Kinetic Roughening in Growth Models with Diffusion in Higher Dimensions

TL;DR

This paper investigates kinetic roughening in higher-dimensional growth models with surface diffusion, revealing larger effective exponents and growth instabilities that lead to mound formation, with implications for understanding surface evolution.

Contribution

It provides numerical simulation results of the Wolf-Villain model in 3+1 and 4+1 dimensions, highlighting the impact of dimensionality on growth instabilities and surface roughness.

Findings

Effective exponents are larger in higher dimensions.

Growth instability causes large mounded structures.

Increasing particle incorporation range reduces roughness but not instability.

Abstract

We present results of numerical simulations of kinetic roughening for a growth model with surface diffusion (the Wolf-Villain model) in 3+1 and 4+1~dimensions using lattices of a linear size up to $L=64$ in 3+1~D and $L=32$ in 4+1~D. The effective exponents calculated both from the surface width and from the height--height correlation function are much larger than those expected based on results in lower dimensions, due to a growth instability which leads to the evolution of large mounded structures on the surface. An increase of the range for incorporation of a freshly deposited particle leads to a decrease of the roughness but does not suppress the instability.