The modification of acoustic phonons in semiconductor nanostructures embedded in a host crystal is investigated including corrections due to strain within continuum elasticity theory. Effective elastic constants are calculated employing ab initio density functional theory. For a spherical $\mathrm{InAs}$ quantum dot embedded in $\mathrm{GaAs}$ as barrier material, the electron-phonon coupling is calculated. Its strength is shown to be suppressed compared to the assumption of bulk phonons.

• Received 15 October 2006

DOI:https://doi.org/10.1103/PhysRevB.75.235320