Optical Response of Semiconductors in Electric Fields: Excitonic Effects

The effects of a uniform electric field on the optical response functions of a semiconductor are calculated, by numerically solving the effective-mass equation for a Wannier exciton. The calculations assume an isotropic effective-mass model of direct transitions at a three-dimensional $M_0$ threshold. The relationship between the real and imaginary parts of the dielectric function are discussed for the purposes of understanding the physics of electroreflection and developing rules of thumb for interpreting electroreflectivity spectra. The theory is compared with the electroreflectivity data at the direct edge of Ge taken by Handler, Jasperson, and Koeppen, and yields very good agreement. The value of the momentum matrix element extracted from the fit of theory to experiment is $0.35\frac{\hslash }{a_0}$, in excellent agreement with experimentally measured values.