本研究建立以氬電漿餘輝態進行矽薄膜沉積之反應機制並進行二維沉積反應之穩態數值模擬，以計算低壓腔體內部矽薄膜成長速率。本研究共考慮17個重要物種，包含電子、質子、自由基氣體、中性氣體等，除求解流場之連續、動量與能量方程式外，本研究使用37個化學反應式，以考慮電漿與工作氣體在反應腔體內部各物種因化學反應生成與消耗，並利用電子能量方程式估算腔體內部電子溫度。此外本研究考慮10個表面反應式，以考慮矽薄膜於基板表面生長的機制。對於所考慮的反應腔體幾何，當工作壓力自0.5 Torr升高為1.0 Torr時，矽薄膜成長率預估將自5.1 Å/s下降至3.8 Å/s；若工作功率自500 W升高為 1000 W時，矽薄膜成長率預估將自3.5 Å/s成長至5.7 Å/s 。數值模擬亦針對不同幾何與工作參數進行計算，當工作氣體中氫氣分量增加，以及氬電槳噴嘴距離增加時，皆不利於提高薄膜成長率，若增加反應器高度，基板溫度以及工作氣體噴嘴間距離，則有利於提高薄膜成長率，但工作氣體噴嘴的高度則對於薄膜成長率無顯著影響。

The growth rate of silicon thin film inside a low-pressure chamber is predicted based on a steady, two-dimensional fluid modeling of deposition process in the afterglow of argon plasma, where silane and hydrogen serve as the working gases. In this study seven-teen species are considered, such as electron, ions, free radicals and neutral species, where thirty seven chemical reactions among them are taken into account in space. The continuity, momentum and energy equations are also solved to predict the gas flow inside the chamber. The electron temperature is additionally calculated by the energy equation of electron. Ten surface reactions are employed to account for the deposition of silicon thin film on substrate surface. By increasing the pressure from 0.5 Torr to 2.0 Torr, the predicted deposition rate decreases from 5.1 Å/s to 3.8 Å/s. In contrast, it increases from 3.5 Å/s to 5.7 Å/s provided the power increases from 500 W to 1000 W. Numerical inves-tigations of the growth of thin film silicon have been also carried out under various condi-tions, such as the change of geometrical and operational parameters. With the increase of the gas flow rate of hydrogen and the distance between two argon orifices, the predicted deposition rate decreases. In contrast, the deposition rate grows when the height of the chamber, the substrate temperature and the distance between two gas rings increase. Be-sides, the distance between gas rings and substrate has little influence on the deposition rate on the substrate.

[1] Franz, G., Low Pressure Plasmas and Microstructuring Technology, Springer, Berlin, 2009.
[2] Chieh T.H., Development of a Parallelized Fluid Modeling Code and Its Applications in Low-Temperature Plasma, Ph.D Thesis, National Chiao Tung University, 2010.
[3] Bruno, G., Capezzuto, P. and Madan, A., Plasma Deposition Processes of Amorphous Silicon-Based Materials, Academic, Boston, 1995.
[4] Street, R.A., Hydrogenated Amorphous Silicon, Cambridge University Press, New York, 2005.
[5] http://www.plasmaequip.com.
[6] http://www.wikipedia.org.
[7] Lieberman, M.A. and Lichtenberg, A.J., Principles of Plasma Discharges and Mate-rials Processing, Wiley, New Jersey, 2005.
[8] Kuo, G. and Kuo, M.T, "Applications of plasma-enhanced chemical vapor deposition (PECVD) in making thin film silicon solar cells", Instruments Today, vol. 31, no. 3, pp. 15-27, 2009.
[9] Fridman, A., Plasma Chemistry, Cambridge University Press, New York, 2008.
[10] Park, J.H., Deposition of Coatings by PECVD, EE7730, Department of Electrical En-gineering, Auburn University, 2003.
[11] Intranuovo, F., Sardella, E., Rossini, P., Agostino, R. and Favia, P., "PECVD of fluo-rocarbon coatings from hexafluoropropylene oxide: glow vs. afterglow", Chemical Vapor Deposition, vol. 15, pp. 95-100, 2009.
