Characterization of random rough surfaces from scattered intensities by neural networks

Optical scatterometry, a non-invasive characterization method, is used to i nfer the statistical properties of random rough surfaces. The Gaussian mode l with rms-roughness sigma and correlation length Lambda is considered in t his paper but the employed technique is applicable to any representation of random rough surfaces. Surfaces with wide ranges of Lambda and sigma, up t o 5 wavelengths (lambda), are characterized with neural networks. Two model s are used: self-organizing map (SOM) for rough classification and multi-la yer 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 theo ry, 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 dis crete classes with resolution Delta Lambda = Delta sigma = 0.5 lambda. The more advanced MLP model is trained for optimal behaviour by providing it wi th known parts of input (scattering) and output (surface parameters). We sh ow that a small amount of data is sufficient for an excellent accuracy on t he order of 0.3 lambda and 0.15 lambda for estimating Lambda and sigma, res pectively.