Bias and variance in single and multiple response surface modeling

This work examines the single response surface (SRS) and multiple response surface (MRS) modeling of wafer uniformity using experimental data from a chemical-mechanical polishing process. It is shown that the SRS estimate of uniformity measures total variation whereas the MRS estimate measures only spatial variation. The experimental results demonstrate that the MRS method is a biased estimator, whereas the SRS method is not. Finally, it is shown that the bias in the MRS estimate can lead one to choose a nonoptimal process recipe.