Franz-Keldysh Effect of the Refractive Index in Semiconductors

Changes in the shape of the fundamental absorption edge of a semiconductor as induced by strong electric fields will lead to correlated changes in the refractive index. Computation of the dispersion integral for an absorption edge that is modified by the Franz-Keldysh effect proves that the refractive index of germanium and gallium arsenide changes by as much as 0.02, for instance, for electric fields characteristically present in a $p-n$ junction. The fact that the refractive index depends upon electric fields extends the Franz-Keldysh effect to reflection phenomena, even if this refractive index is much greater than the extinction coefficient, which is usually the case near the fundamental edge of semiconductors. Based on this dependence of the refractive index upon electric fields, the field effect of the reflectance in germanium is interpreted and good agreement is obtained with experiment. It is pointed out that this mechanism could be relevant for the confinement of the radiation in a gallium arsenide laser.