Persistence of height fluctuation in molecular-beam epitaxy model

Abstract

Persistence probability is an interesting quantity in stochastic process which is the dynamics of surface growth in this study. Persistence probability of height f luctuation is the probability that the height fluctuation does not return to its initial value throughout a time interval. In this work, we use a numerical simulation approach to investigate the persistence probability in Molecular-Beam Epitaxy (MBE) model which is associated with Molecular-Beam Epitaxy technique. First half, we study the effects of temperature and deposition rate on the growth exponent () and persistence exponent (). For the temperature corresponds to 1 diffusion length, we get 017 and positive steady-state persistence exponent, S+ 078. When the temperature increases, the growth exponent value decreases while the persistence exponent rises. The same results happen when the deposition rate is decreased. On the second half, we investigate how the persistence probabilities change with a particular initial value of height fluctuation. The negative persistence probability of positive initial height shows power lawwhentheinitial height is slightly greater than sat. The positive persistence probability of negative initial height does not show power law decay unless the initial height is much greater than sat. We measure the relationship of persistence probability on initial height fluctuation (0), system size, and discreate sampling time to investigate the scaling relation. The persistence probability is a function of three parameters.