Size Effect on the Thermal Conductivity of Thin Metallic Films Investigated by Scanning Joule Expansion Microscopy

A technique to extract in-plane thermal conductivity of thin metallic films whose thickness is comparable to electron mean free path is described. Microscale constrictions were fabricated into gold films of thicknesses $43nm$ and $131nm$⁠. A sinusoidal voltage excitation across the constriction results in a local temperature rise. An existing technique known as scanning joule expansion microscopy, measures the corresponding periodic thermomechanical expansion with a $10nm$ resolution and determines the local temperature gradient near the constriction. A three-dimensional finite-element simulation of the frequency-domain heat transfer fits the in-plane thermal conductivity to the measured data, finding thermal conductivities of $82±7.7W∕mK$ for the $43nm$ film and $162±16.7W∕mK$ for the $131nm$ film, at a heating frequencies of $100kHz$ and $90kHz$⁠, respectively. These values are significantly smaller than the bulk thermal conductivity value of $318W∕mK$ for gold, showing the electron size effect due to the metal-dielectric interface and grain boundary scattering. The obtained values are close to the thermal conductivity values, which are derived from electrical conductivity measurements after using the Wiedemann–Franz law. Because the technique does not require suspended metal bridges, it captures true metal-dielectric interface scattering characteristics. The technique can be extended to other films that can carry current and result in Joule heating, such as doped single crystal or polycrystalline semiconductors.