Quantum mechanical modeling of anharmonic phonon-phonon scattering in nanostructures

TL;DR

This paper develops a quantum mechanical model using NEGF formalism to simulate anharmonic phonon-phonon scattering in nanostructures, enabling better understanding of heat transport at nanoscale.

Contribution

It introduces a comprehensive NEGF-based theoretical framework and computational tool for modeling anharmonic phonon interactions in 1D and 3D nanostructures with first-principles accuracy.

Findings

Phonon-phonon scattering reduces thermal conductivity by about 20% at room temperature in 10 nm silicon films.

The methodology accurately models cross-plane heat transport in silicon thin films.

The framework bridges the gap between quantum heat transport theory and practical nanoscale device simulations.

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.