Overlapping machine groups in semiconductor wafer fabrication

Wafer fabrication is a very complex manufacturing process requiring several hundred process steps. The circuit is grown in layers and a lot visits each of the process areas many times. Machines within a process area may be dedicated to performing particular operations and different visits to the same process area may be to different groups of machines. Machine groups are said to overlap if they have machines in common. Overlapping groups cause many special problems and the potential for error is very high in any kind of analysis or simulation which does not consider overlapping groups if they exist. This paper highlights these problems and proposes solutions to some while leaving others open. Given a grouping, this paper considers three ways of sharing the machines between the groups. The first is to share equally, the second is to share in the ratio of the workload on each process step while the third allows any arbitrary sharing method. Two performance criteria are applied to evaluate the grouping and two linear programming formulations are developed to optimize these criteria. The paper also develops some combinatorial formulae on the number of possible groupings.