近年來矽晶太陽能電池為了降低成本，太陽能晶片尺寸越來越大且厚度越來越薄。以致於燒結過程所產生的翹曲問題越來越被重視，本文提供一套系統化的方法來模擬太陽能電池於燒結過程中的翹曲行為，這套方法包含三個部份: (1) 奈米壓痕實驗求得正面銀膠和背面鋁膠的材料參數；(2)電子顯微鏡求得銀膠和鋁膠的厚度；(3) 利用非線性有限元素分析模擬太陽能電池燒結過程。本文利用這套方法模擬單晶矽太陽能電池於燒結過程所產生的翹曲變形量，和Huster和Hilali建議的翹曲變形量計算公式相比更為貼近實驗數據。並進一步利用這套方法分析澆鑄法(cast method)和限邊薄片狀晶體生長法(Edge-defined film fed growth EFG)所製成的多晶矽太陽能電池，發現矽晶片的材料非等向性對於翹曲的影響很小。這套方法同時可以針對矽晶太陽能電池進行幾何參數分析，當背面鋁膠厚度增加時，翹曲變化量也會跟著增加；正面銀膠則具有抑制翹曲的效果，當正面銀膠厚度每增加10µm時，大約可以減少0.1mm的翹曲變化量。這套方法同時可以提供正面銀膠柵線的設計，以3柵線(3-busbar)太陽能電池為例，當柵線增加銀膠面積時，翹曲變化量也會減少，同時可以檢示柵線於燒結後的塑性應變，其塑性應變較大之處較容易於燒結的過程中發生破壞。這套方法同時提供了矽晶太陽能電池於燒結後的殘留最大主應力的大小與分佈，同時發展出簡單的殘留應力計算公式來計算矽晶太陽能電池於燒結後的殘留應力。

In this thesis, a systematic approach for simulating the cell bowing induced by the firing process is presented. This approach consists of three processes: (1) the material properties are determined using a nanoidentation test; (2) the thicknesses of aluminum (Al) paste and silver (Ag) busbars and fingers are measured using scanning electron microscopy; (3) Non-linear finite element analysis (FEA) is used for simulating the cell bowing induced by the firing process. As a result, the bowing obtained using FEA simulation agrees better with the experimental data than that using the bowing calculations suggested by Huster and Hilali. Bow simulation of single crystalline silicon (sc-Si), cast, and edge-defined film-fed growth (EFG) multi-crystalline silicon wafer of different thickness is presented. The influence of different silicon wafer for cell bowing is not obvious. When the thickness of Al-paste increases, the bowing induced by the firing process increases. Conversely, the increasing thickness of Ag busbar and fingers makes the decreasing bowing. It is also proposed that the metallization pattern, Ag busbars and fingers screen printed on the front of a solar cell, can be designed using this approach. A practical case of a 3-busbar Si solar cell is presented. In addition, the total in-plane residual stress state in the wafer/cell due to the firing process can be determined using the FEA simulation. A detailed analysis of the firing-induced stress state in single crystalline silicon (sc-Si), cast, and edge-defined film-fed growth (EFG) multi-crystalline silicon wafers of different thicknesses is presented. Based on this analysis, a simple residual stress calculation is developed to estimate the maximum in-plane principal stress in the wafers.

[1] Bähr, M., Dauwe, S., Lawerenz, A., mittelstädt, L., “Comparison of bow-avoiding Al pastes for thin, large-area crystalline silicon solar cells,” in: 20th EPSEC, Barcelona, pp. 926-929, (2005).

[2] Best, S. R., Hess, D. P., Belyaev, A., et al., “Audible vibration diagnostics of thermo-elastic residual stress in multi-crystalline silicon wafers,” Applied Acoustics, 67(6): 541-549, (2006).

[3] Bridgman, P. W., “Certain Physical Properties of Single Crystals of Tungsten, Antimony, Bismuth, Tellurium, Cadmium, Zinc, and Tin,” Proceedings of the American Academy of Arts and Sciences, 60(6), pp. 305-383, (1925).

[4] Brito, M. C., Maia Alves, J., Serra, J. M., et al., “Measurement of residual stress in EFG ribbons using a phase-shifting IR photoelastic method,” Solar Energy Materials and Solar cells, 87(1-4), pp. 311-316, (2005a).

[5] Brito, M. C., Pereira, J. P., Maia Alves, J., et al., “Measurement of residual stress in multicrystalline silicon ribbons by a self-calibrating infrared photoelastic method,” Review of Scientific instruments, 76, 013901, (2005b).

[6] Brown, G. R., Levine, R. A., Shaikh, A., et al., “Three-Dimensional Solar Cell Finite-Element Sintering Simulation,” J. Am. Ceram. Soc., 92(7), pp. 1450-1455, (2009).

[7] Chapin, D. M., Fuller, C. S., Pearson, G. L., “A new silicon p­n junction photocell for converting solar radiation into electrical power,” Journal of Applied Physics, Vol. 25, pp. 676, (1954).

[8] Funke, C., Kullig, E., Kuna, M., et al., “Biaxial Fracture Test of Silicon Wafers,” Advanced engineering materials, 6(7), pp. 594-598, (2004).

[9] Hauch, J. A., Holland, D., Marder, M. P., Swinney H. L.,“Dynamic fracture in single crystal silicon,” Physical Review Letters, 82(19), pp. 3823-3826, (1999).

