Three-Sensor 2{\omega} Method with Multi-directional Layout: A General Methodology for Measuring Thermal Conductivity of Solid Materials

Anisotropic thermal transport plays a key role in both theoretical study and engineering practice of heat transfer, but accurately measuring anisotropic thermal conductivity remains a significant challenge. To address this issue, we propose the three-sensor 2{\omega} method in this study, which is capable of accurately measuring the isotropic or anisotropic thermal conductivity of solid materials. In this method, several three-sensor groups following the design guidelines are fabricated upon the sample along different characteristic directions, and each group consists of three parallel metal sensors with unequal widths and distances optimally designed based on sensitivity analysis. Among the three sensors, the outer two serve as AC heaters and the middle one as a DC detector. The 2{\omega} voltage signals across the detector in each three-sensor group are measured, and then the data are processed by the proposed Intersection Method to derive the thermal conductivities along directions of interest. The application of the detector's 2{\omega} instead of the heater's 3{\omega} voltage signals eliminates the errors introduced by the uncertainties of thermal resistance in superficial structures (metal layer, insulation layer, interface, etc.). Meanwhile, by replacing the fitting algorithm with the Intersection Method, the local optimum trap of multivariate fitting is avoided. To verify the accuracy and reliability, four typical monocrystalline semiconductors, i.e., Si, GaN, AlN, and {\beta -Ga _2 O _3}, are measured, and the results are consistent with the literature. This method will provide a comprehensive and versatile solution for the thermal conductivity measurements of solid materials.
Comment: 25 pages, 6 figures