Significant thermal conductivity reduction of CVD graphene with relatively low hole densities fabricated by focused ion beam processing

The detrimental effect of nanoscale hole defects on the in-plane thermal conductivity (k) was first examined for supported CVD graphene. A focused ion beam punctured equally spaced 50-nm diameter holes with different hole spacings (200, 400, and 800 nm) in supported graphene on an 8-nm thin SiO₂ substrate. For the relatively low 4.91% porosity, the thermal conductivity showed a significant reduction to 212.6 W/mK from 1045 W/mK in supported graphene with no holes and even more dramatically so from 3500 W/mK in suspended pristine graphene. The thermal conductivity showed an order-of-magnitude faster reduction with increasing porosity compared to the Eucken model, which is based on the diffusive thermal transport reduction due to the void holes on the macroscale. This is believed to be attributed to the enhanced phonon scattering by the nanoscale hole edges and also by the reduced phonon passage length-scale that became comparable to the phonon mean-free-paths. Furthermore, a phenomenological fitting model is presented to comprehensively describe the k dependence on porosity, hole spacing, and the spectral dependence of the phonon mean-free-path in nanoscale holey graphene.