  Probing detailed spectral dependence of phonon transport properties in bulk
materials is critical to improve the function and performance of structures and
devices in a diverse spectrum of technologies. Currently, such information can
only be provided by the phonon spectral energy density (SED) or equivalently
time domain normal mode analysis (TDNMA) methods in the framework of
equilibrium molecular dynamics simulation (EMD), but has not been realized in
non-equilibrium molecular dynamics simulations (NEMD) so far. In this paper we
generate a new scheme directly based on NEMD and lattice dynamics theory,
called time domain direct decomposition method (TDDDM), to predict the phonon
mode specific thermal conductivity. Two benchmark cases of Lennard-Jones (LJ)
Argon and Stillinger-Weber (SW) Si are studied by TDDDM to characterize
contributions of individual phonon modes to overall thermal conductivity and
the results are compared with that predicted using SED and TDNMA. Excellent
agreements are found for both cases, which confirm the validity of our TDDDM
approach. The biggest advantage of TDDDM is that it can be used to investigate
the size effect of individual phonon modes in NEMD simulations, which cannot be
tackled by SED and TDNMA in EMD simulations currently. We found that the phonon
modes with mean free path larger than the system size are truncated in NEMD and
contribute little to the overall thermal conductivity. The TDDDM provides
direct physical origin for the well-known strong size effects in thermal
conductivity prediction by NEMD.
