Evaluation strategies for multi-layer, multi-material ellipsometric measurements

Abstract

In order to extract the physical properties from an ellipsometric measurement, an optical model of the sample has to be assumed first, because the theory of ellipsometry consists on one-directional computation only (there is no reverse function). Then, the ellipsometric evaluation is an iterative optimising procedure with high time consumption feature and the reliability depends strongly on the a-priori information. The faster the computers are today, the more exactly the physical properties of either the sample or the process can be evaluated. However, the increasing number of the parameters and so, the dimensions of the search space leads to a combinatorial explosion. In the case of larger search space is needed (either less a-priori information is available or more parameters are used), the error surface of the parameter space can be quite “hilly” and may contain even numerous local minima. In the lack of precise a-priori information the Levenberg–Marquardt (LM) gradient search is generally started out of the decreasing area of the global minimum and therefore, it is inappropriate to find the solution. Therefore, there is a hard need of more complex evaluating strategies, which combines the algorithms to make the evaluation more reliable. Different point selection strategies, an extended criteria function and combined algorithms were applied on porous silicon multi-layer and polycrystalline measurements to demonstrate a higher convergence speed (effectiveness) and more reliability.