Effects of surface diffusion length on steady-state persistence probabilities

The dependence of the steady-state persistence probabilities (P s ) and exponents (θ s ) on surface diffusion length ( l ) for four discrete growth models is investigated. The persistence exponents which describe the decay of the persistence probabilities, the probabilities of the average of all initial height ( h 0 ), are increased as l is increased for all models. The results of one-dimensional Family ((1+1)-Family) and Das Sarma-Tamborenea ((1+1)-DT) models with kinetically rough film surface show the decrease of the growth exponent (β) with l . The l >1 results preserve the relation β = max [ 1 − θ + S , 1 − θ − S ] . In contrast, β is observed to increase with l for the two-dimensional larger curvature ((2+1)-LC) and Wolf-Villain ((2+1)-WV) models with mounded morphology. Our results show that the β = max [ 1 − θ + S , 1 − θ − S ] relation is not valid in l >1 cases in models with mounded surfaces. The persistence probabilities of a specific value of initial height ( P s ( h 0 )) for l >1 are found to behave differently between mounded and kinetically rough models.