Environmental Engineering Reference
In-Depth Information
Chapter 4
Ballistic Thermal Transport by Phonons
at Low Temperatures in
Low-Dimensional Quantum Structures
Zhong-Xiang Xie and Ke-Qiu Chen
Department of Applied Physics, Hunan University, Changsha 410082, China
keqiuchen@hnu.edu.cn
Ballistic thermal transport by phonons at low temperature is
analyzed in low-dimensional quantum structures modulated with
inhomogeneities. First, within the Landauer transport theory,
we present a general formula to calculate the ballistic thermal
conductance associated with phonons in the linear response limit.
Then, we introduce a continuum elastic model to describe the
elastic phonon waves with long wavelength and provide the
indispensable details of the scattering-matrix method to calculate
the transmission coe
cient of elastic waves in the low-dimensional
structures. According to the numerical results, the effects of
boundary conditions, dimensions, and inhomogeneities (including
abrupt junctions, structural defects, etc.) on the ballistic thermal
transportbyphononsarediscussedindetail.Acomparativeanalysis
fortheballisticthermaltransportismadebetweentwo-dimensional
(2D) and three-dimensional (3D) models. Some interesting physical
