  We observe unusually narrow donor-bound exciton transitions (0.4 meV) in the
photoluminescence spectra of GaN nanowire ensembles grown on Si(111) substrates
at very high (> 850 degrees Celsius) temperatures. The spectra of these samples
reveal a prominent transition of excitons bound to neutral Si impurities which
is not observed for samples grown under standard conditions. Motivated by these
experimental results, we investigate theoretically the impact of
surface-induced internal electric fields on the binding energy of donors by a
combined Monte Carlo and envelope function approach. We obtain the ranges of
doping and diameter for which the potential is well described using the Poisson
equation, where one assumes a spatially homogeneous distribution of dopants.
Our calculations also show that surface donors in nanowires with a diameter
smaller than 100 nm are ionized when the surface electric field is larger than
about 10 kV/cm, corresponding to a doping level higher than 2 x 10^16 cm^-3.
This result explains the experimental observation: since the (D+,X) complex is
not stable in GaN, surface-donor-bound excitons do not contribute to the
photoluminescence spectra of GaN nanowires above a certain doping level, and
the linewidth reflects the actual structural perfection of the nanowire
ensemble.
