On the consequences of un-modeled dynamics to the optimality of schedules in clustered photolithography tools

Abstract

Clustered photolithography tools (CPTs) are very complex and can substantially influence the throughput of wafer fabrication facilities. Therefore, efficient lot scheduling for CPTs can directly improve fab performance. In order to model their behavior, equipment models of CPTs are often used to predict lot completion times, ranging from simple to complex. In this paper, we develop mixed integer linear programs for linear, affine, exit recursion, and flow line models of CPTs to optimize lot sequence schedules with respect to average mean cycle time, total makespan, and total tardiness. We simulate a true CPT using flow line models and solve the MILPs for each of the reduced models (linear, affine, and exit recursion models) to get optimal lot sequence schedules for each reduced model. These schedules from reduced models are then input into the flow line optimization model in order to evaluate the loss in objective values. Using numerical experiments for a variety of test cases, we show that exit recursion models perform better than both linear and affine models in perspective of error and loss, and are often able to obtain the exact optimal schedules as flow line models.