Thermal transport in free-standing silicon membranes: influence of dimensional reduction and surface nanostructures

Nanostructuring provides a viable route to improve the thermoelectric performance of materials, even of those that in bulk form have very low figure of merit. This strategy would potentially enable the fabrication of thermoelectric devices based on silicon, the cheapest, most integrable and easiest to dope Earth-abundant semiconductor. A drastic reduction of the thermal conductivity, which would lead to a proportional enhancement of the figure of merit, was observed for silicon low-dimensional nanostructures, such as nanowires and ultra-thin membranes. Here we provide a detailed analysis of the phononic properties of the latter, and we show that dimensionality reduction alone is not sufficient to hinder heat transport to a great extent. In turn, the presence of surface roughness at the nanoscale reduces the thermal conductivity of sub-10 nm membranes up to 10 times with respect to bulk