  We study the effects of the nonlinear piezoelectricity and the In
distribution on the exciton energy, the electron-hole electric dipole moment,
and the fine-structure splitting in stress-tunable InGaAs/GaAs quantum dots
integrated onto a piezoelectric actuator. In particular, we investigate in
detail the contributions of various elements of the expansion of the electrical
polarization in terms of externally induced elastic strain on the latter two
important quantum dot properties. Based on the comparison of the effects of
first- and second-order piezoelectricity we provide a simple relation to
estimate the influence of applied anisotropic stress on the quantum dot dipole
moment for quantum dots significantly lattice mismatched to the host crystal.
