Origin of the Temperature Dependence of the Band Gap of PbS and PbSe Quantum Dots

The lead chalcogenides semiconductor materials show in the bulk a shift of the electronic band gap with temperature that is opposite to the majority of direct or indirect band gap semiconductors, namely they show a decreasing of the band gap energy with decreasing temperature. However, in the nanocrystalline form a peculiar behavior has been observed. The shift of the band gap energy with temperature depends on the diameter of the quantum dots, and for sufficiently small quantum dots, the energy shift of the band gap becomes flat and even switches sign, following the behavior of conventional semiconductors. In this manuscript, the temperature dependence of the electronic band gap of PbS and PbSe semiconductor nanocrystals of different diameter was carefully measured. The observed behavior can be reproduced using a simple two-oscillator model used previously in bulk semiconductors without the need to invoke complicated schemes. Furthermore, ab initlo calculations of the phonon density of states of nanocrystals with increasing diameters provide fascinating insights into the embryonic phase of solids. At small cluster sizes, the vibrations are quite localized and little dispersion is noted, as it is expected for almost molecular systems. However, as the nanocrystal size increases to 10 A radius, the vibrational spectra become broader and starts to be quite similar to the bulk.