Ultra-Low Thermal Conductivity of Germanium Nanowires

We theoretically investigate phonon and thermal properties in germanium nanowires with square cross-sections ranging from 2.26 to 27.72 nm. Using a face-centered cubic cell model for lattice vibrations and the Boltzmann transport equation approach, we find that the thermal conductivity of Ge nanowires is 3 to 20 times lower than in bulk c-Ge, depending on the roughness of the nanowire surfaces. This significant decrease in lattice thermal conductivity results from the interplay between two effects: the redistribution of phonon energy spectra due to spatial confinement and phonon boundary scattering. We calculate the temperature distribution in a nanometer-thick porous germanium film with a thermal conductivity of 3.5 W/(m K), typical for rough Ge nanowires. Our results indicate the potential for localized heating in specific regions, reaching temperatures up to ~950 K. This finding aligns well with previous experimental estimations made using Raman spectroscopy.