Application of weighted Voronoi diagrams to analyze nucleation sites of multicrystalline silicon ingots

Analysis of nucleation sites in multicrystalline silicon (mc-Si) grown by directional solidification is required for further grain refinement to reduce dislocation density. In this study, Voronoi diagrams were utilized to analyze nucleation sites of mc-Si grown by single-layer Si beads (SLSB)-seeding method. The grain distribution at the bottom of the ingot was almost reproduced by the weighted Voronoi diagram with a relaxation method to optimize the positions of generating points of the diagram, which correspond to the nucleation sites, and the difference of nucleation timing of each crystal grain. Comparison of the generating points with the optical image indicated that the nucleation started at the remarkably deep portions of the nucleation layer. Further grain refinement by SLSB-seeding method could be achieved by suppressing the formation of the remarkably deep portions of the nucleation layer.