Data reduction in 3ω method for thin-film thermal conductivity determination

The 3ω method has been proven to be very useful for determining the thermal conductivity of thin films and their substrates. Several simplifications are often used in determining the thermal conductivity of the films based on the experimentally measured 3ω signal. These simplifications, however, have limited range of applicability. In this work, we present a detailed analysis and mathematical modeling of the 3ω method applied for different experimental conditions. Effects considered include the finite substrate thickness, anisotropic nature of the film and substrate thermal conductivity, the film-substrate thermal property contrasts, the effect of heat capacitance of the heater, and the effect of thermal boundary resistance. Several experimental results are analyzed using the models presented. This work shows that the 3ω method can be extended to a wide range of sample conditions, with anisotropic conductivities in both the substrate and the film, and with small film-substrate conductivity contrast.