Sequential Screening in Semiconductor Manufacturing, I: Exploiting Spatial Dependence

This paper addresses a problem of simultaneous quality and quantity control motivated by semiconductor manufacturing. After wafers are fabricated, the individual chips on the wafers are probed, or electrically tested, and, in some cases, the probing facility is the bottleneck for the entire IC manufacturing process. Under this assumption, we consider the problem of choosing the optimal start rate of lots of wafers into the fabrication facility and the optimal chip screening policy in front of the probing facility to maximize the expected profit, which is the revenue from good chips minus the variable fabrication and probing costs. These decisions are subject to capacity constraints at both the wafer fabrication and probing facilities. Over 300 wafers from two industrial facilities are analyzed in this paper, and a Markov random field model is employed to capture the spatial clustering of bad chips. Chip screening strategies are proposed that exploit the various types of yield nonuniformities that are detected in the data, such as radial effects, spatial clustering of bad chips, and yield variation by chip location. The numerical results suggest that screening at the chip level can be highly profitable in a semiconductor manufacturing process constrained by its probe capacity.