F. Xavier Alvarez1 Javier Bafaluy1 Juan Camacho1 Xavier Cartoixà2 Pol Torres1 Albert Beardo Ricol1 Lluc Sendra1

1, Physics, Universitat Autonoma de Barcelona, Bellaterra, Barcelona, Spain
2, Electrical Engineering, Universitat Autonoma de Barcelona, Bellaterra, Barcelona, Spain

Two main characteristics make nanoscale thermal transport in semiconductors a complex phenomena full of nuances. The first is the importance of momentum conservation in the phonon-phonon collisions (Normal scattering)[1]. This kind of scattering is not able to destroy momentum and consequently in their presence the phonon distribution cannot relax to its equilibrium form. The second is the large scale range that span the phonon mean free path spectrum[2]. Because of this the connectivity between two regions in a sample (non-locality) depends on the kind of phonons connecting these regions. The consequence is that heat transport at the nanoscale is still an incompletely described topic.

Phonon hydrodynamics has emerged in the last years as a candidate to cover this gap. The appearance of this regime has been associated to the dominance of normal collisions. Its presence has been proven in 2D materials or at low temperatures[3-4], when N-collisions are dominant and in consequence collective effects can be observed easily. But recent works have shown that hydrodynamic effects can still have an important impact when resistive collisions are dominant[5-6]. In this case its presence has to be noticed through indirect evidences. Hydrodynamics has been used, for example, to understand the lack of validity of the Mathiessen rule in silicon or the dependence of the Thermal Boundary Resistance between two materials on the size of the contact.

Kinetic Collective Model (KCM) has been developed to describe heat transport using two key concepts. On one side, the splitting in collective regime (when normal scattering is dominant) and kinetic regime (when it is not important). On the other side, the inclusion of nonlocal and memory effects that introduce hydrodynamic behavior in the description. From the combination of both concepts it can be shown that hydrodynamic phenomena can emerge in both, collective and kinetic regimes, with different particularities in each case.

The equations obtained from the model are simple enough to be solved using finite element computational tools. We will show the results from a recent developed module implemented in COMSOL. Using KCM equations in combination with ab initio calculated parameters we will describe hydrodynamic effects in 2D materials like graphene and in conventional semiconductors like silicon an use the results to interpret some of the most relevant experimental observations of the last years.

[1] Guyer & Krumhansl Phys. Rev., 148(2), 766–778 (1966)
[2] Vermeersch et al. Phys. Rev. B, 91(8), 085202 (2015)
[3] Ding et at. Nano Letters, 18(1), 638–649 (2018)
[4] Cepellotti et al., Nat. Commun., 6, 1-7 (2015)
[5] Torres et al., Phys. Rev. Mat., 2(7) 076001 (2018)
[6] Ziabari et al., Nat. Commun. 9(1), 255 (2018)