Optical investigation of quantum confinement in PbSe nanocrystals at different points in the Brillouin zone

We present detailed investigations on the optical properties of PbSe nanocrystals. The absorption spectra of monodisperse, quasispherical nanocrystals exhibit sharp features as a result of distinct optical transitions. To study the size dependence, absorption spectra of nanocrystals ranging from 3.4 to 10.9 nm in diameter are analysed and a total of 11 distinct optical transitions are identified. The assignment of the various optical transitions is discussed and compared to theoretically calculated transition energies. By plotting all transitions as a function of nanocrystal size (D) we find that the energy (E) changes with the following relationship E proportional to D-1.5 for the lowest energy transitions. The transition energy extrapolates to approximately 0.3 eV for infinite crystal size, in agreement with the bandgap of bulk PbSe at the L-point in the Brillouin zone. In addition, high-energy transitions are observed, which extrapolate to 1.6 eV for infinite crystal size, which is in good agreement with the bulk bandgap of PbSe at the Sigma-point in the Brillouin zone. Tight-binding calculations confirm that the high-energy transitions originate from the Sigma-point in the Brillouin zone. The Sigma-character of the high-energy transitions may be of importance to explain the mechanism behind multiple exciton generation in PbSe nanocrystals.