Effects of electron- and impurity-ion-LO phonon couples on the impurity states in cylindrical quantum wires

The variational method and the effective mass approximation are used to calculate the phonon effects on the hydrogenic impurity states in a cylindrical quantum wire with finite deep potential by taking both the couplings of the electron-confined bulk longitudinal optical (LO) phonons and the impurity-ion-LO phonons into account. The binding energies and the phonon contributions are calculated as functions of the transverse dimension of the quantum wire. The results show that the polaronic effect induced by the electron-LO phonon coupling and the screening effect induced by the impurity-ion-LO phonon coupling tend to compensate each other and the total effects reduce the impurity binding energies.