  We report on stacked multiple quantum dots (QDs) formed inside inverted
pyramidal recesses, which allow for the precise positioning of the QDs
themselves. Specifically we fabricated double QDs with varying inter-dot
distance and ensembles with more than two nominally highly symmetric QDs. For
each, the effect of the interaction between QDs is studied by characterizing a
large number of QDs through photoluminescence spectroscopy. A clear red-shift
of the emission energy is observed together with a change in the orientation of
its polarization, suggesting an increasing interaction between the QDs. Finally
we show how stacked QDs can help influencing the charging of the excitonic
complexes.
