Phonon Mean Free Path Spectroscopy in Silicon and Silicon Carbide Nanomembranes in the 4 - 400 K Range

Knowledge of the phonon mean free path (MFP) in semiconductor nanostructures is essential for thermal engineering in modern microelectronics. Specifically, phonon MFP spectra in silicon and silicon carbide are of particular interest for power electronics that aims to operate in extreme environment at high or ultra-low temperatures. In the past years, the phonon MFPs in bulk samples of these materials have been studied both theoretically and experimentally. However, MEMS and NEMS devices rely on thin membranes, in which the MFP spectra have not been measured experimentally. Moreover, even the thermal conductivity of silicon carbide at nanoscale remains unclear.<br/>In this work, we experimentally study the phonon MFP spectra in suspended membranes made of silicon and silicon carbide at temperatures ranging from 4 to 400 K. First, we measure the thermal conductivity of membranes with arrays of slits. Then, we extract the accumulated thermal conductivity as a function of the MFP using a fully analytical approach based on the semi-analytical procedure proposed by Hao et al. [1]. In both materials, we find that the phonon MFP in 150-nm-thick membranes is an order of magnitude shorter than that in bulk. At room temperature, the phonon MFP spans from 10 to 400 nm in silicon [2] and from 50 to 400 nm in silicon carbide. As the temperature is decreased, the MFP becomes longer, reaching one micron at 4 K [2]. Above room temperature, on the contrary, the MFP becomes shorter, likely due to increased phonon-phonon scattering. These results benchmark the scale at which nanostructuring affects the thermal conductivity in microelectronics above and well below room temperature.<br/><b>References:</b><br/><i>[1] Hao et al., Materials Today Physics 10, 10012 (2019) </i><br/><i>[2] Anufriev et al., Physical Review B 101, 115301 (2020)</i>