Hydrodynamic thermal transport in silicon at temperatures ranging from 100 to 300 K

Abstract

The temperature profile around nano- and microscale heat sources on silicon substrate is technologically important for many integrated circuit applications. Here we present full-field thermal imaging of heater lines and rings with different sizes at temperatures ranging from 100 to 300 K. We show significant deviations compared to Fourier's law which are both size and geometry dependent. This can be explained by a hydrodynamic model for heat transport in silicon based on the Guyer and Krumhansl equation using ab initio calculated parameters within the kinetic collective model framework. One of these parameters, the nonlocal length, is shown to quantitatively determine the situations where nonFourier behavior occurs. This length scale is some orders of magnitude smaller than the longest phonon mean free paths. Ballistic phonons are shown not to manifest directly in these experiments, thus indicating the failure of the multiscale relaxation time approximation. Furthermore, we discuss the differences between Hamiltonian/microscopic and entropic/mesoscopic strategies to address nanoscale heat transport, and the relations between phonon dynamics and thermodynamics. Finally, the nonequilibrium phonon distribution function is used to determine conditions under which hydrodynamic modeling can be used.