Density of States Measured by Scanning-Tunneling Spectroscopy Sheds New Light on the Optical Transitions in PbSe Nanocrystals

Abstract

The density-of-states function of individual colloidal PbSe nanocrystals varying in diameter between 3 and 7 nm is measured by resonant tunneling spectroscopy. It is in semiquantitative agreement with tight-binding calculations, but the energy separation between electron (hole) levels of S and P symmetry is systematically smaller than predicted by the theory. These results provide an explanation for the second and third excitonic optical transitions, which have been debated for a long time.

Optical Investigation of Quantum Confinement in PbSe Nanocrystals at Different Points in the Brillouin Zone

“…We have measured and analyzed the absorption spectrum of PbSe QDs that have a first transition (a) at 0.87 eV (see Supporting Information, Figure S1), allowing for a good comparison with the calculated spectrum by An et al We find that PbSe QDs with transition a at 0.87 eV display a second transition (b) at 1.12 eV, which coincides nicely with the values calculated by An et al [1] This suggests that the second peak in the absorption spectra of PbSe QDs is the 1P h -1P e transition, in line with the assignment by Liljeroth et al, [13] but in contrast with the tight-binding calculations discussed above. Interestingly, An et al calculate two additional transitions as a result of heavily mixed P-and D-like states, located at 1.38 eV and approximately 1.48 eV, respectively.…”

“…Liljeroth et al were able to measure the density of states of single PbSe nanocrystals directly using scanning tunnelling spectroscopy and suggested that transition b corresponds to the 1P h -1P e transition. [13] Below we will compare the experimental absorption spectra and their features with an absorption spectrum that we obtained by tight-binding calculations, as well as an absorption spectrum that was recently calculated by An et al [1] As will become clear, there are still important discrepancies between the experimental data and both theoretical calculations. The purpose of this comparison is to give an overview of the current understanding of the absorption spectrum of PbSe QDs, not to give a final answer on the correct assignment of the different transitions.…”

“…The assignment of the optical transitions is subject to considerable debate in the literature. [1,[10][11][12][13] This debate largely focuses on the assignment of the "second" peak in the absorption spectrum, labelled b here. Based on theoretical calculations of the energy levels and experimental work, this feature has previously been assigned to the 1S h -1P e (or 1P h -1S e ) transition.…”

Reappraisal of Variable-Range Hopping in Quantum-Dot Solids

“…This is in agreement with recent scanning-tunnelingspectroscopy studies on nanocrystal quantum-dots that have revealed a Gaussian shape of the energy-levels with a width of tens of meV. [36][37][38][39] The overlap between g fluc (E) of a donor and an acceptor site in a hopping event, separated by a distance R and an energy mismatch ∆E, determines the rate of nonresonant charge-transfer, 40 which is given by…”

Scanning Tunneling Spectroscopy of Individual PbSe Quantum Dots and Molecular Aggregates Stabilized in an Inert Nanocrystal Matrix

“…The combination of STM and STS has already proved very useful in probing the geometry and electronic structure of individual atoms and molecules and molecular aggregates at the atomic scale. [6][7][8][9][10][11][12] Furthermore, these techniques have been successfully used for the investigation of individual InAs, CdSe, and PbSe QDs, [13][14][15][16][17] as well as their twodimensional arrays. 18,19 In order to study a single, isolated QD or small aggregates of QDs with STM, they have to be immobilized on a conducting substrate.…”