Introduction

A quantum dot is a semiconductor whose excitons are confined in all three spatial dimensions. As a result, they have properties that are between those of bulk semiconductors and those of discrete atoms.
 
Self-organization of nanostructures have been an area of extensive experimental and theoretical research over the past several years.[1]
 
Stranski-Krastanov growth is one mechanism that provides a straightforward route for producing self-assembled quantum dots. This method involves a thin layer-by-layer growth on a crystalline substrate to form various 3D 'islands'. The increase in surface area and corresponding surface energy is mitigated by a strain relaxation mechanism within dots and substrate interface resulting in an energetically favorable process.[2]

We have learned the framework for simulating large shape change due to surface diffusion[3]. Previous project teams have studied the 2D formation of quantum dots, and 3D formulation of the interface migration.[4-5]

In this project, we present a three-dimensional finite element scheme to simulate the growth process of quantum dots under both surface diffusion and interface migration.