This work is devoted to analytical and numerical studies of diffusive heat conduction in configurations considered in 3ω experiments, which aim at measuring thermal conductivity of materials. The widespread 2D …
This work is devoted to analytical and numerical studies of diffusive heat conduction in configurations considered in 3ω experiments, which aim at measuring thermal conductivity of materials. The widespread 2D analytical model considers infinite media and translational invariance, a situation which cannot be met in practice in numerous cases due to the constraints in low-dimensional materials and systems. We investigate how thermal boundary resistance between heating wire and sample, native oxide and heating wire shape affect the temperature fields. 3D finite element modelling is also performed to account for the effect of the bonding pads and the 3D heat spreading down to a typical package. Emphasis is given on the low-frequency regime, which is less known than the so-called slope regime. These results will serve as guides for the design of ideal experiments where the 2D model can be applied and for the analyses of non-ideal ones.
“3ω” experiments aim at measuring thermal conductivities and diffusivities. Data analysis relies on integral expressions of the temperature. In this paper, we derive new explicit analytical formulations of the solution …
“3ω” experiments aim at measuring thermal conductivities and diffusivities. Data analysis relies on integral expressions of the temperature. In this paper, we derive new explicit analytical formulations of the solution of the heat diffusion equation, using Bessel, Struve, and Meijer-G functions, in the 3ω geometry for bulk solids. These functions are available in major computational tools. Therefore numerical integrations can be avoided in data analysis. Moreover, these expressions enable rigorous derivations of the asymptotic behaviors. We also underline that the diffusivity can be extracted from the phase data without any calibration while the conductivity measurement requires a careful one.
A suspended system for measuring the thermal properties of membranes is presented. The sensitive thermal measurement is based on the 3ω dynamic method coupled to a Völklein geometry. The device …
A suspended system for measuring the thermal properties of membranes is presented. The sensitive thermal measurement is based on the 3ω dynamic method coupled to a Völklein geometry. The device obtained using micro-machining processes allows the measurement of the in-plane thermal conductivity of a membrane with a sensitivity of less than 10 nW/K (+∕-5 × 10(-3) Wm(-1) K(-1) at room temperature) and a very high resolution (ΔK/K = 10(-3)). A transducer (heater/thermometer) centered on the membrane is used to create an oscillation of the heat flux and to measure the temperature oscillation at the third harmonic using a Wheatstone bridge set-up. Power as low as 0.1 nW has been measured at room temperature. The method has been applied to measure thermal properties of low stress silicon nitride and polycrystalline diamond membranes with thickness ranging from 100 nm to 400 nm. The thermal conductivity measured on the polycrystalline diamond membrane support a significant grain size effect on the thermal transport.