Scheduling of mask shop E-beam writers

摘要

Reducing wafer fabrication cycle time and providing on-time waferndeliveries are among the top priorities of semiconductor companies. Masknmanufacturing is essential to the overall wafer fabrication processnsince on-time delivery of masks significantly affects wafer fabricationncycle times. Moreover, delivering wafers on time means deliveries ofnmasks must be on time as well. This research studies the schedulingnproblem of the bottleneck machine-the Electrical Beam (E-beam) Writer-ofna mask shop. The criterion of minimum total tardiness is used as ournperformance measure to schedule this bottleneck operation. Using anpredetermined Earliest-Due-Date (EDD) dispatch policy set by management,nthis study first addresses the problem of scheduling batches of a singlenmask size on a single machine. The approach is extended to the problemnof scheduling batches of two mask sizes on a single machine; finally, anheuristic for a multiple-machine problem is developed. For the problemnof a single machine under EDD dispatching policy, the problem can benformulated as a Dynamic Program (DP). Thus, it can be solved for annoptimal solution in polynomial time. For the multiple machines problem,nwe heuristically allocate the masks to each machine. Each machine withnallocated masks can then be solved by the DP formulation designed fornthe single machine problem. Based on the computational experiments innthis study, the proposed DP approach reduces total tardiness by annaverage of 55% from the method currently in use at a major ICnmanufacturing foundry. Furthermore, in the case that due dates are setnrealistically, the DP approach reduces the tardiness about 95% from thenshop's current method and about 88% from a simple full-batch method ofnscheduling