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The concept of the evolution of the distribution function is used to derive an energy‐scale distribution that is able to describe transport phenomena, including inter‐valley transfer effect, in the scale as small as the energy relaxation time. The energy‐scale distribution is used to study the evolution of electrons in n‐type GaAs under the influence of rapid change in field. Results indicate that, near the peak of strong velocity overshoot or the bottom of pronounced undershoot in the Γ valley caused by the rapid change in field, the energy‐scale distribution can not respond as fast as the distribution function calculated from the Monte Carlo method. The average velocity resulting from the energy‐scale distribution therefore leads to less pronounced overshoot and undershoot than those obtained from the Monte Carlo method. However, since velocity overshoot and undershoot are not pronounced in the L‐valleys, the L‐valley energy‐scale distribution is in excellent agreement with that determined by the Monte carlo simulation.

Accuracy of hydrodynamic transport equations using the energy‐dependent relaxation times has been studied for electron transport in Si 〈100〉. The concept of the hydro‐kinetic transport model is used to describe non‐equilibrium electron transport phenomena and to examine the validity for the assumption of energy‐dependent relaxation times. It has been shown that under the influence of a drastic increase in field the relaxation times might also strongly depend on the average velocity near the peak of strong velocity overshoot. In addition, the velocity dependence is found to be more pronounced at lower temperatures in Si 〈100〉.