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The wave property of phonons is employed to explore the thermal transportacross a finite periodic array of nano-scatterers such as circular andtriangular holes. As thermal phonons are generated in all directions, we studytheir transmission through a single array for both normal and obliqueincidences, using a linear dispersionless time-dependent acoustic frame in atwo-dimensional system. Roughness effects can be directly considered within thecomputations without relying on approximate analytical formulae. Analysis byspatio-temporal Fourier transform allows us to observe the diffraction effectsand the conversion of polarization. Frequency-dependent energy transmissioncoefficients are computed for symmetric and asymmetric objects. We demonstratethat the phononic array acts as an efficient thermal barrier by applying thetheory of thermal boundary (Kapitza) resistances to arrays of smooth scatteringholes in silicon for an exemplifying periodicity of 10 nm in the [5-100 K]temperature range. It is observed that the associated thermal conductance hasthe same temperature dependence than that without phononic filtering.

Phononic thermal resistance due to a finite periodic array of nano-scatterers