The Peculiar Electronic Structure of PbSe Quantum Dots

Abstract

PbSe is a pseudo-II-VI material distinguished from ordinary II-VI's (e.g., CdSe, ZnSe) by having both its valence band maximum (VBM) and its conduction band minimum (CBM) located at the fourfold-degenerate L-point in the Brillouin zone. It turns out that this feature dramatically affects the properties of the nanosystem. We have calculated the electronic and optical properties of PbSe quantum dots using an atomistic pseudopotential method, finding that the electronic structure is different from that of ordinary II-VI's and, at the same time, is more subtle than what k.p or tight-binding calculations have suggested previously for PbSe. We find the following in PbSe dots: (i) The intraband (valence-to-valence and conduction-to-conduction) as well as interband (valence-to-conduction) excitations involve the massively split L-manifold states. (ii) In contrast to previous suggestions that the spacings between valence band levels will equal those between conduction band levels (because the corresponding effective-masses me approximately mh are similar), we find a densely spaced hole manifold and much sparser electron manifold. This finding reflects the existence of a few valence band maxima in bulk PbSe within approximately 500 meV. This result reverses previous expectations of slow hole cooling in PbSe dots. (iii) The calculated optical absorption spectrum reproduces the measured absorption peak that had previously been attributed to the forbidden 1Sh --> 1Pe or 1Ph --> 1Se transitions on the basis of k.p calculations. However, we find that this transition corresponds to an allowed 1Ph --> 1Pe excitation arising mainly from bulk states near the L valleys on the Gamma-L lines of the Brillouin zone. We discuss this reinterpretation of numerous experimental results.

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

“…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.…”

“…A different approach for the assignment of the different transitions was recently reported by An et al [1] Using pseudo-potential calculations, it was calculated that a PbSe nanocrystal with a 1S h -1S e transition (a) at 0.89 eV has a 1P h -1P e transition (b) that is 0.24 eV higher in energy, at 1.13 eV. 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.…”

“…As a consequence of the high atomic number of Pb, and the resulting high electron velocities, relativistic effects localize the 6s orbital, transforming Pb into a 6p 2 atom (inert pair effect). [1] Another consequence of the high atomic number of Pb is the relatively large ratio of ionic radii (r Pb,2 + /r Se,2À = 0.59). As a result, the coordination number of PbSe (6) is higher than for, for example, CdSe (4).…”

“…First, the assignment of the multiple features (up to 11) in the absorption spectrum of highly monodisperse PbSe QDs is discussed and compared to calculated spectra of PbSe QDs that were recently published. [1,11] Next, the size dependence of the energy of the various transitions is analyzed for 16 different sizes of PbSe QDs, ranging from 3.4 to 10.9 nm. It follows that the higher-energy transitions can be assigned to optical transitions at a different point in the Brillouin zone than the lower-energy transitions.…”