Atomistic simulations in nanostructures composed of tens of millions of atoms

Strain in self-assembled quantum dots (QDs) is a long-range phenomenon, and its realistic determination requires a large computational domain. To find it for a dome-shaped InAs QD with diameter of 19.2 nm, the nanoelectronic modeling tool NEMO-3D uses the atomistic VFF Keating model with domain sizes of up to 64 million atoms. Interatomic distance changes thus obtained are used to influence the sp3d5s* tight-binding electronic Hamiltonian defined on a subdomain containing up to 21 million atoms (matrix size of order of 4x10$^{8})$. Targeted eigenstates with correct symmetry are found reliably even in such large systems. NEMO-3D is used to analyze the dependence of the QD states on the size of the strain domain and the boundary conditions. The energies of a deeply embedded QD depend dramatically on the strain domain size. For QDs buried under a thin capping layer, on the other hand, the existence of a free surface at the top of the sample allows for an effective relaxation of atoms, and the penetration of strain into the barrier is small.