Thermal Rectification by Ballistic Phonons in Asymmetric Nanostructures

2009 ◽  
Author(s):  
John Miller ◽  
Wanyoung Jang ◽  
Chris Dames
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Monte Carlo Method ◽  
Phonon Transport ◽  
Reverse Direction ◽  
Careful Attention ◽  
Energy Carriers ◽  
Thermal Rectification ◽  
Special Surface ◽  
Ballistic Phonons

In analogy to an electrical diode, a thermal rectifier transports heat more easily in one direction than in the reverse direction. Among various possible nanoscale rectification mechanisms, a ballistic rectifier relies on asymmetric scattering of energy carriers, as has been suggested for phonon transport in a sawtooth nanowire [S. Saha, L. Shi, & R. Prasher, IMECE 2006] or nanowire with special surface specularity function [N.A. Roberts and D.G. Walker, ITherm 2008]. We have used a Landauer-Buttiker method as well as a Monte Carlo method to model the asymmetric heat transport in such nanostructures, with careful attention to boundary conditions that satisfy the 2nd Law of Thermodynamics. The calculations show that ballistic rectification is only significant at relatively large “thermal bias,” which causes significant anisotropy in the distribution function of energy carriers emitted at each of the two thermal contacts. We also propose experiments to observe this phenomenon using either phonons or photons.

Thermal Rectification by Ballistic Phonons

2008 ◽  
Author(s):  
John Miller ◽  
Wanyoung Jang ◽  
Chris Dames
Keyword(s):  
Distribution Function ◽  
Mean Free Path ◽  
Temperature Gradients ◽  
Reverse Direction ◽  
Large Temperature ◽  
Thermal Rectification ◽  
Einstein Distribution ◽  
Ballistic Phonons ◽  
Dimensional Electron Gas ◽  
Bose Einstein

In analogy to the asymmetric transport of electricity in a familiar electrical diode, a thermal rectifier transports heat more favorably in one direction than in the reverse direction. One approach to thermal rectification is asymmetric scattering of phonons and/or electrons, similar to suggestions in the literature for a sawtooth nanowire [1] or 2-dimensional electron gas with triangular scatterers [2]. To model the asymmetric heat transport in such nanostructures, we have used phonon ray-tracing, focusing on characteristic lengths that are small compared to the mean free path of phonons in bulk. To calculate the heat transfer we use a transmission-based (Landauer-Buttiker) method. The system geometry is described by a four-dimensional transfer function that depends on the position and angle of phonon emission and absorption from each of two contacts. At small temperature gradients, the phonon distribution function is very close to the usual isotropic equilibrium (Bose-Einstein) distribution, and there is no thermal rectification. In contrast, at large temperature gradients, the anisotropy in the phonon distribution function becomes significant, and the resulting heat flux vs. temperature curve (analogous to I-V curve of a diode) reveals large thermal rectification.

Monte Carlo Simulation of Steady-State Microscale Phonon Heat Transport

2008 ◽  
Vol 130 (7) ◽  
Author(s):  
Jaona Randrianalisoa ◽  
Dominique Baillis
Keyword(s):  
Heat Transfer ◽  
Thin Films ◽  
Monte Carlo ◽  
Heat Conduction ◽  
Steady State ◽  
Monte Carlo Method ◽  
Silicon Nanowires ◽  
Silicon Film ◽  
Relaxation Times ◽  
Phonon Transport

Heat conduction in submicron crystalline materials can be well modeled by the Boltzmann transport equation (BTE). The Monte Carlo method is effective in computing the solution of the BTE. These past years, transient Monte Carlo simulations have been developed, but they are generally memory demanding. This paper presents an alternative Monte Carlo method for analyzing heat conduction in such materials. The numerical scheme is derived from past Monte Carlo algorithms for steady-state radiative heat transfer and enables us to understand well the steady-state nature of phonon transport. Moreover, this algorithm is not memory demanding and uses very few iteration to achieve convergence. It could be computationally more advantageous than transient Monte Carlo approaches in certain cases. Similar to the famous Mazumder and Majumdar’s transient algorithm (2001, “Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization,” ASME J. Heat Transfer, 123, pp. 749–759), the dual polarizations of phonon propagation, the nonlinear dispersion relationships, the transition between the two polarization branches, and the nongray treatment of phonon relaxation times are accounted for. Scatterings by different mechanisms are treated individually, and the creation and/or destruction of phonons due to scattering is implicitly taken into account. The proposed method successfully predicts exact solutions of phonon transport across a gallium arsenide film in the ballistic regime and that across a silicon film in the diffusion regime. Its capability to model the phonon scattering by boundaries and impurities on the phonon transport has been verified. The current simulations agree well with the previous predictions and the measurement of thermal conductivity along silicon thin films and along silicon nanowires of widths greater than 22nm. This study confirms that the dispersion curves and relaxation times of bulk silicon are not appropriate to model phonon propagation along silicon nanowires of 22nm width.

scholarly journals Deviational Phonons and Thermal Transport at the Nanoscale

2012 ◽  
Author(s):  
Jean-Philippe M. Péraud ◽  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Three Dimensional ◽  
Simulation Method ◽  
Phonon Transport ◽  
Statistical Uncertainty ◽  
Small Temperature ◽  
Efficient Simulation ◽  
Transport Problems ◽  
Individual Particles

We present a new method for simulating phonon transport at the nanoscale. The proposed approach is based on the recently developed energy-based deviational Monte Carlo method by the authors [Phys. Rev. B 84, 205331, 2011] which achieves significantly reduced statistical uncertainty compared to standard Monte Carlo methods by simulating only the deviation from equilibrium. Here, we show that under linearized conditions (small temperature differences) the trajectories of individual particles simulating the deviation from equilibrium can be decoupled and can thus be simulated independently, without introducing any additional approximation. This leads to a particularly simple and efficient simulation method that can be used to treat steady and transient phonon transport problems in arbitrary three-dimensional geometries.

scholarly journals Ring statistics in disordered solids: a parallel algorithm for clusters with hundred thousands of atoms

2017 ◽  
pp. 447-454
Author(s):  
Ф.В. Григорьев ◽  
В.Б. Сулимов ◽  
А.В. Тихонравов
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Monte Carlo Method ◽  
Parallel Algorithm ◽  
Structural Elements ◽  
Disordered Solids ◽  
The Monte Carlo Method

Кольца, состоящие из различного числа атомов, являются основным структурным элементом во многих неупорядоченных веществах. В настоящей статье представлен параллельный алгоритм получения приближенной функции распределения колец по числу атомов, основанный на методе Монте-Карло. Алгоритм применен к кластерам диоксида кремния, содержащим до миллиона атомов. Исследована эффективность алгоритма, как функция числа используемых вычислительных ядер, вплоть до 1024. The rings consisting of various number of atoms are basic structural elements in many disordered solids. In this paper, a parallel algorithm for calculating an approximate ring distribution function by the number of atoms is proposed. The algorithm is based on the Monte Carlo method and is applied to SiO$_2$ clusters consisting of up to $10^6$ atoms. The efficiency of the algorithm is studied using up to 1024 computational cores.

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