Roughness Contributions to Thin-Film Reflectance

In order to find a factor to account for how surface roughness affects reflection and transmission measurements of thin films, we developed a MATLAB program that computes scattering from a rough surface with arbitrary-good accuracy. S-polarized plane waves are reflected off of a perfectly conducting surface with a certain amount of roughness and normalized with reflection from a perfectly smooth surface. In order to best model the kinds of roughness we anticipate in actual thin films, the surfaces were created with cubic splines where the spacing of the knots was varied to control the spatial frequency. The heights of the knots had a random Gaussian distribution. To make these computations useful for extracting index of refraction data from thin-film reflectance measurements, we have developed efficient approximations of the exact calculations that can be used in data fitting programs. These approximations give the roughness correction as a function of incident angle, root-mean-square roughness, and spatial frequency.