Performance analysis of a rapid thermal processor via physics-based modeling and convex optimization

Kim, S.J.; Kang, Sae Byul; Hyun, Sangwon; Cho, Y.M.; Chung, Jae Dong; Lee, J.S.; Jung, Chang Hoon; Choi, Yun‐Jaie; Jung, Kyung-Chul

doi:10.1109/isie.2001.931652

Cited by 3 publications

(11 citation statements)

References 9 publications

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“…Figure 1 shows a schematic of a 300 mm RTP system used as a test-bed in this paper [9]. The wafer is supported by the edge ring, which contacts the chamber wall.…”

Section: Physics-based Modeling and Experimental Validationmentioning

confidence: 99%

“…This paper begins with a parametric model that focuses on the wafer and quartz window, while treating radiant and convective heat flux on the wafer surface and quartz window as boundary conditions [9]. The resulting model is of low order, which is amenable to the performance analysis of an RTP chamber.…”

Section: Introductionmentioning

confidence: 99%

“…In this respect, the performance during transients is crucial to the qualification of a given design. A convex optimization technique based on the validated model is then adopted to determine how small temporal error can be made for a given trajectory by manipulating the lamp power setting within the pre-specified constraints on the lamp power [9][10][11][12][13][14]. It turns out that there is a trade-off between the ramp-up rate and the maximum temperature deviation from the given trajectory.…”

Section: Introductionmentioning

confidence: 99%

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Design-tool for Rapid Thermal Processors for Optimal Trajectory Tracking

Kim¹,

Cho²

2003

Mathematical and Computer Modelling of Dynamical Systems

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It has become an irreversible trend in recent years that the semiconductor wafer fabrication requires shorter processing time, greater flexibility and lower capital cost. Rapid thermal processing (RTP) has demonstrated its potential to meet such requirements while becoming a key process for manufacturing advanced semiconductor devices. Ever decreasing feature sizes require extremely tightly controlled processing conditions, especially the temperature trajectory to be precisely followed across the wafer. This paper presents a systematic methodology for RTP chamber design, based on the 3-dimensional physicsbased model of a generic RTP chamber. After experimentally validated, the physics-based model is reduced to a lower-order model without sacrificing its fidelity for computational efficiency. With a reduced-order model, optimization studies are performed to determine how small the deviation of the wafer temperature from the pre-specified trajectory can be made in a given design. The results of the optimization studies indicate the goodness of the given RTP design, unravel clues for design improvements, and may provide guidelines for control implementation.

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“…Figure 1 shows a schematic of a 300 mm RTP system used as a test-bed in this paper [9]. The wafer is supported by the edge ring, which contacts the chamber wall.…”

Section: Physics-based Modeling and Experimental Validationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design-tool for Rapid Thermal Processors for Optimal Trajectory Tracking

Kim¹,

Cho²

2003

Mathematical and Computer Modelling of Dynamical Systems

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“…Their study was a kind of trial and error method; thus they found the optimum heating lamp configurations among many cases. Kim et al [8] found the optimum powers of heating lamps to maintain uniform temperature distribution on the wafer by the optimization technique.…”

Section: Introductionmentioning

confidence: 99%

Optimization of rapid thermal processing for uniform temperature distribution on wafer surface

Kang

Choi

et al. 2009

J Mech Sci Technol

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An optimization of rapid thermal processing (RTP) was conducted to obtain uniform temperature distribution on a wafer surface by using linear programming and radiative heat transfer modeling. The results show that two heating lamp zones are needed to maintain uniform wafer temperature and the optimal lamp positions are unique for a given geometry and not affected by wafer temperatures. The radii of heating lamps, which were obtained by optimization, are 45 mm and 108 mm. The emissivity and temperature of the chamber wall do not significantly affect the optimal condition. With obtained optimum geometry of the RTP chamber and lamp positions, the wafer surface temperatures were calculated. The uniformity allowance of the wafer surface is less than ±1℃ when the mean temperature of the wafer surface is 1000℃.

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“…It is verified in [2] that the ROM does not lose the accuracy of a full order model (FOM) which takes the whole chamber including gas flow as control volumes.…”

Section: Reduced Order Modeling (Rom)mentioning

confidence: 94%

Design for optimal trajectory tracking in rapid thermal processing

Kim

Hyun

Cho

9th International Conference on Advanced Thermal Processing of Semiconductors, RTP 2001

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It is an irreversible trend that the semiconductor wafer fabrication requires shorter processing time, greater flexibility and lower capital cost. Rapid Thermal Processing (RTP) has shown a potential to meet such requirements while playing a key role in the advanced cluster tool. Ever decreasing feature sizes require extremely tightly controlled processing conditions, especially the temperature trajectory to be precisely followed and the temperature uniformity across the wafer to be closely maintained. In t h i s paper, a 3-dimensional phyics-based model is derived, which is then used in quantifjmg the trajectory following capability of an RTP design via conex optimization. The optimization studies are performed in two ways; the fxst one minimizies the spatial temperature deviation from the set temperature in the steady state while the second one tries to make the temporal trajectory follow the specified trajectory during transient. The outcomes of the optimization studies indicate the goodness of a given RTP design and may serve as a guideline for control implementation when the RTF' chamber is actually built.

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Performance analysis of a rapid thermal processor via physics-based modeling and convex optimization

Cited by 3 publications

References 9 publications

Design-tool for Rapid Thermal Processors for Optimal Trajectory Tracking

Design-tool for Rapid Thermal Processors for Optimal Trajectory Tracking

Optimization of rapid thermal processing for uniform temperature distribution on wafer surface

Design for optimal trajectory tracking in rapid thermal processing

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