Thickness and refractive index measurements of a thin-film using an artificial neural network algorithm

Thin-film thickness and refractive index measurements are important for quality control in many high-tech industrial manufacturing processes, such as the semiconductor, display, and battery. Many studies have been carried out to measure the thickness and refractive index of thin-films, and recently studies using an artificial neural network (ANN) algorithm have also been conducted. However, strict evaluations of ANNs were not reported in all previous studies. In this study, a multilayer perceptron type of ANN algorithm for simultaneously analyzing the thickness and refractive index of a thin-film is designed and verified by using four thin-film certified reference materials (CRMs) being traceable to the length standard. According to the number of hidden layers and the number of nodes for each hidden layer, 12 multilayer perceptron type ANN algorithms were designed and trained with a theoretical dataset generated through optics theory based on multiple interferences. Subsequently, the interference spectra measured by the four CRMs were put into the 12 trained ANNs as input, and it was checked whether or not the output values were in good agreement with the corresponding certified values of both the thickness and refractive index. As a result, an ANN algorithm having two hidden layers with 100 nodes was selected as the final algorithm and an uncertainty evaluation was performed. Finally, the combined uncertainties for the thickness and refractive index were estimated to be 2.0 nm and 0.025 at a wavelength of 632.8 nm, respectively, as measured using a spectral reflectometer with the well-trained ANN algorithm.