Stability of an Exciton bound to an Ionized Donor in Quantum Dots

Total energy, binding energy, recombination rate (of the electron hole pair) for an exciton (X) bound in a parabolic two dimensional quantum dot by a donor impurity located on the z axis at a distance d from the dot plane, are calculated by using the Hartree formalism with a recently developed numerical method (PMM) for the solution of the Schroedinger equation. As our analysis indicates there is a critical dot radius such that for radius less than the critical radius the complex is unstable and with an increase of the impurity distance this critical radius increases. Furthermore, there is a critical value of the mass ratio such that for mass ratio less than the critical value the complex is stable. The appearance of this stability condition depends both on the impurity distance and the dot radius, in a way that with an increase of the impurity distance we have an increase in the maximum dot radius where this stability condition appears. For dot radii greater than this maximum dot radius (for fixed impurity distance) the complex is always stable.Comment: 17 pages, 7 figures Applying a new numerical method which is based on the adiabatic stability of quantum mechanics, we study the stability of an exciton (X) bound in a parabolic two dimensional quantum dot by a donor impurity located on the z axis at a distance d from the dot plan