## Thermal occupation of states It is known that the electrons/holes in the conduction/valence band can be calculated as $n_c(T) = \int_{E_c}^{\infty} D_c(E) \, f(E, T) \, \mathrm{d}E$ $p_v(T) = \int_{-\infty}^{E_v} D_v(E) \, [1 - f(E, T)] \, \mathrm{d}E$ This $f$ is the Fermi-Dirac distribution, $f=\frac{1}{e^{\frac{E-\mu}{k_{B}T}}+1}$. We also show this in [[Orbital, Fermi-Dirac distribution, DOS]]. We may draw how the $f$ and DOS looks like. ![[Drawing 2024-08-31 20.37.56.excalidraw.svg]]