Quantum mechanical modeling of anharmonic phonon-phonon scattering in nanostructures

Abstract

The coherent quantum effect becomes increasingly important in the heat dissipation bottleneck of semiconductor nanoelectronics with the characteristic size shrinking down to few nano-meters scale nowadays. However, the quantum mechanical model remains elusive for anharmonic phonon-phonon scattering in extremely small nanostructures with broken translational symmetry. It is a long-term challenging task to correctly simulate quantum heat transport including anharmonic scattering at a scale relevant to practical applications. In this article, we present a clarified theoretical formulation of anharmonic phonon non-equilibrium Green function (NEGF) formalism for both 1D and 3D nanostructures, through a diagrammatic perturbation expansion and an introduction of Fourier representation to both harmonic and anharmonic terms. A parallelized computational framework with first-principle force constants input is developed for large-scale quantum heat transport simulation. Some crucial approximations in numerical implementation are investigated to ensure the balance between numerical accuracy and efficiency. A quantitative validation is demonstrated for the anharmonic phonon NEGF formalism and computational framework by modeling cross-plane heat transport through silicon thin film. The phonon-phonon scattering is shown to be appreciable and to introduce about 20% reduction of thermal conductivity at room temperature even for a film thickness around 10 nm. The present methodology provides a robust platform for the device quantum thermal modeling, as well as the study on the transition from coherent to incoherent heat transport in nano-phononic crystals. This work thus paves the way to understand and to manipulate heat conduction via the wave nature of phonons.

arXiv comment47 pages, 16 figures

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Cited by in corpus (9)

• Anharmonic phonon-phonon scattering at interface by non-equilibrium Green's function formalism
• Thermal conductivity minimum of graded superlattices due to phonon localization
• Atomistic simulation of phonon heat transport across metallic nanogaps
• Interfacial Thermal Conductance Spectrum in Nonequilibrium Molecular Dynamics Simulations Considering Anharmonicity, Non-homogeneity and Quantum Effects
• Theory of Non-equilibrium Heat transport in anharmonic multiprobe systems at high temperatures
• Revealing molecule-internal mechanisms that control phonon heat transport through single-molecule junctions by a genetic algorithm
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• Local heat current flow in ballistic phonon transport of graphene nanoribbons
• Thermal transport in crystals: from the quantum Dyson equation to mesoscopic phonon hydrodynamics