  The intrinsic fine structure splittings (FSSs) of the exciton states of
semiconductor quantum dots (QDs) are known to be the major obstacle for
realizing the QD-based entangled photon pair emitters. In this study, we
present a theoretical and computational investigation of the excitonic fine
structures of droplet-epitaxial (DE) GaAs/AlGaAs QDs under the
electro-mechanical control of micro-machined piezoelectricity actuators. From
the group theory analysis with numerical confirmation based on the developed
exciton theory, we reveal the general principle for the optimal design of
micro-machined actuators whose application on to an elongated QD can certainly
suppress its FSS. We show that the use of two independently tuning stresses is
sufficient to achieve the FSS-elimination but is not always necessary as widely
deemed. The use of a single tuning stress to eliminate the FSS of an elongated
QD is possible as long as the crystal structure of the actuator material is in
coincidence with that of the QD. As a feasible example, we show that a {\it
single} symmetric bi-axial stress naturally generated from the $(001)$ PMN-PT
actuator can be used as a single tuning knob to make the full FSS-elimination
for elongated DE GaAs QDs.

Mesoscale and Nanoscale Physics