Band-edge excitons in PbSe nanocrystals and nanorods

We investigate the fine structure of band-edge excitons in PbSe nanocrystals and nanorods using circularly polarized magnetophotoluminescence and optically detected magnetic resonance and, based on the results, propose a singlet-triplet model of exciton photoluminescence from nondegenerate conduction and valence bands. From the data and model we extract g-factors for electrons and holes of +1.2 and +0.8, respectively. The splitting of the triplet ground state, which is responsible for the low-temperature photoluminescence, is 88 eV for nanorods, and less than 20 eV for nanocrystals. The intervalley splitting of the electron and hole levels in the nanocrystals is much larger than the electron-hole exchange interaction. ting diodes, 4 lasers, 3,5 detectors, 6 and photovoltaics. 7-11 NCs of the lead chalcogenides PbS, PbSe, and PbTe offer dis- tinct advantages for such applications. Lead chalcogenides are semiconductors with a direct narrow gap that can be tuned by quantum confinement over a range of wavelengths suited to different applications, including ones operating in the infrared transparency windows centered at 1.3 and 1.6 m, as well as planar optical waveguides, 12 in vivo im- aging of biological tissue, 13 and photovoltaic conversion. 7-9 The absorption spectra of lead chalcogenide specifically, PbSe NCs are well understood from the work by Kang and Wise. 14 But their photoluminescence PL properties and the fine structure of the band-edge exciton spectra, which con- trols these properties, are still controversial. 15-17 Lead chalcogenides have a direct gap at the L point of the Brillouin zone. The fourfold degeneracy of the L point means that the 1s ground states of both electrons and holes in lead chalcogenide NCs are eightfold degenerate including spin, and thus there are 88=64 transitions between band- edge excitons. In spherical NCs, these electron and hole states split into two sublevels due to the intervalley interaction, 14 as found in first-principles calculations of NC energy spectra. 16 The fine structure of these states is a com- plicated function of the relative strength of the intervalley interaction, the electron-hole exchange interaction, and de- viations of the NC shape from spherical symmetry. The high degree of degeneracy renders fluorescence line-narrowing experiments which were previously used to study band-edge excitons in CdSe NCs Refs. 18-20 inefficient, highlight- ing the need for a different approach. In this paper we use circularly polarized magnetophotolu- minescence CP-MPL and optically detected magnetic reso- nance ODMR Refs. 21 and 22 to study the fine structure of the band-edge excitons in PbSe NCs and NRs. Our results are well described by the standard singlet-triplet model of the exciton PL from nondegenerate electrons and holes, suggest- ing that intervalley splitting does not significantly affect the PL. Our results also confirm the much-discussed near-mirror symmetry of electron and hole spectra in PbSe NCs. Finally, we extract numerical values for the electron and hole g fac- tors and the electron-hole exchange interaction. We studied PbSe NCs having two basic shapes: either spherically symmetric i.e., NCs or slightly elongated in one direction i.e., NRs, with diameters of approximately 4 nm. Samples were purchased from Evident Technologies as well as synthesized in-house using published techniques. 23 Transmission electron microscopy TEM images of two