Nonequilibrium Green's Function Approach to Thermal Transport in Nanowires

Abstract

Thermal transport in nanowires deviates strongly from bulk behavior once wire diameter approaches the phonon
mean free path, but capturing this crossover quantitatively requires a transport formalism that treats ballistic and
diffusive scattering on equal footing. We apply the nonequilibrium Green's function (NEGF) formalism, combined
with a Born-von Karman lattice dynamics description of the phonon spectrum, to compute phonon thermal
conductance in silicon nanowires across 30 diameters from 5 to 200 nm and temperatures from 100 to 500 K,
incorporating boundary scattering, isotope scattering, and anharmonic phonon-phonon scattering self-energies. At
300 K, computed thermal conductance decreased from a bulk-like value of 1.42 nW/K at 200 nm diameter to 0.081
nW/K at 5 nm diameter, a 94.3% reduction, with the diameter dependence following an effective power law of
conductance proportional to d^1.61 ± 0.05 across the 5-40 nm range, distinctly weaker than the d^2 scaling
expected from cross-sectional area alone, reflecting the growing influence of diameter-dependent phonon boundary
scattering. The apparent phonon mean free path, extracted from the ratio of NEGF-computed conductance to the
diffusive (Fourier) prediction, fell below the corresponding bulk value at all tested diameters and dropped to 38% of
the bulk mean free path at 10 nm, indicating a transport regime intermediate between fully ballistic and fully diffusive
across most of the diameter range studied rather than a sharp crossover at a single diameter. Temperature
dependence of thermal conductance showed a maximum near 150-200 K for wires below 20 nm diameter, in
contrast to the monotonic decrease with temperature seen above 250 K for wires larger than 50 nm, a qualitative
difference attributed to the relative suppression of anharmonic Umklapp scattering, whose phase space is itself
reduced in narrow wires, relative to the boundary-scattering contribution, which is comparatively
temperature-independent. Comparison against a simplified Callaway-model Boltzmann transport calculation
showed agreement with the NEGF results to within 12% at diameters above 40 nm but a systematic underestimate
of NEGF-predicted conductance by 24-31% at diameters below 15 nm, where phonon confinement effects not
captured by the bulk-dispersion Callaway model become significant. These results quantify the diameter- and
temperature-dependent departure of nanowire thermal transport from bulk diffusive behavior and identify the sub-15
nm regime as one requiring full quantum transport treatment for quantitatively accurate thermal conductance
prediction.