[12] Dhayal, M., Forder, D., Parry, K.L., Short, R.D. and Bradley, J.W., "Using an after-glow plasma to modify polystyrene surfaces in pulsed radio frequency (RF) argon dis-charges", Surface and Coatings Technology, vol. 173-174, pp. 872-876, 2003.
[13] Mitchell, R.R., Young, R.M., Partlow, W.D., Bevan, M.J., Chantry, P.J. and Kline, L.E., "Silicon nitride deposition using N2-rare gas radio-frequency afterglows", IEEE International Conference on Plasma Science, Oakland, USA, 21-23 May, 1990.
[14] Nishikawa, K.I., Hardee, P., Hededal, C., Kouveliotou, C., Fishman, G.J. and Mizuno, Y., "Simulation studies of early afterglows observed with SWIFT", The Proceedings of Sixteenth Maryland Astrophysics Conference, pp. 265-270, 2006.
[15] Dhayal, M., Forder, D., Parry, K.L., Short, R.D. and Bradley, J.W., "Using an after-glow plasma to modify polystyrene surfaces in pulsed radio frequency (RF) argon dis-charges", Surface and Coatings Technology, vol. 173-174, pp. 872-876, 2003.
[16] Wada, H. and Oyama, T., "Growth mechanism of electron density in radio frequency afterglow plasmas", Electrical Engineering in Japan (English translation of Denki Gakkai Ronbunshi), vol. 135, no. 2, pp. 26-32, 2001.
[17] Chau, S.W. and Wei, T.C., Flow Simulation of Large-Area and High-Density Plasma Source, ITRI-Report, 2010.
[18] Ward, A.L., "Effect of space charge in cold-cathode gas discharges", Physical Review, vol. 112, no. 6, pp. 1852-1857, 1958.
[19] Bavafa, M., Ilati, H. and Rashidian, B., "Comprehensive simulation of the effects of process conditions on plasma enhanced chemical vapor deposition of silicon nitride", Semiconductor Science and Technology, vol. 23, no. 9, pp. 1-19, 2008.
[20] Boeuf, J.P. and Pitchford, L.C., "Two-dimensional model of a capacitively coupled rf discharge and comparisons with experiments in the Gaseous Electronics Conference reference reactor", Physical Review E, vol. 51, no. 2, pp. 1376-1390, 1995.
[21] Lide, D.R., Handbook of Chemistry and Physics, Taylor and Francis Group LLC, Flor-ida, 2009.
[22] Chiu, Y.M, Hung, C.T, Wu, J.S and Hwang, F.N, "Parallel fluid modeling of silane gas discharge in an inductively coupled plasma source", The 18th Computational Fluid Dynamics Conference in Taiwan, Taiwan, 2011.
[23] Meeks, E., Larson, R.S., Ho, P., Apblett, C., Han, S.M, Edelberg, E. and Aydil, E.S., "Modeling of SiO2 deposition in high density plasma reactors and comparisons of model predictions with experimental measurements", Journal of Vacuum Science and Technology A: Vacuum, Surfaces and Films, vol. 16, pp. 544-563, 1998.
[24] Kushner, M.J., "A model for the discharge kinetics and plasma chemistry during plas-ma enhanced chemical vapor deposition of amorphous silicon", Journal of Applied Physics, vol. 63, no. 8, pp. 2532-2551, 1988.
[25] Bird, R.B., Stewart, W. and Lightfoot, E.N., Transport Phenomena, 2nd Ed., Wiley, New York, 2001.
[26] Krzhizhanovskaya V.V., A Virtual Reaction for Simulation of Plasma Enhanced Chemical Vapor Deposition, Ph.D Thesis, The Institutional Repository of the Univer-sity of Amsterdam, 2008.
[27] Raizer, Y.P, Gas Discharge Physics, Springer, New York, 1991.
