Spectral Parameters of an Exciton in Double Semiconductor Quantum Rings in an Electric Field

The influence of a homogeneous electric field on the exciton energy spectrum and the intensity of interband quantum transitions in double semiconductor (GaAs/AlxGa1 – xAs) cylindrical quantum rings has been studied. Assuming that the lattice constant and the dielectric constant of the nanosystem elements differ slightly from each other, a model of effective masses and rectangular potentials is used to calculate the electron and hole spectra. The corresponding stationary Schrödinger equations for non-interacting electrons and holes in the absence of an electric field are solved analytically exactly. Radial wave functions are obtained as a linear combination of the Bessel, Neumann and modified Bessel functions. The stationary Schrödinger equations for quasiparticles in the presence of an electric field are not analytically solved. For their approximate solution, the unknown wave functions are sought in the form of an expansion over a complete set of cylindrically symmetric wave functions, and the energy of an electron or a hole is found from the solution of the corresponding secular equation. Since the interaction energy between an electron and a hole is much less than the sum of the size-quantized energies of the corresponding quasiparticles, the exciton binding energy is found using perturbation theory. The dependences of the energies of an electron, a hole, and an exciton on the magnitude of the electric field strength are analyzed. It is shown that the electric field significantly affects the localization of quasiparticles in the system of double nanorings. In this case, both the energies of an electron, a hole, and an exciton and the intensities of interband quantum transitions nonmonotonically depend on the magnitude of the electric field strength.