A Sampling Decision System for Virtual Metrology in Semiconductor Manufacturing

In semiconductor manufacturing, metrology operations are expensive and time-consuming, for this reason only a certain sample of wafers is measured. With the need of highly reliable processes, the semiconductor industry aims at developing methodologies covering the gap of missing metrology information. Virtual Metrology turns out to be a promising method; it aims at predicting wafer and/or site fine metrology results in real time and free of costs. In this paper, we present a sampling decision system that relies on virtual measurements suggesting an efficient strategy for measuring productive wafers. Several methods for evaluating when a real measurement is needed (including the expected utility of measurement information, a two-stage sampling decision model and wafer quality risk values) are proposed. We further provide ideas on how to assess and update the reliability of the virtual measurements in a sampling decision system (whenever real measurements become available). In this context, we introduce equipment health factors and virtual trust factors for improving the reliability of the sampling decision system. Finally, the performance of the sampling decision system is demonstrated on a set of virtual and real metrology data from the semiconductor industry. It is shown that wafer measurements are efficiently performed when really needed.