  Silicon nanoparticles have the promise to surpass the theoretical efficiency
limit of single-junction silicon photovoltaics by the creation of a "phonon
bottleneck", a theorized slowing of the cooling rate of hot optical phonons
that in turn reduces the cooling rate of hot carriers in the material. To
verify the presence of a phonon bottleneck in silicon nanoparticles requires
simultaneous resolution of electronic and structural changes at short
timescales. Here, extreme ultraviolet transient absorption spectroscopy is used
to observe the excited state electronic and lattice dynamics in polycrystalline
silicon nanoparticles following 800 nm photoexcitation, which excites carriers
with $0.35 \pm 0.03$ eV excess energy above the ${\Delta}_1$ conduction band
minimum. The nanoparticles have nominal 100 nm diameters with crystalline grain
sized of about ~16 nm. The extracted carrier-phonon and phonon-phonon
relaxation times of the nanoparticles are compared to those for a silicon (100)
single crystal thin film at similar carrier densities ($2$ x $10^{19} cm^{-3}$
for the nanoparticles and $6$ x $10^{19} cm^{-3}$ for the thin film). The
measured carrier-phonon and phonon-phonon scattering lifetimes for the
polycrystalline nanoparticles are $870 \pm 40$ fs and $17.5 \pm 0.3$ ps,
respectively, versus $195 \pm 20$ fs and $8.1 \pm 0.2$ ps, respectively, for
the silicon thin film. The reduced scattering rates observed in the
nanoparticles are consistent with the phonon bottleneck hypothesis.
