The exciton spectrum of the cylindrical quantum dot - quantum ring semiconductor nanostructure in an electric field

In the model of effective masses and rectangular potentials for an electron and a hole, the influence of a uniform electric field on the energy spectrum and wave functions of the exciton and the oscillator strengths of interband quantum transitions in the semiconductor (GaAs/AlxGa1-xAs) quantum dot-quantum ring nanostructure is theoretically investigated. The stationary Schrödinger equations for noninteracting quasiparticles in the presence of an electric field cannot be solved analytically. For their approximate solution, the unknown wave functions are sought in the form of an expansion over the complete set of cylindrically symmetric wave functions, and the electron energy is found by solving the corresponding secular equation. The exciton binding energy is found using perturbation theory. 
The dependences of the energy spectra, the wave functions of an electron, hole, and exciton, and the intensity of interband optical quantum transitions on the magnitude of the electric field strength are analyzed.