Monte Carlo simulation of phonon transport from ab-initio data with Nano-κ

Understanding of heat transport in nanodevices is a challenging issue for several new technologies. It requires specific modelling approaches and dedicated simulation tools. Yet the latter are not numerous, and are often adapted to some "classic" materials or restricted to simple geometries (i.e. thin films, nanowires). Looking to address this deficiency, the present work brings Nano-κ, a Python code to simulate the phonon transport in nano and micro scale devices from ab-initio phonon data. The code has personalizing capabilities that allow to simulate several geometries and materials, offering insights of temperature distribution, heat flux, thermal conductivity, and mode contribution to energy transport. In the present work, a detailed description of the physical model implementation is provided and several simulation test cases are discussed. Nano-κ provides reliable predictions of the thermal conductivity in different materials, and is able to correctly predict the relative effect of size, temperature, and surface roughness on thermal transport properties. Program Title: Nano-κ CPC Library link to program files: https://doi.org/10.17632/tr29mhkjh8.1 Developer's repository link: https://github.com/brunohs1993/Nanokappa Licensing provisions: MIT Programming language: Python Nature of problem: The estimation of heat conduction at nanoscales depends on the estimation of phonon transport, since Fourier's law may not be valid in these situations. The phonon transport is described by the Boltzmann Transport Equation (BTE), that needs to be solved for each phonon mode separately, while estimating temperature distributions that depends on all modes at the same time. The phonon data can be retrieved from ab-initio simulations. Some BTE calculations have been already done through the years for simple geometries, but there is no publicly available code that allows enough flexibility to be used by the scientific community. Solution method: Some previous works [1-3] have had success in applying the Monte Carlo method to solve the BTE for phonon transport. In the more recent works, the ab-initio data is retrieved from density functional theory (DFT) simulations [4-5]. Nano-κ is a Python code built on the same theoretical basis of previous developments, but adds more flexibility so that it can be open for public research use. David Lacroix, Karl Joulain, Denis Lemonnier, Monte Carlo transient phonon transport in silicon and germanium at nanoscales, Phys. Rev. B, 72 (Aug 2005) 064305, https://doi.org/10.1103/PhysRevB.72.064305. Laurent Chaput, Jérôme Larroque, Philippe Dollfus, Jérôme Saint-Martin, David Lacroix, Ab initio based calculations of the thermal conductivity at the micron scale, Appl. Phys. Lett. 112 (3) (2018) 033104, https://doi.org/10.1063/1.5010959. Brice Davier, Jérôme Larroque, Philippe Dollfus, Laurent Chaput, Sebastian Volz, David Lacroix, Jérôme Saint-Martin, Heat transfer in rough nanofilms and nanowires using Full Band Ab Initio Monte Carlo simulation, J. Phys., Condens. Matter, 30 (49) (October 2018) 495902, https://doi.org/10.1088/1361-648X/aaea4f. Atsushi Togo, Laurent Chaput, Isao Tanaka, Distributions of phonon lifetimes in brillouin zones, Phys. Rev. B, 91 (Mar 2015) 094306, https://doi.org/10.1103/PhysRevB.91.094306. Atsushi Togo, Laurent Chaput, Terumasa Tadano, Isao Tanaka, Implementation strategies in phonopy and phono3py. J. Phys., Condens. Matter, 35 (35) (2023) 353001, https://doi.org/10.1088/1361-648X/acd831.