Numerical ellipsometry: Advanced methods for design, testing, and use of artificial intelligence for absorbing films using Jones and/or Mueller measurements

The optical properties and thickness of a thin absorbing film deposited on a known substrate can be determined using ellipsometry in real-time using artificial intelligence (AI) in the form of artificial neural networks (ANNs). The desired film parameters are related to visible light reflection measurements through Maxwell’s equations, wavelength, and geometry. One of the primary advantages of the AI method is speed. Prior work by the authors focused on ITO on silicon and chromium on BK-7 glass. The work here describes further developments in the use of AI methods to potentially enable real-time, in situ monitoring of thin film growth in a broader range of applications for any absorbing film on any homogeneous, isotropic substrate. Examples are given using a single angle of incidence (55°) and three angles of incidence (55°, 65°, and 75°) for comparison. Thin absorbing films (up to a nominal 40 nm) are examined using multilayer perceptron ANNs of either 4 or 12 input neurons and 4 output neurons with two hidden layers of 80 neurons each. A separate network is developed independently at each wavelength. Overall predictions depend upon two steps. The first step is the training step in which a large training data set is presented to the ANN, and an error backpropagation algorithm is employed to incrementally adjust its weights. This step is computationally intensive but only needs to be performed once. The second step is prediction, in which ellipsometry measurements are presented to the trained ANN. Thus, the primary purpose of this work is to lay a foundation that is applicable to a vast array of material combinations, examples of which will be treated with measured data in future work.