Statistical process optimization method for metrology equipment

We developed a statistical method that can be applied to overlay metrology tools to improve performance and time-to-results (TTR) of multi-cycle optimization based on the brute force method. First, we evaluated full response surfaces for each combination of the discrete equipment settings and calculated desirability scores using a normalization function. Second, we combined gradient optimization techniques and response surface methodologies to find the important local maxima (center of the islands in quadratic contour) and stationary response points. Once all the stationary response points have been identified, users can choose to rank the solutions by quality or can choose to use analysis of variance (ANOVA) methods to determine which main effects and/or interactions are of interest. Two separate layers were evaluated and compared to the process of reference (POR) brute force method of optimization. Results showed that the best residuals values from recipes optimized using 1-cycle SPOC-based automatic recipe optimization (ARO) and ARO based on the 2- cycle Brute-Force strategy were comparable to known residuals values from the POR recipes. Moreover, SPOC-based ARO was performed with a TTR of under 2 hours, while a 2-cycle Brute-Force ARO typically took 6~ 20 hours depending on specific configurations. The vast reduction in optimization time is primarily attributed to the elimination of multi-cycle refinement, whose data collection dominated the previously observed TTR. In conclusion, we demonstrated the ability to reduce time to solution by a factor of 3 while maintaining or improving on overlay residuals compared to existing brute force methodologies.