We present the concept of a locally resonant nanophononic metamaterial for thermoelectric energy conversion. Our configuration, which is based on a silicon thin film with a periodic array of pillars erected on one or two of the free surfaces, qualitatively alters the base thin-film phonon spectrum due to a hybridization mechanism between the pillar local resonances and the underlying atomic lattice dispersion. Using an experimentally fitted lattice-dynamics-based model, we conservatively predict the metamaterial thermal conductivity to be as low as 50% of the corresponding uniform thin-film value despite the fact that the pillars add more phonon modes to the spectrum.

Recent work has demonstrated that nanostructuring of a semiconductor material to form a phononic crystal (PnC) can significantly reduce its thermal conductivity. In this paper, we present a classical method that combines atomic-level information with the application of Bloch theory at the continuum level for the prediction of the thermal conductivity of finite-thickness PnCs with unit cells sized in the micron scale. Lattice dynamics calculations are done at the bulk material level, and the plane-wave expansion method is implemented at the macrosale PnC unit cell level. The combination of the lattice dynamics-based and continuum mechanics-based dispersion information is then used in the Callaway-Holland model to calculate the thermal transport properties of the PnC. We demonstrate that this hybrid approach provides both accurate and efficient predictions of the thermal conductivity.

While resonant propagation modes are non-existent within band gaps in infinite periodic structures, it is possible for anomalous band-gap resonances to appear in finite periodic structures. We establish two criteria for the characterization of band-gap resonances and propose approaches for their elimination. By considering flexural periodic beams, we show that as the number of unit-cells is increased the vibration response corresponding to band-gap resonances (1) does not shift in frequency, and (2) drops in amplitude. Both these outcomes are not exhibited by regular pass-band resonances, nor by resonances in finite homogenous beams when the length is changed. Our conclusions stem from predictions based on Timoshenko beam theory coupled with matching experimental observations.

The concept of a phononic crystal can in principle be realized at the nanoscale whenever the conditions for coherent phonon transport exist. Under such conditions, the dispersion characteristics of both the constitutive material lattice (defined by a primitive cell) and the phononic crystal lattice (defined by a supercell) contribute to the value of the thermal conductivity. It is therefore necessary in this emerging class of phononic materials to treat the lattice dynamics at both periodicity levels. Here we demonstrate the utility of using supercell lattice dynamics to investigate the thermal transport behavior of three-dimensional nanoscale phononic crystals formed from silicon and cubic voids of vacuum. The periodicity of the voids follows a simple cubic arrangement with a lattice constant that is around an order of magnitude larger than that of the bulk crystalline silicon primitive cell. We consider an atomic-scale supercell which incorporates all the details of the silicon atomic locations and the void geometry. For this supercell, we compute the phonon band structure and subsequently predict the thermal conductivity following the Callaway-Holland model. Our findings dictate that for an analysis based on supercell lattice dynamics to be representative of the properties of the underlying lattice model, a minimum supercell size is needed along with a minimum wave vector sampling resolution. Below these minimum values, a thermal conductivity prediction of a bulk material based on a supercell will not adequately recover the value obtained based on a primitive cell. Furthermore, our results show that for the relatively small voids and void spacings we consider (where boundary scattering is dominant), dispersion at the phononic crystal unit cell level plays a noticeable role in determining the thermal conductivity

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