A product design problem in semiconductor manufacturing

The authors consider the product design problem of allocating the chip sites on a semiconductor wafer to various types of chips. The manufacturing facility sells chips to its customers in sets (a specific number of several different types of chips), and the objective of the facility is to maximize the average production rate of sets. Variability in the wafer fabrication process, in particular random yield, poses a major obstacle in producing sets in a reliable fashion. A stochastic analysis is employed to develop an effective wafer design, to measure the improvement in performance of the multitype wafer over the traditional single-type wafer, and to determine the cumulative production of sets of nondefective chips as a function of the rate at which lots of wafers are released into the facility. The analysis reveals that multitype wafers regularize the production flow of nondefective chips of each type and cause these flows to be correlated positively, both of which help to improve performance. A numerical example is provided that illustrates the analysis and demonstrates the design’s effectiveness.