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High-Field Distribution and Mobility in Semiconductors

A first-principles theory of carrier distribution in the presence of an electric field of arbitrary strength, which takes into account the quantum-mechanical field-broadening, is described under conditions that the acoustic-phonon scattering is the dominant mechanism of scattering. The general expression of the mobility so obtained reduces to its Ohmic value for vanishing small electric fields, is a quadratic function of electric field in the warm-electron regime, and varies inversely with the electric field at sufficiently high electric fields (hot-electron regime). A saturation current is obtained in the high-field limit, when electron mobility is limited solely by the field-broadening effect; the saturation velocity being comparable to the thermal velocity of an electron. The hot-electron temperature, defined in terms of average energy of an electron, is equal to the lattice temperature in the Ohmic regime, rises quadratically with the increasing electric field in the warm-electron regime, and rises linearly in the hot-electron regime. These results are in agreement with those of experiments on n-Germanium.