  We study the dependence of the quantum yield of photoluminescence of a dense,
periodic array of semiconductor nanocrystals (NCs) on the level of doping and
NC size. Electrons introduced to NCs via doping quench photoluminescence by the
Auger process, so that practically only NCs without electrons contribute to the
photoluminescence. Computer simulation and analytical theory are used to find a
fraction of such empty NCs as a function of the average number of donors per NC
and NC size. For an array of small spherical NCs, the quantization gap between
1S and 1P levels leads to transfer of electrons from NCs with large number of
donors to those without donors. As a result, empty NCs become extinct, and
photoluminescence is quenched abruptly at an average number of donors per NC
close to 1.8. The relative intensity of photoluminescence is shown to correlate
with the type of hopping conductivity of an array of NCs.
