  The phonon renormalization across the semiconductor-to-metal crossover in
FeSi is investigated by inelastic neutron scattering combined with
\textit{ab-initio} lattice dynamical calculations. A significant part of
reciprocal space with a particular focus on the 110$-$001 scattering plane is
mapped by the time-of-flight inelastic neutron scattering data taken below and
above the crossover. Individual momentum values are investigated in more detail
as a function of temperature. The data reveal that the anomalous phonon
softening upon metallization is not exclusive to the high symmetry $R$ and
$\Gamma$ points. Several other phonon modes around the $R$-point as well as the
phonon modes at the $M$ and $X$ points of the Brillouin zone exhibit anomalous
phonon softening with magnitudes comparable to that observed at the $R$-point.
The momentum dependence of the phonon softening is reproduced by the lattice
dynamical calculation based on the density functional perturbation theory. We
discuss our findings with respect to the nature of the semiconductor-to-metal
crossover in FeSi, for which different microscopic origins have been proposed,
i.e., lattice thermal disorder and electronic correlation effects.
