Growth, Structure and Pattern Formation for Thin Films

Abstract

An epitaxial thin film consists of layers of atoms whose lattice properties are determined by those of the underlying substrate. This paper reviews mathematical modeling, analysis and simulation of growth, structure and pattern formation for epitaxial systems, using an island dynamics/level set method for growth and a lattice statics model for strain. Epitaxial growth involves physics on both atomistic and continuum length scales. For example, diffusion of adatoms can be coarse-grained, but nucleation of new islands and breakup for existing islands are best described atomistically. In heteroepitaxial growth, mismatch between the lattice spacing of the substrate and the film will introduce a strain into the film, which can significantly influence the material structure, for example leading to formation of quantum dots. Technological applications of epitaxial structures, such as quantum dot arrays, require a degree of geometric uniformity that has been difficult to achieve. Modeling and simulation may contribute insights that will help to overcome this problem. We present simulations that combine growth and strain showing the structure of nanocrystals and the formation of patterns in epitaxial systems.

Self-assembly of InAs quantum dots on GaAs(001) by molecular beam epitaxy

“…One important reason for the popularity of this dynamic growth scenario may be that it can be fully implemented by a KMC simulation [143][144][145][146][147][148], in addition to being expressible in analytical form on the basis of the surface diffusion equation and MFREs. At present, the KMC simulation is generally regarded as the only method capable of describing surface evolution with atomistic details on experimentally relevant time and length scales.…”