Theory of light scattering from self-affine surfaces: Relationship between surface morphology and effective medium roughness

Using Rayleigh-Rice scattering theory we have studied the influence of surface morphology on the optical response of self-affine surfaces. We have established a mathematical relationship between the surface roughness (d) as determined by spectroscopic ellipsometry (SE) using the effective medium approximation (EMA) and the parameters controlling the morphology of the surface: root-mean-square roughness (w), correlation length (ξ), and roughness (Hurst) exponent ({α}). These three parameters affect the roughness value measured by ellipsometry. However, when the correlation length is smaller than the wavelength, the dependence is contained in a single parameter wδ that is proportional to the product of the surface roughness and the local slope δ=w/wξ^α0.0pt0exξ^α. The fact that the local slope of a surface increases only very slowly during growth explains the linear dependence experimentally found between w as measured by scanning-probe microscopy and the vertical roughness determined by the effective medium approach.