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Ab initio Calculation of the Effective Thermal Conductivity Coefficient of a Superlattice Using the Boltzmann Transport Equation

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Abstract

The effective thermal conductivity coefficient of a binary semiconductor heterostructure is calculated by an example of the GaAs/AlAs superlattice at different layer periods and different ambient temperatures. The applicability of the Fourier-law models is strongly limited on the investigated scale, since they do not take into account the quantum-mechanical properties of materials, which leads to a large deviation from the experimental data. However, the use of molecular dynamics methods allows us to obtain accurate solutions; however, these methods are much more demanding of computing resources and require a nontrivial potential selection problem to be solved. In the investigations of the nanostructures, good results are obtained using the methods based on solving the Boltzmann transport equation for phonons; they make it possible to obtain a fairly accurate solution at a lower computational complexity compared with the molecular dynamics methods. To calculate the thermal conductivity coefficient, a modal suppression model is used, which approximates the solution of the Boltzmann transport equation for phonons. The dispersion and phonon scattering parameters are obtained using ab initio calculations. The two-phonon processes related to the isotopic disorder and the barrier three-phonon scattering processes are taken into account. To increase the accuracy of the calculations, the inhomogeneity of the distribution of materials over the superlattice layers is taken into account. A comparison of the results obtained with the experimental data shows their close agreement.

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ACKNOWLEDGMENTS

The computations were made on a computing cluster of the Federal Research Center “Informatics and Management,” Russian Academy of Sciences.

Funding

This study was supported by the Russian Foundation for Basic Research, project nos. 19-08-01191_a and 18-29-03100.

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Authors and Affiliations

  1. Dorodnitsyn Computing Center, Federal Research Center “Informatics and Management,” Russian Academy of Sciences, 119333, Moscow, Russia

    K. K. Abgaryan & I. S. Kolbin

  2. Moscow Aviation Institute (National Research University), 125993, Moscow, Russia

    K. K. Abgaryan

Authors
  1. K. K. Abgaryan
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  2. I. S. Kolbin
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Corresponding author

Correspondence to K. K. Abgaryan.

Additional information

Translated by E. Bondareva

The article is based on a report presented at the 1st International Conference on “Mathematical Modeling in Materials Science of Electronic Components,” Moscow, 2019.

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Abgaryan, K.K., Kolbin, I.S. Ab initio Calculation of the Effective Thermal Conductivity Coefficient of a Superlattice Using the Boltzmann Transport Equation. Russ Microelectron 49, 594–599 (2020). https://doi.org/10.1134/S1063739720080028

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