Analytical 2D-model of CMOS micromachined gas flow sensors

An analytical 2D model for the theoretical treatment of thermoelectric or thermoresistive integrated gas flow sensors is presented. It allows a detailed understanding and quantitative description of the function of cantilever beam and microbridge sensor structures fabricated using standard CMOS technology followed by an additional etching step. The heat exchange between the solid and the ambient gas along the surface of the respective sensor element is described by a generalized heat transport equation for the spatial temperature distribution. Only a small portion of the Joule heat produced by the integrated heating resistors is transferred to the gas, while the main stream of heat is conducted through the sandwich structure to the bulk silicon. However, there is a significant temperature modulation in the vicinity of the sensor surface, and it is this effect which makes the sensor work. In spite of the simplifying assumptions made, the model reproduces all essential features of the experimental findings and thus may be used to optimize the sensor design.<>