Session: K9-09: NANOSCALE THERMAL TRANSPORT MODELING AND MACHINE LEARNING I

Paper Number: 138026

138026 - A Complex Thermal Conductivity to Model Ballistic Phonon Transport Under Periodic Heating 

Abstract: 

Non-Fourier thermal transport have been investigated both theoretically and experimentally for decades [1-2]. However, the widely used experimental techniques, e.g. the 3ω method, the time/frequency domain thermal reflectance method, rely on solutions to the diffusion equation, leading to inconsistency between measured non-Fourier effects and the Fourier-Law based techniques.

One of the major reasons to the inconsistency above is that the phonon Boltzmann transport equation (BTE), which can deal with the non-Fourier effect, is hard to solve analytically, even under the relaxation time approximation (RTA).  On the other hand, a compact algebraic solution is essential to popularize an experimental technique.  This is evident to the popular Fourier-Law based techniques above.

Here, inspired by the concept of the complex refractive index in the solution to the equation that describes the radiative wave propagation within an absorbing medium, we introduce a complex thermal conductivity.  With this complex thermal conductivity, we can map any existing solution of the diffusion equation under periodic heating to that of the BTE under RTA.  This framework is verified using existing solutions [7-10].

As a concrete example, we extend the classic 3ω method from diffusive to ballistic. We first verify this ballistic 3ω method in various limiting scenarios. Then we develop a formalism to extract materials’ mean free time (MFT) distribution by directly fitting experiments to the ballistic 3ω solution. Finally, we generate synthetic “experiments” to demonstrate the consistency between the “measured” non-Fourier effects and this ballistic 3ω technique. We also discuss the potential combination of this framework and the scattering matrix formalism [11] to model phonon transport in multilayer structures.

 

REFERENCES

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[3]     G. Chen., Nanoscale Energy Transport and Conversion, Oxford: Oxford University Press, (2005).

[4]     M. F. Modest., Radiative Heat Transfer, San Diego: Academic Press, (2003).

[5]    David W. Hahn and M. Necati Ozisik, Heat Conduction, John Wiley & Sons, Inc., (2012).

[6]     H. S. Carslaw and J. C. Jaeger., Conduction of Heat in Solids, Oxford University Press, (1959).

[7]    C. Hua and A. J. Minnich, Phys. Rev. B.,90, 214306 (2014).

[8]    F. Yang, and C. Dames., Phys. Rev. B., 91, pp.165311, (2015).

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[10] G. Wehmeyer, J. Appl. Phys. 126, 124306 (2019).

[11] T. Li and Z. Chen, J. Appl. Phys., 132, 125103, (2022).

Presenting Author: Tao Li Southeast University

Presenting Author Biography: Tao Li focuses on fundamental phonon transport modeling at the micro-nanoscale, including analytical solution of Boltzmann transport equation under relaxation time assumption, especially at thermal conductivity’s size effect and frequency effect.

Authors:

Tao Li Southeast University
Bo Jiang Southeast University
Zhen Chen Southeast University