Overlay sampling optimization by operating characteristic curves empirically estimated

Operating Characteristic (OC) curves, which are probabilities of lot acceptance as a function of fraction defective p, are powerful tools for visualizing risks of lot acceptance errors. The authors have used OC curves for the overlay sampling optimization, and found that there are some differences in probability of acceptance between theoretical calculation and empirical estimation. In this paper, we derive a theoretical formulation of the probability of acceptance for several simple cases by decomposing overlay errors, and show that the origin of the differences is the use of stratified sampling in overlay inspection.