Reduction of the thermal conductivity in free-standing silicon nano-membranes investigated by non-invasive Raman thermometry

We report on the reduction of the thermal conductivity in ultra-thin suspended Si membranes with high crystalline quality. A series of membranes with thicknesses ranging from 9 nm to 1.5 μm was investigated using Raman thermometry, a novel contactless technique for thermal conductivity determination. A systematic decrease in the thermal conductivity was observed as reducing the thickness, which is explained using the Fuchs-Sondheimer model through the influence of phonon boundary scattering at the surfaces. The thermal conductivity of the thinnest membrane with d = 9 nm resulted in (9 ± 2) W/mK, thus approaching the amorphous limit but still maintaining a high crystalline quality.