Effects of quantum statistics of phonons on the thermal conductivity of silicon and germanium nanoribbons
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NANO EXPRESS
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Effects of quantum statistics of phonons on the thermal conductivity of silicon and germanium nanoribbons Yuriy A Kosevich1,2* , Alexander V Savin1 and Andr´es Cantarero2
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. Keywords: Thermal conductivity, Molecular dynamics simulation, Nanoribbon, Silicon, Germanium, Isotopic effect
Background 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 not only by the alloy disorder, but also by the decrease of the phonon mean free path by reduced-dimensional effects. The effect of temperature on the thermal conductivity of silicon and germanium may be quite different since the Debye temperature of silicon almost doubles that of germanium. The purpose of the present work is to analyze quantum statistic effects on thermal phonon conductivity in silicon and germanium nanoribbons with the use of the novel semiquantum molecular dynamics simulation [2].
*Correspondence: [email protected] 1 Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, 119991, Russia 2 Materials Science Institute, University of Valencia, PO Box 22085, Valencia, 46071, Spain
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. On the other hand, 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 [3-9]. The most conve
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