Research Papers

Computational Study of Contact Solidification for Silicon Film Growth in the Ribbon Growth on Substrate System

[+] Author and Article Information
Ronghui Ma

e-mail: roma@umbc.edu
Department of Mechanical Engineering,
University of Maryland, Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250

1Corresponding author.

Manuscript received February 28, 2013; final manuscript received July 9, 2013; published online October 25, 2013. Assoc. Editor: Ranganathan Kumar.

J. Thermal Sci. Eng. Appl 6(1), 011011 (Oct 25, 2013) (9 pages) Paper No: TSEA-13-1040; doi: 10.1115/1.4025050 History: Received February 28, 2013; Revised July 09, 2013

Ribbon growth on substrate (RGS) has emerged as a new method for growing silicon films at low cost for photovoltaic applications by contact solidification. Thermal conditions play an important role in determining the thickness and quality of the as-grown films. In this study, we have developed a mathematical model for heat transfer, fluid flow, and solidification in the RGS process. In particular, a semi-analytical approach is used in this model to predict solidification with a sharp solid–liquid interface without using a moving grid system. A more realistic analytical relationship that considers the varying rate of heat removal at the interface has been developed to evaluate the effective heat transfer rate, solidification rate, and solidification front. These models were used to predict the flow patterns in the crucible, the temperature distributions in the system, the velocity fields in the crucible, the solidification rates, and the film thicknesses. The effects of important operational parameters, such as pulling speed, preheat temperature, and thermal properties of the substrate material, have been examined. In addition, an order of magnitude analysis has been performed to understand heat transfer in the growing film and substrate. This analysis leads to a simplified mathematical model for heat transfer and solidification, which can be resolved analytically to derive theoretical solutions for the effective heat transfer coefficient, the rate of solidification, and the film thickness. The results show that the solidification rate varies largely on the substrate. The non-uniformity can be mitigated by altering the temperature distribution in the silicon melt through manipulating heat generation in the top heater. The rates of solidification and film thickness are very sensitive to both the thermal conductivity and preheat temperature of the substrate. Increasing pulling velocity will increase the rate of solidification at the leading edge but reduce the film thickness. The numerical model and the theoretical solution provide an important tool for thermal design and optimization of the RGS system.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Braga, A. F. B., Moreira, S. P., Zampieri, P. R., Bacchin, J. M. G., and Mei, P. R., 2008, “New Processes for the Production of Solar-Grade Polycrystalline Silicon: A Review,” Sol. Energy Mater. Sol. Cells, 92(4), pp. 418–424. [CrossRef]
Müller, A., Ghosh, M., Sonnenschein, R., and Woditsch, P., 2006, “Silicon for Photovoltaic Applications,” Mater. Sci. Eng., B, 134, pp. 257–262. [CrossRef]
Möller, H. J., Funke, C., Rinio, M., and Scholz, S., 2005, “Multicrystalline Silicon for Solar Cells,” Thin Solid Films, 487, pp. 179–187. [CrossRef]
Janoch, R. E., Anselmo, A. P., Wallace, R. L., Martz, J., Lord, B. E., and Hanoka, J. I., 2000, “PVMaT Funded Manufacturing Advances in String Ribbon Technology,” Photovoltaic Specialists Conference, Anchorage, AK, pp. 1403–1406.
Surek, T., 2005, “Crystal Growth and Materials Research in Photovoltaics: Progress and Challenges,” J. Cryst. Growth, 275, pp. 292–304. [CrossRef]
Hahn, G., Seren, S., Kaes, M., Schonecker, A., Kalejs, J. P., Dube, C., Grenko, A., and Belouet, C., 2006, “Review on Ribbon Silicon Techniques for Cost Reduction in PV,” Photovoltaic Energy Conversion, Conference Record of the 2006 IEEE 4th World Conference, Waikoloa, HI, pp. 972–975.
Steinbach, I., and Hofs, H. U., 1997, “Microstructural Analysis of the Crystallization of Silicon Ribbons Produced by the RGS Process,” Photovoltaic Specialists Conference, Conference Record of the Twenty-Sixth IEEE, Anaheim, CA, pp. 91–93.
Lange, H., and Schwirtlich, I. A., 1990, “Ribbon Growth on Substrate (RGS)—A New Approach to High Speed Growth of Silicon Ribbons for Photovoltaics,” J. Cryst. Growth, 104, pp. 108–112. [CrossRef]
Schonecker, A., Laas, L.,Gutjahr, A.,Wyers, P., Reinink, A., and Wiersma, B., 2002, “Ribbon-Growth-on-Substrate: Progress in High-Speed Crystalline Silicon Wafer Manufacturing,” Photovoltaic Specialists Conference, Conference Record of the Twenty-Ninth IEEE, Petten, The Netherlands, pp. 316–319.
Kalejs, J. P., 2002, “Silicon Ribbons and Foils—State of the Art,” Sol. Energy Mater. Sol. Cells, 72, pp. 139–153. [CrossRef]
Seren, S., Hahn, G., Gutjahr, A., Burgers, A. R., and Schonecker, A., 2005, “Screen-Printed Ribbon Growth on Substrate Solar Cells Approaching 12% Efficiency,” Photovoltaic Specialists Conference, Conference Record of the Thirty-First IEEE, Konstanz University, Germany, pp. 1055–1058.
Hahn, G., Seren, S.,Sontag, D., Gutjahr, A., Laas, L., and Schonecker, A., 2003, “Over 10% Efficient Screen Printed RGS Solar Cells,” Proceedings of 3rd World Conference Photovoltaic Energy Conversion, Osaka, Japan, 2, pp. 1285–1288.
Seren, S., Hahn, G., Gutjahr, A., Burgers, A. R., Schonecker, A., Grenko, A., and Jonczyk, R., 2006, “Ribbon Growth on Substrate and Molded Wafer-Two Low Cost Silicon Ribbon Materials for PV,” Photovoltaic Energy Conversion, Conference Record of the 2006 IEEE 4th World Conference on, Waikoloa, HI, pp. 1330–1333.
Lu, J., Rozgonyi, G., Schonecker, A., Gutjahr, A., and Liu, Z., 2005, “Impact of Oxygen on Carbon Precipitation in Polycrystalline Ribbon Silicon,” J. Appl. Phys., 97, p. 033509. [CrossRef]
Appapillai, A., and Sachs, E., 2010, “The Effect of Substrate Material on Nucleation Behavior of Molten Silicon for Photovoltaics,” J. Cryst. Growth, 312, pp. 1297–1300. [CrossRef]
Appapillai, A. T., Sachs, C., and Sachs, E.M., 2011, “Nucleation Properties of Undercooled Silicon at Various Substrates,” J. Appl. Phys, 109, p. 084916. [CrossRef]
Apel, M., Franke, D., and Steinbach, I., 2002, “Simulation of the Crystallisation of Silicon Ribbons on Substrate,” Sol. Energy Mater. Sol. Cells, 72, pp. 201–208. [CrossRef]
Jeong, H.-M., Chung, H.-S., and Lee, T. W., 2010, “Computational Simulations of Ribbon-Growth on Substrate for Photovoltaic Silicon Wafer,” J. Cryst. Growth, 312, pp. 555–562. [CrossRef]
Lee, J.-S., Jang, B.-Y., and Ahn, Y.-S., 2012, “Effect of Processing Parameters on Thickness of Columnar Structured Silicon Wafers Directly Grown From Silicon Melts,” Int. J. Photoenergy, 2012, p. 5.
Hu, H., and Argyropoulos, S., 1996, “Mathematical Modelling of Solidification and Melting: A Review,” Model. Simul. Mater. Sci. Eng., 4, p. 371. [CrossRef]
Voller, V. R., Swaminathan, C. R., and Thomas, B. G., 1990, “Fixed Grid Techniques for Phase Change Problems: A Review,” Int. J. Numer. Methods Eng., 30, pp. 875–898. [CrossRef]
Basu, B., and Date, A. W., 1988, “Numerical Modelling of Melting and Solidification Problems—A Review,” Sadhana, 13, pp. 169–213. [CrossRef]
Jaluria,Y., 2003, “Thermal Processing of Materials: From Basic Research to Engineering,” J. Heat Transfer, 125, pp. 957–979. [CrossRef]
Faghri, A., and Zhang,Y., 2006, Transport Phenomena in Multiphase Systems, Elsevier, New York, Chap. 6.
Prasad, V., Zhang, H., and Anselmo, A. P., 1997, “Transport Phenomena in Czochralski Crystal Growth Processes,” Adv. Heat Transfer, 30, pp. 313–435. [CrossRef]
Ma, R. H., Zhang, H., Ha, S., and Skowronski, M., 2003, “Integrated Process Modeling and Experimental Validation of Silicon Carbide Sublimation Growth,” J. Cryst. Growth, 252, pp. 523–537. [CrossRef]
Myers,G., 1971, Analytical Methods in Conduction Heat Transfer, McGraw-Hill, New York, Chap. 6.


