Exchange Energy of a Hole Gas and the Thomas-Fermi-Dirac Approximation in p-Type ?-Doped Quantum Wells in Si and GaAs

Abstract

We present the electronic structure of p-type δ-doped quantum wells in Si and GaAs including exchange effects in the Thomas-Fermi-Dirac approximation. We also carry out Schrodinger-Poisson self-consistent calculations considering the particularities the exchange potential has in the Local Density Approximation in the case of a hole gas. Using the Thomas-Fermi-Dirac approximation, we present an analytical expression for the Hartree-Fock potential. We compare the results obtained from this model with those obtained through Schrodinger-Poisson self-consistent calculations. As a result of this comparison, we saw that the model presented, in spite of its simplicity, gives very good results. In particular, it practically fixes the energy differences between the occupied levels of the well. There is agreement between the results of our two calculations (self-consistent and with Thomas-Fermi-Dirac model) with the experimental results in the three systems (B δ-doped quantum wells in Si, Be δ-doped quantum wells in GaAs, and p-type Si δ-doped quantum wells in GaAs).