Analysis of heat transfer in a chemical vapor deposition reactor: an eigenfunction expansion solution approach

Chang, Hsiao-Yung; Adomaitis, Raymond A.

doi:10.1016/s0142-727x(98)10042-5

Cited by 10 publications

(7 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These and related functions can be obtained from http://www.ench.umd.edu/software/MWRtools. These methods primarily have been used for simulation of chemical vapor deposition reactors and other unit operations in semiconductor device fabrication [18] and model reduction studies [19,20]. In the latter, the eigenfunction expansion methods are instrumental for identifying optimized trial functions for reduced-basis discretizations as well as in the implementation of nonlinear Galerkin methods [21] for the reducing the dynamic degrees of freedom in discretized boundary-value problems.…”

Section: Discussionmentioning

confidence: 99%

A collocation/quadrature-based Sturm–Liouville problem solver

Adomaitis

Lin

2000

Applied Mathematics and Computation

Self Cite

View full text Add to dashboard Cite

ISR develops, applies and teaches advanced methodologies of design and analysis toKeywords: Sturm-Liouville problems; collocation; quadrature; eigenfunction expansions; computational methods. AbstractWe present a computational method for solving a class of boundary-value problems in Sturm-Liouville form. The algorithms are based on global polynomial collocation methods and produce discrete representations of the eigenfunctions. Error control is performed by evaluating the eigenvalue problem residuals generated when the eigenfunctions are interpolated to a finer discretization grid; eigenfunctions that produce residuals exceeding an infinity-norm bound are discarded. Because the computational approach involves the generation of quadrature weights and discrete differentiation operations, our computational methods provide a convenient framework for solving boundary-value problems by eigenfunction expansion and other projection methods.

show abstract

Section: Discussionmentioning

confidence: 99%

A collocation/quadrature-based Sturm–Liouville problem solver

Adomaitis

Lin

2000

Applied Mathematics and Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…This analysis gives an accurate first look at gas/wafer energy transport mechanisms and sheds light on the relative importance of the different heat transfer mechanisms ( [7] and Fig. 2).…”

Section: Cvd System Heat Transfer -Eigenfunction Expansionsmentioning

confidence: 94%

A Computational Framework for Boundary-Value Problem Based Simulations

2000

Self Cite

View full text Add to dashboard Cite

ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract A framework is presented for step-by-step implementation of weighted-residual methods (MWR) for simulations that require the solution of boundary-value problems. A set of Matlab-based functions of the computationally common MWR solution steps has been developed and is used in the application of eigenfunction expansion, collocation, and Galerkin-projection discretizations of time-dependent, distributed-parameter system models. Four industrially relevant examples taken from electronic materials and chemical processing applications are used to demonstrate the simulation approach developed.

show abstract

“…In this article, we continue our work 16 of developing a low-order gas/wafer heat transfer model with true predictive capabilities. The model accounts for gas flow across the wafer, the three-dimensional gas temperature field, heat conduction within the wafer, and heat transfer between the wafer, gas, and reactor chamber.…”

Section: Introductionmentioning

confidence: 92%

“…The overall solution algorithm begins by using the gas composition and measured wafer temperature to compute corresponding physical properties and to set the flow velocity and temperature field boundary conditions. The gas flow velocity field is computed using a Galerkin discretization technique 16 based on globally defined eigenfunctions; this solution approach determines the flow velocity component v x and the pressure drop term ␤ v .…”

Section: Solution Proceduresmentioning

confidence: 99%

Influence of gas composition on wafer temperature in a tungsten chemical vapor deposition reactor: Experimental measurements, model development, and parameter identification

Chang

Adomaitis

Kidder

et al. 2001

Journal of Vacuum Science &Amp; Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena

Self Cite

View full text Add to dashboard Cite

Experimental measurements of wafer temperature in a single-wafer, lamp-heated chemical vapor deposition system were used to study the wafer temperature response to gas composition. A physically based simulation procedure for the process gas and wafer temperature was developed in which a subset of parameter values were estimated using a nonlinear, iterative parameter identification method, producing a validated model with true predictive capabilities. With process heating lamp power held constant, wafer temperature variations of up to 160 K were observed by varying the feed gas H2/N2 ratio. Heat transfer between the wafer and susceptor was studied by shifting the instrumented wafer off the susceptor axis, exposing a portion of the wafer backside to the chamber floor. Model predictions and experimental observations both demonstrated that the gas velocity field had little influence on the observed wafer and predicted gas temperatures.

show abstract

Analysis of heat transfer in a chemical vapor deposition reactor: an eigenfunction expansion solution approach

Cited by 10 publications

References 10 publications

A collocation/quadrature-based Sturm–Liouville problem solver

A collocation/quadrature-based Sturm–Liouville problem solver

A Computational Framework for Boundary-Value Problem Based Simulations

Influence of gas composition on wafer temperature in a tungsten chemical vapor deposition reactor: Experimental measurements, model development, and parameter identification

Contact Info

Product

Resources

About