Independent-particle theory of the Franz-Keldysh effect including interband coupling: Application to calculation of electroabsorption in GaAs

We calculate the linear optical absorption spectrum for a semiconductor in the presence of a strong constant (dc) electric field (the Franz-Keldysh effect). An independent particle theory is developed that treats the dc field nonperturbatively and the optical field perturbatively. Results are presented from a calculation using a 14-band $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ model for the band structure of GaAs that includes remote band effects to order ${k}^{2}$. We also include remote band effects in the matrix elements for consistency. Coupling between nearly degenerate bands due to the dc field plays an important role, both near the valence band degeneracy in the center of the Brillouin zone and along lines where spin-split bands become degenerate. We calculate the electroabsorption spectrum with a dc field pointing along various crystal directions and predict experimentally accessible effects due to band warping. Calculations using the 14-band model show a change in the absorption spectrum that depends on the sign of the electric field, reflecting the lack of a center of inversion symmetry in GaAs. The theoretical framework presented can be easily extended to nonlinear absorption.