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.
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