Jonathan Mendoza | Searcharxiv

arXiv2021

Green's Functions of the Boltzmann Transport Equation with the Full Scattering Matrix for Phonon Nanoscale Transport beyond the Relaxation Time Approximation

The phonon Boltzmann transport equation (BTE) has been widely utilized to study thermal transport in solids. While for a number of materials the exact solution to the BTE has been obtained for a uniform heat flow, problems arising in micro/nanoscale heat transport have been analyzed within the relaxation time approximation (RTA). Since the RTA breaks down at temperatures low compared to the Debye temperature, this approximation prevents the study of an important class of high Debye temperature materials such as diamond, graphite, graphene and some other 2D materials. We present a full scattering matrix formalism that goes beyond the RTA approximation and obtain a Green's function solution for the linearized BTE, which leads to an explicit expression for the phonon distribution and temperature field produced by an arbitrary spatio-temporal distribution of heat sources in an unbounded medium. The presented formalism is capable of describing a wide range of phenomena, from heat dissipation by nanoscale hot spots to the propagation of second sound waves. We provide numerical results for graphene for a spatially sinusoidal heating profile and discuss the importance of using the full scattering matrix compared to the RTA.

cond-mat.mes-hall↗

arXiv2016

Phonon Localization in Heat Conduction

Departures in phonon heat conduction from diffusion have been extensively observed in nanostructures through their thermal conductivity reduction and largely explained with classical size effects neglecting phonon's wave nature. Here, we report localization-behavior in phonon heat conduction due to multiple scattering and interference of phonon waves, observed through measurements of the thermal conductivities of GaAs/AlAs superlattices with ErAs nanodots randomly distributed at the interfaces. Near room temperature, the measured thermal conductivities increased with increasing number of SL periods and eventually saturated, indicating a transition from ballistic-to-diffusive transport. At low temperatures, the thermal conductivities of the samples with ErAs dots first increased and then decreased with an increasing number of periods, signaling phonon wave localization. This Anderson localization behavior is also validated via atomistic Green's function simulations. The observation of phonon localization in heat conduction is surprising due to the broadband nature of thermal transport. This discovery suggests a new path forward for engineering phonon thermal transport.

cond-mat.mes-hall↗