Dimensionless Analysis of Micro Pirani Gauges for Broad Pressure Sensing Range

This article proposes a dimensionless thermal analysis of micro-fabricated membranes as Pirani gauges for pressure measurements. Use of dimensionless numbers simplifies the mode l and facilitates understanding. Our model's predictions are consistent with experimental results obtained from heated suspended SiO2/SiN membranes with a sub-micrometer separation distance with the substrate (500 nm). Other systems reported in the literature also confirmed the modelling. This framework is a powerful prediction tool as it allows a study of the effects of key parameters on the sensing pressure range, including geometry, material properties and radiative heat fluxes. It also addresses the effect of the operating mode, either constant temperature or constant power. Furthermore, we propose a methodology for rapid design of Pirani gauge arrays to reach a broad range of pressure measurements from atmospheric pressure to high vacuum (10
^-3
Pa) without microcontroller use. We prove that this new formalism offers a way to optimize the geometry to reach the target application, which essentially depends on the power consumption, material choice and the pressure measurement range.