Measurements of Thermal Conductivity of Thin Films by 3-Omega Method

In this study, the thermal conductivity of a bismuth-telluride (Bi₂Te₃) thin film is measured at room temperature by using the 3ω method [1, 2]. The 3ω method for thin films uses a single metal-line as both the heater and thermometer. An alternating-current driving current at angular frequency ω heats the surface of the sample at a frequency of 2ω. Since the resistance of a metal increases with temperature, temperature oscillations produce an oscillation of the electrical resistance at a frequency of 2ω. Consequently, the voltage drop across the metal line has a small component at 3ω that can be used to measure the temperature oscillations and the thermal response of the sample with a Bismuth-telluride thin film. Differential amplifiers are used to subtract the ω component of the voltage for the measurement of the small 3ω signal as shown in Fig.1. The amplified 3ω component and the attenuated reference voltage are acquired to a personal computer through a 16bit DAC card. The bismuth-telluride thin films are manufactured by flash evaporation and coating. The narrow Aluminum lines for the 3ω method are made by vacuum deposition through metal masks. The measured temperature oscillation ΔT versus ln(ω) yields the thermal conductivity of the substrates. The thermal conductivity of the glass is measured as 0.97 W/(m·K), and that of alumina is 15.4 W/(m·K). These results agree well with the reference data. The thermal conductivities of Bismuth-telluride thin films are calculated from the measured thermal resistances of the films. The measured value for a flash evaporated Bismuth-telluride is 1.20 W/(m·K), and the coated film is 0.51 W/(m·K).