Electron-phonon interaction in a spherical quantum dot with finite potential barriers: The Fröhlich Hamiltonian

A Fröhlich Hamiltonian describing the electron-phonon interaction in a spherical quantum dot embedded in another polar material is derived, taking into account interactions with both bulk longitudinal optical and surface optical phonons. The Hamiltonian is appropriate to the general case of a finite confining potential originating from a bandgap mismatch between the materials of the dot and the surrounding matrix. This Hamiltonian is then used to treat the electron-phonon interaction in the adiabatic approximation for CdSe/ZnSe and CuCl/NaCl quantum dot systems. It is found that, as the radius of the dot decreases, the magnitude of the electron-phonon interaction energy first increases, passes through a maximum, and then gradually decreases to the value appropriate to the situation where the electron is weakly localized inside the dot. As the height of the interface barrier decreases, the absolute value of the electron-phonon interaction energy also decreases. These results indicate that the dependence of the electron-phonon interaction on the radius of the dot is much smaller than predicted from the simplified model with infinite value of the bandgap mismatch.