Influences of growth front surfaces on the grain boundary development of multi-crystalline silicon during directional solidification: 2D/3D multi-phase-field study

In order to control the grain structure of multi-crystalline silicon during directional solidification, the development process of grain boundaries (GBs) should be more fully understood. A phase-field model incorporated with anisotropic surface energy and anisotropic attachment kinetic coefficient has produced the silicon crystal shape, which agrees well with the experimental observation. In the growth simulation of coupled silicon grains, the morphology of the growth front surfaces and the development of the GBs are found to be influenced by the growth mode of the groove surfaces, which swings between the kinetic mode and energetic mode, depending on both the orientation relationship and cooling condition. The simulation of the growth of three grains in 3D provides a more complete view of the grain structure with grain-grain-liquid and grain-grain-grain triple lines, which are absent in the two-dimensional observations. The phase-field model developed in this work can be used for predicting GB development and the formation of the grain structure of multi-crystalline silicon, which can potentially contribute to the production of high-efficiency and low-cost solar cells.