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In systems where deposition rates are high compared to diffusion, desorptionand other mechanisms that generate correlations, a crossover from random tocorrelated growth of surface roughness is expected at a characteristic timet_0. This crossover is analyzed in lattice models via scaling arguments, withsupport from simulation results presented here and in other authors works. Weargue that the amplitudes of the saturation roughness and of the saturationtime scale as {t_0}^{1/2} and t_0, respectively. For models with lateralaggregation, which typically are in the Kardar-Parisi-Zhang (KPZ) class, weshow that t_0 ~ 1/p, where p is the probability of the correlated aggregationmechanism to take place. However, t_0 ~ 1/p^2 is obtained in solid-on-solidmodels with single particle deposition attempts. This group includes models invarious universality classes, with numerical examples being provided in theEdwards-Wilkinson (EW), KPZ and Villain-Lai-Das Sarma (nonlinear molecular-beamepitaxy) classes. Most applications are for two-component models in whichrandom deposition, with probability 1-p, competes with a correlated aggregationprocess with probability p. However, our approach can be extended to othersystems with the same crossover, such as the generalized restrictedsolid-on-solid model with maximum height difference S, for large S. Moreover,the scaling approach applies to all dimensions. In the particular case ofone-dimensional KPZ processes with this crossover, we show that t_0 ~ nu^{-1}and nu ~ lambda^{2/3}, where nu and lambda are the coefficients of the linearand nonlinear terms of the associated KPZ equations. The applicability ofprevious results on models in the EW and KPZ classes is discussed.Comment: 14 pages + 5 figures, minor changes, version accepted in Phys. Rev.

Scaling in the crossover from random to correlated growth