The dependence of the crystallization front shape on the heat exchange regime in the Bridgman-Stockbarger method
DOI:
https://doi.org/10.7242/1999-6691/2019.12.1.10Keywords:
crystal growth from the melt, the Bridgman-Stockbarger method, conjugate convective heat transfer, the phase transition heat, numerical simulation, the finite element methodAbstract
The growth of a silicon ingot in the Bridgman-Stockbarger crystal-melt-crucible system, similar to that used in real technology is studied numerically in the axisymmetric formulation by the finite element method. The simulation was carried out taking into account the heat of phase transition under conditions of unsteady thermal conductivity and natural convection at the initial heating of the melt up to 40 K and two rates of crucible lowering. The temperature gradient along the lower part of the side wall of the crucible is linear and equal to 35 K/cm or 70 K/cm. A comparison between the crystallization processes in the unsteady heat conduction regime and the natural convection regime is carried out. The dependence of the shape of the crystallization front on the heat transfer modes is investigated. It has been shown that in all heat conduction modes being considered, the crystallization front has a convex shape during the entire crystallization process. Moreover, the shape of the crystallization front in the examined range of parameters weakly depends on the crucible lowering rate, but is drastically influenced by the temperature gradient on the crucible walls. Under conditions of hermogravitational convection the shape of the crystallization front strongly depends on the crucible lowering rate and temperature gradient on the side walls of the crucible. At some parameters, a secondary convective vortex can be generated over the crystal during the crystallization process. Depending on the combinations of temperature gradient on the side walls and the lowering rate of the crucible, the shape of the crystallization front can be either concave or convex.
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