Session: 09-03: Computational Methods in Micro/ Nanoscale Transport

Paper Number: 140769

140769 - Nanoscale Heat Conduction With Electrons and Phonons From the Discrete Ordinate Method 

Abstract: 

It is well established that heat conduction requires to be modelled by the Boltzmann transport equation (BTE) when the sizes involved start to be similar to the mean free path of the energy carriers. It is the case for both phonons, which carry heat in nonmetallic materials and possess room-temperature mean free path averaged at around 200 nm, and electrons, which carry heat in metals with smaller mean free path of dozens of nanometers. There are various ways to simulate heat conduction at the nanoscale. Monte-Carlo methods are currently popular due to their capability to address complex geometries, but deterministic methods can also be used in less-complex geometries such as nanowires or deposited metallic lines standing on substrates or multilayers, which are used in a broad variety of applications. Various techniques to solve the BTE have been described since decades in the community dealing with Radiative Transfer Equation (RTE), including the Discrete Ordinate Method (DOM), which is addressed in the current paper. In particular, early analyses of thermal conductivity in nanowires was done with this method [1].

Here, we first analyze the interplay between heat source sizes and layer thicknesses. When the thickness is large, the heat source effect, when it is smaller than the mean free path and leads to ballistic dissipation, can be considered independently. However, when thickness is small, it is not the case anymore and treating the effects independently is not justified. We analyze numerically such effect in Cartesian 2D geometry in the case of phonons in silicon.
In a second step, we implement an electron-phonon solver and analyze the interplay between their respective mean free paths and layer thicknesses. It is shown that depending on coupling strength temperature fields are identical or differ.
Finally, we introduce an interative technique to address multiscale heat conduction by coupling the DOM solver dealing with nanoscale to a solver of the heat equation that deals with larger scales [2]. In particular, we discuss the condition for fast convergence of the numerical code and explain the difficulties inherent to large dimensionalities.

 

[1] S. Volz, D. Lemonnier, J.-B. Saulnier, Clamped nanowire thermal conductivity based on phonon transport equation, Microscale Thermophysical Engineering 5 (3), 191-207 (2001)

[2] W. Cheng, A.Alkurdi, P.-O. Chapuis, Coupling mesoscopic Boltzmann transport equation and macroscopic heat diffusion equation for multiscale phonon heat conduction, Nanoscale and Microscale Thermophysical Engineering 24, 150 (2020)

We acknowledge funding by EU project EFINED and French project ANR EFICACE.

Presenting Author: P-Olivier Chapuis CNRS

Presenting Author Biography: P-Olivier Chapuis is a CNRS researcher at the Centre for Energy and Thermal Sciences of Lyon (CETHIL), where he leads the 'Micro and nanoscale heat transfer' (MiNT) group. The centre is located on the campus of INSA, the National Institute of Applied Sciences, in Lyon.

Authors:

Ali Alkurdi CNRS
Weizheng Chen INSA Lyon
P-Olivier Chapuis CNRS