Field learning and production planning for semiconductor manufacturing systems

This paper is motivated by the so-called “yield learning” problem encountered in semiconductor manufacturing processes. The problem involves controlling the production rate of a process so as to maximize cumulative rewards over some time interval. Because improving yield can only occur as a result of discrete events coinciding with finished lots, a basic tradeoff arises as high production rates increase rewards for a given yield, but also cause longer average lot lead times, which delays the events that cause yield improvement. The problem is further complicated by the short life cycles of many semiconductor products, which implies fast price declines over time. We show that in some cases simple bang-bang solutions can be obtained for this problem through standard optimal control techniques. We also describe a general framework for solving this problem through iterative techniques that make use of “rapid modeling” software tools for the performance analysis of semiconductor manufacturing systems