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Frontiers in Energy

Front Energ    2011, Vol. 5 Issue (3) : 305-312
Computer modeling of crystal growth of silicon for solar cells
Lijun LIU1(), Xin LIU1, Zaoyang LI1, Koichi KAKIMOTO2
1. MOE Key Laboratory of Thermo-Fluid Science and Engineering, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China; 2. Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan
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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     
Corresponding Authors: LIU Lijun,   
Issue Date: 05 September 2011
 Cite this article:   
Lijun LIU,Xin LIU,Zaoyang LI, et al. Computer modeling of crystal growth of silicon for solar cells[J]. Front Energ, 2011, 5(3): 305-312.
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Lijun LIU
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Fig.1  Configuration and computational mesh of a DS furnace
(a) Configuration; (b) global mesh; (c) local mesh
Fig.2  Configuration, domain partition, and computational mesh of a CZ furnace
(a) Configuration and domain partition; (b) local view of the 2D/3D mesh
Fig.3  Dynamic behavior of the thermal field and mc interface of an industrial CZ-Si growth process
(a)–(c) dynamic behavior of the thermal field; (d) mc interface
Fig.4  3D features of TMCZ-Si growth
(a) Melt convection, thermal field, and mc interface profiles in symmetric planes (right) =0 and =0 (left); (b) a local view of the mc interface and the temperature distribution on the melt top surface
Fig.5  Instability of the melt flow of large volume
(a) Fluctuation of temperature; (b) fluctuation of radial velocity; (c) fluctuation of azimuthal velocity; (d) fluctuation of axial velocity
Fig.6  Temperature and oxygen distributions in the melt of an EMCZ-TMF configuration
(a) Temperature; (b) oxygen
Fig.7  Thermal fields in the furnace
(a) Temperature distribution and flow fields in the furnace; (b) temperature distribution in the melt, crystal, crucibles, and pedestal (unit of temperature, K)
Fig.8  Melt-solid interface shape, temperature distributions in the melt-crystal domain, and melt convective flow field
(a) Interface profiles and temperature distributions on the boundary surfaces of the melt-crystal domain; (b) velocity fields of the melt flow in three perpendicular cross-planes
Fig.9  Impurity distributions
(a) Distribution of iron concentration in a solidified silicon ingot (atom/cm); (b) distributions of substitutional carbon (left) and SiC particles (right) in a cross-plane of a solidified ingot ()
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