Optimization of the resonant frequency MEMS pressure sensor based on numerical simulation

   Silicon microelectromechanical pressure sensors of the resonant-frequency type are distinguished by high linearity and stability of their output characteristics, making them particularly promising for precision measurements. This paper presents a study of the influence of membrane geometry and stress-strain state on the sensitivity of resonant-frequency pressure sensors. Recommendations for optimal resonator placement and the selection of a process route for membrane formation are also developed. Using three-dimensional models of membranes of various geometric shapes, numerical simulation of their stress-strain state under static pressure was performed using the finite element method. This method allowed us to identify the zones of localized deformation most suitable for resonator placement. Wet etching with preliminary wafer thinning and subsequent finishing machining was used to fabricate test samples of silicon membranes. It is shown that maximum sensitivity is achieved by positioning the resonator in zones of peak tensile and compressive stresses. An analysis of the membrane shape relationship to stress distribution and resonator response was conducted, enabling the identification of optimal resonator locations in terms of manufacturing tolerances and sensitivity. Membrane preparation methods were compared: chemical and mechanical thinning followed by polishing. Based on roughness measurements for membranes manufactured using different methods, the optimal preparation technology was described. The obtained results enable optimization of the geometry and manufacturing process of the resonant-frequency pressure sensor, which contributes to increased sensitivity, wider manufacturing tolerances, reduced production costs, and improved reliability in industrial operation.

1. Jha C.M., Bahl G., Melamud R., Chandorkar S.A., Hopcroft M.A., Kim B., Agarwal M., Salvia J., Mehta H., Kenny T.W. High resolution microresonator-based digital temperature sensor. Applied Physics Letters, 2007, vol. 91, no. 7, pp. 074101 doi: 10.1063/1.2768629

2. Kudriavtceva D.A. Use of silicon resonator in resonant pressure transducers. Transactions of the International Symposium on Reliability and Quality, 2015, vol. 2, pp. 118–121. (in Russian)

3. Lu Y., Zhang S., Yan P., Li Y., Yu J., Chen D., Wang J., Xie B., Chen J. Resonant pressure micro sensors based on dual double ended tuning fork resonators. Micromachines, 2019, vol. 10, no. 9, pp. 560. doi: 10.3390/mi10090560

4. Andreev K.A., Tinyakov Yu.N., Shakhnov V.A. Mathematical models hybrid sensing elements transducers pressure. Sensors & Systems, 2013, no. 9 (172), pp. 2–9. (in Russian)

5. Tinyakov Yu.N., Nikolaeva A.S. Computation of pressure sensor membrane. Herald of the Bauman Moscow State Technical University. Series Instrument Engineering, 2015, no. 6 (105). pp. 135–142. (in Russian). doi: 10.18698/0236-3933-2015-6-135-142

6. Clark S.K., Wise K.D. Pressure sensitivity in anisotropically etched thin-diaphragm pressure sensors. Proc. of the IEEE Transactions on Electron Devices, 1979, vol. 26, no. 12, pp. 1887–1896. doi: 10.1109/T-ED.1979.19792

7. Yu Z., Zhao Y., Li L., Tian B., Li C. Geometry optimization for micropressure sensor considering dynamic interference. Review of Scientific Instruments, 2014, vol. 85, no. 9, pp. 095002. doi: 10.1063/1.4895999

8. Gulieva D.A., Tsypin B.V., Kuchumov E.V. Increasing of the string primary converter sensitivity by changing the overall and mass characteristics of the sensitive element. University Proceedings. Volga Region. Technical Sciences, 2020, no. 3 (55), pp. 88–97. (in Russian). doi: 10.21685/2072-3059-2020-3-9

9. Munas F.R., Amarasinghe Y.W.R., Kumarage P., Dao D.V., Dau V.T. Design and simulation of MEMS based piezoresitive pressure sensor for microfluidic applications. Proc. of the Moratuwa Engineering Research Conference (MERCon), 2018, pp. 215–220. doi: 10.1109/MERCon.2018.8421908

