Nonlinear field dependence of carrier mobilities and irreversible thermodynamics in semiconductors

Irreversible thermodynamics and transport processes in semiconductors are studied by means of the Boltzmann equation for carrier distribution functions. By solving the equation by the modified moment method, we derive the extended Gibbs relation for entropy change and the evolution equations for fluxes. The steady-state solutions of the evolution equations yield diffusion fluxes and drift velocities which are nonlinear with respect to the field strength. Depending on the wave-number dependences of the scattering cross sections and the affinity of electrons in different valleys in the conduction band, the drift velocity and the mobility can exhibit a plateau or a negative differential mobility in the high-field regime. Calculated carrier drift velocities are compared with experimental data on the electron drift velocities in Si and $n$-Ge. The comparisons are in good agreement and show that the theory generally predicts qualitatively correct field dependences of electron drift velocities.