Electron correlations in semiconductor heterostructures

The theory of a two-dimensional electron gas is reexamined in the case of GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterojunctions and quantum wells. A new and accurate method was employed to calculate the static structure factor within the mean-field approximation. The influence of the finite width of the electron layer was investigated by calculation of the plasmon dispersion, the local-field function, and exchange and correlation energies in the random-phase approximation (RPA), the Hubbard approximation, and the self-consistent Singwi-Tosi-Land-Sjölander approximation.