  Nanostructured silicon is a promising material for thermoelectric conversion,
because the thermal conductivity in silicon nanostructures can be strongly
reduced with respect to that of bulk materials. We present thermal conductivity
measurements, performed with the 3$\omega$ technique, of suspended
monocrystalline silicon thin films (nanomembranes or nanoribbons) with smooth
and rough surfaces. We find evidence for a significant effect of surface
roughness on phonon propagation: the measured thermal conductivity for the
rough structures is well below that predicted by theoretical models which take
into account diffusive scattering on the nanostructure walls. Conversely, the
electrical conductivity appears to be substantially unaffected by surface
roughness: the measured resistance of smooth and rough nanostructures are
comparable, if we take into account the geometrical factors. Nanomembranes are
more easily integrable in large area devices with respect to nanowires and are
mechanically stronger and able to handle much larger electrical currents (thus
enabling the fabrication of thermoelectric devices that can supply higher power
levels with respect to current existing solutions).
