Numerical ellipsometry: Artificial intelligence for real-time, in situ absorbing film process control

Abstract

Ellipsometry is a material analytical method in which the desired parameters, for example, film thickness and index of refraction, are related to the instrument measurements through Maxwell’s equations, light wavelength, and measurement geometry. Consequently, obtaining the desired parameters has required solving the model equations using a wide variety of methods. A commonly used method is least squares curve fitting, frequently the Levenberg–Marquardt method. This numerical method depends upon not only the model but also the initial estimates of solution, the possible interference of local minima, and the algorithm stopping conditions. Being iterative, it also takes nonzero time. The work here demonstrates the use of artificial intelligence in the form of a multilayer perceptron artificial neural network to avoid these problems and find solutions in the millisecond time scale. This noniterative, stable, and fast performance lends itself to real-time, in situ monitoring of thin film growth. Examples for thin (up to 30 nm) films will be given using a multilayer perceptron configuration consisting of four input and four output neurons with two hidden layers of 40 neurons each. Solutions are predicted by the artificial neural network at each wavelength independently and do not rely on fitting functions which express a relationship between optical properties and wavelength.