A frequency-modulated 3ω method (FM-3ω) for thermal conductivity measurements

The 3ω technique is a prominent thermal conductivity measurement methodology for thin films, substrates, nanowires, and thermal boundary conductance. The extraction of the thermal conductivity typically relies on measuring the thermal response across a wide range of frequencies and determining the slope within acceptable limiting conditions, which can be a time-consuming process prone to error from the amplification of noise when taking the derivative of discrete temperature data to determine thermal conductivity. Here, we develop and demonstrate a frequency-modulated 3ω method (FM-3ω) with which we directly measure the derivative of the 3ω signal by varying the center frequency ω, eliminating the need to postprocess the data, thereby reducing the time to take such measurements from hours to minutes. Our modulation approach is a frequency modulation method in which the frequency ω of the excitation current is sinusoidally varied over time. We show that our new method produces results with similar accuracy to the traditional method on bulk sapphire and borofloat 33 samples, and we further explore the limitations of modulation depth and center frequency on the results. We find that thermal conductivity measurements from the FM-3ω method agree well with thermal conductivities extracted through linear fits to temperature data over similar frequency windows of the traditional method. Our method provides a new strategy using frequency modulation and tandem demodulation to directly measure the derivative of temperature, thus contributing to the advancement of thermal transport sciences by increasing the ease and pace of measuring the thermal conductivity of thin films and multilayer structures.