Optimization of the Optical Measuring Converter’s Geometric Properties for the Microelectromechanical Pressure Sensor

Nowadays development and production of microelectromechanical systems is one of the most promising directions in the world's economy. One of the innovative fields in the development of microsystems is integration of optical devices as measuring transducers. Goal of the paper is optimization of the optical measuring transducer geometry for microelectromechanical pressure sensor which provides a required value and linearity of the optical transmission coefficient. Microelectromechanical pressure sensor comprises the optical measuring transducer represented by a pair of waveguides that form an optical directional coupler. Linearity of the optical transmission coefficient of the transducer is provided by the selection of the initial gap between the waveguides at the linear section of the curve representing dependence of the optical transmission coefficient on the gap. Calculation of the required characteristics of such transducer requires a combination of the Finite-difference time-domain method and the mode overlapping method. This allows calculating the magnitude of the optical transmission coefficient for different geometric parameters of the transducer. Two models of the directional coupler with silicon and silicon nitride waveguides were used to determine dependencies of the transducer's optical transmission coefficient on the optical coupling length and the waveguide bending radius. The data obtained were used to plot the dependencies of the transmission coefficient on the gap between the waveguide for both models. The plots show the optimal initial gaps and the length of the linear section. The results allow designing a device with predetermined working section at which the optical measuring transducer can measure membrane displacements that are linearly proportional to an acting pressure. Such working section is characterized by the initial gap in the middle of the linear section that amounts to 500 nm for silicon waveguides and 600 nm for silicon nitride ones. The linear section of the transducer's transmission characteristic for the waveguides of both types is estimated as ±80 nm in relation to the initial gap. In this section, the optical transmission coefficient of the transducer with silicon waveguides alters from 0 to 0.86 which corresponds to a value of 5.375‧106 m-1. For the waveguide with silicon nitride waveguides the coefficient varies from 0.09 to 0.53 which corresponds to a value of 2.75‧106 m-1. The computer aided analysis methods allow for determining the optimal geometry of the evanescent coupling-based measuring transducer that is used in the microelectromechanical pressure sensor. The presented models of two transducers with two waveguides made of different materials demonstrate different characteristics. The optimal parameters for each of the models are achieved at different waveguide bending radii and optical coupling lengths.

1. Bhat KN, Nayak MM. MEMS Pressure SensorsAn Overview of Challenges in Technology and Packaging. Inst. Smart Struct. Syst. J. 2013;2(1):39-71.

2. Barlian AA, Park W-T, Mallon JR, Rastegar AJ, Pruitt BL. Review: Semiconductor Piezoresistance for Microsystems. Proceedings of the IEEE. 2009;97(3):513-552. DOI: 10.1109/JPROC.2009.2013612

3. Kanekal D, Jindal SK. Investigation of MEMS Piezoresistive Pressure Sensor with a Freely Supported Rectangular Silicon Carbide Diaphragm as a Primary Sensing Element for Altitudinal Applications. Silicon. 2023;(15):19471959. DOI: 10.1007/s12633-022-02146-z

4. Kyoung-Ho Ha, Heeyong Huh, Zhengjie Li, Nanshu Lu. Soft Capacitive Pressure Sensors: Trends, Challenges, and Perspectives. ACS Nano. 2022;16(3):3442-3448. DOI: 10.1021/acsnano.2c00308

5. Yulan Lu, Pengcheng Yan, Chao Xiang, Deyong Chen, Junbo Wang, Bo Xie and Jian Chen. A Resonant Pressure Microsensor with the Measurement Range of 1 MPa Based on Sensitivities Balanced Dual Resonators. Sensors. 2019;19(10):2272. DOI: 10.3390/s19102272

6. Shahiri Tabarestani M. Analytical Analysis of Capacitive Pressure Sensor with Clamped Diaphragm. Int. J. Eng. 2013;26(3(C)):297-302. DOI: 10.5829/idosi.ije.2013.26.03c.09

7. Boukabache A. [et al.]. Characterization and modelling of the mismatch of TCRs and their eff on the drift of the off voltage of piezoresistive pressure sensors. Sensors Actuators, A Phys. 2000;84(3):292-296. DOI: 10.1016/S0924-4247(00)00406-4

8. Belwanshi V. Analytical modeling to estimate the sensitivity of MEMS technology-based piezoresistive pressure sensor. J Comput Electron. 2021;(20):668-680. DOI: 10.1007/s10825-020-01592-5

9. Park S-H, Lee HB, Yeon SM, Park J, Lee NK. Flexible and Stretchable Piezoelectric Sensor with ThicknessTunable Confi of Electrospun Nanofi Mat and Elastomeric. Substrates. ACS Applied Materials & Interfaces. 2016;8(37):24773-81. DOI: 10.1021/acsami.6b07833

10. Xu MG, Geiger H, Dakin JP. Fibre grating pressure sensor with enhanced sensitivity using a glass-bubble housing. Electronics Letters. 1996;32(2):128-129. DOI: 10.1049/el:19960022

11. Arkwright JW, Underhill ID, Maunder SA, Jafari A, Cartwright N, Lemckert C. Fiber Optic Pressure Sensing Arrays for Monitoring Horizontal and Vertical Pressures Generated by Traveling Water Waves. IEEE Sensors Journal. 2014;14(8):2739-2742. DOI: 10.1109/JSEN.2014.2311806

12. Wang T, Ge Y, Ni H, Chang J, Zhang J, Ke W. Miniature fi pressure sensor based on an in-fi confocal cavity. Optik. 2018;(171):869-875. DOI: 10.1016/j.ijleo.2018.06.151

13. Guo F, Fink T, Han M, Koester L, Turner J, Huang J. High-sensitivity, high-frequency extrinsic Fabry– Perot interferometric fi sensor based on a thin silver diaphragm. Optics Letters. 2012;37(9):1505-1507. DOI: 10.1364/OL.37.001505

14. Evgenii Barbin, Tamara Nesterenko, Aleksej Koleda, Evgeniy Shesterikov, Ivan Kulinich, Andrey Kokolov and Anton Perin. The Design, Modeling and Experimental Investigation of a Micro-G Microoptoelectromechanical Accelerometer with an Optical Tunneling Measuring Transducer. Sensors. 2024;24(3):765. DOI: 10.3390/s24030765