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Capacity Planning in a Semiconductor Wafer Fabrication Facility with Time Constraints
Between Process Steps
Author:
Jennifer Robinson
University of Massachusetts
Abstract:
Central to the advancement of the U.S. economy is the efficient production of
semiconductors, which in turn depends upon having accurate methods of planning
semiconductor wafer fabrication facility capacity. A characteristic of wafer fabrication
that makes capacity planning particularly difficult is the presence of time constraints
between process steps, also known as time bound sequences. In a time bound sequence, there
exists a step that must be completed within some fixed time interval of an earlier step.
An example in semiconductor manufacturing is a furnace operation that must be started
within two hours of a prior clean operation. If more than two hours elapse before the
furnace operation can begin, the job must be sent back to the clean operation for
reprocessing.
The capacity of a time bound sequence can be difficult to predict. At low equipment
utilizations, lots flow through with few delays, and are rarely sent back for
reprocessing. At higher arrival rates, however, or for highly variable systems, time bound
sequences can rapidly become unstable. To know the capacity of some time bound sequences
requires knowing the entire distribution of lot cycle times. This research uses simulation
to understand the behavior of time bound sequences, and then develops analytic models to
estimate their capacity.
This dissertation focuses first on the simplest type of time bound sequences, those
that involve only two operations. For such sequences, the time constraint only applies to
the time in queue for the second operation. In this case, a simple approximation based on
M/M/c queueing formulas is shown to perform quite well in predicting the probability of
reprocessing. This approximation provides a bound that can easily be included in
spreadsheet capacity models. A fluid model is then developed for the more complex
situation of time bound sequences with intermediate operations. Based on the behavior of
the model, several practical guidelines are given for planning capacity in the presence of
time bound sequences. The most significant of these guidelines is a method for selecting
time constraint values for which the probability of reprocessing is very small, so that
systems will be well-behaved.
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