Nonequilibrium capture of impurities that completely block kinks during crystal growth

Abstract

Some impurities cannot integrate into isolated kinks because they completely block the growth of the kinks to which they adsorb. For this class of impurity, we derive an equation for the amount that incorporates into a crystal during growth of the elementary step by assuming that such an impurity incorporates if and only if it gets captured between a kink and an antikink. We show that the impurity concentration in the crystal increases monotonically with the impurity concentration in the mother phase, but that it can vary non-monotonically with both the supersaturation of the mother phase and the kink density of the step. In contrast to other capture mechanisms, we find that weakly adsorbed impurities incorporate to an extent that is independent of the supersaturation when the supersaturation is high. Irrespective of the growth conditions, the amount of impurity that can incorporate into a crystal is limited by an upper bound determined by the kink density.