Disparate quasiballistic heat conduction regimes from periodic heat sources on a substrate

Abstract

We report disparate quasiballistic heat conduction trends for periodic nanoscale line heaters deposited on a substrate, depending upon whether measurements are based on the peak temperature of the heaters or the temperature difference between the peak and the valley of two neighboring heaters. The degree of quasiballistic transport is characterized by the effective thermal conductivities of the substrate which are obtained by matching the diffusion solutions to the phonon Boltzmann transport equation results. We find that while the ballistic heat conduction effect based on the peak temperature diminishes as the two heaters become closer, it becomes stronger based on the peak-valley temperature difference. Our results also show that the collective behavior of closely spaced heaters can counteract the nonlocal effects caused by an isolated nanoscale hot spot. These results are relevant to thermal conductivity spectroscopy techniques under development and also have important implications for understanding nonlocal heat conduction in integrated circuits and carbon nanotube array thermal interface materials.