Chapter 2: Theory of Size-Dependent Optical Properties

Experimental observations of spherical CdSe nanocrystals have shown that as the average radius, R, increases from 0.6 nm to 4.15 nm, the photoluminescence emission color changes from blue to red, and the photon energy of the first absorbance peak, E12, decreases from 3.02 eV to 1.88 eV 24 and eventually approaches the bandgap energy, Eg = 1.7 eV, of bulk CdSe. Various theoretical approaches have been developed to explain the relationship between R and E12. The effective mass approximation predicts that a positive, size-dependent energy shift will be proportional to 1/R, based on quantum confinement, while classical physics predicts a positive energy shift will be proportional to1/R, based on the dielectric properties of spheres. Complex simulations of the band structure in semiconductor nanocrystals attempt to provide more accurate predictions of the allowed photon transitions for quantum dots of a particular size, but these results do not produce analytical expressions for E versus R. Empirically, a positive energy shift proportional to 1/R closely follows experimental observations and is useful for converting observed absorbance spectra into estimates of particle size in order to track quantum dot growth kinetics.