Analytical solutions for the optical absorption of semiconductor superlattices

The anisotropic medium approach is used to obtain an exact and easily programmable generalization of Elliot's formula describing the excitonic absorption of semiconductor superlattices. The theory is applied to the computation of excitation binding energies and absorption spectra of GaAs-Alₓ{Ga}_{1{{-}}x}$As superlattices, and the transition between two-dimensional and three-dimensional systems is discussed in good agreement with recent experimental results. For high carrier densities, the Hulthen approximation for the screened Coulomb potential is used within a partly phenomenological approach to obtain an analytical expression for the nonlinear optical absorption.