The Energetics of Hut-Cluster Self-Assembly in Ge/Si(001) from Linear-Scaling DFT Calculations

Density functional theory (DFT) in a linear-scaling implementation is used to study the energetics of three-dimensional (3D) Ge islands (hut clusters) grown on Si(001) surface. DFT calculations on the fully relaxed energies of a series of hut clusters of increasing size are reported, finding a 2D to 3D cross-over near three monolayers; the number of atoms in the largest simulated system is over 20,000. A variety of technical issues which are important in addressing the accuracy and validity of the calculations are described and assessed. The results suggest that energetics alone is responsible for the initial transition from 2D to 3D growth.