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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Item Influence of Gas Composition on Wafer Temperature Control in a Tungsten Chemical Vapor Deposition Reactor(2000) Chang, Hsiao-Yung; Adomaitis, Raymond A.; Kidder, John N., Jr.; Rubloff, Gary W.; ISRExperimental measurements of wafer temperature in a single-wafer,lamp-heated CVD system were used to study the wafer temperature responseto gas composition. A physically based simulation procedure for theprocess gas and wafer temperature was developed in which a subset ofparameter values were estimated using a nonlinear, iterative parameteridentification method, producing a validated model with true predictivecapabilities.With process heating lamp power held constant, wafertemperature variations of up to 160 degrees K were observed by varying feed gasH_2/N_2 ratio. Heat transfer between the wafer and susceptor wasstudied by shifting the instrumented wafer off the susceptor axis,exposing a portion of the wafer backside to the chamber floor. Modelpredictions and experimental observations both demonstrated that the gasvelocity field had little influence on the observed wafer and predictedgas temperatures.
Item Spectral Filtering for Improved Performance of Collocation Discretization Methods(2000) Adomaitis, Raymond A.; ISRSpectral filtering methods are investigated for use in reducing the Gibbs oscillations that result when discontinuous functions are projected onto globally definedtrial function expansions. Several physical-space filters are studied in the context of a high-degree, mixed collocation method used for time integration of a nonlinear boundary value problem with a piece-wise continuous, time-dependentboundary condition. Improved accuracy is reported, both in terms of point-wiseand norm-wise solution convergence, making the filtered global collocationapproach a potential alternative to spline formulations in some applications.Item A Spectrally Filtered, Least-Squares Projection Method for Stokes Flow Problems in Driven Cavities(1999) Adomaitis, Raymond A.; ISRA least-squares, weighted residual projection method is presented forcomputingStokes flow solutions to driven cavity problems in rectangular andcylindrical geometries.In this procedure, thevelocity field components are first defined by eigenfunction expansionsolutions to the Stokes flow problem in terms of an unknown pressure fieldwhich is subsequentlycomputed by minimizing the continuity equation residual norm by theleast-squaresprojection. The role of spectral filtering methods for improving pointwisesolutionconvergence is also discussed.Item A Collocation/Quadrature-Based Sturm-Liouville Problem Solver(1999) Adomaitis, Raymond A.; Lin, Yi-hung; ISRWe present a computational method for solving a class of boundary-value problemsin Sturm-Liouville form. The algorithms are based on global polynomialcollocation methods and produce discrete representationsof the eigenfunctions. Error control is performed by evaluating theeigenvalue problem residuals generated when the eigenfunctions are interpolatedto a finer discretization grid; eigenfunctions thatproduce residuals exceeding an infinity-norm bound are discarded.Because the computational approach involves the generationof quadrature weights and discrete differentiation operations, our computationalmethods provide a convenient framework for solving boundary-value problemsby eigenfunction expansion and other projection methods.Item A Computational Framework for Boundary-Value Problem Based Simulations(1998) Adomaitis, Raymond A.; Lin, Yi-hung; Chang, Hsiao-Yung; ISRA framework is presented for step-by-step implementation of weighted-residualmethods (MWR) for simulations that require the solution ofboundary-value problems. A set of Matlab-based functions ofthe computationally common MWR solution steps has beendeveloped and is used in the application of eigenfunction expansion,collocation, and Galerkin-projection discretizations oftime-dependent, distributed-parameter system models. Fourindustrially relevant examples taken from electronic materialsand chemical processing applications are used to demonstrate thesimulation approach developed.Item Analysis of Heat Transfer in a Chemical Vapor Deposition Reactor: An Eigenfunction Expansion Solution Approach(1997) Chang, Hsiao-Yung; Adomaitis, Raymond A.; Adomaitis, Raymond A.; ISRA numerical solution procedure combining several weighted residual methods and based on global trial function expansion is developed to solve a model for the steady state gas flow field and temperature distribution in a low-pressure chemical vapor deposition reactor. The enthalpy flux across the wafer/gas boundary is calculated explicitly and is found to vary significantly as a function of wafer position. An average heat transfer coefficient is estimated numerically and is compared to typical radiative heat transfer rates in the system. The convergence properties of the discretization method developed also are discussed.Item Software and Other Teaching Tools Applied to Modeling and Analysis of Distributed Parameter Systems(1997) Adomaitis, Raymond A.; ISROver the last two years, we have been developing a library of Matlab subprograms integrated with on-line lecture notes in the form of WWW documents which are used in both undergraduate and graduate-level Chemical Engineering Applied Mathematics classes. The goal has been to make as transparent as possible the relationships between model development, solution, and analysis of systems described by partial differential equation models. This paper presents the results of our initial efforts to create computational modules which have a one-to-one correspondence with each step of implementing eigenfunction expansion, Galerkin's, and other weighted residual methods. Examples representing heat transfer in a cylinder, and gas flow and heat transfer in a chemical vapor deposition reactor are presented.Item An Orthogonal Collocation Technique for Rapid Thermal Processing System Discretization(1997) Adomaitis, Raymond A.; ISRA model of a multiple heating zone Rapid Thermal Processing (RTP) system is developed to study wafer thermal dynamics during a processing cycle. The system is discretized with trial functions generated from the linearized wafer energy balance equation eigenfunctions, and careful analysis of the solution residual reveals a slow, but predictable, convergence rate. A modified set of trial functions is derived from a subset of the original eigenfunctions combined with the dominant modes identified by the Karhunen-Loeve expansion of the wafer temperature variance component that contributes most to the slow convergence. Since the wafer temperature variance is computed explicitly from an eigenfunction expansion solution of the linearized system with specified processing statistics, the collocation procedure effectively links RTP model reduction and simulation in one discretization procedure. The convergence rate of the modified collocation method is shown to be superior to collocation methods based on the original eigenfunction and polynomial sequences.Item Model Reduction for RTCVD Optimization(1996) Theodoropoulou, A.; Adomaitis, Raymond A.; Zafiriou, E.; ISRA model of a three-zone Rapid Thermal Chemical Vapor Deposition (RTCVD) system is developed to study the effects of spatial wafer temperature patterns on polysilicon deposition uniformity. A sequence of simulated runs is performed, varying the lamp power profiles so that different wafer temperature modes are excited. The dominant spatial wafer thermal modes are extracted via Proper Orthogonal Decomposition and subsequently used as a set of trial functions to represent both the wafer temperature and deposition thickness. A collocation formulation of Galerkin's method is developed to discretize the original modeling equations, giving a low-order model which looses little of the original, high-order model's fidelity. We make use of the excellent predictive capabilities of the reduced model to optimize power inputs to the lamp banks to achieve a desired polysilicon deposition thickness at the end of a run with minimal deposition spatial nonuniformity.Item RTCVD Model Reduction: A Collocation on Empirical Eigenfunctions Approach(1995) Adomaitis, Raymond A.; ISRA model of a three-zone Rapid Thermal Chemical Vapor Deposition (RTCVD) system is developed to study the effects of spatial wafer temperature patterns and gas-phase reactant depletion on polysilicon deposition uniformity. A sequence of simulated runs is performed, varying the lamp power profiles so that different temperature modes are excited. The dominant spatial wafer thermal modes are extracted via proper orthogonal decomposition. A collocation formulation of Galerkin's method is used to discretize the original modeling equations, giving a low-order model which loses little of the original's fidelity. We make use of the excellent predictive capabilities of the reduced model in a real-time RTP system simulator.