[28] Salabas, A., Gousset, G. and Alves, L.L., "Two-dimensional fluid modelling of charged particle transport in radio-frequency capacitively coupled discharges", Plasma Sources Science and Technology, vol. 11, no. 4, pp. 448-465, 2002.
[29] Perrin, J., Leroy, O. and Bordage, M.C., "Cross-sections, rate constants and transport coefficients in silane plasma chemistry", Contributions to Plasma Physics, vol. 36, no. 1, pp. 3-49, 1996.
[30] Sakiyama, Y. and Graves, D.B., "Neutral gas flow and ring-shaped emission profile in non-thermal RF-excited plasma needle discharge at atmospheric pressure", Plasma Sources Science and Technology, vol. 18, no. 2, pp. 1-11, 2, 2009.
[31] Hsu, C.C., Diagnostic Studies and Modeling of Inductively Coupled Plasma, Ph.D Thesis, University of California, 2006.
[32] Denysenko, I.B., Ostrikov, K., Xu, S., Yu, M.Y. and Diong, C.H., "Nanopowder man-agement and control of plasma parameters in electronegative SiH4 plasmas", Journal of Applied Physics, vol. 94, no. 9, pp. 6097-6107, 2003.
[33] Kessels, W.M.M., Van De Sanden, M.C.M., Severens, R.J. and Schram, D.C., "Sur-face reaction probability during fast deposition of hydrogenated amorphous silicon with a remote silane plasma", Journal of Applied Physics, vol. 87, no. 7, pp. 3313-3320, 2000.
[34] Amanatides, E., Stamou, S. and Mataras, D., "Gas phase and surface kinetics in plasma enhanced chemical vapor deposition of microcrystalline silicon: The combined effect of rf power and hydrogen dilution", Journal of Applied Physics, vol. 90, no. 11, pp. 5786-5798, 2001.
[35] Hsin, W.C., Tsai, D.S. and Shimogaki, Y., "Surface reaction probabilities of silicon hydride radicals in SiH4/H2 thermal chemical vapor deposition", Industrial and Engi-neering Chemistry Research, vol. 41, no. 9, pp. 2129-2135, 2002.
[36] Comet User Manual, Institute of Computational Continuum Mechanics GmbH, Ham-burg, 2000.
[37] Khosla, P.K. and Rubin, S.G., "A diagonally dominant second-order accurate implicit scheme", Computers & Fluids, vol. 2, pp. 207-209, 1974.
[38] Kee, R.J., Rupley, F.M. and Miller, J.A., CHEMKIN Release 4.1, Reaction Design, San Diego, California, 2006.
[39] Tsai, R.Y., Kuo, L.C. and Ho, F.C., "Amorphous silicon and amorphous silicon nitride films prepared by a plasma-enhanced chemical vapor deposition process as optical coating materials", Applied Optics, vol. 32, no. 28, pp. 5561-5566, 1993.
[40] Ong, Y.Y., Chen, B.T., Tay, F.E.H. and Iliescu, C., "Process analysis and optimization on PECVD amorphous silicon on glass substrate", Journal of Physics: Conference Se-ries, vol. 34, no. 1, pp. 812-817, 2006.
[41] Sleeckx, E., Schaekers, M., Shi, X., Kunnen, E., Degroote, B., Jurczak, M., Depotterde Ten Broeck, M. and Augendre, E., "Optimization of low temperature silicon nitride processes for improvement of device performance", Microelectronics Reliability, vol. 45, no. 5-6, pp. 865-868, 2005.
[42] Guo, L., Kondo, M., Fukawa, M., Saitoh, K. and Matsuda, A., "High rate deposition of microcrystalline silicon using conventional plasma-enhanced chemical vapor deposi-tion", Japanese Journal of Applied Physics, Part 2: Letters, vol. 37, no. 10 , Part A, pp. L1116-L1118, 1998.
[43] Martin, P.M, Handbook of Deposition Technologies for Films and Coatings, 3rd Ed., Elsevier Inc, Washington, 2010.
[44] Rossnagel, S.M., Cuomo, J.J. and Westwood, W.D., Handbook of Plasma Processing Technology, Park Ridge, New Jersey, 1990.
