  We investigate acceptor and donor states in GaN nanocrystals doped with a
single substitutional impurity. Quantum dots (QD's) of zinc-blende structure
and spherical shape are considered with the radius ranging from 4.5 to 67.7 A.
The size-dependent energy spectra are calculated within the sp3d5s*
tight-binding model, which yields a good agreement with the confinement-induced
blue shifts observed in undoped QD's. The computed binding energy is strongly
enhanced with respect to the experimental bulk value when the dopant is placed
at the center of the smallest QD's. It decreases with increasing QD size
following a scaling law that extrapolates to the bulk limit. In order to
estimate the degree of localization of the bound carriers we analyze their wave
functions and average radii. The resulting physical picture points to a highly
localized acceptor hole, mostly distributed over the nearest-neighbor anion
shell, and a much more extended donor electron. We also study off-center
impurities in intermediate-size QD's. The acceptor binding energy is
approximately independent of the dopant position unless it is placed within a
surface shell of thickness of the order of the bulk Bohr radius, where the
ionization energy abruptly drops. On the contrary, the donor binding energy
gradually decreases as the impurity is moved away from the center toward the QD
surface.
