Thermal transport in semiconductors at the nanoscale: from phonon hydrodynamics to phonon resonances

Thermal management in nanostructured semiconductor devices is critical to the advancement of nanotechnologies, as temperature affects device performance and reliability. However, macroscopic modeling based on heat diffusion fails to describe experimental observations, even with the use of effective parameters such as apparent thermal conductivities or interfacial resistances [1].

The appropriate methods to construct nanoscale heat transport models beyond effective diffusion and their validation against experiments are intensely debated. Here we discuss the applicability of hydrodynamic modeling derived from the linearized Boltzmann Transport equation (BTE) [2] at length scales comparable to the average phonon mean free path (100s of nanometers in silicon at 300 K). For example, we predict non-diffusive thermal evacuation from nanoscale heat sources [1] and the influence of rapidly varying thermal fields [3] using parameters calculated from first principles [2]. The deviations from diffusion are shown to manifest in the form of heat vorticity, viscosity and memory effects. To understand the microscopic origin of phonon hydrodynamics, we use atomistic simulations to identify hydrodynamic signatures such as Poiseuille-like heat flux profiles between system boundaries [4].

At length-scales smaller than the average phonon mean free path, phonons can display coherent wave-like interactions. In this scenario, particle-like descriptions such as the BTE are insufficient to fully describe the influence of nanoscale structural constrains. A paradigmatic example of coherent phonon behavior is phonon localization due to atomic-scale local resonances [5]. To elucidate the role of this kind of dynamical constraint in anharmonic thermalized environments, we demonstrate a novel analysis framework enabling the characterization of fundamental thermodynamic quantities such as the rate of entropy production in non-equilibrium molecular dynamics simulations [6], thus hinting at new routes to understand phonon evolution far from equilibrium beyond conventional approaches.

[1] ACS Nano 15, 13019 (2021).

[2] Phys. Rev. B 103, L140301 (2021).

[3] Science Advances 7, 27 (2021)

[4] Nano Letters 23, 6, 2129–2136 (2023)

[5] Phys. Rev. B, to appear; arXiv:2406.04097 (2024)

[6] arXiv:2404.15831 (2024)