Dynamic scaling and temperature effects in thin film roughening

Abstract

The dynamic scaling of mesoscopically thick films (up to $10^{4}$ atomic layers) grown with the Clarke-Vvedensky model is investigated numerically for broad ranges of values of the diffusion-to-deposition ratio $R$ and lateral neighbor detachment probability $\epsilon$, but with no barrier at step edges. The global roughness scales with the film thickness $t$ as $W \sim t^{\beta}/\left[R^{3/2}\left(\epsilon + a\right)\right]$, where $\beta \approx 0.2$ is the growth exponent consistent with Villain-Lai-Das Sarma (VLDS) scaling and $a=0.025$. This general dependence on $R$ and $\epsilon$ is inferred from renormalization studies and shows a remarkable effect of the former but a small effect of the latter, for $\epsilon\leq 0.1$. For $R\geq {10}^4$, very smooth surfaces are always produced. The local roughness shows apparent anomalous scaling for very low temperatures ($R\leq {10}^2$), which is a consequence of large scaling corrections to asymptotic normal scaling. The scaling variable $R^{3/2}\left( \epsilon + a\right)$ 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 $z\approx 3.3$ also consistent with the VLDS class.