K⋅p theory of the Franz-Keldysh effect

We use the k⋅p formalism to calculate Franz-Keldysh (FK) absorption spectra in direct-band-gap III-V semiconductors. This method allows us to include band anisotropy and nonparabolicity as well as band mixing. With k⋅p models of various complexity, we investigate how these phenomena influence the main features of the electroabsorption using GaAs as an example. We show that the dependence of the FK absorption on the polarization of the incoming light can be understood in analogy to quasi-two-dimensional systems by mostly decoupled heavy- and light-hole bands involving the anisotropy of the bulk-momentum matrix elements. On the other hand, the FK absorption tail and the periods of the FK oscillations are mainly determined by the realistic energy dispersions of the bands. We discuss the applicability and the limits of simplified models and demonstrate that for most cases the field-induced interband mixing is negligible in comparison with the zero-field coupling of the bands. As an application, we show the consequences for the widely used method to determine the electric field from the FK oscillation periods measured by absorption or photoreflectance experiments. Most of the basic features have been observed in experiments. The qualitative details are of general validity.