Institute for Systems Research
Permanent URI for this communityhttp://hdl.handle.net/1903/4375
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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 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 Model Reduction for a Tungsten Chemical Vapor Deposition System(1998) Chang, Hsiao-Yung; Adomaitis, Raymond A.; ISRA model of a tungsten chemical vapor deposition (CVD) system isdeveloped to study the CVD system thermal dynamics and wafer temperaturenonuniformities during a processing cycle. We develop a model for heattransfer in the system's wafer/susceptor/guard ring assembly and discretizethe modeling equation with a multiple-grid, nonlinear collocation technique.This weighted residual method is based on the assumption that the system'sdynamics are governed by a small number of modes and that the remaining modesare slaved to these slow modes. Our numerical technique produces a model thatis effectively reduced in its dynamical dimension, while retaining theresolution required for the wafer assembly model. The numerical techniqueis implemented with only moderately more effort than the traditional collocationor pseudospectral techniques. Furthermore, by formulating the technique in termsof a collocation procedure, the relationship between temperature measurementsmade on the wafer and the simulator results produced with the reduced-ordermodel remain clear.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 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.Item Spatially Resolved Compressor Characteristics for Modeling and Control of Blade-Scale Flow Instabilities(1995) Adomaitis, Raymond A.; ISRA numerical techniques cable of simulating blade-scale compression system flow instabilities over times scales spanning tens of rotor revolutions is presented. Simulations of stall inception, growth to fully-developed rotating stall, and evidence for hysteresis, secondary instabilities, and other nonlinear phenomena are presented. signal processing techniques for flow asymmetry characterization are discussed in the context of obtaining low-order representations of the flow disturbances with the ultimate goal of active stall suppression.Item Local Nonlinear Control of Stall Inception in Axial Flow Compressors(1993) Adomaitis, Raymond A.; Abed, Eyad H.; ISRA combination of theoretical and computational nonlinear analysis techniques are used to study the scenario of bifurcations responsible for the initiation of rotating stall in an axial flow compressor model. It is found that viscosity tends to damp higher-frequency modes and so results in a sequence of bifurcations along the uniform-flow solution branch to stall cells of different mode number. Lower-mode stalled flow solutions are born in subcritical bifurcations, meaning that these equilibria will be unstable for small amplitudes. Secondary bifurcations, however, can render them stable, leading to hysteresis. Using throttle position as a control, we find that while the stall bifurcations are not linearly stabilizable, nonlinear state feedback of the first mode amplitude will reduce the hysteresis. This improves the nonlinear stability of the compression system near the stall margin.Item Bifurcation Analysis of Nonuniform Flow Patterns in Axial-Flow Gas Compressors(1992) Adomaitis, Raymond A.; Abed, Eyad H.; ISRWe study the transition from steady, spatially uniform-flow to nonuniform and time-dependent gas axial velocity profiles in an axial flow compression system. Local bifurcation analysis of the uniform-flow solution reveals a series of bifurcations to traveling waves of different mode number as a function of throttle opening. The number of bifurcating modes is found to depend on the gas viscosity parameter, an effect introduced in this work. Using the local approximations of the bifurcating solutions as starting points of our numerical analysis, we uncover a complicated scenario of secondary bifurcations ultimately resulting in parameter ranges where locally asymptotically stable stalled-flow solutions of different mode number coexist.