  Randomly blinking nanocrystals have given rise to numerous and intense
theoretical and experimental investigations recently. An experimental
breakthrough was finally made by fabricating the non-blinking
Cd$_{1-x}$Zn$_x$Se/ZnSe graded nanocrystal [Nature 459 (2009) 686]. Here, we
report (1) an unequivocal and detailed theoretical investigation to understand
the properties of the potential-well and the distribution of Zn content with
respect to the nanocrystal radius and (2) develop a strategy to find the
relationship between the photoluminescence (PL) energy peaks and the
potential-well due to Zn distribution in nanocrystals. We found that the
non-square-well potential can be varied in such a way that one can indeed
control the PL intensity and the energy-level difference (PL energy peaks) in
any non-free-electron nanocrystals accurately. This implies that we can either
suppress the blinking altogether, or alternatively, manipulate the PL energy
peaks and intensities systematically to give non-random blinking. Our
theoretical strategy developed here is generic and can be applied to any
non-free-electron nanocrystals.
