Electric-Field Effects on Optical Absorption near Thresholds in Solids

Abstract

The weak-field effective-mass-approximation calculations of the absorption coefficient in the presence of an electric field for direct and indirect transitions at a normal (${M}_{0}$) threshold are extended to an arbitrary orientation of the electric field in an anisotropic solid. To do this, a systematic method of evaluating density-of-states integrals arising in the electroabsorption or Franz-Keldysh effect is presented. Certain integrals obtained in prior calculations at the ${M}_{0}$ threshold which have not been previously evaluated are given in closed form. This method is also used to derive the change in absorption coefficient, $\ensuremath{\Delta}\ensuremath{\alpha}(\mathcal{E})$, occuring at the saddle-point edges ${M}_{1}$ and ${M}_{2}$, as well as the edge ${M}_{3}$, for an arbitrary field direction in an anisotropic solid. It is shown that there is a direct correlation between $\ensuremath{\Delta}\ensuremath{\alpha}(\mathcal{E})$ for the ${M}_{0}$ and ${M}_{3}$ edges, and also for the ${M}_{1}$ and ${M}_{2}$ thresholds. Reduced masses of opposite signs, as in the ${M}_{1}$ and ${M}_{2}$ edges, give rise to two branches in $\ensuremath{\Delta}\ensuremath{\alpha}(\mathcal{E})$.