[10] He, S., Danyluk, S., “Residual stresses in polycrystalline silicon sheet and their relation to electron-hole lifetime,” Applied physics letters, 89, 111909, (2006).

[11] He, S., Zheng, T., Danyluk, S., “Analysis and determination of the stress-optic coefficients of thin single crystal silicon samples,” Journal of Applied Physics, 96(6): 3103-3109, (2004).

[12] Hilali, M. M., Gee, J. M., Hacke, P., “Bow in screen-printed back-contact industrial silicon solar cells,” Solar Energy Material & Solar Cells, 2007, 91(13):1228-1233, (2007).

[13] Hopcroft, M. A., Nix, W. D., Kenny, T. W., “What is the Young’s modulus of silicon,” Journal of Microelectromechamical System, 19(2), pp. 229-238, (2010).

[14] Huster, F., 2005a, “Aluminium-back surface field: bow investigation and elimination,” 20th EPSEC, Barcelona, Spain, pp. 635-638, (2005a).

[15] Huster, F., “Investigation of the alloying process of screen printed aluminium pastes for the BSF formation on silicon solar cells,” in: 20th EPSEC, Barcelona, pp. 1466-1469, (2005b).

[16] Kohn, C., Faber, T., Kübler, R., Beinert, J., Kleer, G., Clement, F., Erath, D., Reis, I., Martin, F., Müller, A., “Analyses of warpage effects induced by passivation and electrode coatings in silicon solar cells,” in: EU PVSES, pp. 1270-1273, (2007).

[17] Li, F., Garcia, V., Danyluk, S., “Full Field Stress Measurements in Thin Silicon Sheet,” Proceedings of the Fouth World conference on Photovoltaic Energy Conversion, Waikoloa, HI, USA, 1, pp. 363-368, (2006)

[18] Merle B., Göken, M., “Fracture toughness of silicon nitride thin films of different thicknesses,” Acta Materialia, 59, pp. 1772-1779, (2011).

[19] Möller, H. J., “Basic Mechanisms and Models of Multi-wire Sawing,” Advanced Engineering Materials, 6(7), pp. 501-513, (2004).

[20] Oliver, W. C., Pharr, G. M., “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiment,” J. Mater. Res., 7(6), pp. 1564-1583, (1992).
[21] Nelson, J., The physics of solar cells, Imperial College Press, (2003).

[22] Parretta, A., Sarno, A., Tortora, P., Yakubu, H., Maddalena, P., Zhao, J., Wang, A. “Angle-dependent reflectance measurements on photovoltaic materials and solar cells,” Optics Communications, 172, pp. 139-151, (1999).

[23] Ravl, K. V., “The growth of EFG silicon ribbons,” Journal of Crystal Growth, 39, pp.1-16, 1977.

[24] Schneider, A., Gerhards, C., Huster, F., Neu, W., Spiegel, M., Fath, P., Bucher, E., Young, R. J. S., Prince, A. G., Raby, J. A., Carroll, A. F., “Al BSF for thin screen-printed multicrystalline Si solar cells,” in: 17th European Photovoltaic Solar Energy Conference, Munich, Germany, pp. 1768-1771, (2001).

[25] Schneider, A., Gerhards, C., Fath, P., Bucher, E., “Bow reducing factors for thin screen-printed mc-Si solar cells with Al BSF,” in: 29th IEEE Photovoltaic Specialists Conference, pp. 336-339, (2002).

[26] Stockbarger, D. C., “The production of large single crystals of lithium fluoride,” Review of Scientific Instruments, 7, pp. 133, (1936).

[27] Szlufcik, J., Duerinckx, F., Horzel, J., Kerschaver, E. V.,Dekkers, H., Wolf, S. D., Choulat, P., Allebe, C., Nijs, J.,“High-efficiency low-cost integral screen-printing multicrystalline silicon solar cells,” Solar Energy Material & Solar Cells, 74, pp. 155-163, (2002).

[28] Teal, G. K., Little, J. B., “Growth of germanium single crystals”, Physical Review Letters, 78, pp. 647, (1950).

[29] Timoshenko, S., “Analysis of Bi-Metal Thermostats,” journal of the Optical Society of America, 11(3), pp.233-255, (1925)

[30] Williams, R., “Becquerel photovoltaic effect in binary compounds,” The journal of Chemical Physics, 32(5), pp. 1505-1514, (1960).

[31] Wu, P. H., Lin, I. K., Yan, H. Y., Ou, K. S., Chen, K. S., Zhang, X., “Mechanical property characterization of sputtered and plasma enhanced chemical deposition (PECVD) silicon nitride films after rapid thermal annealing,” Materials Science and Engineering A, 168, pp. 117-126, (2011).

[32] Yasutake, K., Uemno, M., Kawabe, H., et al., “Measurement of Residual stress in Bent Silicon Wafers by Means of Photoluminescence”, Japanese Journal of Appied Physics, 21(1):1715-1719, (1982).

[33] Yu, L., Jiang, Y., Lu, S., et al., “3D FEM for sintering of Solar Cell with Boron Back Surface Field Based on Solidwork Simulation,” IERI Procedia 1, pp. 81-86, (2012).

[34] 中華民國經濟部能源局, 新及再生能源領域-105年度研發規劃報告書(大綱), 2014

[35] 台灣太陽光電產業協會, 矽晶太陽電池技術、成本與性能, 2012

[36] 元晶太陽能科技股份有限公司(TSEC), http://www.tsecpv.com/zh-tw