  The thermoelectric properties of nanostructured silicon are not fully
understood despite their initial promise. While the anomalously low thermal
conductivity has attracted much work, the impact of nanostructuring on the
power factor has mostly escaped attention. While initial reports did not find
any significant changes to the power factor compared to the bulk, subsequent
detailed measurements on p-type silicon nanowires showed a stark reduction in
the Seebeck coefficient when compared to similarly doped bulk. The reduction is
consistent with the disappearance of the phonon drag contribution, due to
phonon boundary scattering. Here, we report measurements on a different
nanostructure, holey silicon films, to test if similar loss of phonon drag can
be observed. By devising experiments where all properties are measured on the
same sample, we show that though these films possess electrical conductivity
close to that in the bulk at comparable doping, they exhibit considerably
smaller thermopower. The data are consistent with loss of phonon drag. At neck
distances between 120 - 230 nm, the power factor at optimal doping is $\sim$ 50
percent that of the bulk. These insights are useful in the practical design of
future thermoelectric devices based on nanostructured silicon.
