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-xZn_xSe/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

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... he 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.