In equilibrium, carrier occupation is governed by $f(E)=\left[1+\exp\left((E-E_F)/k_B T\right)\right]^{-1}$. For nondegenerate semiconductors, the electron and hole densities can often be approximated by Maxwell-Boltzmann statistics, but this breaks down at high doping or low temperature.

Under weak fields, carrier motion is described by drift-diffusion equations coupled to Poisson's equation. The current density may be written as $\mathbf{J}_n=q n \mu_n \mathbf{E}+q D_n \nabla n$ for electrons, with analogous expressions for holes. The Einstein relation $D/\mu = k_B T/q$ applies in the simplest nondegenerate case.

Mobility is reduced by phonon scattering, ionized impurity scattering, neutral defects, alloy disorder, interface roughness, and in low dimensions by remote charge traps. At low temperatures, impurity and defect scattering often dominate; at high temperatures, phonons dominate. The detailed temperature dependence can reveal the microscopic scattering mechanism.