Phase-Field Modeling of Step Dynamics on Growing Crystal Surface: Step Pinning Induced by Impurities

The step pinning hypothesis is widely accepted as an explanation for the inhabitation of crystal growth by impurity molecules. This hypothesis enables us to evaluate the average step velocity and the critical impurity density above which no step can move on the crystal surface polluted by impurities. The average step velocity and the critical impurity density were obtained analytically in some literature; however, they have not been verified with other approaches. Here, we propose a new method for the numerical simulation of the step pinning by impurities in the framework of a phase-field technique and report a quantitative study on the average step velocity and critical impurity density for the first time. Our results clarify the limitations of the physical assumptions of the analytical formulas and their applications. Our phase-field method provides a good numerical tool for the quantitative investigation of the effect of impurities on step dynamics if step pinning works as described in the Cabrera–Vermilyea model