Analytical solution for temperature oscillation in the heater/thermometer film in 3ω method and its application to thermal conductivity measurement of micro/nanometer-films

Abstract

Analytical solution in terms of series for temperature oscillation in the heater/thermometer film is derived for 3ω measurements. The complex temperature solution is seperated into the real and imaginary parts. Analysis is performed to show the effect of the combined parameters of ac frequency, heater width and sample thermal properties on the temperature oscillation. The mathematical model for the measurement is corrected based on the solution. Accordingly, a 3ω setup is developed to determine thermal conductivity of 500 nm-thick thin film on Si substrate. Uncertainty analysis and comparison with the results of differential-3ω methods and published values are made, the results show good mutual agreement. The thermal conductivities of SiO2 film and Si substrate are determined simultaneously with the series solution and by extension to high frequency. The method is also employed to measure the thermal conductivity of the multi-layer antireflective coating of ZrO2/SiO2 deposited on Nd:YAG surface. The ZrO2 film has a thermal conductivity smaller than the volume value. The established 3ω setup and analytical method can be applied to investigate the thermal performance of thin film-substrate structures for use with micro-systems such MEMS.