Quasy-Two- and Quasy-One-Dimensional Excitons in Uniform Electric Field

The states of interacting electron-hole pair in semiconductor nanotube in the presence of strong lateral homogeneous electric field are considered theoretically. It is shown in single-particle approximation that along with the size-quantization of charge carriers` motion by the radial direction the external strong electric field leads to the additional (field) localization of particles also by the angular variable. At the same time the strong external field polarizes the electron–hole pair and traps them on the opposite ends of tube`s diameter. Consequently, the excitonic complex with transversal dimensions of the order of the system`s diameter is formed in a nanotube. By using the variation approach the binding energies and wave functions of the first two states of such field exciton-like complex (FELC) in the tube are calculated. The specificities of interacting electron-hole pair states in semiconductor quantum ring in the presence of strong lateral homogeneous electrostatic field are also considered. The influence of the longitudinal uniform electrostatic field on two- dimensional and one-dimensional excitonic states in the quantum film and quantum wire are considered, respectively. In the quasiclassical approximation the probabilities of ionization of two-dimensional and one-dimensional excitons under the influence of a longitudinal external electric field are calculated. The dependence of the ionization probability on the external field strength is obtained in the explicit analytical form. The results show that when the dimensionality of the system is reduced, the dependence of the exciton ionization probability on the value external field as compared to the three-dimensional case is weakened.

Keywords: Adiabatic approximation, Boundary conditions, Coulomb interaction, Cylindrical nanolayer, Effective mass, Energy spectrum, E-h pair, 1D-exciton, 2D-exciton, Ionization, Longitudinal field, Quantum well, Quantum wire, Quasiclassical approximation, Strong field, Strong quantization, Transversal field, Uniform field, Variation method, Wave function.