Strain and Piezoelectric Effects on the Electronic Structure of Coupled In$_{x}$Ga$_{1-x}$As/GaAs Self-Assembled Quantum Dots

In$_{x}$Ga$_{1-x}$As/GaAs coupled quantum dot systems have gained much attention for optical and quantum computing applications. Due to strain, originating from the assembly of lattice- mismatched semiconductors, the quantum dot arrays tend to grow in the vertical direction. These vertically stacked quantum dots are strongly coupled through the strain field, which is atomistically inhomogeneous and penetrates deep into the GaAs buffer layer surrounding the dots. Crystal symmetry and atomistic details of interfaces are extremely important in such systems. Also piezoelectric fields must be taken into account to properly model the experimentally observed symmetry breaking and the introduction of a global shift in the energy spectra of the system. In this work, we present a detailed description of strain and piezoelectric potential effects on the electronic structure of closely coupled identical and non-identical quantum dot systems using sp$^{3}$d$^{5}$s* nearest neighbor empirical tight binding model. We show that strain causes strong mixing of s- and p- electron energy levels in strongly coupled quantum dot, splits heavy hole and light hole bands and even reverses their order within dots.