Analytical model for phonon transport analysis of periodic bulk nanoporous structures

Abstract

Phonon transport analysis in nano- and micro-porous materials is critical to their energy-related applications. Assuming diffusive phonon scattering by pore edges, the lattice thermal conductivity can be predicted by modifying the bulk phonon mean free paths with the characteristic length of the nanoporous structure, i.e., the phonon mean free path (ΛPore) for the pore-edge scattering of phonons. In previous studies (Jean et al., 2014), a Monte Carlo (MC) technique have been employed to extract geometry-determined ΛPore for nanoporous bulk materials with selected periods and porosities. In other studies (Minnich and Chen, 2007; Machrafi and Lebon, 2015), simple expressions have been proposed to compute ΛPore. However, some divergence can often be found between lattice thermal conductivities predicted by phonon MC simulations and by analytical models using ΛPore. In this work, the effective ΛPore values are extracted by matching the frequency-dependent phonon MC simulations with the analytical model for nanoporous bulk Si. The obtained ΛPore values are usually smaller than their analytical expressions. These new values are further confirmed by frequency-dependent phonon MC simulations on nanoporous bulk Ge. By normalizing the volumetric surface area A and ΛPore with the period length p, the same curve can be used for bulk materials with aligned cubic or spherical pores up to dimensionless p·A of 1.5. Available experimental data for nanoporous Si materials are further analyzed with new ΛPore values. In practice, the proposed model can be employed for the thermal analysis of various nanoporous materials and thus replace the time-consuming phonon MC simulations.