Hall effect with Electrons and Holes FormulaHall constant (Electron and Hole Mobilities, Charge Carrier Density) $$ A_{\text H} ~=~ \frac{ \class{red}{p} \,{\mu_{\text +}}^2 ~-~ \class{blue}{n} \, {\mu_{\text -}}^2}{e \, (\class{red}{p} \, \mu_{\text +} ~+~ \class{blue}{n} \, \mu_{\text -})^2} $$
Scattering of an Electron - Drude Model FormulaDrude Model (Current Density, Mean Free Time, E-field) $$ j ~=~ \frac{n \, e^2 \, \tau}{m_{\text e}} \, E $$
Lorentz force: electron in a magnetic field FormulaCyclotron Frequency (B-field, Charge, Mass) $$ f ~=~ \frac{|q| \, \class{violet}{B}}{2\pi \, \class{brown}{m}} $$
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) $$ U_\text{H} ~=~ \frac{1}{n \, q} ~ \frac{I \, \class{violet}{B}}{d} $$
Hall effect with Electrons FormulaHall Effect (Voltage, Hall Coefficient, Current, B-Field) $$ U_{\text H} ~=~ A_{\text H} \, \frac{I \, \class{violet}{B}}{d} $$
Bragg reflection on two lattice planes FormulaBragg's Law (Diffraction Order, Wavelength, Lattice Constant, Angle) $$ m \, \class{violet}{\lambda} ~=~ 2\class{blue}{d} \, \sin(\class{gray}{\theta}) $$
Fermi distribution graph at finite temperature FormulaFermi Distribution (Probability, Energy, Temperature) $$ P(W) ~=~ \frac{1}{\mathrm{e}^{ \frac{ W - \mu }{ k_{\text B} \, T}} ~+~ 1} $$
Banddiagramm: Metall, Halbleiter, Isolator FormulaFree Electron Gas in 3d (Fermi Temperature) $$ T_{\text F} ~=~ \frac{\hbar^2}{2m \, k_{\text B}} \, (3\pi^2 \, n)^{2/3} $$
