  Differences in the confinement of electrons and holes in quantum dots are
shown to profoundly impact the magnitude of scattering with acoustic phonons in
materials where crystal deformation shifts the conduction and valence band in
the same direction. Using an extensive model that includes the non-Markovian
nature of the phonon reservoir, we show how the effect may be addressed by
photoluminescence excitation spectroscopy of a single quantum dot. We also
investigate the implications for cavity QED, i.e. a coupled quantum dot-cavity
system, and demonstrate that the phonon scattering may be strongly quenched.
The quenching is explained by a balancing between the deformation potential
interaction strengths and the carrier confinement and depends on the quantum
dot shape. Numerical examples suggest a route towards engineering the phonon
scattering.
