Dynamic scaling in thin-film growth with irreversible step-edge attachment

Abstract

We study dynamic scaling in a model with collective diffusion (CD) of isolated atoms in terraces and irreversible aggregation at step edges. Simulations are performed in two-dimensional substrates with several diffusion to deposition ratios R identical with D/F. Data collapse of scaled roughness distributions confirms that this model is in the class of the fourth-order nonlinear growth equation by Villain, Lai, and Das Sarma (VLDS) with negligible finite-size effects, while estimates of scaling exponents show some discrepancies. This result is consistent with the prediction of a recent renormalization group approach and improves previous numerical works on related models. The roughness follows dynamic scaling as W=Lalpha/R1/2f(xi/L), with correlation length xi=(Rt)1/z, where z is the dynamic exponent. We also propose a limited mobility (LM) model where the incident atom executes up to G steps before a new atom is adsorbed, and irreversibly aggregates at step edges. This model is also shown to belong to the VLDS class. The size of the plateaus in the film surface increases as G1/2 and the lateral correlation scales as G1/2t1/z. The time evolution of the roughness reproduces that of the CD model if an equivalent parameter G approximately R2/z is chosen. This suggests the possibility of using LM models with tunable diffusion length to simulate processes with simultaneous diffusion of many atoms. A scaling approach is used to justify exponent values and dynamic relations for both models, including the significant decrease of surface roughness as R or G increases.