Low-order modeling and dynamic characterization of rapid thermal processing

Schaper, Charles D.; Cho, Y. M.; Kailath, T.

doi:10.1007/bf00324195

Cited by 28 publications

(19 citation statements)

References 8 publications

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“…They need complicated computations such as Monte Carlo simulations [9]. Schaper et al [8] showed that the off-diagonal terms in Γ ij are small and can be ignored for the purpose of control system…”

Section: Single Wafer Rapid Thermal Processing and Temperature Controlmentioning

confidence: 99%

“…4). Then we have (8) Applying the above test procedure, we obtain the multivariable steady state gain matrix, , between and . A refined (k+1)-th gain matrix of RTP becomes (9) When the process is not ill-conditioned, two or three iterations are sufficient.…”

Section: Iterative Refinementmentioning

confidence: 99%

“…To design these control systems, accurate models for RTP are required. Models based on the first principles are available [6,[8][9][10]. They have been shown to be approximated by diagonal nonlinear first order dynamics with multivariable static gains [5,7,11].…”

Section: Introductionmentioning

confidence: 99%

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Iterative identification of temperature dynamics in single wafer rapid thermal processing

Cho

Edgar

Lee

2009

Korean J. Chem. Eng.

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As the standard size of silicon wafers grows and performance specifications of integrated circuits become more demanding, a better control system to improve the processing time, uniformity and repeatability in rapid thermal processing (RTP) is needed. Identification and control are complicated because of nonlinearity, drift and the time-varying nature of the wafer dynamics. Various physical models for RTP are available. For control system design they can be approximated by diagonal nonlinear first order dynamics with multivariable static gains. However, these model structures of RTP have not been exploited for identification and control. Here, an identification method that iteratively updates the multivariable static gains is proposed. It simplifies the identification procedure and improves the accuracy of the identified model, especially the static gains, whose accurate identification is very important for better control.

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Section: Single Wafer Rapid Thermal Processing and Temperature Controlmentioning

confidence: 99%

Section: Iterative Refinementmentioning

confidence: 99%

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Iterative identification of temperature dynamics in single wafer rapid thermal processing

Cho

Edgar

Lee

2009

Korean J. Chem. Eng.

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“…Many research studies have focused on modeling transport mechanisms in single wafer rapid thermal processing ͑RTP͒ systems, [7][8][9][10][11] where nonuniform heat transfer mechanisms can prevent across-wafer temperature uniformity during the process cycle. Typical modeling studies of RTP chemical vapor deposition ͑CVD͒ systems include a gas phase transport submodel and a wafer submodel to account for the interactions between the gas phase and wafer itself.…”

Section: Introductionmentioning

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

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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.

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“…The model for wafer heat transfer is a modified version of models presented in [2,8,28,41,42]. It is based on an energy balance for a heat conducting solid which emits and absorbs heat radiation at its boundary surfaces.…”

Section: Wafer Heat Transfermentioning

confidence: 99%

Modeling and Model Reduction for Control and Optimization of Epitaxial Growth in a Commercial Rapid Thermal Chemical Vapor Deposition Reactor

Newman¹,

Krishnaprasad²,

Ponczak³

et al. 1998

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ISR develops, applies and teaches advanced methodologies of design and analysis to solve complex, hierarchical, heterogeneous and dynamic problems of engineering technology and systems for industry and government. ISR is a permanent institute of the University of Maryland, within the Glenn L. Martin Institute of TechnolAbstract In December 1996, a project was initiated at the Institute for Systems Research (ISR), under an agreement between Northrop Grumman Electronic Sensors and Systems Division (ESSD) and the ISR, to investigate the epitaxial growth of silicon-germanium (Si-Ge) heterostructures in a commercial rapid thermal chemical vapor deposition (RTCVD) reactor. This report provides a detailed account of the objectives and results of work done on this project as of September 1997. The report covers two main topics -modeling and model reduction. Physics-based models are developed for thermal, fluid, and chemical mechanisms involved in epitaxial growth. Experimental work for model validation and determination of growth parameters is described. Due to the complexity and high computational demands of the models, we investigate the use of model reduction techniques to reduce the model complexity, leading to faster simulation and facilitating the use of standard control and optimization strategies. Some of the contents of this report are contained in [34].

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Low-order modeling and dynamic characterization of rapid thermal processing

Cited by 28 publications

References 8 publications

Iterative identification of temperature dynamics in single wafer rapid thermal processing

Iterative identification of temperature dynamics in single wafer rapid thermal processing

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

Modeling and Model Reduction for Control and Optimization of Epitaxial Growth in a Commercial Rapid Thermal Chemical Vapor Deposition Reactor

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