Multiscale modelling of nanostructures

Most materials phenomena are manifestations of processes that are operative over a vast range of length and time scales. A complete understanding of the behaviour of materials thereby requires theoretical and computational tools that span the atomic-scale detail of first-principles methods and the more coarse-grained description provided by continuum equations. Recent efforts have focused on combining traditional methodologies-density functional theory, molecular dynamics, Monte Carlo methods and continuum descriptions-within a unified multiscale framework. This review covers the techniques that have been developed to model various aspects of materials behaviour with the ultimate aim of systematically coupling the atomistic to the continuum descriptions. The approaches described typically have been motivated by particular applications but can often be applied in wider contexts. The self-assembly of quantum dot ensembles will be used as a case study for the issues that arise and the methods used for all nanostructures. Although quantum dots can be obtained with all the standard growth methods and for a variety of material systems, their appearance is a quite selective process, involving the competition between equilibrium and kinetic effects, and the interplay between atomistic and long-range interactions. Most theoretical models have addressed particular aspects of the ordering kinetics of quantum dot ensembles, with far fewer attempts at a comprehensive synthesis of this inherently multiscale phenomenon. We conclude with an assessment of the current status of multiscale modelling strategies and highlight the main outstanding issues.