CourseLevel 3 (for advanced students)Introduction to solid state physics Here you will learn the basics of solid state physics - that is, electrical / thermal transport in solid matter, its crystal structure and interactions.
FormulaFree electron gas in 1d (density of states) $$ D(W) ~=~ \frac{L}{\pi} \, \left(\frac{2m}{\hbar^2}\right)^{1/2} \, \frac{1}{\sqrt{W}} $$
FormulaFree electron gas in 3d (density of states) $$ D(W) ~=~ \frac{V}{2\pi^2} \, \left(\frac{2m}{\hbar^2}\right)^{3/2} \, \sqrt{W} $$
FormulaEnergy band gap of GaAs (temperature dependence) $$ E_{\text g} ~=~ 1.522\,\text{eV} - \frac{ 5.8 \cdot 10^{-4} \, \frac{ \text{eV} }{ \text{K} } \, T^2 }{ 300 \,\text{K} + T } $$
FormulaEnergy band gap of germanium (temperature dependence) $$ E_{\text g} ~=~ 0.742\,\text{eV} - 3.90 \cdot 10^{-4} \, \frac{ \text{eV} }{ \text{K} } \cdot T $$
FormulaEnergy band gap of silicon (temperature dependence) $$ E_{\text g} ~=~ 1.165\,\text{eV} - 2.84 \cdot 10^{-4} \, \frac{ \text{eV} }{ \text{K} } \cdot T $$
FormulaBoltzmann distribution function (Probability, Energy, Temperature) $$ P(W) ~=~ \mathrm{e}^{ -\frac{ W - \mu }{ k_{\text B} \, T}} $$
FormulaFermi distribution (Probability, Energy, Temperature) $$ P(W) ~=~ \frac{1}{\mathrm{e}^{ \frac{ W - \mu }{ k_{\text B} \, T}} ~+~ 1} $$
