Spectroscopic ellipsometric evaluation of multilayer thin-film roughness using a genetic algorithm

Accurate characterization of thin films with complex surface roughness requires precise modeling of both the film and its interfaces. In ellipsometry, surface roughness can be described using Bruggeman, Lorenz-Lorenz, or Maxwell-Garnett effective medium approximations (EMAs). Here, we adopt the Maxwell-Garnett EMA because it provides a simple yet physically meaningful representation of a composite air/material layer, accurately accounting for the volumetric fraction of inclusions while remaining computationally efficient. The model comprises two roughness sublayers atop a dense SiO2 layer, each represented as an air/SiO2 mixture with decreasing volume fractions according to Maxwell-Garnett theory. The substrate optical constants are known, and the dense layer is described using a fixed Lorentz model. Ellipsometric intensities (Is and Ic) are computed via the transfer matrix method (TMM) in MATLAB and treated as simulated data. A genetic algorithm (GA) is used to invert these data and extract key opto-geometrical parameters, including the dense layer’s refractive index, layer thicknesses, and porosity fractions. Results show that the multilayer EMA combined with GA enables more accurate and robust parameter retrieval, particularly for complex roughness profiles. The approach is experimentally validated on a resin thin film deposited on a silicon substrate, providing a reliable framework for optical characterization of rough thin-film surfaces.