Ab Initio Plasmonics of Externally Doped Silicon Nanocrystals

Heavily doped semiconductor nanocrystals (NCs) represent a novel class of plasmonic materials: their hypertunable plasmonic resonances play a key role in different nanotechnology applications. The plasmonic properties of doped semiconductor NCs have been, to date, mainly modeled using (semi)classical theoretical approaches in contrast to conventional metallic NCs for which ab initio plasmonics based on Time-Dependent Density Functional Theory (TD-DFT) calculations have now become the standard reference. In this work, we aim at filling this gap by presenting a TD-DFT study on the optical properties of silicon NCs doped with an increasing number of excess electrons (dynamical doping). We have considered spherical NCs of different sizes (up to a diameter of 2.4 nm) embedded into an external polarizable medium, which turned out to be very important to obtain stable ground-state configurations. TD-DFT results show the presence of a plasmon peak at low energy with an intensity increasing with the number of excess electrons. We use the recently proposed Generalized Plasmonicity Index, with a novel implementation and interpretation in terms of transition densities, to verify the plasmonic properties of this peak. Our analysis demonstrates that the low energy peak is a plasmon peak, but it is strongly screened by the valence electrons. A detailed comparison between TD-DFT and classical results shows that the latter can be safely applied only for NCs with a diameter larger than 2 nm. The presented TD-DFT results can also be used as a reference for other theoretical approaches that aim at modeling quantum effects beyond the classical regime.