Oblique-incidence optical reflectivity difference from a rough film of crystalline material

Formation of a rough film of crystalline material on a smooth substrate resulting from kinetic roughening in epitaxy or erosion causes disproportionate changes in reflectivity for s- and p-polarized light. I present a mean-field theory of optical reflectivity difference defined as (r_p-r _p0)/r_p0-(r_s-r_s0)/r _s0≡Δ_p-Δ_s from such a rough film, with r_p0 and r_s0 being the reflectivities of the bare substrate, and r_p and r_s being the reflectivities after the rough film forms on the substrate. In the limit that the average film thickness is less than the optical wavelength λ, I found that Δ_p - Δ_s consists of a term that varies linearly with the average film thickness and a term that is proportional to the surface density of step edge atoms. I apply such a theory to the analysis of growth and ion erosion of a number of crystalline materials studied with the oblique-incidence optical reflectivity difference (OI-RD) technique.