General theory of optical reflection from a thin film on a solid and its application to heteroepitaxy

Light reflection from an optically smooth yet atomically rough film on a smooth solid substrate formed by deposition or erosion is a convenient source of information on morphology and chemical makeup of the film. We show that changes in optical reflectivity for s -polarized (TE mode) and p -polarized (TM mode) components, defined as (rp - rp0) rp0 - (rs - rs0) rs0 Δp - Δs induced by such a film, are generally related to structural and chemical properties of such a film through a mean-field theory. Here, rp0 and rs0 are the reflectivities of the substrate, and rp and rs are the reflectivities when the film is added. According to the theory, Δp - Δs consists of a term that is proportional to the thickness of the rough portion of the film, a term that is proportional to the density of unit cells embedded in terraces, and a term that is proportional to the density of unit cells situated at step edges. The proportionality constants are functions of the overall thickness and chemical makeup of the film. We apply the theory to the analysis of a wide range of growth and adsorption experiments studied with the oblique-incidence reflectivity difference technique.