Characterization of random rough surfaces from scattered intensities by neural networks

Optical scatterometry, a non-invasive characterization method, is used to infer the statistical properties of random rough surfaces. The Gaussian model with rms-roughness sigma and correlation length Lambda is considered in this paper but the employed technique is applicable to any representation of random rough surfaces. Surfaces with wide ranges of Lambda and sigma, up to 5 wavelengths (lambda), are characterized with neural networks. Two models are used: self-organizing map (SOM) for rough classification and multi-layer perceptron (MLP) for quantitative estimation with nonlinear regression. Models infer Lambda and sigma from scattering, thus involving the inverse problem. The intensities are calculated with the exact electromagnetic theory, which enables a wide range of parameters. The most widely known neural network model in practise is SOM, which we use to organize samples into discrete classes with resolution Delta Lambda = Delta sigma = 0.5 lambda. The more advanced MLP model is trained for optimal behaviour by providing it with known parts of input (scattering) and output (surface parameters). We show that a small amount of data is sufficient for an excellent accuracy on the order of 0.3 lambda and 0.15 lambda for estimating Lambda and sigma, respectively.