Heat conduction in microstructured materials

The phonon Boltzmann equation is solved numerically in order to study the phonon thermal conductivity of micro/nanostructured thin films with open holes in a host material. We focused on the size effect of embedded pores and film thickness on the decrease in thermal conductivity of the film. Simulations have revealed that the temperature profiles in the micro/nanostructured materials are very different from those in their bulk counterparts, due to the ballistic nature of the microscale phonon transport. These simulations clearly demonstrate that the conventional Fourier heat conduction equation cannot be applied to study heat conduction in solids at microscale. The effective thermal conductivity of thin films with micro/nanoholes is calculated from the applied temperature difference and the heat flux. In the present paper, the effective thermal conductivity is shown as a function of the size of the micro/nanoholes and the film thickness. For example, when the size of the hole becomes approximately 1/20th the phonon mean free path in a film, the thickness is 1/10th the mean free path of phonons and the effective thermal conductivity decreases to as low as 6% of the bulk value. The distribution of holes also affects the reduction in the effective thermal conductivity. Thin films embedded with staggered-hole arrays have slightly lower effective thermal conductivities than films with aligned-hole arrays. The cross-sectional area in the thermal transport direction is a significant parameter with respect to the reduction of thermal conductivity. The results of the present study may prove useful in the development of artificial micro/nanostructured materials, including thermoelectrics and low-k dielectrics.