  We study emission of photoelectrons from plasmonic nanoparticles into
surrounding matrix. We consider two mechanisms of the photoelectric effect from
nanoparticles - surface and volume ones, and use models of these two effects
which allow us to obtain analytical results for the photoelectron emission
rates from nanoparticle. Calculations have been done for the step potential at
surface of spherical nanoparticle, and the simple model for the hot electron
cooling have been used. We highlight the effect of the discontinuity of the
dielectric permittivity at the nanoparticle boundary in the surface mechanism,
which leads to substantial (by 5 times) increase of photoelectron emission rate
from nanoparticle compared to the case when such discontinuity is absent. For
plasmonic nanoparticle, a comparison of two mechanisms of the photoeffect was
done for the first time and showed that surface photoeffect, at least, does not
concede the volume one, which agrees with results for the flat metal surface
first formulated by Tamm and Schubin in their pioneering development of
quantum-mechanical theory of photoeffect in 1931. In accordance with our
calculations, this predominance of the surface effect is a result of effective
cooling of hot carriers, during their propagation from volume of the
nanoparticle to its surface in the scenario of the volume mechanism. Taking
into account both mechanisms is essential in development of devices based on
the photoelectric effect and in usage of hot electrons from plasmonic
nanoantenna.
