High-field transport phenomenology: Hot-electron generation at semiconductor interfaces.

Abstract

The transport of electrons in large, inhomogeneous electric fields is described using a phenomenological approach. The competing effects of acceleration and deceleration of the carriers due to the electric field and the scattering by phonons, respectively, are described by a drift-diffusion equation (Fokker-Planck equation) in energy space. In the Fokker-Planck equation, the scattering processes are treated in an averaged manner: First, inelastic scattering gives rise to an average friction force, which opposes the acceleration by the electric field. Second, the random character of the scattering introduces an energy dispersion. The combination of electric field and friction force determines the drift of the particle flow in energy space, whereas the energy-dispersion term determines its diffusion. The formalism is applied to the problem of hot-electron and minority-carrier generation in the depletion region of charged semiconductor interfaces. The friction force and the energy dispersion are determined for the case of polar-optic-phonon scattering. Acoustic-phonon scattering and pair creation are taken into account. We find that the isotropic character of the polar-optic-phonon scattering at very low carrier energies greatly enhances the friction force experienced by the electrons. The resulting peak in the friction force found at low energies is suppressed in the presence of large electric fields. As a result, we find that the yields for hot-electron and minority-carrier generation depend critically on the field strength via the donor concentration in the semiconductor. These results have implications for the breakdown behavior of a varistor.