Institute for Systems Research Technical Reports

Permanent URI for this collectionhttp://hdl.handle.net/1903/4376

This archive contains a collection of reports generated by the faculty and students of the Institute for Systems Research (ISR), a permanent, interdisciplinary research unit in the A. James Clark School of Engineering at the University of Maryland. ISR-based projects are conducted through partnerships with industry and government, bringing together faculty and students from multiple academic departments and colleges across the university.

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Author: search.filters.author.Newman, Andrew J.Subject: search.filters.subject.mathematical modeling

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    Modeling and Optimization for Epitaxial Growth: Transport and Growth Studies
    (1999) Newman, Andrew J.; Krishnaprasad, Perinkulam S.; Krishnaprasad, Perinkulam S.; ISR; CDCSS
    This report details the objectives, methodologies, and results for Phase II ofthe project, "Modeling and Optimization for Epitaxial Growth"(see~cite{NKPB98} for Phase I report). This project is a joint effort betweenthe Institute for Systems Research (ISR) and Northrop Grumman'sElectronic Sensors and Systems Sector (ESSS), Baltimore, MD.

    The overallobjective is to improve manufacturing effectiveness for epitaxial growth ofsilicon and silicon-germanium (Si-Ge) thin films on a silicon wafer. Growthtakes place in the ASM Epsilon-1 chemical vapor deposition (CVD) reactor, aproduction tool currently in use at ESSS. Phase II project results includedevelopment of a new comprehensive process-equipment model capable ofpredicting gas flow, heat transfer, species transport, and chemical mechanismsin the reactor under a variety of process conditions and equipment settings.

    Applications of the model include prediction and control of deposition rate andthickness uniformity; studying sensitivity of deposition rate to processsettings such as temperature, pressure, and flow rates; and reducing the use ofconsumables via purge flow optimization. The implications of varioussimulation results are discussed in terms of how they can be used to reducecosts and improve product quality, e.g., thickness uniformity of thin films. We demonstrate that achieving deposition uniformity requires some degree oftemperature non-uniformity to compensate for the effects of other phenomenasuch as reactant depletion, gas heating and gas phase reactions, thermaldiffusion of species, and flow patterns.

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    Model Reduction via the Karhunen-Loeve Expansion Part II: Some Elementary Examples
    (1996) Newman, Andrew J.; Krishnaprasad, P. S.; ISR
    In Part II of this paper we present some elementary examples of distributed parameter system model reduction using the techniques described in Part I. In particular, we focus on using theKarhunen-Loeve expansion and Galerkin's method to formulated reducedorder models for a heat diffusion system and temperature field dynamicsin a Rapid Thermal Chemical Vapor Deposition reactor. Simulationresults are presented.
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    Model Reduction via the Karhunen-Loeve Expansion Part I: An Exposition
    (1996) Newman, Andrew J.; Krishnaprasad, P.S.; ISR
    In formulating mathematical models for dynamical systems, obtaining a high degree of qualitative correctness (i.e. predictive capability) may not be the only objective. The model must be useful for its intended application,and models of reduced complexity are attractive in many cases.

    In Part I of this paper we provide an exposition of some techniques that are useful in finding models of reduced complexity for dynamical systems involving flows. The material presented here is not new. The techniques we discussare based on classical theory such as the Karhunen-Loeve expansion and the method of Galerkin, and the more recent concept of "coherent structures." They have been heavily exploited in a wide range of areas in science and engineering.

    The attempt here is to present this collectionof important methods and ideas together, at a high level of detail, in coherent form, and in the context of model reduction for simulation and control. In this manner we lead in to Part II which illustrates theirusefulness in model reduction by applying them to some elementary examples of distributed parameter systems which are related to processes found in semiconductor manufacturing.