Scattering of an Electron - Drude Model FormulaDrude Model (Current Density, Mean Free Time, E-field) $$ j ~=~ \frac{n \, e^2 \, \tau}{m_{\text e}} \, E $$
Fermi, Bose and Boltzmann distribution - Graphs FormulaBoltzmann Distribution Function (Probability, Energy, Temperature) $$ P(W) ~=~ \mathrm{e}^{ -\frac{ W - \mu }{ k_{\text B} \, T}} $$
Dispersion relation of lattice vibrations for monatomic crystal lattice FormulaThermal Capacity (Debye Approximation) $$ C_{\text V} ~=~ 9N \, k_{\text B} \left( \frac{T}{T_{\text D}} \right)^3 \int_{0}^{T_{\text D}/T} \frac{u^4 \, \mathrm{e}^u}{(\mathrm{e}^u-1)^2} ~ \text{d}u $$
Banddiagramm: Metall, Halbleiter, Isolator FormulaFree Electron Gas in 3d (Fermi Temperature) $$ T_{\text F} ~=~ \frac{\hbar^2}{2\class{brown}{m} \, k_{\text B}} \, (3\pi^2 \, n)^{2/3} $$
Fermi distribution graph at finite temperature FormulaFermi Distribution (Probability, Energy, Temperature) $$ P(W) ~=~ \frac{1}{\mathrm{e}^{ \frac{ W - \mu }{ k_{\text B} \, T}} ~+~ 1} $$
Electric Current Density in a 3D Conductor FormulaSpecific Resistance of a Wire (Length, Cross-Sectional Area) $$ \rho ~=~ R \, \frac{A}{l} $$
Hall effect with Electrons and Holes FormulaHall constant (Electron and Hole Mobilities, Charge Carrier Density) $$ A_{\text H} ~=~ \frac{ \class{red}{p} \,{\mu_{\text +}}^2 ~-~ \class{blue}{n} \, {\mu_{\text -}}^2}{e \, (\class{red}{p} \, \mu_{\text +} ~+~ \class{blue}{n} \, \mu_{\text -})^2} $$
Hall plate with holes FormulaHall Effect (Voltage, Drift Velocity) $$ U_\text{H} ~=~ v \, \class{violet}{B} \, h $$
Hall effect with Electrons and Holes FormulaHall Effect (Hall Voltage, Charge Carrier Density) $$ U_\text{H} ~=~ \frac{1}{n \, q} ~ \frac{I \, \class{violet}{B}}{d} $$
