Interband Dielectric Properties of Solids in an Electric Field

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Abstract
A general expression for the imaginary part of the one-electron interband dielectric function of a solid in the presence of an electric field is derived. The result is valid for all regions of k space and explicitly takes into account the variation of the dipole matrix element and effective mass throughout the Brillouin zone. Under certain approximations the finite-electric-field dielectric function reduces to the convolution of the zero-field dielectric function with an Airy function. This result can be used in conjunction with band-structure calculations which have already been done in order to predict the line shape of the electroreflectance spectra as a function of electric field. The convolution expression reduces further at nondegenerate critical points, and the forms for the four types of critical points are presented. In certain instances it is possible to unfold the convolution integral and obtain the zero-field dielectric function from either the finite-field dielectric constant or the electroreflectance data at isolated critical points.