  Using Localized Surface Plasmon Resonance (LSPR) as an optical probe we
demonstrate the presence of free carriers in phosphorus doped silicon
nanocrystals (SiNCs) embedded in a silica matrix. In small SiNCs, with radius
ranging from 2.6 to 5.5 nm, the infrared spectroscopy study coupled to
numerical simulations allows us to determine the number of electrically active
phosphorus atoms with a precision of a few atoms. We demonstrate that LSP
resonances can be supported with only about 10 free electrons per nanocrystal,
confirming theoretical predictions and probing the limit of the collective
nature of plasmons. We reveal a phenomenon, unique to embedded nanocrystals,
with the appearance of an avoided crossing behavior linked to the hybridization
between the localized surface plasmon in the doped nanocrystals and the silica
matrix phonon modes. Finally, a careful analysis of the scattering time
dependence versus carrier density in the small size regime allows us to detect
the appearance of a new scattering process at high dopant concentration.
