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 Δx is the energy difference between the lowest-energy optically dark exciton state and the first optically bright exciton state. We find that Δx 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.