Nonequilibrium total dielectric function approach to the electron Boltzmann equation for inelastic scattering in doped polar semiconductors
This paper describes a simple and general method for deriving the inelastic collision term in the electron Boltzmann equation for scattering from a coupled electron-phonon system, and applies the method to the case of doped polar semiconductors. In the Born approximation, the inelastic differential...
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Zusammenfassung: | This paper describes a simple and general method for deriving the inelastic
collision term in the electron Boltzmann equation for scattering from a coupled
electron-phonon system, and applies the method to the case of doped polar
semiconductors. In the Born approximation, the inelastic differential
scattering rate $W^{inel}$ can be expressed in terms of the nonequilibrium
total dynamic dielectric function, which includes both electronic and lattice
contributions. Within the random-phase approximation $W^{inel}$ separates into
two components: an electron-electron interaction containing the nonequilibrium
distribution function for excitations of the electron gas, and a Fr\"{o}hlich
interaction including the phonon distribution function and self-energy due to
polarization of the electrons. Each of these two interactions is screened by
only the electronic part of the total dielectric function which contains the
high frequency dielectric constant, unlike commonly used expressions which
contain the static dielectric constant. Detailed balance between plasmons and
electron-hole pairs in steady state is used to eliminate the nonequilibrium
plasmon distribution from the Boltzmann equation, resulting in a dynamically
screened electron-electron collision term. The phonon self-energy modifies the
longitudinal optical phonon dispersion so that two hybrid normal modes
contribute to the electron-phonon collision term. |
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DOI: | 10.48550/arxiv.cond-mat/9501083 |