e for diffusion in DT when a single lateral bound is enough to irreversibly stick the adatom on a site. In the WV case, where diffusion happens more readily, mound morphologies with quasiregular structures emerge more clearly.

![\[hh\_corr\_Ns\] Main plot: Height-height correlation function dependence with the parameter $N_s$ (indicated in the legends) for the WV model in two-dimensional substrates at a time $t=10^5$. Inset: Same as the main plot for one dimension at a time $t=10^7$. Curves correspond to averages over 100 independent samples.](gamma_wv2d1d.pdf){width="0.8\linewidth"}

A standard tool to characterize the morphology of interfaces in growth process is the height-height correlation function defined as [@Evans2006; @Murty2003; @Chatraphorn2001] $$\Gamma({\mathbf}r) = \left\langle \tilde h({\mathbf}x) \tilde h({\mathbf}x + {\mathbf}r) \right\rangle_x,$$ here $\tilde h({\mathbf}x)$ is the height interface at position ${\mathbf}x$ relative to the mean height and $\left\langle \ldots \right\rangle_x$ denotes an average over the surface. The height-height correlation for ${\mathbf}r = 0$ is related to the interface width by $$\sqrt{\left\langle\Gamma(0)\right\rangle} = w$$ here $\left\langle\ldots\right\rangle$ denotes an average over independent runs. A self-affine interface is characterized by a height-height correlation function that goes monotonically to zero while those characterized by mounds exhibit oscillatory behavior around $0$. In the latter case, the first zero of $\Gamma(r)$, denoted by $\xi$, is a characteristic lateral length of the mounds in the surface.

Figure \[hh\_corr\_time\] shows the height-height correlation function for the WV model with kinetic barrier in one- and two-dimensional substrates. The curves clearly exhibit oscillatory behavior even for averages over 100 independent samples. Conversely, the irregular oscillatory behavior observed for the original WV model shown in insets of Fig. \[hh\_corr\_time\] is lumped after averaging. Therefore, interfaces obtained with kinetic