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Phonons strongly influence the optical control of semiconductor quantum dots.When modeling the electron-phonon interaction in several theoretical approachesthe quantum dot geometry is approximated by a spherical structure, thoughtypical self-assembled quantum dots are strongly lens-shaped. By explicitlycomparing simulations of a spherical and a lens-shaped dot using awell-established correlation expansion approach we show that indeed lens-shapeddots can be exactly mapped to a spherical geometry when studying the phononinfluence on the electronic system. We also give a recipe to reproduce spectraldensities from more involved dots by rather simple spherical models. On theother hand, breaking the spherical symmetry has a pronounced impact on thespatio-temporal properties of the phonon dynamics. As an example we show thatfor a lens-shaped quantum dot the phonon emission is strongly concentratedalong the direction of the smallest axis of the dot which is important for theuse of phonons for the communication between different dots.

Phonon impact on optical control schemes of quantum dots: The role of quantum dot geometry and symmetry