Dynamic scaling and temperature effects in thin film roughening

The dynamic scaling of mesoscopically thick films (up to 104 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 , but with no barrier at step edges. The global roughness scales with the film thickness t as W ~ tβ/[R3/2( + 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 is inferred from renormalization studies and shows a remarkable effect of the former but a small effect of the latter, for ≤ 0.1. For R ≥ 104, very smooth surfaces are always produced. The local roughness shows apparent anomalous scaling for very low temperatures (R ≤ 102), which is a consequence of large scaling corrections to asymptotic normal scaling. The scaling variable R3/2( + 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.