  The understanding and modeling of inelastic scattering of thermal phonons at
a solid/solid interface remain an open question. We present a fully quantum
theoretical scheme to quantify the effect of anharmonic phonon-phonon
scattering at an interface via non-equilibrium Green's function (NEGF)
formalism. Based on the real-space scattering rate matrix, a decomposition of
the interfacial spectral energy exchange is made into contributions from local
and non-local anharmonic interactions, of which the former is shown to be
predominant for high-frequency phonons whereas both are important for
low-frequency phonons. The anharmonic decay of interfacial phonon modes is
revealed to play a crucial role in bridging the bulk modes across the
interface. The overall quantitative contribution of anharmonicity to thermal
boundary conductance is found to be moderate. The present work promotes a
deeper understanding of heat transport at the interface and an intuitive
interpretation of anharmonic phonon NEGF formalism.
