With a reasonable balance between cost and efficiency, multicrystalline silicon (mc-Si) has been a mainstream material for solar cells, and these cells make up approximately 50% of the market of today’s photovoltaics industry. There are significant opportunities for increasing quality and reducing cost of the mc-Si substrate material via a better understanding of crystal growth processes. One challenge is the formation of silicon carbide and silicon nitride precipitates in the melt due to carbon and nitrogen impurities coupled with their relatively small segregation coefficients. These solid particles can be engulfed by the solidification front to form inclusions in the mc-Si solid. The presence of inclusions lowers cell efficiency and can lead to wafer breakage and sawing defects, even breakage of the wire saw.

To better understand the physical mechanisms responsible for these inclusions, we are applying finite-element, moving-boundary analyses to assess particle dynamics during engulfment via solidification fronts.  Two-dimensional steady-state and dynamic models are developed using the Galerkin finite element method and elliptic mesh generation techniques.  Such an approach is particularly well suited for rigorous and accurate representation of geometrical and interfacial interactions in this system, and we demonstrate how this model is able to represent very large deformations of the melt-solid interface during the process of engulfing a solid particle.

We discuss model formulation, implementation, validation, and its performance with respect to prior models of this process. We also present initial results to investigate various factors' influence on particle-solidification front dynamics, such as i) particle size, ii) different materials’ densities and thermal conductivities, iii) interfacial premelting, iv) Gibbs-Thomson effects, v) temperature gradient, vi) gravity, and vii) the bulk flow caused by the density change upon solidification. Criteria to establish the all-important pushing/engulfing transition of a particle near a solid-melt interface are investigated via transient simulations. The significance of introducing a premelting film into the system is also discussed.

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Supported in part by U.S. National Aeronautics and Space Administration, NNX10AR70G, the content of which does not necessarily reflect the position or policy of the United States Government, and no official endorsement should be inferred.

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