Quasi-two-dimensional electron-hole plasma in a quantum well: Hartree, exchange, and correlation energies.

Abstract

We calculate the {ital T}=0 total Coulomb energy of a quasi-two-dimensional electron-hole plasma in a quantum well, taking into account the finite width of the well. We consider 2D plasma densities low enough to have electrons and holes in their lowest subband only, but large enough to ensure the validity of the usual perturbative expansion in Coulomb interaction. We derive explicit expressions of the Hartree, exchange, and correlation energies in terms of the {ital exact} free-electron and hole wave functions in the well, in order to allow calculations of these energies for finite barrier heights. In a last part, we recover the intuitive Schr{umlt o}dinger equation for excitons in a quantum well, using the ladder diagram approach. {copyright} {ital 1996 The American Physical Society.}