Green's functions of the Boltzmann transport equation with the full scattering matrix for phonon nanoscale transport beyond the relaxation-time approximation

被引：13

作者：

Chiloyan, Vazrik ^{[1
]}

Huberman, Samuel ^{[1
,2
]}

Ding, Zhiwei ^{[1
]}

Mendoza, Jonathan ^{[1
]}

Maznev, Alexei A. ^{[3
]}

Nelson, Keith A. ^{[3
]}

Chen, Gang ^{[1
]}

机构：

[1] MIT, Dept Mech Engn, Cambridge, MA 02139 USA

[2] McGill Univ, Dept Chem Engn, Montreal, PQ H3A 0C5, Canada

[3] MIT, Dept Chem, Cambridge, MA 02139 USA

来源：

PHYSICAL REVIEW B | 2021年 / 104卷 / 24期

基金：

加拿大自然科学与工程研究理事会;

关键词：

D O I：

10.1103/PhysRevB.104.245424

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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 two-dimensional 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 spatiotemporal 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.

引用

页数：5

共 26 条

[21] Flexural phonons and thermal transport in graphene [J].