Size-dependent optical spectrum of CdSe nanocrystals

An empirical $sp^3d^5$ tight-binding model has been employed to describe the optical properties of CdSe nanocrystals over a wide range of sizes. The $sp^3d^5$ model explains successfully the single-particle electron levels and excitonic effects including the evolution of both the emission and absorption peaks with confinement. We provide an interpretation of the band-edge fine structure in agreement with both the one- and two- photon spectroscopies and the PLE resonant and non-resonant Stokes shifts. Previous effective mass, pseudopotential and $sp^3s^*$ tight-binding models were unable to explain such experiments. The wurtzite lattice structure splits the lowest $S$- and $P$- hole states into two doublets that overlap, in accordance to the indistinguishability observed between the one-photon and two-photon spectroscopies. A correct description of the spin-orbit coupling allows the non-resonant Stokes shift to be reproduced. Finally, for dot radius below 2.3 nm, an optically passive $P-$ level becomes the ground hole state giving rise to the large resonant Stokes shift observed experimentally.