Electro-optical properties of semiconductor superlattices in the regime of Franz-Keldysh oscillations

Abstract

We show how to compute the optical functions (reflectivity, transmissivity, and absorption) for semiconductor superlattices exposed to a uniform electric field in the growth direction, including the excitonic effects. The field strength is chosen to be small enough to avoid Stark localization but strong enough to observe Franz-Keldysh (FK) oscillations. For superlattices of total thicknesses large compared to the exciton Bohr radius, polaritonic effects are taken into account. For small values of the applied field the optical spectra are ``excitonlike'' but with the excitonic transition energy shifted by the applied field. For great values of the electric field the excitonic binding energy decreases, and an absorption tail appears below the gap. Above the gap FK oscillations appear. Our approach automatically includes the nonlocal behavior of the susceptibility, and the coherence between the carriers and the electromagnetic field. Numerical examples appropriate to GaAs/${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As superlattices are given, and a comparison with experiments is discussed.