Investigations of the low- and high-frequency response of 3ω-sensors used in dynamic heat capacity measurements

The 3 omega-method is used to study time dependent processes through measurements of dynamic heat capacity. The 3 omega-sensor is a thin (similar to 0.1 mu m) metal strip which is evaporated onto a substrate. The sample is probed by periodic diffusive thermal waves of frequency 2 omega emitted from the strip. The heater temperature T-0 measured at frequency 3 omega yields the dynamic heat capacity. The validity of a one-dimensional heat flow model, assuming an infinitely thin heater, is here studied using a finite element modelling (FEM) technique as well as experiments. T-0 obtain results within 1% of the theory, FEM shows that the ratio between the heater width and the heat wave penetration depth (=root D/omega, where D is the thermal diffusivity) must be greater than 30, which sets a tow-frequency limit for the model. At high frequencies, the finite thickness of the heater causes a deviation from the model. For a thickness of 0.1 mu m, the deviation is <1% at 200 Hz, reaching 5% at 5 kHz. A small 3 omega-component intrinsic to the electronics together with a thermal resistance between heater and sample can explain deviations from T-0 proportional to omega(-upsilon), at high frequencies, where upsilon = 0.5 is predicted by the model but experiments generally show smaller values.