Phonon Thermal Transport in Semiconductors Studied Using a Neural Network Assisted Solution of The Peierls-Boltzmann Equation

Unusual thermal transport phenomena such as the hydrodynamic and Poiseuille phonon flow arise out of strong coupling among phonons in certain solid-state crystalline materials, and find applications in thermal cloaking and shielding of semiconductor devices and in the development of low thermal noise detectors. The linearized Peierls-Boltzmann equations (LPBE), which form a set of multi-dimensional and coupled partial differential equations, govern the coupled dynamics, transport and equilibriation of phonons in these systems. Hence, solving the LPBE is a crucial step towards discovering new materials that display these unusual, yet technologically important phenomena.<br/><br/>However, predictive solutions of the LPBE including lowest-order interactions among three phonons and higher-order interactions among four phonons with <i>ab initio</i> inputs from density functional theory, which will serve as search tools for new materials, have been computationally intractable until recently [1, 2]. Even considering these recent advances, the computational cost due to the high dimensionality of the LPBE, large number of phonon polarization for the materials with complex crystal geometries and the need to resolve highly localized, temporally evolving interactions among phonons makes these conventional methods unsuitable for the rapid search of new materials that show exceptional hydrodynamic phonon transport.<br/><br/>To overcome this problem, here we develop a neural network scheme to solve the steady-state and the transient LPBE, which enables rapid convergence of the steady-state solution of the LPBE and allows for computationally efficient high temporal resolution of localized interactions among phonons under transient transport conditions, which is particularly important to search for materials with strongly hydrodynamic phonon flow. We show that, for materials with complex crystal structures beyond the cubic geometry such as bulk MoS₂, graphite, w-GaN and hBN, where hydrodynamic transport is possible at cryogenic conditions, the neural network scheme significantly outperforms the conventional iterative solution of the LPBE under both steady-state and transient conditions. Our findings highlight the computational advantages of adopting this new neural network-based first principles solver for the LPBE, which can have significant impact in the research areas of developing robust, efficient computational tools for materials discovery.<br/><br/>This work is supported by India's Science and Engineering Research Board through the Core Research Grant No. CRG/2020/006166 and the Mathematical Research Impact Centric Support Grant No. MTR/2022/001043. The presenter also acknowledges the Infosys Young Investigator award for support.<br/><br/>[1] Tianli Feng, Lucas Lindsay, and Xiulin Ruan, Phys. Rev. B 96, 161201(R), 2017.<br/>[2] Navaneetha K. Ravichandran and David Broido, Phys. Rev. X 10, 021063, 2020.