Application of covariance based models to fit response surfaces to experimental data

Experimental design together with the response surface methodology (RSM) are important tools that can be employed to help optimise IC processes (Walton et al, 1997). This paper presents a method of fitting a response surface to experimental data when there are one or more data points that are poorly fitted by conventional polynomial models. The method is based on first fitting the data with a polynomial model and using this to calculate a worksheet for the combinations of control factors that were used in the original experiment. The actual experimental conditions for the poorly fitting points are then substituted into this worksheet and a covariance fit used to fit the data. The resulting surface follows the general trend while also fitting measurement points where there is confidence that there is no significant experimental error.