Institute for Systems Research

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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.; ISR
A 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.
Bifurcation Analysis of Nonuniform Flow Patterns in Axial-Flow Gas Compressors
(1992) Adomaitis, Raymond A.; Abed, Eyad H.; ISR
We 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.
A Collocation/Quadrature-Based Sturm-Liouville Problem Solver
(1999) Adomaitis, Raymond A.; Lin, Yi-hung; ISR
We 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.
A Comparative Study of Reactor Designs for the Production of Graded Films with Applications to Combinatorial CVD
(2007-10-24) Sreenivasan, Ramaswamy; Adomaitis, Raymond A.
Segmented CVD reactor designs enabling spatial control of across-wafer gas phase composition were evaluated for depositing graded films suitable for combinatorial studies. Specifically two reactor designs were constructed and evaluated with experiments and response surface model (RSM) based analysis to quantify the reactor performance in terms of film thickness uniformity, sensitivity to adjustable reactor operating conditions, range of thickness over which uniformity could be achieved and each reactor’s ability to control the thickness gradient across the wafer surface. Design features distinguishing the two reactor systems and their influence on gradient control versus deposition rate performance are summarized. RS models relating wafer state properties to process recipes are shown to be effective tools to quantify, qualify and compare different reactor designs.
A Comparative Study of Reactor Designs for the Production of Graded Films with Applications to Combinatorial CVD
(2007) Sreenivasan, Ramaswamy; Adomaitis, Raymond A.; Rubloff, Gary W.; ISR
Segmented CVD reactor designs enabling spatial control of across-wafer gas phase composition were evaluated for depositing graded films suitable for combinatorial studies. Specifically two reactor designs were constructed and evaluated with experiments and response surface model (RSM) based analysis to quantify the reactor performance in terms of film thickness uniformity, sensitivity to adjustable reactor operating conditions, range of thickness over which uniformity could be achieved and each reactor ability to control the thickness gradient across the wafer surface. Design features distinguishing the two reactor systems and their influence on gradient control versus deposition rate performance are summarized. RS models relating wafer state properties to process recipes are shown to be effective tools to quantify, qualify and compare different reactor designs.
A Computational Framework for Boundary-Value Problem Based Simulations
(1998) Adomaitis, Raymond A.; Lin, Yi-hung; Chang, Hsiao-Yung; ISR
A 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.
Control of Nonlinear Phenomena at the Inception of Voltage Collapse
(1993) Wang, H.O.; Abed, Eyad H.; Adomaitis, Raymond A.; Hamdan, Anan M. A.; ISR
Nonlinear Phenomena, including bifurcations and chaos, occurring in power system models exhibiting voltage collapse have been the subject of several recent studies. These nonlinear phenomena have been determined to be crucial factors in the inception of voltage collapse in these models. In this paper, the problem of controlling voltage collapse in the presence of these nonlinear phenomena is addressed. The work focuses on an example power system model that has been studied in several recent papers. The bifurcation control approach is employed to modify the bifurcations and to suppress chaos. The control law is shown to result in improved performance of the system for a greater range of parameter values.
A Global Basis Function Approach to DC Glow Discharge Simulation
(1997) Lin, Yi-hung; Adomaitis, Raymond A.; ISR
A global discretization approach was taken to solve a self- consistent DC glow discharge model to study the interplay between modeling assumptions and convergence of the numerical solution techniques. It was found that the assumed form of electron diffusivity temperature dependence had a profound influence on the computed solutions. The numerical techniques developed offer a simple to implement alternative for plasma model discretization.
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.; ISR
Experimental 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.
Local Nonlinear Control of Stall Inception in Axial Flow Compressors
(1993) Adomaitis, Raymond A.; Abed, Eyad H.; ISR
A 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.
Model Reduction for a Tungsten Chemical Vapor Deposition System
(1998) Chang, Hsiao-Yung; Adomaitis, Raymond A.; ISR
A 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.
Model Reduction for RTCVD Optimization
(1996) Theodoropoulou, A.; Adomaitis, Raymond A.; Zafiriou, E.; ISR
A 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.
A NEW APPROACH TO SPATIALLY CONTROLLABLE CVD
(2004) Choo, Jae-Ouk; Adomaitis, Raymond A.; Rubloff, Gary W.; Henn-Lecordier, Laurent; Cai, Yuhong; Adomaitis, Raymond A.; ISR
This paper describes the continuing design evolution of a new approach to spatially controllable chemical vapor deposition for electronic materials manufacturing. Based on the success of a previous prototype reactor, we describe construction of a newer version of the prototype reactor system to assess its performance and identify its key operational characteristics. This new design includes a fully automated feed gas control system, allowing the reprogramming of reactor operation without hardware modifications and a time-shared gas sampling mass spectrometer for spatially resolved across-wafer gas composition analysis.
