Electron-Phonon Interaction In Cylindrical Quantum Wires

With the development of molecular-beam epitaxy and microfabrication techniques, people can arrange the atoms and moleculars at will and make various zero-dimensional, one-dimensional and two-dimensional systems even single molecular devices. Those low-dimensional systems not only have unique physical properties, but also extra wide application prospects. Therefore, it is important to study those systems in the modern physics, the material physics and the developing technique. In this paper, variational method and Lee-Low-Pines (LLP)-like transformations are applied to investigate the impurity states and exciton states in effective mass approximation in a cylindrical quantum wire. The properties of the impurity states with the influences of the electron- confined longitudinal optical (LO) phonon and interface optical (10) phonon interactions in the infinite and finite quantum wires are studied. In addition, the contributions of the electron polaronic effects and impurity center-phonon couplings to the impurity binding energies are discussed in detail. Finally, the phonon effects on the impurity and exciton binding energies under an external electric field are investigated. Some main results obtained in the thesis are generalized as following:[1] Variational method and effective mass approximation are applied to calculate the phonon effects on the impurity binding energy in a GaAs cylindrical quantum wire surrounded by a nonpolar material. For the electron-phonon interaction we use the electron-confined LO and IO phonon interaction Hamiltonian and take both the electron- phonon couplings as well as the impurity-ion phonon couplings into account. The results show that the binding energies with only the electron polaronic effects are slightly higher than that without any phonon influence. Once taking ion-phonon couplings into account, the binding energies are obviously lower than that without phonon contributions. The impurity binding energies for different impurity position in the quantum wire are also calculated and find that the binding energies and the LO phonon effects on the binding energies decrease rapidly as the impurity shifts away from the center. Besides, the renormalization effective mass of the electron bound to the impurity center in quantum wire center is also concluded.[2] Variational approach is applied to calculate the binding energy of bound impurity states in a cylindrical quantum wire under an external electric field perpendicular to the quantum wire axes. The results show that the binding energies of shallow donor impurity states strongly depend not only on the wire radius, but also on the applied electric field and the impurity position in the wire. The binding energy is reduced by the external electric field and the phonon effects. The effect of the electric field direction becomes significant when the impurity departs from the wire center. Compared with the GaAs (III-V) quantum wire, the impurity binding energy is higher in the CdTe (II-VI) quantum wire, and the phonon effects and Stark shifts are larger in the CdTe quantum wire.[3] The binding energies of the hydrogenic impurity states in a cylindrical quantum wire with finite deep potential well are discussed. The phonon effects on the impurity states are considered by taking both the couplings of the electron- confined LO and IO phonon and the impurity ion-LO and IO phonon into account. As an example, we have performed numerical calculation in a GaAs cylindrical quantum wire. It is found that the ion-phonon interactions reduce the impurity binding energy and supply a key contribution to the energy shifts, but the electron polaronic effects enhance the binding energy less. LO phonon effect plays more important role than IO phonon in the impurity potential screening. The electron polaronic effect caused by IO phonon is more important when the wire is thinner, while the LO phonon effect is dominant for the thicker wires.[4] The effects of the external electric field on the hydrogenic impurity states in the GaAs quantum wire with a finite confining potential are studied by a variational method. The binding energies are calculated as functions of the transverse dimension of the quantum wire, and the donor-impurity position for different electric fields. The calculated results confirm that the phonon effects both reduce the binding energies of impurity states and the Stark shifts. The peak of the binding energies shifts toward a larger radius when the external electric field is applied.[5] The effects of the exciton- phonon interactions on the binding energies of an exciton in a cylindrical quantum wires with infinite potential in present an external electric filed are discussed. The exciton binding energies for III-V and II-VI compound semiconductor quantum wire structure are calculated as functions of the transverse dimension of the quantum wires and the electric fields. Theoretical results show that the exciton-phonon coupling reduces both the exciton binding energies and the Stark shifts by screening the Coulomb interaction and cannot be neglected.