EVOLUTION OF NONEQUILIBRIUM ELECTRON-DISTRIBUTION FUNCTIONS AT HYDRODYNAMIC SCALES IN MULTI-VALLEY SEMICONDUCTORS

The concept of the physical evolution process for the distribution fun ction is used to derive a non-equilibrium hydro-kinetic transport theo ry. The hydro-kinetic distribution that is interpolated between the ki netic and hydrodynamic levels is introduced to elucidate the physics o f evolution for the distribution. The evolution scales of the distribu tion are decomposed into characteristic scales of hydrodynamic paramet ers, such as carrier density, energy and momentum characteristic times . The coarseness of the hydro-kinetic distribution function is determi ned by scales of the chosen hydrodynamic parameters. The hydro-kinetic distribution is used to close the infinite set of moments and to dete rmine the rate coefficients in the closed set of hydrodynamic equation s. In this paper, the hydro-kinetic distribution at the energy charact eristic scale is applied to study evolution of the electron energy/mom entum distribution and transport parameters, including inter-valley tr ansfer, in GaAs subjected to a fast varying electric field. Monte Carl o (MC) simulations are also included to illustrate the difference betw een evolution scales of the kinetic and tau(epsilon)-scale hydro-kinet ic distributions. The study indicates that the electron distribution i s strongly dependent on the mean energy but weakly on the average mome ntum. In GaAs subjected to a rapid increase in field, effects of the m omentum dependence is enhanced only near the peak of strong velocity o vershoot, such as the overshoot in the Gamma valley. The Gamma-valley energy scale hydro-kinetic (energy dependent) distribution thus apprec iably deviates from the kinetic distribution near the peak of strong o vershoot. As a result, the hydro-kinetic model leads to a smaller over shoot in the Gamma valley than the Me method. In the case of less pron ounced velocity overshoot, the energy scale hydro-kinetic distribution can reasonably follow the evolution scale of the kinetic distribution function.