Related papers: New Epitaxial Thin Film Models and numerical appro…
In this article we study a model from epitaxial thin-film growth. It was originally introduced as a phenomenological model of growth in the presence of a Schwoebbel barrier, where diffusing particles on a terrace are not allowed to jump…
The formation of three-dimensional structures during the epitaxial growth of films is associated to the reflection of diffusing particles in descending terraces due to the presence of the so-called Ehrlich-Schwoebel (ES) barrier. We…
The formation of mounded surfaces in epitaxial growth is attributed to the presence of barriers against interlayer diffusion in the terrace edges, known as Ehrlich-Schwoebel (ES) barriers. We investigate a model for epitaxial growth using a…
The random deposition model must be enriched to reflect the variety of surface roughness due to some material characteristics of the film growing by vacuum deposition or sputtering. The essence of the computer simulation in this case is to…
A discrete solid-on-solid model of epitaxial growth is introduced which, in a simple manner, takes into account the effect of an Ehrlich-Schwoebel barrier at step edges as well as the local relaxation of incoming particles. Furthermore a…
A theoretical framework is developed to describe experiments on the structure of epitaxial thin films, particularly niobium on sapphire. We extend the hypothesis of dynamical scaling to apply to the structure of thin films from its…
\emph{Wolf-Villain (WV) model} is a simple model used to study \emph{ideal} molecular beam epitaxy (MBE) growth by using computer simulations. In this model, an adatom diffuses instantaneously within a finite diffusion length to maximize…
In the present contribution we review basic mathematical results for three physical systems involving self-organising solid or liquid films at solid surfaces. The films may undergo a structuring process by dewetting,…
We consider following fourth-order parabolic equation with gradient nonlinearity on the two-dimensional torus with and without advection of an incompressible vector field in the case $2<p<3$: \begin{equation*} \partial_t u + (-\Delta)^2 u =…
Frank's prediction of the spiral growth mode in 1949 defined a pivotal moment in the history of crystal growth. In recent decades the topic has received less attention, and instead we have seen a resurrection of two-dimensional nucleation…
The article consists of four sections all dealing with the computational modeling of the sputtering process. The first section deals with the difference in Bismuth atomic layer deposition at different polar angle and ion flounce. In the…
We study, through large scale stochastic simulations using the noise reduction technique, a large number of simple nonequilibrium limited mobility solid-on-solid growth models. We find that d=2+1 dimensional surface growth in several noise…
Epitaxial films evolve on time and length scales that are inaccessible to atomistic computer simulation methods like molecular dynamics (MD). To numerically predict properties for such systems, a common strategy is to employ kinetic Monte…
The energetically driven Ehrlich-Schwoebel (ES) barrier had been generally accepted as the primary cause of the growth instability in the form of quasi-regular mound-like structures observed on the surface of thin film grown via molecular…
The functional properties of devices based on perovskite oxides depend strongly on the growth modes that dramatically affect surface morphology and microstructure of the hetero-structured thin films. To achieve atomically flat surface…
Thin films are ubiquitous, with uses ranging from optoelectronics to antibacterial coatings. Unfortunately, precisely quantifying how the choice of substrate influences epitaxial growth remains an unsolved problem. Here, a novel thin film…
In this paper we propose and analyze a (temporally) third order accurate exponential time differencing (ETD) numerical scheme for the no-slope-selection (NSS) equation of the epitaxial thin film growth model, with Fourier pseudo-spectral…
We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method…
A continuum one dimensional model of homoepitaxial growth under oblique incidence is investigated. We carried out numerical integration of a continuum equation incorporating a shadowing search algorithm. The interplay between the…
This paper addresses a two-dimensional sharp interface variational model for solid-state dewetting of thin films with surface energies, introduced by Wang, Jiang, Bao, and Srolovitz in \cite{jiang2016solid}. Using the $H^{-1}$-gradient flow…