Variational tight-binding theory of excitons in compositionally modified semiconductor superlattices

Abstract

We present results for the binding energy of an exciton formed when an electron–hole pair is photoexcited within a single, compositionally modified layer of a semiconductor superlattice, for example by adding a small percentage of In atoms to a single GaAs layer of a GaAs/AlGaAs system. Such a system could serve as the basis for spatially-selective photoexcitation, a process whereby a laser pulse would create electron–heavy-hole pairs exclusively in the modified layer.We first derive an effective one-dimensional (1D) Hamiltonian for an electron, by averaging the 3D electron–hole Hamiltonian using a one-parameter trial wavefunction, which is dependent on the in-plane relative coordinates, as well as a normalized Wannier orbital for a single hole. The exciton binding energy is then obtained by computing the lowest bound-state energy of the effective 1D electron Hamiltonian in the nearest-neighbor tight-binding approximation. As a demonstration of the effectiveness of our approach, we find that for periodic superlattices our results for the exciton binding energy are in very good agreement both with experiment and the results of other theoretical calculations.