Electron-electron interactions in the nonparabolic conduction band of narrow-gap semiconductors

Abstract

The Lindhard dielectric function is evaluated at nonzero temperatures with Fermi-Dirac statistics and a nonparabolic conduction band for bulk, narrow-gap semiconductors. This is used to study two problems of current interest: (i) inelastic scattering of single, energetic electrons by a system of plasmons, phonons, and quasiparticle excitations; and (ii) cooling of a hot, quasiequilibrium plasma by dynamically screened LO-phonon emission. Scattering of high-energy electrons injected into $n$-doped InAs at room temperature is analyzed and compared to the case where nonparabolicity is neglected. Plasmon losses and a larger density of states are shown to be more important for electrons in a nonparabolic conduction band with energy above the Fermi level. The energy-loss rate of a hot-electron--donor ion plasma to a cold lattice via screened LO-phonon emission in parabolic and nonparabolic bands is also obtained. It is found that even though dynamic screening of LO phonons is stronger in a nonparabolic band, the cooling rate of hot electrons in InAs can be significantly faster because of the increased density of conduction-band states.