  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.
