QUASI-2-DIMENSIONAL ELECTRON-HOLE PLASMA IN A QUANTUM-WELL - HARTREE,EXCHANGE, AND CORRELATION ENERGIES

We calculate the T=0 total Coulomb energy of a quasi-two-dimensional e lectron-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 int eraction. We derive explicit expressions of the Hartree, exchange, and correlation energies in terms of the exact free-electron and hole wav e functions in the well, in order to allow calculations of these energ ies for finite barrier heights. In a last part, we recover the intuiti ve Schrodinger equation for excitons in a quantum well, using the ladd er diagram approach.