Extracting optical constants of solid materials with micro-rough surfaces from ellipsometry without using effective medium approximation

Abstract

The effective medium approximation (EMA) model may cause a large deviation in the data analysis of spectroscopic ellipsometry (SE) for solid materials with randomly microrough surfaces since it ignores the influence of the lateral irregularities of the rough surfaces on the electromagnetic scattering. In this work, a novel inversion framework is developed to extract optical constants from the SE parameters for solid materials with randomly microrough surfaces. Our approach enables the integration of the Levenberg-Marquardt optimization algorithm and the first-principles calculations of electromagnetic scattering. In each iterative step, the electromagnetic interactions with rough surfaces are accurately obtained from first-principles calculations without using the EMA model for rough estimation, which significantly guarantees the precision and wide applicability of our method for actual surfaces without a perfectly Gaussian height distribution. Furthermore, a superior advantage of our approach is that its error can be feasibly evaluated from the instrumental errors of the surface morphology detectors and the SE.

Spectro-ellipsometric modeling and optimization of two-dimensional Ge layer and three-dimensional Ge dot/island structures on SiO2 substrates

“…48) The influence of the shadowing effect on randomly rough surfaces cannot be neglected either. 49) Liu et al 50,51) theoretically studied the effect of lateral irregularities in the microstructure on scattering of light. They identified the limitations of using EMA to determine the optical constants of randomly rough solid surfaces.…”