Microscopic origin of heat vorticity in quasi-ballistic phonon transport

Abstract

The microscopic constraints required for the emergence of hydrodynamic-like heat conduction in semiconductors as predicted by the Guyer-Krumhansl equation (GKE) are determined through energy-based deviational Monte Carlo simulations of the Boltzmann Transport Equation (MC-BTE). We simulate the process of heat release from a nanoscale heat source towards a semi-infinite Silicon substrate in steady-state by solely considering resistive phonon collisions with an average mean free path. We obtain good agreement between the microscopic (MC-BTE) and mesoscopic (GKE) approaches in capturing significant deviations from diffusive transport, such as the emergence of vorticity. The analysis shows that heat vortices appear in the vicinity of sufficiently small energy sources in the absence of momentum-conserving scattering. The GKE is able to capture the resulting non-diffusive transport effects at moderate Knudsen numbers in consistency with previous experimental work.