Electronic excitations in semiconductors. General theory

Abstract

A general theory is presented that allows for the computation of excitation energies in semiconductors with proper inclusion of electron correlations. It is a natural extension to excited states of a local approach to the electron-correlation problem that has been formulated and tested before for ground-state calculations. The electronic correlations can be treated thereby with the same accuracy as is customary in quantum-chemistry calculations for small molecules. The formulation does not have the shortcomings that prevent conventional quantum-chemistry methods to be carried over to a treatment of delocalized excited states in solids. The theory is formulated in terms of a set of basis functions. Computation of the correlation energy is reduced to the computation of a number of expectation values. They are explicitly evaluated by applying a set of rules which are described in detail. By means of a simple model, special aspects of the correlation problem are discussed, such as electronic polarizations, local-field effects, the dependence of the correlation energy on the energy of the excited electron, and changes in the ground-state correlations due to the presence of the excited electron. It is pointed out that the general theory also contains dynamic relaxation effects.