  We study phonon-assisted electron tunneling in semiconductor quantum dot
molecules. In particular, singlet-singlet relaxation in a two-electron doped
structure is considered. The influence of Coulomb interaction is discussed via
comparison with a single electron system. We find that the relaxation rate
reaches similar values in the two cases but the Coulomb interaction shifts the
maximum rates towards larger separations between the dots. The difference in
electron-phonon interaction between deformation potential and piezoelectric
coupling is investigated. We show that the phonon-induced tunneling between
two-electron singlet states is a fast process, taking place on the time scales
of the order of a few tens of picoseconds.
