Dynamic scaling and temperature effects in thin film roughening. (12th June 2015) - Assis, T A de; Aarão Reis, F D A
Abstract: The dynamic scaling of mesoscopically thick films (up to 10 4 atomic layers) grown with the Clarke–Vvedensky model is investigated numerically in 2 + 1 dimensions for broad ranges of values of the diffusion-to-deposition ratio R and lateral neighbor detachment probability ϵ, but with no barrier at step edges. The global roughness scales with the film thickness t as W  ∼  t β /[ R 3/2 ( ϵ  +  a )], where β  ≈ 0.2 is the growth exponent consistent with Villain–Lai–Das Sarma (VLDS) scaling and a  = 0.025. This general dependence on R and ϵ is inferred from renormalization studies and shows a remarkable effect of the former but a small effect of the latter, for ϵ  ⩽ 0.1. For R  ⩾ 10 4, very smooth surfaces are always produced. The local roughness shows apparent anomalous scaling for very low temperatures ( R  ⩽ 10 2 ), which is a consequence of large scaling corrections to asymptotic normal scaling. The scaling variable R 3/2 ( ϵ  +  a ) also represents the temperature effects in the scaling of the correlation length and appears in the dynamic scaling relation of the local roughness, which gives dynamic exponent z  ≈ 3.3 also consistent with the VLDS class.