Thermal conductivity prediction of nanoscale phononic crystal slabs using a hybrid lattice dynamics-continuum mechanics technique

Abstract

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.

Thermal transport in phononic crystals and the observation of coherent phonon scattering at room temperature

“…Fig. 2 shows the computed phonon dispersion normalized with the transverse wave speed (c t ) using the plane wave expansion technique 8 . Implicit in this calculation is the assumption that phase information is retained throughout the entire spectrum.…”

“…2) is used for o(q), which implicitly accounts for the existence of the air holes; hence we set f(f) ¼ 1 in equation (1). Incoherent scattering from the surface boundaries of the sample was still accounted for by setting L ¼ t. A total of over 46,000 modes were used in the calculation of the PnC dispersion 8 . It is worth noting here that this method is quite accurate for the acoustic phonon branches but to a lesser degree for the optical branches.…”

“…Recently, it has been proposed that coherent boundary scattering in phononic crystals (PnCs) with relatively large feature sizes (Z100 nm) may hold the key to solving this problem by scattering phonons with minimal influence on electrons [7][8][9] . As phonons traverse such a lattice, they can undergo two types of scattering processes: simple particle-like incoherent scattering as a result of encountering a boundary, and wave-like coherent Bragg 10 scattering due to the periodic geometry of the artificial lattice of air holes.…”

“…Thus, the possibility of coherent phonon boundary scattering in Si-air PnCs at room temperature has generated widespread debate in the literature, given the relatively small wavelength of the phonon population dominating the thermal transport 6,8,[12][13][14][15] . Experimentally, however, the thermal conductivity (k) of PnC samples has consistently been measured to be significantly lower than that of an unpatterned film 6,7,9,14,15 , even after taking into account the combination of material removal and simple incoherent boundary scattering 7,9,14 .…”

“…Several methods exist for calculating k that assume partially coherent and partially incoherent phonon boundary scattering 6,8,12,14,15 . In particular, Hao et al 12 , used Monte Carlo simulations combined with frequency-dependent phonon MFPs 16 to study phonon transport in a 2D square-lattice PnC, and concluded that phonon size effects caused by the periodic arrangement of the holes can be remarkable even when the hole size and spacing are much greater than the average phonon MFP.…”