In-plane lattice thermal conductivity predictions of thin films within columnar grains

Polycrystalline thin films are widely used for devices and energy-related applications, such as power electronics, solar cells, and thermal management of devices. In many cases, large-scale crystallization during thin-film growth is challenging, so columnar grains are often found in metal and semiconductor thin films. These rough columnar grain boundaries may also have different phonon specularities from that for typically smoother top/bottom film surfaces. A simple analytical model to separately treat these boundaries and interfaces for phonon scattering is currently unavailable, although the in-plane thermal transport is critical to heat spreading within thin-film devices. In this paper, we extend the effective medium formulation from three-dimensional polycrystalline bulk materials to columnar-grained thin films. The model predictions agree well with those given by frequency-dependent phonon Monte Carlo simulations, considering varied phonon specularity at top/bottom film surfaces and grain-boundary phonon transmissivity. The analytical model is further used to analyze the existing data on polycrystalline ZnO thin films with columnar grains.