Surface roughness measurement with optical scatterometry

Scattering of light by random rough surface scan be numerically simulated by using an exact electromagnetic scattering theory. Unfortunately, the characterization of surfaces is almost impossible owing to the non-uniqueness of the inverse scattering problem and highly nonlinear relationship between the surface parameters and the scattering. Thus, existing practical methods for qualitative or quantitative characterization are almost entirely experimental. Here we apply neural networks for estimating statistically the surface parameters. Previously, we have successfully demonstrated that neural network as a statistical estimator for optical scatterometry is an efficient tool for characterizing periodic microstructures. We generate numerically random surfaces, which are characterized with the degree of roughness, i.e., rot-mean- square (rms) amplitude of the roughness and correlation length. Here we are mainly interest in the most demanding region of the rms amplitude in the so-called resonance domain, corresponding to height fluctuations and correlations up to 5 times the wavelength of light. The neural network model, which is her a self-organizing map, is first trained and calibrated with the known surface parameter and scattering data pairs. At characterization stage, using only measured intensity distributions, the neural network theory classifies surface parameters into discrete classes of the rms amplitude and the correlation length. For most cases the classification result deviates at most one class, corresponding to 0.5 wavelengths, from the correct values.