Surface effects on reflectance: role of the crystal termination

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Abstract
The reflectivity coefficient of a semi-infinite medium is found, taking into account the effect of the crystal termination on the electron wavefunctions. Maxwell equations are solved for light propagating in a weakly inhomogeneous medium and the reflectivity coefficient is related to an effective dielectric function, which is expressed in terms of the electron wavefunctions. The method is applied to the case of direct transitions between parabolic bands in a semiconductor and the effect of the crystal termination is explicitly considered. An analytic expression is found for the effective dielectric function, which turns out to be quite different from the dielectric function of the infinite crystal. The effect of the surface on modulated reflectivity is expected to be significant. The lambda -modulated reflectivity at the direct gap of Ge is computed and it is shown that it is strongly modified by the surface. The lineshape is sufficiently different to allow, in principle, detection of this effect by an accurate experiment.