Nonlinear Dynamics of Axial Flow Compressors: A Parametric Study
(1991) Liaw, Der-Cherng; Adomaitis, Raymond A.; Abed, Eyad H.; ISR
This paper presents the analysis of the dynamics of a representative axial flow compressor model, emphasizing the influence of two important control parameters. These are a nondimensional parameter B (previously introduced by Greitzer (1976) as a primary determinant of post-stall behavior) and the setting of the throttle line. Greitzer's lumped-parameter model is employed in this study, with a specific choice of compressor and throttle characteristics. Our analysis shows the presence of a rich variety of global as well as local bifurcations as the two control parameters are varied. The analysis leads to a characterization of compressor operation into three major zones: the stalled zone, the pre-stall zone, and the normal (unstalled) zone. Simulation results demonstrate the qualitatively different dynamical behaviors within each regime of parameter space.
Nonlinear Dynamics of Axial-Flow Compressors: A Parametric Study
(1992) Adomaitis, Raymond A.; Liaw, Der-Cherng; Abed, Eyad H.; ISR
Analysis of the post-instability dynamical behavior of an axial- flow compression system model is carried out in a bifurcation- theoretic setting. Using global analysis techniques, we uncover the sequence of bifurcations in parameter space which allows us to rigorously determine whether the compressor stalls or surges when the throttle is slowly closed beyond the instability margin. Using these computational techniques, we also determine the conditions under which stalled and/or surging flow solutions coexist with the desired uniform-flow operating point and quantify the perturbations which destabilize this operating point.
Objects for MWR
(2001) Adomaitis, Raymond A.; ISR
A computational framework has been developed for step-by-step implementation of global spectral projection methods used for solving boundary-value problems and analyzing solutions produced using the numerical techniques of this framework. A set of Matlab-based functions corresponding to each step in a Galerkin discretization procedure has been developed with emphasis on simplifying the implementation of discretization methods for nonlinear, distributed-parameter system models in up to three-dimensional physical domains. A key feature of this computational approach is that a set of object classes were developed to facilitate implementation of the weighted residual methods (MWR) in an effort to make the connection between the solution procedures and modeling equations as clear as possible. The utility of the computational procedures is demonstrated through applications to two-dimensional reaction-diffusion and fluid flow problems, and a three-dimensional heat transfer problem in semiconductor manufacturing.
On the Dynamics and Global Stability Characteristics of Adaptive Systems
(1991) Adomaitis, Raymond A.; Frouzakis, Christos E.; Kevrekidis, Ioannis G.; ISR
We consider the dynamics of some representative adaptively- controlled systems and focus on situations where the desired operating point is locally, but not globally, stable. Perturbations which drive the system from the set point are quantified by computing the boundaries separating the basin of attraction of the set point from the basins of attraction of the other, undesirable attractors. The basins are found to sometimes consist of complicated, disconnected structures in phase space. This results from the nonunique reverse-time dynamics often exhibited by these systems and can be studied by considering the behavior of the reverse-time map along the basin boundaries. The effect of noninvertibility on the forward-time dynamical behavior is also explored.
An Orthogonal Collocation Technique for Rapid Thermal Processing System Discretization
(1997) Adomaitis, Raymond A.; ISR
A 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.
Parameter Identification and Simulation of a Thin Film Conducting Polymer Gas Sensor
(2001) Li, Yong; Adomaitis, Raymond A.; McAvoy, Thomas J.; ISR
Thin film conducting polymer gas composition sensors can be used forindustrial safety monitoring, environmental pollution control, and numerousother applications. In this paper, a sensor system model is developed andthis model is used to compare a lumped circuit to a transmission lineformulation of the equivalent circuits describing the polymer film andelectrodes; the sensor model includes the adsorption/desorption processand the electric properties of the sensor. The simulation approachcombines physically based modeling and parameter estimation, in which asubset of model parameters are estimated using published experimentaldata. The simulation results are found to be useful for interpretingconduction polymer sensor responses to different gas species.
Predicting the Complexity of Disconnected Basins of Attraction for a Noninvertible System
(1991) Adomaitis, Raymond A.; Kevrekidis, Ioannis G.; Llave, Rafael de la; ISR
A noninvertible, two-dimensional, discrete-time system featuring multistability is presented. Because the preimage behavior of this system is a function of location in phase space, the boundary separating the basins of attraction can be disconnected. These "polka-dot" basins of attraction have either a finite number of preimages (giving a finitely-complicated basin) or infinitely many (giving infinite complexity). A complexity criterion based on following the noninvertible region forward in time is presented and a fixed-point algorithm for computing the boundary of the "complete" noninvertible region is discussed.