[45] Ferziger, J.H. and Perić, M., Computational Methods for Fluid Dynamics, Springer, Berlin, 2002.
[46] Versteeg, H.K. and Malalaserkera, W., An Introduction to Computational Fluid Dy-namics: The Finite Volume Method, Longman Scientific and Technical, New York, 1995.
[47] Yoon, J.S., Song, M.Y., Han, J.M., Hwang, S.H., Chang, W.S., Lee, B. and Itikawa, Y., "Cross sections for electron collisions with hydrogen molecules", Journal of Phys-ical and Chemical Reference Data, vol. 37, no. 2, pp. 913-931, 2008.
[48] Chau, S.W., Numerical Investigation of Free-Stream Rudder Characteristics Using a Multi-Block Finite Volume Method, PhD Thesis, Universität Hamburg, 1997.
[49] Niikura, C., Kondo, M. and Matsuda, A., "High rate growth of device-grade micro-crystalline silicon films at 8 nm/s", Solar Energy Materials and Solar Cells, vol. 90, no. 18-19, pp. 3223-3231, 2006.
[50] Itabashi, N., Nishiwaki, N., Magane, M., Naito, S., Goto, T., Matsuda, A., Yamada, C. and Hirota, E., "Spatial distribution of SiH3 radicals in RF silane plasma", Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Pa-pers, vol. 29, no. 3, pp. 505-507, 1990.
[51] Sakiyama, Y. and Graves, D.B., "Non-thermal atmospheric RF plasma in 1-D spherical coordinates: A parametric study", IEEE Transactions on Plasma Science, vol. 35, no. 5 I, pp. 1279-1286, 2007.
[52] Bukowski, J.D., Graves, D.B. and Vitello, P., "Two-dimensional fluid model of an in-ductively coupled plasma with comparison to experimental spatial profiles", Journal of Applied Physics, vol. 80, no. 5, pp. 2614-2623, 1996.
[53] Hsu, C.C., Nierode, M.A., Coburn, J.W. and Graves, D.B., "Comparison of model and experiment for Ar, Ar/O2 and Ar/O2/Cl2 inductively coupled plasmas", Journal of Physics D: Applied Physics, vol. 39, no. 15, pp. 3272-3284, 2006.
[54] Owan D.C., Thin Film Amorphous Silicon Cells by Inductive PECVD with a View to-wards Flexible Substrates, Ph.D Thesis, University of Southampton, 2009.
[55] Shirafuji, T., Chen, W., Yamamuka, M. and Tachibana, K., "Monte-Carlo simulation of surface reactions in plasma-enhanced chemical vapor deposition of hydrogenated amorphous silicon thin films", Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers, vol. 32, no. 11 A, pp. 4946-4947, 1993.
[56] Matsuda, A., "Thin-film silicon growth process and solar cell application", Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Pa-pers, vol. 43, pp. 7909-7920, 2004.
[57] Oversluizen, G. and Lodders, W.H.M., "Optimization of plasma-enhanced chemical vapor deposition of hydrogenated amorphous silicon", Journal of Applied Physics, vol. 83, no. 12, pp. 8002-8009, 1998.
[58] Ho, P., Coltrin, M.E. and Breiland, W.G., "Laser-induced fluorescence measurements and kinetic analysis of Si atom formation in a rotating disk chemical vapor deposition reactor", Journal of Physical Chemistry, vol. 98, no. 40, pp. 10138-10147, 1994.
[59] Nowling, G.R., Babayan, S.E., Jankovic, V. and Hicks, R.F., "Remote plasma-enhanced chemical vapor deposition of silicon nitride at atmospheric pressure", Plasma Sources Science and Technology, vol. 11, no. 1, pp. 97-103, 2002.
[60] Babayan, S.E., Ding, G., Nowling, G.R., Yang, X. and Hicks, R.F., "Characterization of the active species in the afterglow of a nitrogen and helium atmospheric-pressure Plasma", Plasma Chemistry and Plasma Processing, vol. 22, no. 2, pp. 255-269, 2002.