Abstract
A modeling approach combining the lattice Boltzmann (LB) method and the cellular automaton (CA) technique are developed to simulate the faceted front to equiaxed structure transition (FET) of directional solidification of multi-crystalline silicon. The LB method is used for the coupled calculation of velocity, temperature and solute content field, while the CA method is used to compute the nucleation at the silicon-crucible interface and on SiC particles, as well as the mechanism of growth and capturing. For silicon, the interface kinetic coefficient is rather low, which means that the kinetic undercooling can be large. A strong anisotropy in the surface tension and interfacial kinetics are considered in the model. A faceted front in conjunction with a sufficiently high carbon content can lead to equiaxed growth by nucleation on SiC. The temperature gradient in Si melt at the interface is negative, which leads to the occurrence of a faceted interface. The higher the absolute value of thermal gradients, the faster the growth velocity. Due to differences in the degree of undercooling, there will be the unification of facets in front of the solid-liquid interface. Transitions from faceted front to thermal equiaxed dendrites or faceted equiaxed grains are observed with smaller or larger impurity contents, respectively.
Highlights
Multi-crystalline solidification of silicon is a low-cost way of producing photovoltaic cells it is less efficient than single crystalline silicon [1]
In order to verify the correctness of the cellular automaton (CA) model for faceted growth, this paper simulates the faceted growth for strong anisotropy of kinetic coefficient and compares the simulation results with faceted growth for strong anisotropy of kinetic coefficient and compares the simulation results with the literature and experimental observations
We simulate the transition of a planar faceted front to equiaxed growth in directional solidification of a multi-crystalline silicon ingot using a CA-lattice Boltzmann (LB)
Summary
Multi-crystalline solidification of silicon is a low-cost way of producing photovoltaic cells it is less efficient than single crystalline silicon [1]. Hwang [11] developed a three-dimensional cellular automaton-finite element (CA-FE) model to simulate the microstructural evolution of multi-crystalline silicon ingots This model can represent the occurrence of equiaxed grains observed ahead of a planar faceted interface due to carbon segregation during solidification. Zhao et al [15] set up a three-dimensional cellular automaton (CA) model to simulate the microstructure change of iron carbon alloy in the solidification process This model took into account the solid-liquid interface curvature, surface energy and dendrites anisotropy. In this work, a new cellular automaton-lattice Boltzmann (CA-LB) model was established for calculating the transition of the planar faceted front of columnar grains to equiaxed growth in the directional solidification of a multi-crystalline silicon ingot, which is on the basis of exploring the calculation of faceted interface of multi-crystalline silicon with cellular automaton (CA) method
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