A sampling decision system for semiconductor manufacturing - relying on virtual metrology and actual measurements

In semiconductor manufacturing, optimization of the sampling measurement plan through production steps is key to maximize productive performances. The measurement plan must guarantee high quality and compliance to wafer specifications limits. In this article, the relationships between virtual metrology (VM) and actual measurements are investigated with respect to a sampling decision system (SDS); specifically, a multilevel VM strategy is relied on to provide predictive information. Such virtual measurements serve as input for the sampling decision system, which in turn suggests the optimal measurement strategy. Two approaches relying on decision-theoretical concepts are discussed: the expected value of measurement information (EVofMI) and a two stage sampling decision model. The basic assumption of the SDS-VM system is that it is not necessary to perform a real measurement until it is strictly needed. The two methodologies are then validated relying on simulation studies and actual chemical vapor deposition (CVD) process and measurement data. The ability of the proposed system to sample dynamically the wafer measurements in dependence of the calculated risk is then evaluated and discussed.