Computer modeling of crystal growth of silicon for solar cells

Abstract

A computer simulator with a global model of heat transfer during crystal growth of Si for solar cells is developed. The convective, conductive, and radiative heat transfers in the furnace are solved together in a coupled manner using the finite volume method. A three-dimensional (3D) global heat transfer model with 3D features is especially made suitable for any crystal growth, while the requirement for computer resources is kept permissible for engineering applications. A structured/unstructured combined mesh scheme is proposed to improve the efficiency and accuracy of the simulation. A dynamic model for the melt-crystal (mc) interface is developed to predict the phase interface behavior in a crystal growth process. Dynamic models for impurities and precipitates are also incorporated into the simulator.

Applications of the computer simulator to Czochralski (CZ) growth processes and directional solidification processes of Si crystals for solar cells are introduced. Some typical results, including the turbulent melt flow in a large-scale crucible of a CZ-Si process, the dynamic behaviors of the mc interface, and the transport and distributions of impurities and precipitates, such as oxygen, carbon, and SiC particles, are presented and discussed. The findings show the importance of computer modeling as an effective tool in the analysis and improvement of crystal growth processes and furnace designs for solar Si material.

Keywords

computer modeling / silicon / crystal growth / solar cells

References

[1] Li J F, Wang S C, Zhang M J, Ma L J. China Solar PV Report. Beijing: China Environmental Science Press, 2007 (in Chinese)

[2] Derby J J, Brown R A. Thermal-capillary analysis of Czochralski and liquid encapsulated Czochralski crystal growth I. Simulation. Journal of Crystal Growth, 1986, 74(3): 605–624

[3] Kobayashi N. Computational simulation of the melt flow during Czochralski growth. Journal of Crystal Growth, 1978, 43(3): 357–363

[4] Kakimoto K, Liu L J. Numerical study of the effects of cusp-shaped magnetic fields and thermal conductivity on the melt-crystal interface in CZ crystal growth. Crystal Research and Technology, 2003, 38(7, 8): 716–725

[5] Krauze A, Muiznieks A, Muhlbauer A, Wetzel T. Ammon W. Numerical 3D modelling of turbulent melt flow in large CZ system with horizontal DC magnetic field I. Flow structure analysis. Journal of Crystal Growth, 2004, 262(1-4): 157–167

[6] Atherton L J, Derby J J, Brown R A. Radiative heat exchange in Czochralski crystal growth. Journal of Crystal Growth, 1987, 84(1): 57–78

[7] Dupret F, Nicodeme P, Ryckmans Y, Wouters P, Crochet M J. Global modelling of heat transfer in crystal growth furnaces. International Journal of Heat and Mass Transfer, 1990, 33(9): 1849–1871

[8] Li M W, Li Y R, Imaishi N, Tsukada T. Global simulation of a silicon Czochralski furnace. Journal of Crystal Growth, 2002, 234(1): 32–46

[9] Kalaev V V, Evstratov I Yu. Makarov Yu N. Gas flow effect on global heat transport and melt convection in Czochralski silicon growth. Journal of Crystal Growth, 2003, 249(1, 2): 87–99

[10] Liu L J, Kakimoto K. Partly three-dimensional global modeling of a silicon Czochralski furnace I. Principles, formulation and implementation of the model. International Journal of Heat and Mass Transfer, 2005, 48(21, 22): 4481–4491

[11] Liu L J, Kakimoto K. Partly three-dimensional global modeling of a silicon Czochralski furnace II. Model application: Analysis of a silicon Czochralski furnace in a transverse magnetic field. International Journal of Heat and Mass Transfer, 2005, 48(21, 22): 4492–4497

[12] Kakimoto K, Liu L, Miyazawa H, Nakano S, Kashiwagi D, Chen X J, Kangawa Y. Numerical investigation of crystal growth process of bulk Si and nitrides-a review. Crystal Research and Technology, 2007, 42(12): 1185–1189

[13] Kashiwagi D, Gejo R, Kangawa Y, Liu L J, Kawamura F, Mori Y, Sasaki T, Kakimoto K. Global analysis of GaN growth using a solution technique. Journal of Crystal Growth, 2008, 310(7-9): 1790–1793

[14] Chen X J, Liu L J, Tezuka H, Usuki Y, Kakimoto K. Numerical investigation of induction heating and heat transfer in a SiC growth system. Crystal Research and Technology, 2007, 42(10): 971–975

[15] Chen X J, Liu L J, Tezuka H, Usuki Y, Kakimoto K. Optimization of the design of a crucible for a SiC sublimation growth system using a global model. Journal of Crystal Growth, 2008, 310(7-9): 1810–1814

[16] Liu L J, Kakimoto K. 3D global analysis of CZ-Si growth in a transverse magnetic field with rotating crucible and crystal. Crystal Research and Technology, 2005, 40(4, 5): 347–351

[17] Liu L J, Nakano S, Kakimoto K. An analysis of temperature distribution near the melt-crystal interface in silicon Czochralski growth with a transverse magnetic field. Journal of Crystal Growth, 2005, 282(1, 2): 49–59

[18] Liu L J, Nakano S, Kakimoto K. Investigation of oxygen distribution in electromagnetic CZ-Si melts with a transverse magnetic field using 3D global modeling. Journal of Crystal Growth, 2007, 299(1): 48–58

[19] Liu L J, Nakano S, Kakimoto K. Three-dimensional global modeling of a unidirectional solidification furnace with square crucibles. Journal of Crystal Growth, 2007, 303(1): 165–169

[20] Liu L J, Nakano S, Kakimoto K. Dynamic simulation of temperature and iron distributions in a casting process for crystalline silicon solar cells with a global model. Journal of Crystal Growth, 2006, 292(2): 515–518

[21] Liu L J, Nakano S, Kakimoto K. Carbon concentration and particle precipitation during directional solidification of multi-crystalline silicon for solar cells. Journal of Crystal Growth, 2008, 310(7-9): 2192–2197

[22] Miyazawa H, Liu L J, Hisamatsu S, Kakimoto K. Numerical analysis of influence of tilt of crucibles on interface shape and fields of temperature and velocity in a unidirectional solidification process. Journal of Crystal Growth, 2008, 310(6): 1034–1039

[23] Evstratov I Yu, Kalaev V V, ZhmakinA I,MakarovYu N,AbramovA G,IvanovN G,SmirnovE M,DornbergerE,VirbulisJ,TomzigE,von AmmonW. Modeling analysis of unsteady three-dimensional turbulent melt flow during Czochralski growth of Si crystals. Journal of Crystal Growth, 2001, 230(1, 2): 22–29

[24] Hirata H, Hoshikawa K. Oxygen incorporation and melt convection in CZ silicon crystal growth. Journal of the Japanese Association of Crystal Growth, 1988, 15(2): 207–216

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 50876084), NCET-08-0442, RFDP (No. 20100201110016) and the Fundamental Research Funds for the Central Universities of China.

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg