Effect of the electron-phonon interaction on the subband structure of inversion layers in compound semiconductors

Abstract

Recently electron inversion layers have been fabricated on a number of compound (principally III–V) semiconductors. Because of the polar nature of these materials, the effect of the electron-optical phonon interaction is expected to be significant. This has certainly been true in recent calculations of the ground state energy and equilibrium density of electron-hole liquids in a number of compound semiconductors [1]. We have calculated the subband structure of inversion layers in polar semiconductors. The starting point of our many-body calculation is the Hartree subband structure determined using a variational method described in ref. [2]. Using the Hartree wavefunctions as basis functions we have calculated the self-energy of the ground and first excited subbands to lowest order in the effective interaction. This interaction is the sum of Coulomb (direct and image) and electron-phonon terms which are screened by a dielectric function that includes both e-e and e-ph effects. The screening by inversion layer electrons has been treated in the plasmon-pole approximation. We have obtained the electron self-energy, the quasi-particle energy, and the subband separations as a function of inversion layer concentration for parameters corresponding to GaAs. The coupling of electrons to bulk phonons is considered. Our results are compared to those obtained using the simpler ϵ 0 ∗ approximation [1]. Here, explicit phonon terms are neglected, but the bare band mass is replaced by the polaron mass, and the high frequency dielectric constant (ϵ ∞) is replaced by the static dielectric constant (ϵ 0). This approximation has been applied to the electron-hole liquid for situations in which the optical phonon frequency is larger than the electron plasma frequency. The idea behind the ϵ 0 ∗ approximation is to account in a very rough way for vertex corrections to the electron-phonon interaction. A principal criticism of our dynamic RPA calculations is the neglect of vertex corrections in the effective interaction. In three-dimensional metallic systems (high density), Migdal's theorem applies and vertex corrections are small. However, it is not clear that we may neglect such corrections in inversion layers. This point will be discussed further.