Atomistic simulations in nanostructures composed of tens of millions of atoms: Importance of long-range strain effects in quantum dots

Strain in self-assembled quantum dots is a long-range phenomenon, and its realistic determination requires a large computational domain. To tackle this problem for an embedded InAs quantum dot NEMO-3D uses the atomistic VFF Keating model containing up to 64 million atoms. Interatomic distance changes obtained are used to influence the sp3d5s* tight-binding electronic Hamiltonian defined in a subdomain containing up to 21 million atoms (matrix size of order of 4×10⁸). Targeted eigenstates with correct symmetry are found reliably even in such large systems. NEMO-3D is used to analyze the dependence of the dot states on the size of the strain domain and the boundary conditions. The energies of a deeply embedded dot depend dramatically on the strain domain size. For dots 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.