Improved combination of scalar diffraction theory and Rayleigh-Rice theory and its application to spectroscopic ellipsometry of randomly rough surfaces

Expressions for ellipsometric quantities and reflectance presented are based on a heuristic combination of the Rayleigh-Rice theory and the scalar diffraction theory. The latter takes into account the local slopes and shadowing. The second-order Rayleigh-Rice theory is used to express the local electric field on the rough surface and the obtained expressions are then used in the scalar diffraction theory instead of the expressions corresponding to a smooth surface. A numeric method of evaluation of the quadruple integral resulting from this combination of the two theories is developed, utilising a Gauss-like quadrature. The efficiency of the formulae is illustrated by optical characterisation of rough silicon and gallium arsenide surfaces created using anodic and thermal oxidation, respectively, and covered with native oxide layers. The optical characterisation employs variable-angle spectroscopic ellipsometry and spectroscopic reflectometry.