Density of states and Wannier-Stark levels of superlattices in an electric field

The density of states is calculated for superlattices in the presence of an electric field, using the concept of a generalized transmission probability. Various ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As-based quantum-well structures with up to 200 periods are examined for electric fields ranging from 4×${10}^2$ V/cm to 1×${10}^6$ V/cm. Different field effects are observed in the below- and above-barrier regions of the density-of-states spectra. In the below-barrier region the spectra embody the occurrence of Wannier-Stark localization. The above-barrier region is dominated by two kinds of structures, one similar to Franz-Keldysh oscillations, and another resembling a Wannier-Stark-ladder behavior.