Phonon transport in periodic silicon nanoporous films with feature sizes greater than 100 nm

Abstract

The thermal conductivities of solid silicon thin films and silicon thin films with periodic pore arrays are predicted using a Monte Carlo technique to include phonon-boundary scattering and the Boltzmann transport equation. The bulk phonon properties required as input are obtained from harmonic and anharmonic lattice dynamics calculations. The force constants required for the lattice dynamics calculations are obtained from forces calculated using density functional theory. For both solid and porous films, the in-plane thermal conductivity predictions capture the magnitudes and trends of previous experimental measurements. Because the prediction methodology treats the phonons as particles with bulk properties, the results indicate that coherent phonon modes associated with the secondary periodicity of the pores do not contribute to thermal transport in porous films with feature sizes greater than 100 nm.

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

“…Since this is the smallest physically-meaningful value of L, it corresponds to the maximum possible reduction from models assuming solely incoherent scattering and actually predicts a larger reduction in conductivity than that predicted by ref. 13, which argues in favour of purely incoherent scattering. There, the effective sample characteristic length L eq is seen to be consistently larger than L c by more than 100 nm for each corresponding sample.…”

“…In this formulation, assuming a sufficiently large sample thickness [23][24][25][26] and feature sizes 13 , if coherent boundary scattering were absent, the Si phonon dispersion would remain basically unaltered before and after the PnC patterning and fixing L c would lead to a constant incoherent boundary scattering limit (Supplementary Table 1). We thus set out to realize an experiment where the geometry of the PnC lattice is varied, while L c is kept constant.…”

“…Room temperature Monte Carlo simulations accounting for purely incoherent boundary scattering via the Boltzmann transport equation were used. The apparent agreement between theory and experiment 13 led the authors to conclude the absence of any coherent phonon boundary scattering. Although the incoherent nature of the model should have made it insensitive to propagation direction and scatterer geometry, the model was surprisingly deficient in reproducing the k measured for unperforated slabs and the cross-plane PnC 7 direction, raising doubts that incoherent boundary scattering is solely responsible for the experimentally observed k reduction in such PnCs.…”

“…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 .…”

“…Their study found some agreement with recent experimental work on nano-scale PnCs 9 , highlighting the importance of zone folding, however the model failed to reproduce the cross-plane data 7 possibly because of the lack of lattice periodicity in that direction. Conversely, Jain et al 13 argued that a major deficiency in the previous models is their 2D nature, and proposed a full 3D model. Room temperature Monte Carlo simulations accounting for purely incoherent boundary scattering via the Boltzmann transport equation were used.…”