Phase Field Modeling of Twin-related Faceted Dendrites

Dendritic growth behaviors of semiconductors (e.g. Si and Ge) have attracted much attention due to their unique crystal morphologies. The appearance of the dendrite is bounded by habit planes, and more than two parallel twin planes can be found at the center of these dendrites. The growth orientation of twin-related faceted silicon dendrites depends on the undercooling ΔT in the melt, which cannot be explained by the existing models. The aim of this thesis is to investigate the faceted dendrite growth via our phase field model. In this study, we first investigate the faceting condition for equilibrium shapes and dynamic situations. We propose a new anisotropic function of surface energy for the phase-field simulations in three dimensions, and negative stiffness is further considered. Then we investigate the growth of a twin-related silicon dendrite through a novel phase field model. The correctness of the model for an equilibrium twined crystal is examined first before we model the faceted dendrite growth. The simulated morphologies of <112> and <110> faceted dendrites are consistent with experimental observations. The growth orientation of the simulated dendrite depend on the growth rates at the ridges and the re-entrant corners. Moreover, we propose a model to explain the growth behavior showing that the re-entrant corners would lead to the growth of <112> dendrites, while the <110> branch is due to continuous growth. Such a selection could be determined by the velocity ratio Vre-entrant/Vridge that is a function of ΔT. An analytical expression for this ratio is derived and compared to the experimental observations.