Grahic Jump Location
Fig. 1

Schematic diagram of the RGS system

Grahic Jump Location
Fig. 2

Diagram of heat transfer in the growing film and substrate

Grahic Jump Location
Fig. 3

Comparisons of the growth rates (a) and film thicknesses (b) on graphite substrate predicted by numerical and theoretical solutions, Tph = 1388 K, Vp = 0.1 m/s

Grahic Jump Location
Fig. 4

Effective heat transfer coefficient heff for a graphite substrate, Vp = 0.1 m/s

Grahic Jump Location
Fig. 5

Global temperature distribution in the RGS system (a); stream function and velocity vectors in the melt (b); temperature distribution in melt (c); temperature distribution in substrate (d); Vp = 0.1 m/s, Tph = 1388 K

Grahic Jump Location
Fig. 6

Silicon film growth rates (a) and film thicknesses (b) for different Vp on a graphite substrate, Tph = 1388 K

Grahic Jump Location
Fig. 7

Silicon film growth rates (a) and film thicknesses (b) for different thermal conductivities, Tph = 1388 K, Vp = 0.05 m/s

Grahic Jump Location
Fig. 8

Silicon film growth rates (a) and thicknesses (b) for different Tph on graphite substrate, Vp = 0.1 m/s

Grahic Jump Location
Fig. 9

Schematic of the moving substrate



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In