10. Tun P.V., Simonov B.M., Timoshenkov S.P. Investigation of the possibilities of increasing the sensitivity of a capacitive-type MEMS pressure sensor with membranes of various geometric shapes. Proceedings of Universities. Electronics, 2023, vol. 28, no. 2, pp. 222–231. (in Russian). doi: 10.24151/1561-5405-2023-28-2-222-231

11. Volkov V.S., Frantsuzov M.V., Ryblova E.A. Analytical and numerical simulation of semiconductor piezoresistive pressure sensing elements. Measuring. Monitoring. Management. Control, 2016, no. 2 (16). pp. 110–117. (in Russian)

12. Tcibizov P.N. Sensitive Elements for Microelectronic Pressure Sensors in Information-Measuring Systems. Penza, PNZGU, 2007, 173 p. (in Russian)

13. Tcypin B.V., Ariskina E.V., Shchipanov V.D., Iaroslavtceva D.A., Volkov V.S., Barinov I.N. Simulation of sensing element characteristic for micromechanical pressure sensor for use for heavy duty. Measuring. Monitoring. Management. Control, 2013, no. 2 (4), pp. 30–36. (in Russian)

14. Li Y., Lu Y., Xie B., Chen J., Wang J., Chen D. A micromachined resonant differential pressure sensor. IEEE Transactions on Electron Devices, 2020, vol. 67, no. 2, pp. 640–645. doi: 10.1109/TED.2019.2957880

15. Lu Y., Yan P., Xiang C., Chen D., Wang J., Xie B., Chen J. A resonant pressure microsensor with the measurement range of 1 MPa based on sensitivities balanced dual resonators. Sensors, 2019, vol. 19, no. 10, pp. 2272. doi: 10.3390/s19102272

16. Xiang C., Lu Y., Cheng C., Wang J., Chen D., Chen J. A resonant pressure microsensor with a wide pressure measurement range. Micromachines, 2021, vol. 12, no. 4, pp. 382. doi: 10.3390/mi12040382

17. Yan P., Lu Y., Xiang C., Wang J., Chen D., Chen J. A temperature-insensitive resonant pressure micro sensor based on silicon-on-glass vacuum packaging. Sensors, 2019, vol. 19, no. 18, pp. 3866. doi: 10.3390/s19183866

18. Harada K., Ikeda K., Kuwayama H., Murayama H. Various applications of resonant pressure sensor chip based on 3-D micromachining. Sensors and Actuators A: Physical, 1999, vol. 73, no. 3, pp. 261–266. doi: 10.1016/S0924-4247(98)00245-3

19. Danilina T.I., Smirnova K.I., Iliushin V.A., Velichko A.A. Study Guide on Micro- and Nanotechnology Processes. Tomsk, TUSUR, 2004, 260 p. (in Russian)

20. Sundaram K.B., Vijayakumar A., Subramanian G. Smooth etching of silicon using TMAH and isopropyl alcohol for MEMS applications. Microelectronic Engineering, 2005, vol. 77, no. 3-4, pp. 230–241. doi: 10.1016/j.mee.2004.11.004

21. Mitsumori K. Silicon etching. Scientific Wet Process Technology for Innovative LSI/FPD Manufacturing, 2018, pp. 252–263. doi: 10.1201/9781315221076

22. Pal P., Swarnalatha V., Rao A.V.N., Pandey A.K., Tanaka H., Sato K. High speed silicon wet anisotropic etching for applications in bulk micromachining: a review. Micro and Nano Systems Letters, 2021, vol. 9, no. 1, pp. 4. doi: 10.1186/s40486-021-00129-0

23. Yu X., Ye Y., Zhu P., Wu L., Shen R., Zhu C. Wet anisotropic etching characteristics of Si{111} in KOH-based solution. ACS Omega, 2025, vol. 10, no. 3, pp. 2940–2948. doi: 10.1021/acsomega.4c09272