Hydrodynamic Experimental Observations in Bulk Semiconductors

A large number of experimental observations incompatible with the classical Fourier description of thermal transport at the nanometer and in the picosecond scales has been reported in the last decade [1,2]. Despite the theoretical efforts done in the topic, a model able to describe the gathered data at all length and time scales is still not available.<br/>Two different descriptions have been proposed. Phonon hydrodynamics has been used as a framework to model thermal transport in materials where momentum conservation in phonon-phonon collisions is important. For other situations, a kinetic description based on the propagation of independent phonons, in what is called quasiballistic description, has been developed. The fundamental difference between them is in the number of length or time scales required to describe the observations. While in the hydrodynamic approach, a single scale is enough, in the quasiballistic description, the full set of phonon scales is necessary.<br/>Traditionally, for graphene and other 2D materials, the hydrodynamic approach has been the traditional main stream, while the quasiballistic approach has been more used for classical bulk semiconductors. But in the last years, some experiments and theoretical descriptions seems to be challenging this traditional splitting. On the one side, some predictions of the hydrodynamic regime for 2D materials like the second sound velocity have put on doubt the standard approach. On the other side, collective phonon behavior like the use of a single time scale to describe thermal decay in a silicon substrate [3] or the observation of second sound in germanium [4] seem to indicate that the hydrodynamic description could be used in these semiconductors. This could be an indication that a more unified framework could be proposed.<br/>The talk will cover some of the most recent evidences in the theoretical and experimental research on thermal transport and we will analyze them in the framework of the Kinetic/Collective model (KCM) [5], developed to give a more generalized framework to describe thermal experiments.<br/><br/><br/><b>References </b><br/>[1] Wilson, R., Cahill, D. Anisotropic failure of Fourier theory in time-domain thermoreflectance experiments. <i>Nat Commun</i> 5, 5075 (2014). doi: 10.1038/ncomms6075<br/>[2] Hoogeboom-Pot KM, Hernandez-Charpak JN, Gu X, Frazer TD, Anderson EH, Chao W, Falcone RW, Yang R, Murnane MM, Kapteyn HC, Nardi D. A new regime of nanoscale thermal transport: Collective diffusion increases dissipation efficiency. Proc Natl Acad Sci USA. 2015 Apr 21;112(16):4846-51. doi: 10.1073/pnas.1503449112<br/>[3] Beardo A, Knobloch JL, Sendra L, Bafaluy J, Frazer TD, Chao W, Hernandez-Charpak JN, Kapteyn HC, Abad B, Murnane MM, Alvarez FX, Camacho J. A General and Predictive Understanding of Thermal Transport from 1D- and 2D-Confined Nanostructures: Theory and Experiment. ACS Nano. 2021 Aug 24;15(8):13019-13030. doi: 10.1021/acsnano.1c01946<br/>[4] A. Beardo, M. López-Suárez, L.A. Pérez, L. Sendra, M.I. Alonso, C. Melis, J. Bafaluy, J. Camacho, L. Colombo, R. Rurali, F.X. Alvarez, J.S. Reparaz<b>. Observation of second sound in a rapidly varying temperature field in Ge. </b>Sci. Adv., 7 (27) (2021), doi: 10.1126/sciadv.abg4677<br/>[5] A. Beardo, M. Calvo-Schwarzwälder, J. Camacho, T.G. Myers, P. Torres, L. Sendra, F.X. Alvarez, J. Bafaluy. Hydrodynamic Heat Transport in Compact and Holey Silicon Thin Films. Physical Review Applied <b>2019,</b> <i>11 </i>(3) doi: 10.1103/PhysRevApplied.11.034003