Analytical Model for Lattice Thermal Conductivity Predictions of Periodic Nanoporous Structures

Phonon transport within nanoporous bulk materials or thin films is of importance to applications in thermoelectrics, gas sensors, and thermal insulation materials. Considering classical phonon size effects, the lattice thermal conductivity K_L can be predicted assuming diffusive pore-edge scattering of phonons and bulk phonon mean free paths. In the kinetic relationship, k_L can be computed by modifying the phonon mean free paths with the characteristic length Λ_Pore of the porous structure. Despite some efforts using the Monte Carlo ray tracing method to extract Λ_Pore, the resulting K_L often diverges from that predicted by phonon Monte Carlo simulations. In this work, the effective Λ_Pore is extracted by directly comparing the predictions by the kinetic relationship and phonon Monte Carlo simulations. The investigation covers a wide range of period sizes and volumetric porosities. In practice, these Λ_Pore values can be used for thermal analysis of general nanoporous materials.