|
Recently developed statistical inference methods permit detailed process information to be developed from experiments without relying on particular physical process models. Generalized Cross Validation is a powerful calculational method that can be used to find the smooth function that best approximates noisy, scattered experimental data. Already employed in applications in such fields as geology, biology, and meteorology, its three principal benefits for process engineering are: - The method does not require a parameterized model of the experiment, so it can be used in situations where no model, or no sufficiently detailed model, is available. - The results of the calculation are expressed in terms of piecewise polynomial or polylogarithm functions, rather than the global polynomials, which are used by traditional Response Surface Methods, that can fail if the experimental data cannot be described well by a polynomial. - The method can be used effectively in situations where the errors in the experimental results are not known precisely. These qualities make Generalized Cross Validation (GCV) a very attractive tool for analyzing and optimizing processes. We present an overview of the GCV method with two examples that show how it can be applied to solve problems in process modeling and optimization. In our first example, we efficiently determine the best values for the GHOST proximity-effect correction parameters (defocused-beam diameter and dose) by using the GCV method to fit and interpolate experimental data. For the 50-kV electron-beam system we studied, the best values were predicted to be a defocused beam diameter of 20 μm and a dose of 34 per cent of the pattern dose. These results are in good agreement with earlier work that employed a much more time-consuming method. In our second example, the GCV method is applied to interpolate experimental data to predict the developer concentration and prebake temperature that produce maximum contrast for a particular deep-UV resist.
|
