Abstract
We have studied the electron-confined LO phonon interaction effects in Cylindrical Quantum Dot (CQD) systems. We investigated the variation of the electron binding energy caused by the electron-confined LO phonon interaction and the energy shift due to the external magnetic field for a wide range of the radius and the coupling strength. We performed the calculations with standard unitary transformation treatment and the variational method. It was found that the binding energy has a minimum at a particular radius as the electron binding energy is considered as a function of the radius. The origin of the occurrence of the minimum might be ascribed to the boundary confinement effect of the quantum dot. We also found that the effect of the magnetic field on the binding energy in the quantum dot with larger radius is more important than that in the quantum dot with small radius. The effect is negligible when the dot radius becomes very small. We also calculated the phonon-coupling-induced potential well strength and the average virtual phonon number. The induced potential well strength provides us a simple picture to investigate the polaronic effect, and the virtual phonon numbers usually predicts the electron-phonon coupling strength. Our result also showed that the maximum binding energy of the CQD can be obtained if the height of the CQD equals to the diameter of the CQD. This might be attributed to the symmetry of the wave function in such a situation.