Exact diagonalization approach for atomistic calculation of piezoelectric effects in semiconductor quantum dots

We present an exact diagonalization approach for atomistic calculation of excitonic properties of semiconductor nanostructures under piezoelectric field. The method allows for efficient treatment of both single particle and many-body states at a small computational cost and results in a very good agreement with the full diagonalization treatment. We illustrate our approach by analyzing the effect of a piezoelectric field on a spectra of a self-assembled InAs/GaAs lens-shaped quantum dot. We study the influence of linear and quadratic piezoelectric terms on the quantum dot electronic structure and importantly we found that the non-linear, density functional based theory of piezoelectricity produces results very similar to those obtained by a well-established linear approach utilizing empirical parameters.