Measurement of the Thermal Conductivity and Heat Capacity of Freestanding Shape Memory Thin Films Using the 3ω Method

Abstract

The 3ω method (17) is a powerful tool for thermophysical property measurement and has been used extensively for a wide variety of materials including dielectrics (18,33), superlattice materials (34), complex alloys (19), etc. The 3ω method is based on the temperature-dependent electrical resistivity of metals. A thin metal line is deposited on the material of interest, and a small sinusoidal electric current is passed through it. Since the electric current is sinusoidal at frequency ω, the resultant Joule heating, and hence the temperature of the metal line, has a component that oscillates at a frequency of 2ω. The amplitude of this temperature oscillation is a function of the heating power, geometry, and thermophysical properties of the material of interest. Thus, the measurement of the 2ω temperature oscillation amplitude provides a means of determining the thermal properties of the material. This measurement is performed indirectly by measuring the 3ω voltage induced due to the electric current that oscillates at frequency ω and the temperature-dependent electrical resistance of the metal heater, which oscillates at frequency 2ω. The two quantities are related by the following equation (17,35):Display FormulaΔT2ω=2dTdRRVV3ω (1) The 3ω method was first used for measurements on a substrate that was much thicker than the thermal penetration depth of the thermal wave produced by the sinusoidal current. In this case, a semi-infinite assumption was used to simplify and solve the governing energy equation. This method fails for freestanding thin films since the current frequency would have to be unrealistically high to still satisfy the semi-infinite assumption. The 3ω method has been modified for measuring thermal properties of thin films deposited on a substrate with well-known properties (20). In this case, the thermal resistances through the thin film and the substrate are assumed to add up in series. Thus, the temperature oscillation amplitude with the thin film exhibits a constant frequency-independent difference from the value expected if only the substrate were present. This difference is used to determine the thermal conductivity of the thin film. This method cannot measure the heat capacity of the thin film. In addition, the boundary thermal resistance between the thin film and substrate remains unaccounted for. Some work has also been done on using numerical simulations for applying the 3ω method for freestanding thin films (36). However, the development of an analytical method for thermal measurements remains highly desirable.