Improvement of Temperature Uniformity in Rapid Thermal Processing Systems Using Multivariable Control

Norman, Stephen A.; Schaper, Charles D.; Boyd, Stephen

doi:10.1557/proc-224-177

Cited by 24 publications

(11 citation statements)

References 6 publications

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“…The effort detailed within this paper produced this finding. However, other researchers (in independent work done concurrently) arrived at the same conclusion-two of which are reported in [lll, [12].…”

Section: Transient Temperature Uniformity Processingsupporting

confidence: 57%

Thermal uniformity and stress minimization during rapid thermal processes

Perkins

Riley

Gyurcsik³

1995

IEEE Trans. Semicond. Manufact.

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Abstruct-The practical development and implementation of rapid thermal processes will significantly influence the semiconductor fabrication industry. With the capability to perform heat cycles quickly and with low thermal budgets, rapid thermal processors have the potential to supplant conventional thermal systems in the years to come. Currently, rapid thermal processors are unable to match the thermal process uniformity produced in conventional convective-based systems. Using a thermal model to approximate the heating characteristics of silicon wafers, it is possible to determine the effects of time-varying intensity profiles on a wafer during a rapid thermal process. Interpretation of this model shows idealized intensity profiles can maintain thermal uniformity at steady-state temperatures. During thermal transients a dynamic continuously changing profile is required to maintain thermal uniformity. As a predictive tool, this analysis can be used to determine and evaluate dynamic uniformity producing intensity profiles before thermal transients occur within a process. This approach can reduce the accumulation of error during high temperature steps not only by providing thermal uniformity at steady states, but by reducing the initial nonuniformities produced by transitions. This paper will review the wafer model, show the results of an idealized profile for steady-state and transient temperatures, and explain the dynamic profiles required for continuous uniformity.

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Section: Transient Temperature Uniformity Processingsupporting

confidence: 57%

Thermal uniformity and stress minimization during rapid thermal processes

Perkins

Riley

Gyurcsik³

1995

IEEE Trans. Semicond. Manufact.

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“…The optimal speed setting popt that minimizes the maximum error can then be obtained by solving the following linear programming problem (Norman 1991):…”

Section: Problem Formulationmentioning

confidence: 99%

Coordinate control of air movement for optimal thermal comfort

Liu

Yin

Schiavon

et al. 2018

Science and Technology for the Built Environment

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Personally controlled air movement can maintain or enhance thermal comfort in warm environments and reduce energy consumption. Unlike controlling a personal fan, using a system of fans for multiple occupants is difficult as it is hard to find an appropriate fan speed setting that maximizes occupants' satisfaction. Since limited work has been carried out on this issue, in this paper, a novel cooperative control approach for a system of fans is proposed to provide optimized air movement for multiple occupants. This is the first time that a system of fans is controlled cooperatively in the research of built environment. The proposed approach predicts airflow in a cost-effective manner by calibrating the fans in the real environment. The operation of the fans is optimized by minimizing the worst-case deviation between the actual air speed and the desired air speed, which can be determined based on either the PMV -SET model or the occupants' feedback. This minimax-error problem is formulated as an equivalent linear programming problem which can be solved using standard methods. The proposed approach was tested in two different indoor scenarios respectively by 1) measuring air speed directly in a business conference room and 2) involving human subject surveys in a university classroom. In the first experiment, the measured air speeds after optimization are closer to the target values at all tested temperature levels (26 °C, 27.5 °C and 29 °C) indicating improved thermal comfort. In the second experiment, only 62% of the occupants (totally 34) are satisfied with slightly increased room temperature (around 26.5 °C) before optimization, while this number increased to 94% after optimization.

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“…The RTP system under consideration, developed at Stanford University [2], has a three-ringed circular symmetric lamp configuration with independent control of power to each ring (see Fig. 2).…”

Section: A Structure Of Rtpmentioning

confidence: 99%

“…This section presents a mathematical thermal model for axisymmetric RTP systems [1], [2], which is the approximation to the heat equation in cylindrical coordinates. The wafer is partitioned into concentric elements, one cylindrical and the others annular.…”

Section: B Model Equation Of Rtpmentioning

confidence: 99%

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A learning approach of wafer temperature control in a rapid thermal processing system

Choi

Min

2001

IEEE Trans. Semicond. Manufact.

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This paper presents a learning approach for wafer temperature control in a rapid thermal processing system (RTP). RTP is very important for semiconductor processing system and requires an accurate trajectory following. Numerous studies have addressed this problem and most research on this problem requires exact knowledge of the system dynamics. The various approaches do not guarantee the desired performance in practical applications when there exist some modeling errors between the model and the actual system. In this paper, iterative learning control scheme is applied to RTP without exact information on the dynamics. The learning gain of the iterative learning law is estimated by neural networks instead of a mathematical model. In addition, the control informations obtained by the iterative learning controller (ILC) are accumulated in the feedforward neuro controller (FNC) for generalization to various reference profiles. Through numerical simulations, it is demonstrated that the proposed method can achieve an accurate output tracking even without an exact RTP model. The output errors decrease rapidly through iterations when using the learning gain estimated and the FNC yields a reduced initial error, and so requires small iterations.Index Terms-Iterative learning control, neural network, rapid thermal processing.

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Improvement of Temperature Uniformity in Rapid Thermal Processing Systems Using Multivariable Control

Cited by 24 publications

References 6 publications

Thermal uniformity and stress minimization during rapid thermal processes

Thermal uniformity and stress minimization during rapid thermal processes

Coordinate control of air movement for optimal thermal comfort

A learning approach of wafer temperature control in a rapid thermal processing system

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