Adiabatic approach to the dynamics of nonequilibrium electron ensembles in semiconductors

We describe an approach to the solution of the Boltzmann kinetic equation for the evolution of non- equilibrium electron ensembles in semiconductors under the influence of both phonon scattering and electron-electron interaction. This approach works well when the interaction with optical phonons is the dominant scattering mechanism. In this case, the ensemble evolution can be separated into two stages, the first of which corresponds to the establishment of an intermediate distribution, corresponding to a quasiequilibrium with the optical-phonon subsystem. To describe the subsequent evolution, we assume that this quasiequilibrium is maintained while the ensemble progresses toward the true equilibrium. This assumption implies a certain form of the time-dependent distribution function and renders the full kinetic equation tractable. The solution thus obtained has been checked against Monte Carlo simulations for both polar and nonpolar semiconductors.