摘要
本文以中山科學研究院正在發展中的快速熱處理機台為對象，
進行快速熱處理過程的熱傳研究，發展加熱燈、
腔體及直徑 厘米的晶圓之間的熱輻射交換及被加熱的晶圓的熱傳導的數值模擬。
本文採用封閉面模式計算熱輻射交換，
再結合熱輻射交換的結果和晶圓熱傳導的有限差分解，
求得快速熱處理過程晶圓溫度的分佈。
以加熱燈表相放射率為 ，
表相吸收率為 及單一加熱燈的放射功率為 的典型計算而言，
加熱 秒後晶圓的溫度約為 。當燈座吸收率減少，各時刻晶圓溫度會增加。
這是因為燈座吸收率愈小，燈座外流的能量會愈少。
另外，腔壁放射率的減少會造成晶圓溫度的增加。

Abstract
In this work, we consider heat transfer in Rapid Thermal Processing
(RTP) for the RTP equipment under development in CSIST. Numerical
schemes simulating radiative heat exchange among the lamps, chamber and a
300mm wafer and heat conduction in the wafer are developed. The enclosure
model is applied to solve the radiative heat exchange, and the results are
combined with the finite-difference solutions of the heat conduction in the
wafer to obtain the temperature distribution of the wafer in the RTP. For a
typical case with the apparent emissivity of a lamp 0.426, the apparent
absorptivity 0.408 and the emissive power of a single lamp 510W, the
temperature of wafer achieves about 1300K after 10-second heating. The
temperature of the wafer at a certain instant increases, as the absorptivity of
the lamp-stands decreases. This is because the energy leakage through the
lamp-stands decreases with the decrease of the absorptivity. Besides, the
temperature of the wafer increases with the decrease of the emissivity of
chamber wall.

參考文獻

1. Lord, H. A., 1988, "Thermal and Stress Analysis of Semiconductor Wafers in a Rapid Thermal Processing Oven," IEEE Transactions on Semiconductor Manufacturing, 1, pp. 105-114.
2. Kakoschke, R., Bubmann, E., 1989, "Simulation of Temperature Effects during Rapid Thermal Processing," Rapid Thermal Annealing/Chemical Vapor Deposition and Integrated Processing, 146, pp.473-482.
3. Sorrell, F. Y., Fordham, M. J., Ozturk, M. C., and Wortman, J. J., 1992, "Temperature Uniformity in RTP Furnace," IEEE Transactions on Electron Devices, 39, pp. 75-80.
4. Anderson, D. A., Tannchill, J. C., and Pletcher, R. H., 1984, Computational Fluid Mechanics and Heat Transfer, Cambridge, MA：Hemisphere Pub.
5. Richtmyer, R. D., and Morton, K. W., 1967, Difference Methods for Initial Value Problems, New York：Wily Interscience.
6. Leitz, G., Pezoldt, J., Patzschke, I., Zollner, J. P., and Eichhorn, G., 1993, "Investigation of Dynamical Temperature Behavior in RTP," Materials Research Society Symposium Proceedings, 303, pp. 171-176.
7. Lin, Y. T., Subrahmanyan, R., Sitaram, A. R., and Orlowski, M., 1993, "Combined Simulation and Measurement Study of Temperature Uniformity in Rapid Thermal Processing," Materials Research Society Symposium Proceedings, 303, pp. 231-236.
8. Lie, K. H., Merchant, T. P., and Jensen, K. F., 1993, "Simulation of Rapid Thermal Processing Equipment and Processes," Materials Research Society Symposium Proceedings, 303, pp. 197-209.
9. Zollner, J. P., Patzschke, I., Pietzuch,V., Pezoldt, J. and Eichhorn, G., 1993, "To the Influence of the Wafer Edge on RTP ," Materials Research Society Symposium Proceedings, 303, pp. 177-182.
10. Henda, R., Scheid, E., and Bielle-Daspet, D., 1994, "A 3-Dimensional Temperature Uniformity Model for a Rapid Thermal Processing Furnace," Materials Research Society Symposium Proceedings, 342, pp. 419-424.
11. Acharya. N., and Timans P. J., 1998, "The Effect of Chamber Components on Wafer Temperature Response in an RTP System," Materials Research Society Symposium Proceedings , 525, pp.21 -26.
12. Riley, T. J. and Gyurcsik, R. S., 1993, "Rapid Thermal Processor Modeling Control and Design for Temperature Uniformity," Materials Research Society Symposium Proceedings, 146, pp. 223-229.
13. Dilhac, J. M., Nolhier, N., Ganibal, C., and Zanchi, C., 1995, "Thermal Modeling of a Wafer in a Rapid Thermal Processor," IEEE Transactions on Semiconductor Manufacturing, 8, pp. 432-439.
14. Peuse, B., Miner, G., Yam, M., and Elia, C., 1998, "Advances in RTP Temperature Measurement and Control," Materials Research Society Symposium Proceedings, 525, pp.71 -85.
15. Jan, Y. K., and Lin, C. A., 1998, "Lamp Configuration Design for Rapid Thermal Processing Systems," IEEE Transactions on Semiconductor Manufacturing , 11, pp.75 -84.
16. Siegel, R., and Howell, J. R., 1992, Thermal Radiation Heat Transfer, Taylor & Franics, Washington. D.C.
17. 蘇俊傑, 2000 , "快速熱處理製程之晶圓加熱模擬分析, " 第17屆,中國機械工程學會, 高雄.
18. Hill, C., Jones, S., and Boys, D., 1989, Rapid Thermal Annealing-Theory and Practice, in Reduced Thermal Processing for ULSI, NATO ASI Series B: Physics, pp. 143-180.
19. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical Recipes in Fortran The Art of Scientific Computing second ed., Cambridge, New York.
20. 王振源,吳志陽, 2001, "快速熱處理機台即時溫度量測系統最佳化設計, " 機械關鍵系統技術研究發展第二期三年計畫,中山科學研究院.
21. Ozisik, M. N., 1993, Heat Conduction second ed., John Wiley & Sons, New York.
22. Modest, M., 1993, Radiative Heat Transfer, Mc Graw Hill, New York.
23. Howell, J. R., 1982, A Catalog of Radiation Configuration Factors, McGraw-Hill, New York.