of vacuum; multiplied by a material’s relative permittivity ${\epsilon }_r$ to obtain ${\epsilon }_s$ for use in Poisson’s equation and capacitance formulas.
Speed of light (vacuum)	$c$	$2.99792458\times 10^{8}m/s$	Fundamental constant relating energy and photon wavelength ($E=hc/\lambda$); central to optoelectronic devices such as LEDs, lasers, and photodetectors.
Avogadro’s number	$N_A$	$6.02214076\times 10^{23}\mathrm{mo}{\mathrm{l}}^{-1}$	Number of entities per mole; used when converting between molar and per-unit-volume quantities, e.g. dopant concentrations specified in mol/cm³.
Thermal voltage (at $T=300\mathrm{K}$)	$V_T=k_{B}T/q$	$\approx 0.0259\mathrm{V}$	The characteristic voltage scale of Boltzmann carrier statistics and diode I-V behavior at room temperature; appears in the Einstein relation and the ideal diode equation.

Important Questions

Ques: Why is $k_{B}T/q$ (the thermal voltage) treated as a single combined constant rather than computed from $k_B$ and $T$ separately in most device equations?

Because $k_B$, $T$, and $q$ appear together as the ratio $k_{B}T/q$ in nearly every exponential carrier-statistics expression (Boltzmann approximation, diode law, Einstein relation), it is conventional in device physics to precompute this ratio at a reference temperature, most commonly $T=300\mathrm{K}$, where $k_{B}T/q\approx 0.0259\mathrm{V}$. This is a notational convenience rather than a new physical constant, and the value must be recalculated whenever the operating temperature differs from 300 K, since $V_T$ scales linearly with $T$. Reference: S.M. Sze and Kwok K. Ng, Physics of Semiconductor Devices, 3rd ed., Wiley, 2007; D.A. Neamen, Semiconductor Physics and Devices, 4th ed., McGraw-Hill, 2012.