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In this article, we are proposing a thorough analysis of the cross, and thein-plane thermal conductivity of thin-film materials based on the 3$\omega$method. The analysis accommodates a 2D mathematical heat transfer model of asemi-infinite body and the details of the sample preparation followed by themeasurement process. The presented mathematical model for the system considersa two-dimensional space for its solution. It enables the calculation of thecross-plane thermal conductivity with a single frequency measurement, thederived equation opens new opportunities for frequency-based andpenetration-depth dependent thermal conductivity analysis. The derived equationfor the in-plane thermal conductivity is dependent on the cross-plane thermalconductivity. Both in and cross-plane thermal conductivities enable themeasurements in two steps of measurements, the resistance-temperature slopemeasurement and another set of measures that extracts the third harmonic of thevoltage signal. We evaluated the methodology in two sets of samples, siliconnitride and boron nitride, both on silicon wafers. We observed anisotropicthermal conductivity in the cross and the in-plane direction, despite theisotropic nature of the thin films, which we relate to the total anisotropy ofthe thin film-substrate system. The technique is conducive to the thermalanalysis of next-generation nanoelectronic devices.

Thermal Conductivity Measurement of Supported Thin Film Materials Using the 3$\omega$ method