Effect of surface roughness on the electromagnetic properties of multilayered solids

The expressions for the scattered electric fields Ei and Ej of plane waves incident on a statistically rough interface of two isotropic, homogeneous halfspaces i and j are derived using Kirchhoff approximation. By constructing the mean intensity (correlation function) of the scattered fields in medium i (incidence medium) and medium j, respectively, the coherent (specular) and incoherent (diffuse) component of reflection and transmission coefficients and the so called (introduced by the author) 'reflection and transmission attenuation factors' are derived. These reflection and transmission attenuation factors are used to develop a mathematical-physical model which is used to derive reflectance and transmittance expressions of a planeparallel plate (silicon-wafer) with and randomly rough surface from that of a planeparallel plate with smooth surfaces. Using this model the roughness-parameters (standard deviation 'sigma' and autocorrelation length 'tau' ) of the surface of an industrial manufactured silicon-wafer are specified from spectroscopic reflectance and transmittance measurements. The results are in best agreement with the values of the roughness-parameters which have been specified by using Atomic Force Microscope (TMAFM). (author)