Abstract
Mathematical Modeling of Solid-Liquid Interface Morphology in The Process of Polycrystalline Silicon Directional Solidification
Highlights
Directional solidification is an important process in the physical purification of polycrystalline silicon, the solid-liquid interface morphology in solidification process is directly related to grain size arrangement, grain length and stress distribution [1,2], the study of the solid-liquid (S-L) interface morphology has important technological value for improving the quality of purification
The theoretical research of S-L interface in directional solidification is often simulated by numerical simulation software [3,4], but the numerical method cannot reveal the intrinsic relation of the parameters, and the analytic method is almost ignored [5,6]
The S-L interface occupies only a thin area of the silicon melt, the vertical axis of the melt is set to y, using the symmetry of the crucible
Summary
Directional solidification is an important process in the physical purification of polycrystalline silicon, the solid-liquid interface morphology in solidification process is directly related to grain size arrangement, grain length and stress distribution [1,2], the study of the solid-liquid (S-L) interface morphology has important technological value for improving the quality of purification. The analytic method, as an exact solution, has an irreplaceable use for the design, process control and experiment of the directional solidification Equipment. Because the latent heat is released in solidification process, the system has an internal thermal source, so the temperature field satisfies the Poisson. 1. When the q > 0, the heat flux is the x axis positive direction, this means that the computational area is losing heat; 2. When q < 0, the heat flux direction is negative along the x axis, this means that the computational area is obtaining heat; 3. Mathematical Modeling of Solid-Liquid Interface Morphology in The Process of Polycrystalline Silicon Directional Solidification. ∑ u = (A0x + B0 )(C0 y + D0 )+ [Ansh(knx) + Bn c h(knx)][Cn sin(kn y) + Dn cos(kn y)] [23] the analytic solution of Eq (7) can be deduced by Eq (35). Eq (23) can be transformed into expression t(x,y) in computational area can be obtained
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