Coupling between electrons and acoustic phonons in semiconductor nanostructures.

We show that the coupling between electrons and acoustic phonons in semiconductor confined structures ocurs via an interaction, which we call the ``ripple mechanism,'' in addition to the usual deformation potential coupling. Coupling due to the ripple mechanism arises from the perturbation of the electron wave function by the motion of interfaces. In this work we provide a general derivation of this coupling mechanism and give detailed expressions for it that are valid for all nanostructure systems, including those with quasi-zero-, one-, and two-dimensional geometries. For the purposes of illustration, calculations of the electron scattering rates due to acoustic phonons are given here for semiconductor quantum dots in a variety of shapes, including spheres, cubes, and rectangular parallelepipeds. From these results it is found that scattering due to the ripple mechanism dominates that from the deformation potential for dot sizes less than \ensuremath{\sim}500 \AA{} and that for smaller dot sizes the ripple mechanism contribution can be much larger than that from the deformation potential.