Numerical Investigation of Macro-Scale Step Morphology in Long-Term Solution Growth of SiC

During the solution growth of off-axis SiC crystal, undesirable step morphology on the growth interface, namely excessive step bunching and inhomogeneous distribution, strongly affects the quality of bulk crystal by introducing defects like inclusion and 2D nucleation. Previous study has investigated the effect of flow direction on local step behavior, but for practical growth of large-scale crystal, it is crucial to understand the relationship between the macroscopic controlling parameters and global step morphology to maintain a smooth and uniform step distribution on the whole crystal surface.<br/>In this study, a numerical method was proposed to investigate the relationship between macroscopic controlling parameters (e.g., crystal&crucible rotation speed, and growth temperature) and macro-scale step morphology evolution during solution growth of SiC crystal. This simulation method comprises two parts: a 2D global steady CFD model to calculate the temperature, flow and carbon concentration fields inside the growth system under certain controlling parameters, and a 3D local transient CFD model to calculate the surface step kinetics coupled with the carbon transport near the crystal. The boundary conditions of the 3D simulation are extracted from the 2D simulation result, and one macro-scale “step” on the crystal surface is assumed as the aggregation of <i>n</i> atom-scale steps.<br/>A 2-inch SiC solution growth system was taken as an example. Parameter studies were conducted to illuminate the effects of crystal&crucible rotation and growth temperature on step morphology evolution, which match well with the experiment results in previous studies. Moreover, two improved unsteady rotation patterns were proposed and it was found that by periodically rotating the crystal and cruicble in both CW and CCW directions, step distribution on the whole grown surface is more homogeneous without local intense bunching, which presents better long-term stability. The simulation results were also validated by experiments.