Linear harmonic atomic chain. K and a refer to the force and the lattice constant, u_{i } to the displacement of atom i and F_{ij } to the force between atoms i and j .

Schematic of a superlattice period showing the predominance of phonon–phonon interactions (blue line) when the phonon mean free path Λ is smaller than the period. In this situation, heat transfer is diffusive, Fourier's law can be applied, and the effective thermal conductivity is an averaged of the bulk thermal conductivities of both layers. The quantity q refers here to a Fourier heat flux.

Schematic of a superlattice period showing the predominance of interfacial scattering (blue line) when the phonon mean free path Λ is larger than the period. The total superlattice thermal resistance is defined by the sum of the interfacial resistances, and the effective thermal conductivity is equal to the ratio of the period to the interfacial resistance.

Schematic figure of the twinning SL with the stacking sequence (left) and TCs of the Si twinning SL NWs as a function of the period for different diameters D at 300 K (right).

Y –Z components of the LA-mode vectors around the frequency 4.0 cm^{−1} for (a) the pristine, (b) L_{p} =1.25 nm, (c) L_{p} =1.9 nm, and (d) L_{p} =10.6 nm NWs with 2 nm in diameter. The colour represents the number of modes and the maximum value has been normalized to 1. The corresponding structures are schematically indicated in each panel.

Schematic of a one-side branched Si NW where the side branches are served as resonator structures (left) and the TC of resonant NWs with the change of period L_{p} .

Phonon dispersion in the frequency range [0;3] THz for pristine Si NWs (a), two-side branched Si NWs with L_{h} =1.63 nm (b); visualization of the phonon modes indicated by the circle (c), the square (d), the triangle (e) symbols in (b).

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