Abstract
We study ballistic interfacial thermal transport across atomic junctions. Exact expressions for phonon transmission coefficients are derived for thermal transport in one-junction and two-junction chains, and verified by numerical calculation based on a nonequilibrium Green's function method. For a single-junction case, we find that the phonon transmission coefficient typically decreases monotonically with increasing freqency. However, in the range between the point of equal frequency spectrum and that of equal acoustic impedance, it first increases then decreases, which explains why the Kapitza resistance calculated from the acoustic mismatch model is far larger than the experimental values at low temperatures. The junction thermal conductance reaches a maximum when the interfacial coupling equals the harmonic average of the spring constants of the two semi-infinite chains. For three-dimensional junctions, in the weak coupling limit, we find that the conductance is proportional to the square of the interfacial coupling, while for a intermediate coupling strength the conductance is approximately proportional to the interfacial coupling strength. For two-junction chains, the transmission coefficient oscillates with the frequency due to interference effects. The oscillations between the two envelope lines can be understood analytically, thus providing guidelines for designing phonon frequency filters.
Highlights
In the past decade there has been a significant research focus on thermal transport in micro scale[1]
For three-dimensional junctions, in the weak coupling limit, we find that the conductance is proportional to the square of the interfacial coupling, while for intermediate coupling strength the conductance is approximately proportional to the interfacial coupling strength
III, we have derived the analytical expressions for the phonon transmission coefficient for pointjunction and extended-junction
Summary
Is Zi = ρivi = (mi/ai)vi, and We note that in acoustic mismatch model the transmission coefficient is frequency independent, and in reality it only applies in the limit of low frequency/long wavelengths. In this case the phonon sees the interface only as a discontinuity between two semiinfinite media and the transmission does not depend on the coupling spring strength kij.
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