Draft: Phonon Transport in Asymmetric Sawtooth Nanowires

Thermal transport in asymmetric sawtooth nanowires was investigated. The boundaries reflect phonons differently depending on the frequency and momentum of the phonon. These systems show thermally rectifying behavior when the boundary reflections are a function of both the direction the phonon is traveling and the frequency of the phonon. This rectifying effect could be useful for thermal management applications at all size scales, but would have to be built up from the nanoscale because of a strong dependence on the device aspect ratio and the Knudsen number of the system. Monte Carlo simulations show an accumulation of phonons at the boundary which emits phonons in a perceived rough direction where those phonons have some probability of diffuse reflections at the boundary while phonons emitted in the smooth direction only experience specular reflections at the boundary and are eventually thermalized at the opposite boundary. In this study the level of rectification of the system was linearly dependent on the device aspect ratio as long as the length of the device was near or below the phonon mean free path of the phonons. NOMENCLATURE B scattering constants D density of states (1/J-m3) E energy (J) F normalized density function F exchange factor k wave vector (1/m) kb Boltzmann constant ∗Address all correspondence to this author. l device length (m) N phonon number 〈n〉 Bose-Einstein distribution p probability R random number T temperature (K) t time (s) Vg phonon group velocity (m/s) w device width (m) α aspect ratio (l/w) η characteristic roughness (m) ε level of rectification κ thermal conductivity (W/m-K) λ phonon wavelength (m) τ relaxation time (1/s) ω phonon frequency (Hz) INTRODUCTION Thermal rectification is a phenomenon where transport through a material or device is dependent on the sign of the applied temperature gradient or heat current along a specific axis. Reports of this phenomenon date back to 1936 when Starr observed a system consisting of an interface between copper and copperous oxide exhibited both electrical and thermal rectification [1]. In the 1960s and 70s there was a surge of interest in the area of thermal rectification when studies were being performed on composite systems for aerospace applications and additional mechanisms of thermal rectification were discovered. These mechanisms are summarized in ref. [2]. After this explosion of research in the area followed a period of little work 1 Copyright c © 2011 by ASME