Theoretical consideration of the effect of porosity on thermal conductivity of porous materials

The thermal conductivity of porous materials is theoretically studied in connection with nanoporous materials used in recent semiconductor devices. The effects of porosity and pore size on the thermal conductivity are discussed. The thermal conductivity of insulating materials is determined by the heat capacity of phonons, the average phonon velocity and the phonon mean free path. We investigate the porosity dependence of these quantities, especially by taking into account phonon scatterings by pores, and present an expression for the thermal conductivity as a function of porosity. Our model consideration predicts that the thermal conductivity of nanoporous materials depends on the ratio of the pore size R p to the phonon mean free path for zero-porosity, l 0. The thermal conductivity for l 0/R p > 1 decreases steeply with increasing porosity because of effective phonon scatterings by pores. On the other hand, the thermal conductivity for l 0/R p < 0.1 decreases moderately with increasing porosity because phonon scatterings by pores are no longer effective. On the basis of the present theoretical consideration, we discuss the principal factor dominating the porosity dependence of thermal conductivity in nanoporous materials. We also discuss how one can design nanoporous materials with lower or higher thermal conductivity.