2D and 3D Modeling of Directional Solidification of Multi-Crystalline Silicon Ingots
Directional Solidification (Casting) of silicon in squared large-scale crucibles is a cost effective technique to grow multi-crystalline Si ingots, which are used to make wafers for solar cells. Crystallization of silicon is initiated on the bottom of the crucible and is maintained in vertical direction by decreasing the heater powers and/or moving of insulation or crucible.
Example of 2D unsteady modeling of DS of multi-Si in CGSim
On the right you can see the animated results of computer modeling: the temperature distributions in the furnace, melt and gas flows, crystallisation process simulated with CGSim software.
Crystallization front predictions
It is quite important to keep crystallization front geometry close to a flat shape, especially during the beginning of crystallization. A concave melt/crystal interface results in decreasing grain size and deteriorating wafer quality. CGSim can predict geometry of the melt/crystal interface very well. Below you can see comparison of the computed profile to the experimental data published in : the interface is flat in the center of the crystal with larger grain size and concave in the crystal periphery with a smaller grain size.
Global heat transfer, flows, and crystallization dynamics in a DS system (P = 50000 Pa, Vinlet = 0.3 m/s, Process time: 25 h, Vcryst about 15 mm/h). Furnace design 
Four large vortices are observed in the melt as the combined effect of buoyancy and Marangoni surface tension
Comparison of experiment by SAS (left) and simulation results (right). Vertical cut of the ingot is 250x700x700 mm. Data: Y. Y. Teng et al., Proceedings of PVSEC-18 conference
Species transport and segregation
Oxygen, nitrogen, carbon transport and segregation during crystallization are very important for avoiding SiC, Si3N4, and Si2N2O particles formation in the melt and their incorporation into the crystal. Formation of particles along the melt/crystal interface dramatically decreases grain size in the ingot and deteriorates wafer quality. CGSim is a robust tool to simulate species transport including chemical reactions in the melt and gas. 2D or fully 3D unsteady approximations can be used for modeling of convection, diffusion, and segregation of species (see below). As an example, SiO transport in the gas is coupled to oxygen transport in the melt flow via relations of mass fluxes and equilibrium concentrations along the melt/crystal interface, considering deposition reactions on reactor walls .
The results of 3D unsteady computation considering heat transfer, melt flow, and carbon mass transfer including the effect of species segregation along moving melt/crystal interface is shown below. By melt flow engineering, carbon concentration in the melt can be managed to be lower than the equilibrium solubility level to avoid formation of SiC particles in the crystal.
The model of carbon segregation illustrated here was successfully verified and used for technology optimization in . The authors of  report 10% decrease of carbon concentration in the crystal by using CGSim modeling results, which was obtained by modifications changing the melt flow and crystallization front profile.
3D computational grid of crystallization domain and gas flow above the melt free surface
Carbon concentration distribution in a vertical cross section of growing crystal computed in 3D unsteady approximation
Comparison of experimental and computed vertical carbon concentration profiles in the crystal grown with standard and optimized conditions
3D analysis of heater design in a DS system
STR provides advanced research and consulting projects to study and to optimize crystal growth from the melt and solution. Illustrated here is a detailed study of 3D features of heater design and cooling of graphite rods supplying electric current to the side and top heaters of a Directional Solidification System (see  for details of the DSS).
Depending on a heater design and engineering of electric current supply, there is particular generation of the Lorenz force in the melt flow as a result of electro-magnetic interactions between heaters and other conductive materials. The Lorenz force can change considerably the melt flow, heat, and mass transfer , affecting crystallization front geometry and effective segregation of impurities.
Top: Temperature distribution in the heater and crucible
Left: Temperature distribution in the DSS furnace
 Bei Wu et al., Journal of Crystal Growth, Volume 310, Issues 7-9, pp. 2178-2184
 “Crystalline front control of growing multicrystalline Si ingots during the directional solidification process” ,Ying-Yang Teng, Jyh-Chen Chen, Chung-Wei Lu, V.V. Kalaev and S. E. Demina, 18th International photovoltaic Science and Engineering, PVSEC, January 19-23, 2009, Kolkata, India
 “Analysis of impurity transport and deposition processes on the furnace elements during Cz silicon growth”, AD Smirnov, VV Kalaev, Journal of Crystal Growth, Volume 311, 2009, pp. 829–832
 “The carbon distribution in multicrystalline silicon ingots grown using the directional solidification process“, Ying-Yang Teng, Jyh-Chen Chen, Chung-Wei Lu, Chi-Yung Chen, Journal of Crystal Growth, Volume 312, Issue 8, April 2010, pp. 1282-1290
”Computer modeling of diamond single crystal growth by the temperature gradient method in carbon-solvent system“, S.E. Demina, V.V. Kalaev, V.V. Lysakovskyi, M.A. Serga, T.V. Kovalenko, S.A. Ivahnenko, Journal of Crystal Growth, 311 (2009) p.680