Proceedings of the 2011 Winter Simulation Conference
S. Jain, R. R. Creasey, J. Himmelspach, K. P. White, and M. Fu, eds.
AGGREGATE MODELING OF SEMICONDUCTOR EQUIPMENT
USING EFFECTIVE PROCESS TIMES
L.F.P. Etman
C.P.L. Veeger
E. Lefeber
I.J.B.F. Adan
J.E. Rooda
Department of Mechanical Engineering
Eindhoven University of Technology
PO Box 513, 5600 MB Eindhoven, THE NETHERLANDS
ABSTRACT
Performance evaluation using queueing models is common practice in semiconductor manufacturing.
Analytical closed-form expressions and simulation models are popular in capacity planning and the analysis
of equipment configurations. However, the complexity of semiconductor processes complicates the modeling
of the equipment. Analytical models lack the required accuracy, whereas simulation models require too
many details, making them impractical. Aggregation is a way to overcome this difficulty. The various
details are not modeled in detail, but their contribution is lumped in the aggregate model, which makes
the model more appropriate for both analysis and simulation.
This paper gives an overview of our efforts to develop a top-down aggregate modeling approach for
semiconductor equipment, starting from the effective process time concept inspired by the Factory Physics
book of Hopp and Spearman. The strong feature of our modeling approach is that the aggregate model
parameters are estimated directly from industrial data (arrival and departure times), without the need to
quantify the various details.
1 INTRODUCTION
The development of simple and accurate models for queueing performance analysis in semiconductor
manufacturing is an open research problem. With “simple” we mean models that have only few model
parameters, and that can be easily used and estimated. With “accurate” we mean models that provide a
prediction accuracy that is of practical use in semiconductor applications. This may depend of course on
the type of application, but we assume that in most cases an accuracy of 10% or better is desired.
Commonly-used simple models are closed form G/G/m queueing expressions, such as the approximation
due to Sakasegawa (1977) and Whitt (1993), which is used in the popular Factory Physics book of Hopp
and Spearman (2008). Although useful and insightful, this model lacks the necessary accuracy for the
typical equipment encountered on the semiconductor factory floor. Modifications to (partially) account for
typical semiconductor equipment characteristics such as the simultaneous processing of wafers of multiple
lots have been proposed in e.g., Morrison and Martin (2007b) and Morrison and Martin (2007a).
Alternatively, discrete-event simulation may be used to arrive at a sufficiently accurate representation
of the semiconductor equipment. Simulation modeling allows the inclusion of all relevant factory floor
details. This obviously requires the collection of all the necessary input data regarding the various model
elements. A a result, a detailed simulation model becomes computationally very expensive and requires
significant development time. Including too many details makes simulation modeling impractical.
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