Establishment of metrological references for the measurement of thermal conductivity by scanning thermal microscopy

The increasing demand for thermal management in various industries (energy, micro and nanoelectronics…), has driven the need for reliable thermal characterization techniques at micro- and nanoscale. Scanning thermal microscopy (SThM) is a valuable tool for thermal properties characterization and heat transfer mechanisms investigation at these scales. However, some metrological aspects remain a challenge for quantitative and traceable thermal conductivity measurement with the SThM technique. The aim of this work is to improve the metrology associated with the SThM thermal conductivity measurement for quantitative, traceable, and reliable measurements.

A key contribution of this work is the establishment of a new 3D FEM model (three-dimension model established with finite elements method) for the second generation of the Pd probe. This new model aims to describe more accurately the heat dissipation in the probe and the different heat transfer mechanisms occurring between the probe, the sample and the environment with different measurement configurations (vacuum, air, and probe in contact with the sample or out of contact). Simulation results highlight the respective contribution of main influencing parameters. These reveal notably the critical influence of the interfacial thermal resistance on the thermal response and on the sensitivity of the technique both in air and in vacuum environments. The ballistic heat conduction regime (at the contact), which is generally neglected in existing models in the literature, was integrated into the 3D model. The simulation study highlights the necessity to consider this heat transfer when the measurements are done in vacuum.

A comparative study between the 3D FEM model and an analytical model used experimentally to calibrate SThM probes evaluates the applicability of the analytical approach for thermal conductivity measurements and highlights its limitation and potential improvement.

The experimental part of this work focuses on improving the experimental setup developed at the French National Metrology Institute and measurement protocols for a more accurate and repeatable measurement. Additionally, an experimental calibration curve is established and the associated uncertainty is evaluated with a new approach.

The results have shown that the improvements of the setup and the measurement protocols have reduced the uncertainty associated to the measurand thus reducing the uncertainty associated with the thermal conductivity estimation. Experimental analysis shows that quantitative and traceable measurements of thermal conductivity (for samples where heat transfer is predominantly diffusive) using the SThM technique are possible for low thermal conductivity materials (currently limited to the range from 0.187 W.m^-1.K^-1 to 10 W.m^-1.K^-1) with an relative associated uncertainty lower than 20% (k=2).

finite element method modeling, uncertainty evaluation, thermal conductivity, scanning thermal microscopy (SThM), resistive probe, nanoscale.