Multiclass Flow Line Models of Semiconductor Manufacturing Equipment for Fab-Level Simulation

Abstract

For multiclass flow line models, we identify a class of service times that allow a decomposition of the system into subsets of servers called channels. In each channel, the customer delay is well structured and we develop a recursion to calculate it. The recursions provide an alternative to the elementary evolution equations. By considering batch arrivals and restricting the structure of the model, the recursions can require nearly one order of magnitude less computation than is otherwise possible. Flow lines can be used as models for semiconductor manufacturing equipment such as multicluster or clustered photolithography tools. The models allow for internal wafer buffers and setups that are wafer location dependent. The models have shown to be very accurate in tests with data from clustered photolithography tools in production. As such, the models may serve as good candidates to improve the fidelity of existing equipment models in fab-level simulation. Note to Practitioners-Clustered photolithography and multicluster tools in semiconductor manufacturing feature internal wafer buffers and setups that depend on wafer location. These features are important to system performance when product diversity and small wafer lots are common as in high-mix fabs and in the anticipated 450 mm fabs. Unfortunately, existing fab-level simulation models do not include these equipment features. We develop flow line models that allow for diverse products, wafer lots and wafer location dependent setups. The models developed can require about one order of magnitude less computation than otherwise possible to model practical tools. In addition, the models have given throughput and cycle time values to within 1.0% and 4.0% of actual values from production clustered photolithography tools. As such, a flow line can serve to replace existing equipment models in fab-level simulators with reasonable computational cost while retaining high accuracy.