Basic Equations
Density of States in Conduction and Valence Band
$$N_C(E)=\frac{\left(m_n^\ast\right)^\sfrac{3}{2}\sqrt2}{\pi^2\hbar^3}\sqrt{E-E_C}$$
$$N(E)=\frac{\left(m_p^\ast\right)^\sfrac{3}{2}\sqrt2}{\pi^2\hbar^3}\sqrt{E_V-E}$$
Fermi function: $$f(E)=\frac{1}{1+exp{\left(\frac{E-E_F}{kT}\right)}}$$
