Hydrodynamic states of electron plasma of semiconductors in the generalized Chapman–Enskog method

  • S. A. Sokolovsky Prydniprovska State Academy of Civil Engineering and Architecture, Dnipro, Ukraine
  • A. I. Sokolovsky Oles Honchar Dnipro National University, Dnipro, Ukraine
  • O. A. Hrinishyn Oles Honchar Dnipro National University, Dnipro, Ukraine
Keywords: semiconductor, electron-phonon interaction, Bogolyubov kinetic equation, temperature and velocity relaxation, hydrodynamics, local equilibrium, collision integral operator, spectral theory, functional hypothesis


The hydrodynamic states of polar semiconductors are investigated. Such states are described by the temperature, mass velocity, and density of the number of particles of the electron subsystem, which is considered as rarefied one. The phonon subsystem of a semiconductor is considered to be equilibrium. The electron-phonon interaction in the system is described by the Fröhlich Hamiltonian. The theory is based on Bogolyubov’s linear kinetic equation for the electron distribution function in the presence of a weak electric field. The reduced description of the system is investigated by the generalized Chapman–Enskog method, which leads to a nonlinear equation for the electron distribution function in the reduced description. The zone structure of the system is neglected, focusing on the study of fundamental issues of relaxation of temperature and velocity. Gradients of hydrodynamic parameters are considered small; the same small
parameters determine the smallness of the electric field. In the basic order of the perturbation theory, the distribution function of the system satisfies a nonlinear equation. The method of spectral theory of the collision integral operator shows that the study of the basic approximation is reduced to an analysis of a first-order quasilinear equation, which, in particular, has a solution that we found earlier.