Symmetry Analysis of Electroreflectance Spectra

A systematic study is undertaken of the polarization anisotropies observed in electroreflectance, with the objective of obtaining information about the Brillouin zone (BZ) location and $E\left(k\right)\mathrm{}$ topology of the transition. The analysis permits the extraction of such symmetry information from properly designed experiments, independent of the details of the spectral line shape, and magnitude and inhomogeneity of the modulating field. It is shown that transitions originating from $〈111〉$ and $〈100〉$ directions in the BZ can be identified. Criteria are established for determining the validity of the weak-field approximation in calculations of the electro-optic effect, and for determining the effect of the electric field on the transition matrix element. The effect of the electric field on band degeneracies is considered, and their correlation to observed anisotropies is discussed. Comparison of the analytical results with electroreflectance measurements in germanium is made.