Within the relaxation-time approximation, carrier dynamics can be modeled by the Boltzmann transport equation. Macroscopically, the drift current density is $\mathbf{J}_{\text{drift}} = q n \mu_n \mathbf{E}$ and diffusion current is $\mathbf{J}_{\text{diff}} = q D_n \nabla n$, with analogous expressions for holes.

Mobility is reduced by phonon scattering, ionized impurity scattering, alloy disorder, interface roughness, and dislocations. At high temperatures, phonon scattering often dominates; at low temperatures and high dopant densities, impurity scattering becomes critical. In low-dimensional systems, boundary and surface scattering can strongly modify transport.

When device dimensions become comparable to the mean free path, transport becomes quasi-ballistic or ballistic. In this regime, classical drift-diffusion models may fail, and Landauer-type descriptions, non-equilibrium Green's function methods, or Monte Carlo simulations become more appropriate.