  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.
