Anomalous quantum confinement of the longitudinal optical phonon mode in PbSe quantum dots

Abstract

We have investigated the diameter dependence of the Raman spectra of lead selenide nanocrystals. The first-order Raman peak at about 136 cm${}^{\ensuremath{-}1}$ and its second-order overtone at twice this wavenumber move up in energy with decreasing nanocrystal diameter. This anomalous behavior is interpreted in terms of quantum confinement of the longitudinal optical (LO) phonon whose frequency displays a minimum at \ensuremath{\Gamma} in the dispersion of bulk PbSe. We perform ab initio calculations of the phonons of PbSe slabs with up to 15 layers. The LO mode perpendicular to the slab shifts indeed upwards with decreasing layer thickness, thus validating the interpretation of the anomalous radius dependence of the Raman spectra in terms of quantum confinement.