Optical-phonon modes and Frِhlich potential in quantum dots

By extending the microscopic dipole model on optical-phonon modes as applied in quantum wells and quantum wires, to rectangular quantum dots (QD), optical phonon modes and their accompanying Frِhlich potentials in QD are calculated and classified. When the bulk phonon dispersion is ignored, the optical phonon modes in QD can be clearly divided into the confined LO- and TO-bulk-like modes and the extended interface-like modes. Among the interface-like modes, a special attention is given to the corner modes, whose anisotropic behavior is depicted in the long wavelength limit. Based on the numerical results, a set of analytical formula are proposed to approximately describe the bulk-like modes, for which both the optical displacements and Frِhlich potentials vanish at the interfaces.