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

We present results for the binding energy of an exciton formed when an elec tron-hole pair is photoexcited within a single, compositionally modified la yer of a semiconductor superlattice, for example by adding a small percenta ge of In atoms to a single GaAs layer of a GaAs/AlGaAs system. Such a syste m could serve as the basis. for spatially-selective photoexcitation, a proc ess whereby a laser pulse would create electron-heavy-hole pairs exclusivel y in the modified layer. We first derive an effective one-dimensional (ID) Hamiltonian for an electron, by averaging the 3D electron-hole Hamiltonian using a one-parameter trial wavefunction, which is dependent on the in-plan e relative coordinates, as well as a normalized Wannier orbital for a singl e 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 effectiven ess of our approach, we find that for periodic superlattices our results fo r the exciton binding energy are in very good agreement both with experimen t and the results of other theoretical calculations. (C) 1999 Academic Pres s.