The Excitonic Exchange Splitting and Radiative Lifetime in PbSe Quantum Dots

Abstract

An exciton evolving from an m-fold degenerate hole level and an n-fold degenerate electron level has a nominal m × n degeneracy, which is often removed by electron−hole interactions. In PbSe quantum dots, the degeneracy of the lowest-energy exciton is m × n = 64 because both the valence-band maximum and the conduction-band minimum originate from the 4-fold degenerate (8-fold including spin) L valleys in the Brillouin zone of bulk PbSe. Using a many-particle configuration-interaction approach based on atomistic single-particle wave functions, we have computed the fine structure of the lowest-energy excitonic manifold of two nearly spherical PbSe quantum dots of radius R = 15.3 and 30.6 Å. We identify two main energy splittings, both of which are accessible to experimental probe: (i) The intervalley splitting δ is the energy difference between the two near-edge peaks of the absorption spectrum. We find δ = 80 meV for R = 15.3 Å and δ = 18 meV for R = 30.6 Å. (ii) The exchange splitting Δ x is the energy difference between the lowest-energy optically dark exciton state and the first optically bright exciton state. We find that Δ x ranges between 17 meV for R = 15.3 Å, and 2 meV for R = 30.6 Å. We also find that the room-temperature radiative lifetime is τR ∼ 100 ns, considerably longer than the ∼10 ns radiative lifetime of CdSe dots, in quantitative agreement with experiment.

Temperature-Dependent Optical Properties of Colloidal IV-VI Quantum Dots, Composed of Core/Shell Heterostructures with Alloy Components

“…This abnormal climax was previously explained 21 as a thermal activation between dark and bright states, with activation energy (E a ) close to the LO phonon energy (LO (PbSe) = 16.8 meV, LO (PbS) = 26 meV). The values of E a of the investigated samples are listed in Table 3, spanning a range that is in close agreement to the suggested theoretical values of the dark-bright splitting in pure PbSe cores; 27 (ii) unexplained a minor decrease of the intensity <10 K with an activation energy ~ 0.4 meV, way below the acoustic phonon energy (LA, TA ~ 4-6 meV). 40 Worth to note, that the best fit shown in Panel (a) also show some deviation from perfection > 150 K, in correlation with the abrupt climax shown in Panel (b), due to a change in the emission mechanism from a dark to a bright state emission.…”

“…27,30 and exsperimentally 21,23,29,[31][32][33] . These studies have suggested that splitting within the exciton fine structure near the band gap may be responsible 23,27,29 . We proposed that the problem of two emitting bands need supplementary evidence, which can be gained from the temporal and spectrally resolved PL measurements.…”

In-Gap State of Lead Chalcogenides Quantum Dots

“…The linear fitting slope of E PL ~ E 1 is 0.75, which is larger than 0.50, meaning the emission state or G.S is not fixed with respect to the bottom of the bulk conduction band, as previously reported for an in-gap hybrid state [41]. We also rule out G.S to be a dark exciton state in PbS quantum dots, since the gap state is too 'deep' for dark exciton state from exchange splitting, which was calculated to be less than 10 meV below the lowest bright exciton for a 4.2 nm PbS QD [18], on the other hand, the activation energy of G.S was measured to be about 20 meV [24]. In terms of Stokes shift, even counting the total splitting due to exchange and intervalley interactions, the calculated value was less than 80 meV, whereas the Stokes shift we measured is 332 meV for this size QD [24].…”

“…Although the properties of excitonic states have been thoroughly studied in the past decade, mostly employing transient spectroscopies [13][14][15][16][17], relatively less attention has been paid to the states within the quantum dots bandgap. Conventionally, there are two types of in-gap states: one is the dark exciton state, which is due to the exchange splitting from confinement-enhanced exchange interaction [18,19]; another type is trap state(s) associated with surface defects [20][21][22]. These in-gap states are of great importance since they affect the final destiny of excitons.…”

Four-wave-mixing imaging and carrier dynamics of PbS colloidal quantum dots

“…Therefore, the ground-state exciton is 64-fold degenerate, compared to the eightfold degeneracy of excitons in CdSe CQDs with a direct band gap at the ⌫ point. 14 Owing to the strong quantum confinement, significant carrier-carrier Coulomb interaction and, in particular, Auger recombination is expected in PbX CQDs. Strong carrier-carrier scattering can also result in the generation of multiexcitons by a single high-energy photon, an effect known as carrier multiplication ͑CM͒ or multiexciton generation, which can be understood as the reverse of Auger recombination.…”