Generalized phonon hydrodynamics in nanostructured semiconductors.

During the last decade, experiments have revealed non-Fourier thermal conduction at the nanoscale in general semiconductors such as silicon [1,2]. Recent work has demonstrated that the hydrodynamic heat transport equation provides a unifying description of this behavior in terms of new phenomena like phonon vorticity and viscosity [4-6] or memory [7]. In contrast to direct solvers of the phonon Boltzmann Transport equation, the hydrodynamic equation can be solved in arbitrarily complex geometries using finite element methods [8], which is crucial for modeling modern nanoelectronic devices.

The microscopic picture of phonon hydrodynamics is usually associated to the abundance of momentum-conserving collisions in 2D materials, such as graphene at low temperatures. Here, I will show that the applicability of the hydrodynamic heat equation is not restricted to this regime, and can be extended to describe boundary effects in 3D semiconductors. I will introduce recently uncovered general connections between the Boltzmann Transport equation and the mesoscopic hydrodynamic equation [9]. Furthermore, I will discuss the modeling of a variety of experiments displaying non-Fourier behavior in terms of the hydrodynamic framework, including the process of energy release from a nanoscale heat source towards a silicon substrate [5,6], or the unlocking of non-drifting second sound in germanium under a high-frequency laser excitation [7] . Finally, I will compare this interpretation with alternative models like the ballistic suppression of phonons in nanostructures [5].

[1] R.B. Wilson, D. Cahill, Nat. Comm. 5, 5075 (2014)

[2] K. M. Hoogeboom-Pot et. al., PNAS 112 16 4851 (2015)

[4] A. Beardo, et al. Phys. Rev. B 101, 075303 (2020)

[5] A. Beardo, S. Alajlouni, et al. Phys. Rev. B 105, 165303 (2022)

[6] A. Beardo, J. Knobloch, et al. ACS Nano 15, 8, 13019–13030 (2021)

[7] A. Beardo, et al. Sc. Adv. 7, eabg4677 (2021)

[8] A. Beardo, et al. Phys. Rev. Applied 11, 034003 (2019)

[9] L. Sendra, et al. Phys. Rev. B 103, L140301 (2021)