Numerical Study of Impurity-Induced Growth Hysteresis on a Growing Crystal Surface

Growth hysteresis is one of the remarkable phenomena of crystal growth induced by impurities; namely, the growth rates of crystal take different values between when supersaturation is decreased and is increased. The appearance of hysteresis has been explained on the basis of the mean field theory, in which the physical quantities such as step velocity, step interval, and density of impurities adsorbed on the crystal surface are averaged over space and time. Here, we propose a new method for the numerical simulation of step dynamics with impurity adsorption–desorption kinetics on a growing crystal surface. We numerically reproduce the growth hysteresis in a more realistic situation, in which the physical quantities fluctuate. The calculated hysteresis agrees with the prediction of the mean field theory. We have also found that the supersaturation should be changed within a period that is similar to the impurity adsorption time scale or slightly longer in order to observe obvious growth hysteresis. Measurement of growth hysteresis may be useful in obtaining data of impurity adsorption–desorption kinetics