The excitonic exchange splitting and radiative lifetime in PbSe quantum dots

An exciton evolving from an m-fold degenerate hole level and an n-fold degenerate electron level has a nominal m x n degeneracy, which is often removed by electron-hole interactions. In PbSe quantum dots, the degeneracy of the lowest-energy exciton is m x 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 A. We identify two main energy splittings, both of which are accessible to experimental probe: (i) The intervalley splitting delta is the energy difference between the two near-edge peaks of the absorption spectrum. We find delta = 80 meV for R = 15.3 A and delta = 18 meV for R = 30.6 A. (ii) The exchange splitting Delta(x) is the energy difference between the lowest-energy optically dark exciton state and the first optically bright exciton state. We find that Delta(x) ranges between 17 meV for R = 15.3 A, and 2 meV for R = 30.6 A. We also find that the room-temperature radiative lifetime is tau(R) similar to 100 ns, considerably longer than the similar to 10 ns radiative lifetime of CdSe dots, in quantitative agreement with experiment.