Abstract
In diaphragm-based micromachined calorimetric flow sensors, convective heat transfer through the test fluid competes with the spurious heat shunt induced by the thin-film diaphragm where heating and temperature sensing elements are embedded. Consequently, accurate knowledge of thermal conductivity, thermal diffusivity, and emissivity of the diaphragm is mandatory for design, simulation, optimization, and characterization of such devices. However, these parameters can differ considerably from those stated for bulk material and they typically depend on the production process. We developed a novel technique to extract the thermal thin-film properties directly from measurements carried out on calorimetric flow sensors. Here, the heat transfer frequency response from the heater to the spatially separated temperature sensors is measured and compared to a theoretically obtained relationship arising from an extensive two-dimensional analytical model. The model covers the heat generation by the resistive heater, the heat conduction within the diaphragm, the radiation loss at the diaphragm’s surface, and the heat sink caused by the supporting silicon frame. This contribution summarizes the analytical heat transfer analysis in the microstructure and its verification by a computer numerical model, the measurement setup, and the associated thermal parameter extraction procedure. Furthermore, we report on measurement results for the thermal conductivity, thermal diffusivity, and effective emissivity obtained from calorimetric flow sensor specimens featuring dielectric thin-film diaphragms made of plasma enhanced chemical vapor deposition silicon nitride.
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Acknowledgments
The authors would like to thank Dr. Artur Jachimowicz (Institute of Sensor and Actuator Systems, Vienna University of Technology) for his support regarding fabrication of the devices. This work was financially supported in part by the European Regional Development Fund and the province of Lower Austria.
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Appendix: Linearized Stefan‐Boltzmann law
Appendix: Linearized Stefan‐Boltzmann law
The radiative heat loss at the surface of a body can be expressed by the (nonlinear) Stefan-Boltzmann law as heat flux density
where ɛ is the emissivity, σ the Stefan-Boltzmann constant, T the local temperature, and T 0 the ambient temperature (Carslaw and Jaeger 1990). In general, this equation is owing to the term T 4 highly nonlinear. However, in case of small temperature differences |T − T 0| ≪ 1 it can be linearized to
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Beigelbeck, R., Cerimovic, S., Talic, A. et al. Measurement technique for the thermal properties of thin-film diaphragms embedded in calorimetric flow sensors. Microsyst Technol 18, 973–981 (2012). https://doi.org/10.1007/s00542-011-1422-8
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DOI: https://doi.org/10.1007/s00542-011-1422-8