Bound and Resonant States of Shallow Donors in Quantum Antidots

The energy spectrum and the wave functions of a shallow donor placed at the center of a spherical quantum antidot are computed within the effective mass approximation. The wave functions for discrete bound states and for continuum states are obtained in a closed form. We show that, due to the local potential of the microstructure, resonances occur in the continuum. Their energies are close to those of hydrogen-like levels lying under the top of the barrier when the quantum antidot radius is large as compared to the effective Bohr radius. The lifetimes of the resonant states and the oscillator strengths for optical transitions from the ground state are computed. We show how the energy spectrum and the oscillator strengths depend on the antidot parameters.