Hydrodynamic heat transport in semiconductors at the nanoscale*

Recent experiments in heat transport on silicon using ultrafast laser heating techniques have shown significant discrepancies with Fourier like behaviour[1-3]. The interpretations of these results using only a ballistic to diffusive transition of the carriers have shown to be unfruitful. 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[4-5], 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[6-7]. In this case its presence has to be noticed through indirect evidences. Hydrodynamics has been used to understand the lack of validity of the Mathiessen rule in silicon or the dependence of the Thermal Boundary Resistance 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.
[1] PRL, 110, 025901 (2013).
[2] Nat. Commun., 5, 5075 (2014).
[3] PNAS, 112, 201503449 (2015).
[4] Nano Lett., 18, 638–649 (2018)
[5] Nat. Commun., 6, 1-7 (2015)
[6] Phys. Rev. Mat., 2 076001 (2018)
[7] Nat. Commun. 9, 255 (2018)