Skewness and kurtosis of height distribution of thin films simulated by larger curvature model with noise reduction techniques

Abstract

Time varying skewness (S) and kurtosis (Q) of height distribution of (2+1)-dimensional larger curvature (LC) model with and without noise reduction techniques (NRTs) are investigated in both transient and steady state regimes. In this work, effects of the multiple hit NRT (m>1 NRT) and the long surface diffusion length NRT (ℓ>1 NRT) on the surface morphologies and characteristics of S and Q are studied. In the early growth time, plots of S and Q versus time of the m>1 morphologies show pronounced oscillation indicating the layer by layer growth. Our results show that S=0 and Q<0 at every half layer while S=0 and Q>0 at every complete layer. The results are confirmed by the same plots of the results from the Das Sarma–Tamborenea (DT) model. The ℓ>1 LC model, on the other hand, has no evidence of the layer by layer growth mode due to the rapidly damped oscillation of S and Q. In the steady state, the m>1 and ℓ>1 NRTs affect weakly on the values of S and Q and the mounded morphologies of the film. This lead to the evidence of universality of S and Q in the steady state of the LC models with various m and ℓ. The finite size effect on the values of S and Q is found to be very weak in the LC model. By extrapolating to L→∞, we obtain SL→∞≈0.05 and QL→∞≈−0.62 which are in agreement with the NRTs results.