A modified learning strategy for neural networks to support spectroscopic ellipsometric data evaluation

Abstract

It has been shown that worst-case learning, a slightly modified strategy in backpropagation network (BPN) training, results in constrained maximal error at the expense of slightly increased root mean squared error (RMSE) using BPN in spectroscopic ellipsometry (SE). Traditionally the evaluation of SE needs an anticipated multifilm optical model possessing initial parameters close enough to the targeted ones, because a non-linear gradient descent algorithm is performed on the basis of the selected initial guesses. If the initial guesses are not close enough, erroneous results may appear when the algorithm inadvertently falls into the trap of a local minimum. Backpropagation-trained feedforward neural networks prove to be able to give initial estimations that are sufficient for avoiding problems in most cases. Nevertheless, such a network trained with a traditional backpropagation algorithm cannot guarantee error free operation at high confidence levels as it aims for minimised RMSE. The suggested worst-case method gives high confidence levels of convergence from the neural network performed pre-evaluation results to the actual physical parameters. We present two types of problems as demonstrations. Firstly, Separation by Implantation of Oxygen (SIMOX) structural models were used. The maximal errors of structural prediction have fallen from 37% to 7.8% of the entire training region when using a worst-case strategy instead of a traditional backpropagation. Meanwhile RMSE values rose from 3.2 to 4.61%. Secondly, porous silicon layer (PSL) investigations show the effectiveness of using trained BPNs successively. Using a second BPN trained in a smaller region after the first one, we get a more precise approximation for the parameters. Further tips are given for exploiting the advantages of the worst-case learning method, to facilitate creating a more effective and safe apparatus for real-time material parameter determination.