Frohlich electron-phonon interaction Hamiltonian in a quantum dot quantum well

The phonon modes of a quantum dot quantum well (QDQW) in the nonpolar dielectric surrounding medium are deduced by using the dielectric continuum model. The confined longitudinal-optical (LO) phonon modes both in the core material (LO1) and in the shell material (LO2), interface optical (IO) and surface optical (SO) phonon modes, as well as the corresponding Frohlich electron-phonon interaction Hamiltonians are derived. A proper eigenfunction for LO1 modes is adopted and a legitimate eigenfunction for LO2 modes is constructed to describe the vibrating of the LO phonons. Numerical calculations are performed on a HgS/CdS QDQW, and the results reveal that there are three branches of IO or SO phonon frequencies in the system. With increasing quantum number l, the frequencies of two branches approach those in the single HgS/CdS heterostructure and the reason for this feature is explained. Bigger l and a thicker spherical shell make the potentials of IO or SO phonon modes more localized at a certain interface or surface. The study also reveals that the electron-SO phonon coupling is more significant.