Performance Evaluation of Blended Metrology Schemes Incorporating Virtual Metrology

This paper formulates and explores the tradeoff between re-calibration and off-line metrology to find the optimal number of samples that maximizes the profit. A sequence of metrology samples using a regression model with linearly drifting coefficients is simulated, a model realistically applying to a manufacturing process with linearly drifting hidden variables. Three different types of statistical models, linear regression, exponentially-weighted linear regression (EWLR), and the Kalman Filter are used as VM prediction tools. We simulate two blended metrology sampling scenarios, one that automatically discards flagged wafers and another that allows re-inspection and process re-tuning. We alternate between training sets and testing sets, and compare the resulting net profit, Type I, and Type II errors as a function of varying VM prediction sample sizes. Results show that each VM prediction model has a different tradeoff between the Type I and Type II errors that determine the optimal sampling scheme. The ultimate goal is to create a general framework that quickly leads to the optimal design of such schemes given the characteristics of the process in question.