*Article* **Analytic Optimization of Cantilevers for Photoacoustic Gas Sensor with Capacitive Transduction**

**Wioletta Trzpil, Nicolas Maurin, Roman Rousseau, Diba Ayache, Aurore Vicet and Michael Bahriz \***

IES, University Montpellier, CNRS, 34095 Montpellier, France; wioletta.trzpil@umontpellier.fr (W.T.); nicolas.maurin@ies.univ-montp2.fr (N.M.); roman.rousseau@ies.univ-montp2.fr (R.R.); diba.ayache@ies.univ-montp2.fr (D.A.); aurore.vicet@umontpellier.fr (A.V.)

**\*** Correspondence: michael.bahriz@umontpellier.fr

**Abstract:** We propose a new concept of photoacoustic gas sensing based on capacitive transduction which allows full integration while conserving the required characteristics of the sensor. For the sensor's performance optimization, trial and error method is not feasible due to economic and time constrains. Therefore, we focus on a theoretical optimization of the sensor reinforced by computational methods implemented in a Python programming environment. We present an analytic model to optimize the geometry of a cantilever used as a capacitive transducer in photoacoustic spectroscopy. We describe all the physical parameters which have to be considered for this optimization (photoacoustic force, damping, mechanical susceptibility, capacitive transduction, etc.). These parameters are characterized by opposite trends. They are studied and compared to obtain geometric values for which the signal output and signal-to-noise ratio are maximized.

**Keywords:** MEMS; gas sensor; photoacoustics; cantilever; capacitive detection; analytic model
