Hierarchical Decision-Making for Qualification Management in Wafer Fabs: A Simulation Study

Abstract

A qualification management problem arising in semiconductor wafer fabrication facilities (wafer fabs) is discussed. The stepper equipment needs to be qualified to process lots that belong to different families. Stepper- and family dependent qualification time windows exist. Time windows can be reinitialized if required and can be extended by on-time processing of lots from qualified families. A hierarchical approach is proposed. The base-level provides a dispatching strategy that takes into account qualification decisions, while the mid-level consists of a mixed integer linear program (MILP) for making qualification decisions. The top-level comprises a linear program (LP) that computes target quantities for the families on the steppers in each period of the planning window taking into account fab-wide objectives. In addition to an LP formulation with conventional capacity constraints, we provide a formulation where clearing functions are used to represent the congestion of the wafer fab. We also discuss how to anticipate the behavior of the mid-level on the top-level. Results of simulation experiments where the hierarchical approach is applied in a rolling horizon manner demonstrate that the LP-based approaches outperform a heuristic to determine the target quantities. Among the LP formulations, the ones with clearing functions perform best. We also demonstrate the value of anticipation. Note to Practitioners—A hierarchical approach is designed to decide when tools in wafer fabs have to be qualified for a certain lot family. Qualification-related decisions are highly relevant because qualifications are costly and take a lot of time. The top-level determines target quantities for each family based on linear programming. The mid-level is formed by a MILP. A dispatching scheme to implement the qualification decisions provides the base-level. The hierarchical approach is assessed in a rolling horizon setting using a simulation model of a 200mm wafer fab. The benefit of the different levels of the hierarchy is demonstrated by simulation experiments.