Persistence probabilities of height fluctuation in thin film growth using discrete models with up-down symmetry

Abstract

The problem of persistence of height fluctuations in non-equilibrium surface growth and interface dynamics has been widely studied in recent years. The persistence concept is interesting theoretically and also has practical applications in many areas. The persistence probability is the probability that the height fluctuation of a growing film does not return to its initial value over a specified time interval. For several models of surface growth, the persistence probability decreases in time as a power law. The persistence probability and the corresponding exponents appear to change when the initial height changes. The persistence probability also depends on the discrete sampling time (discrete time interval between two measurements used to calculate the persistence probability). The main purpose of this study is to understand how the persistence probability of up-down symmetric models change as the initial height and the discrete sampling time are varied and determine a scaling description for it. Another goal is to study effects of patterned substrate. The healing times of thin films simulated by Family and Das Sarma-Tamborenea models grown on the smooth triangular substrate, and the rough pillar and groove substrate are studied. The healing time is the time when influences of the initial pattern in the substrate disappear and characteristics of the growing interface are healed to those obtained by a film grown on a flat substrate. The healing time is determined via the study of the nearest-neighbor height difference correlation function. The theoretical solution of the correlation function describing dynamics of film surface of the Family model grown on both patterns is also investigated.