Electric-field effects on interband transitions

Abstract

The effect of an electric field on the optical properties due to interband transitions has been investigated in the two-dimensional and three-dimensional periodic structures. The approach of Franz and Keldysh is followed, and expressions forɛ2 (ω,F) are obtained, which are extensions of previous expressions given in the literature to all types of critical points and to all directions of the electric field. It is shown that the electric field effect occurs only at critical points and, though a limited volume ofk-space must be considered, the result under appropriate conditions does not depend on this volume. The results for the three-dimensional case presented here are in complete agreement with those recently obtained by Aspnes with a different procedure, using an infinite volume of integration. Detailed results are given for a structure which is periodic in two dimensions. For the critical pointM0 we find an effect very similar to the Franz-Keldysh effect. For the critical pointM1, the strong logarithmic singularity is broadened and shifted, while additional oscillations appear on one side of the peak. A strong anysotropy is present both atM0 andM1. The present results may be useful in clarifying the nature of the critical points responsible for the structure in the optical constants and for obtaining the values of the effective masses.