Planar 3$\omega$ and 2$\omega$ Method for Increased Sensitivity to Through-Plane Thermal Properties

Accurately measuring the thermal properties of buried interfaces is crucial for understanding heat transport in multilayered materials, particularly in applications such as batteries and integrated circuits. The conventional 3$\omega$ method, which uses a line heater, has limited sensitivity to through-plane thermal properties due to lateral heat spreading, especially when a highly conductive layer overlays a resistive one. Additionally, when using a line heater, there is a lower limit to the frequency of heating, below which the analytical solution assuming infinite lateral dimension is not valid. This limits analytical interpretation of 2$\omega$ temperature oscillation at lower frequencies where the sensitivity to the conductivity of a buried layer is greater. To overcome these limitations, we propose a planar 3$\omega$ and 2$\omega$ method that enhances the sensitivity to buried layers by ensuring planar heat flow. We implement this technique using a planar metallic heater across the entire sample and validate it experimentally against the analytical solution using Feldman's algorithm. We also discuss the practical implementation details of the approach, including ensuring uniform current distribution and the required sensor layout. Our results demonstrate improved measurement sensitivity for polymer layers in silicon stacks and buried interfaces in battery electrodes, with sensitivity improvements by factors of 2-5 compared to conventional technique using a line heater.