Index of refraction of GaAsAl_xGa_1-xAs superlattices and multiple quantum wells

Recent research of superlattices and multiple quantum wells has generated considerable interest in the optical waveguiding properties of these structures for optoelectronic applications. As a result we present a theoretical study of the index of refraction of superlattices and determine its variation as a function of frequency and the superlattice parameters, i.e., layer width and AlAs composition. Γ-region exciton and valence-band mixing effects are included in the model. It is found that these two effects have an important influence on the value of the index of refraction and that superstructure effects rapidly decrease for energies greater than the superlattice potential barriers. Because of the quasi-two-dimensional character of the Γ-region excitons, our results indicate that the superlattice index of refraction can vary by ∼ 2% at the quantized, bound-exciton, transition energies. Overall, the theoretical results are in good agreement with the experimental data.