An Accurate and Computationally Efficient Model for Membrane-Type Circular-Symmetric Micro-Hotplates

Abstract

Ideally, the design of high-performance micro-hotplates would require a large number of simulations because of the existence of many important design parameters as well as the possibly crucial effects of both spread and drift. However, the computational cost of FEM simulations, which are the only available tool for accurately predicting the temperature in micro-hotplates, is very high. As a result, micro-hotplate designers generally have no effective simulation-tools for the optimization. In order to circumvent these issues, here, we propose a model for practical circular-symmetric micro-hot-plates which takes advantage of modified Bessel functions, computationally efficient matrix-approach for considering the relevant boundary conditions, Taylor linearization for modeling the Joule heating and radiation losses, and external-region-segmentation strategy in order to accurately take into account radiation losses in the entire micro-hotplate. The proposed model is almost as accurate as FEM simulations and two to three orders of magnitude more computationally efficient (e.g., 45 s versus more than 8 h). The residual errors, which are mainly associated to the undesired heating in the electrical contacts, are small (e.g., few degrees Celsius for an 800 °C operating temperature) and, for important analyses, almost constant. Therefore, we also introduce a computationally-easy single-FEM-compensation strategy in order to reduce the residual errors to about 1 °C. As illustrative examples of the power of our approach, we report the systematic investigation of a spread in the membrane thermal conductivity and of combined variations of both ambient and bulk temperatures. Our model enables a much faster characterization of micro-hotplates and, thus, a much more effective optimization prior to fabrication.

An analytical method to design annular microfilaments with uniform temperature

“…Khan and co-workers presented an effective model for circular symmetric microhotplates to calculate the temperature profile of the heated area (Khan and Falconi 2014). Based on similar thermal management strategy and FEM assisted design procedure, a 75 lm radius circular shaped microfilament was optimised with improved temperature uniformity by Ali et al (2009).…”

Modeling, Fabrication and Testing of a Customizable Micromachined Hotplate for Sensor Applications

“…The models are based on a multiphysics approach involving electrical, thermal and fluidics aspects. The multiphysics approach has become the leading method to deal with high complex systems that cannot be uniformed on a single physics, and this is particularly evident for MEMS [ 16 , 17 , 18 ], where electrical, thermal and, sometimes, mechanical behaviors are responsible, at the same time, of the good functionality of the device The geometries, materials and physics are derived from the actual devices to obtain the best possible accuracy. In particular the Pt characteristics were investigated to obtain the experimental Temperature Coefficient of Resistance (TCR) to be included as an input in the models.…”