An analytic model for cantilever optimization for photoacoustic gas sensing with capacitive transduction

Gas sensing find tremendous applications in various fields like medicine, air quality, food processing or security and defence. The main challenge in industry is to create an integrated and compact sensor while maintaining its performance and power consumption. Photoacoustic spectroscopy (PAS) gains particular interest in this field due to its excellent selectivity while maintaining compactness. In tunable laser diode absorption spectroscopy (TDLS) the signal is proportional to optical path. Sensitivity in photoacoustic spectroscopy is proportional to the power of the laser, which allows to keep a good sensitivity even with small gas cells. The use of mechanical resonator with high quality factor allows improving the signal-to-noise ratio and avoid the use of an acoustic chamber. Micro-electro mechanical systems (MEMS) fabricated in silicon technology remain a reasonable choice to realize a compact and integrated sensor, including laser source and electronics. We propose a capacitive transduction method, which can be easily integrated, compact and highly sensitive. Due to the multi-physics problem, time and financial contains, a theoretical model seems to be a first step towards sensor performance improvement. We propose an analytical model for a new concept of photoacoustic gas sensing using capacitive transduction mechanism. The model was reinforced with computational methods implemented in Python programming environment. The study was carried out using silicon cantilever as a model, which brings an opportunity to obtain an analytical solution for all physical parameters. The goal of this research stands maximization of electrical signal output and signal-to-noise (SNR) ratio. Conducted study provides a solution to retrieve a cantilever dimensions and frequency for integrated compact gas sensor. Beyond optimization, the model provides a comprehensive tool to understand mechanisms of sensor working principles and therefore stands as a tool allowing a mechanical resonator to be developed with a more complex geometry and/or different transduction mechanism.