Effects of quantum statistics of phonons on the thermal conductivity of silicon and germanium nanoribbons

Yuriy A Kosevich,Alexander V Savin,Andrés Cantarero

doi:10.1186/1556-276x-8-7

Abstract

We present molecular dynamics simulation of phonon thermal conductivity of semiconductor nanoribbons with an account for phonon quantum statistics. In our semiquantum molecular dynamics simulation, dynamics of the system is described with the use of classical Newtonian equations of motion where the effect of phonon quantum statistics is introduced through random Langevin-like forces with a specific power spectral density (color noise). The color noise describes interaction of the molecular system with the thermostat. The thermal transport of silicon and germanium nanoribbons with atomically smooth (perfect) and rough (porous) edges are studied. We show that the existence of rough (porous) edges and the quantum statistics of phonon change drastically the low-temperature thermal conductivity of the nanoribbon in comparison with that of the perfect nanoribbon with atomically smooth edges and classical phonon dynamics and statistics. The rough-edge phonon scattering and weak anharmonicity of the considered lattice produce a weakly pronounced maximum of thermal conductivity of the nanoribbon at low temperature.

Highlights

It has been recently shown [1] that silicon and germanium nanowires can give a figure of merit of over 2 at 800 K due to strong reduction of phonon thermal conductivity in nanowires as compared with their equivalent bulk material, i.e., the reduction is caused by the alloy disorder, and by the decrease of the phonon mean free path by reduced-dimensional effects
In the semiquantum molecular dynamics approach, the dynamics of the system is described with the use of the classical Newtonian equations of motion while the effects of phonon quantum statistics are introduced through random Langevin-like forces with a specific power spectral density
The semiquantum molecular dynamics approach has allowed us to model the transition in the rough-edge nanoribbons from the thermal insulator-like behavior at high temperature, when the thermal conductivity decreases with the conductor length, to the ballistic conductor-like behavior at low temperature, when the thermal conductivity increases with the conductor length

Summary

Introduction

It has been recently shown [1] that silicon and germanium nanowires can give a figure of merit of over 2 at 800 K due to strong reduction of phonon thermal conductivity in nanowires as compared with their equivalent bulk material, i.e., the reduction is caused by the alloy disorder, and by the decrease of the phonon mean free path by reduced-dimensional effects. Molecular dynamics is a method of numerical modeling of molecular systems based on classical Newtonian mechanics It does not allow for the description of pure quantum effects such as the freezing out of highfrequency oscillations at low temperatures and the related decrease to zero of heat capacity for T → 0. Because of its complexity, a pure quantummechanical description does not allow, in general, the detailed modeling of the dynamics of many-body systems. To overcome these obstacles, different semiclassical methods, which allow to take into account quantum effects, have been proposed [3,4,5,6,7,8,9]

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