Abstract

Modeling a MEMS (Micro Electro-Mechanical Systems) electrostatic actuator in electrical domain is important for system simulation of the actuator along with its associated electronics. For instance, an integrated MEMS resonator used in a serial I/O PLL design modeled in electrical domain enables to optimize the system with the rest of the electronics. In this work, we have developed a simplified equivalent circuit model for MEMS electrostatic actuator and simulated it using Natspice, a U.C. Berkeley SPICE3f5-based in-house circuit simulator. The equations governing the actuator are implemented using coupled RL and RLC circuit, defined in SPICE and Verilog-A. Natspice simulation results are presented and compared with Matlab results which show very high correlation. A system consisting of an array of MEMS devices can be quickly simulated using this simplified model.

References

• Schröpfer, Gerold, et al. "Advanced process emulation and circuit simulation for co-design of MEMS and CMOS devices." Proceedings Symposium on Design, Test, Integration and Packaging of MEMS/MOEMS (DTIP). 2005.
• Cheng, J., Zhe, J., Wu, X., Farmer, K. R., Modi, V., & Frechette, L. (2002, May). Analytical and FEM simulation pull-in study on deformable electrostatic micro actuators. In Technical Proc. of the International Conf on Modeling and Simulation of Microsystems, MSM (pp. 298-301).
• Wang, C. K., Chen, C. S., & Wen, K. A. (2011, May). A monolithic CMOS MEMS accelerometer with chopper correlated double sampling readout circuit. In Circuits and Systems (ISCAS), 2011 IEEE international Symposium on (pp. 2023-2026). IEEE.
• Senturia, S. D. (1998). CAD challenges for microsensors, microactuators, and microsystems. Proceedings of the IEEE, 86(8), 1611-1626.
• Cheng, J., Zhe, J., Wu, X., Farmer, K. R., Modi, V., & Frechette, L. (2002, May). Analytical and FEM simulation pull-in study on deformable electrostatic micro actuators. In Technical Proc. of the International Conf on Modeling and Simulation of Microsystems, MSM (pp. 298-301).
• Camon, H., Larnaudie, F., Rivoirard, F., & Jammes, B. (1999, May). Analytical simulation of a 1D single crystal silicon electrostatic micromirror. In International Conference on Modeling and Simulation of Microsystems (pp. 628-631).
• Certon, D., Teston, F., & Patat, F. (2005). A finite difference model for cMUT devices. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 52(12), 2199-2210.
• Clark, J. V., Zhou, N., & Pister, K. S. J. (1998, June). MEMS simulation using SUGAR v0. 5. In Solid-State Sensor and Actuator Workshop (pp. 191-196).
• Lohfink, A., Eccardt, P. C., Benecke, W., & Meixner, H. (2003, October). Derivation of a 1D CMUT model from FEM results for linear and nonlinear equivalent circuit simulation. In Ultrasonics, 2003 IEEE Symposium on (Vol. 1, pp. 465-468). IEEE.
• Lohfink, A., & Eccardt, P. C. (2005). Linear and nonlinear equivalent circuit modeling of CMUTs. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 52(12), 2163-2172.
• Wygant, I. O., Kupnik, M., & Khuri-Yakub, B. T. (2008, November). Analytically calculating membrane displacement and the equivalent circuit model of a circular CMUT cell. In Ultrasonics Symposium, 2008. IUS 2008. IEEE (pp. 2111-2114). IEEE.
• Mita, M., & Toshiyoshi, H. (2009). An equivalent-circuit model for MEMS electrostatic actuator using open-source software Qucs. IEICE Electronics Express, 6(5), 256-263.
• Sathe, A. A., Groll, E. A., & Garimella, S. V. (2008). Analytical model for an electrostatically actuated miniature diaphragm compressor. Journal of micromechanics and microengineering, 18(3), 035010.
• Cicek, İ., Bozkurt, A., & Karaman, M. (2005). Design of a front-end integrated circuit for 3D acoustic imaging using 2D CMUT arrays. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 52(12), 2235-2241.
• Konishi, T., Machida, K., Masu, K., & Toshiyoshi, H. (2013). Multi-Physics Equivalent Circuit Model for MEMS Sensors and Actuators. ECS Transactions, 50(14), 55-61.
• Koymen, H., Atalar, A., Aydogdu, E., Kocabas, C., Oguz, H. K., Olcum, S., ... & Unlugedik, A. (2012). An improved lumped element nonlinear circuit model for a circular CMUT cell. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 59(8).
• Wygant, I. O., Kupnik, M., & Khuri-Yakub, B. T. (2016, September). CMUT design equations for optimizing noise figure and source pressure. In Ultrasonics Symposium (IUS), 2016 IEEE International (pp. 1-4). IEEE.
• Oguz, H. K., Atalar, A., & Köymen, H. (2013). Equivalent circuit-based analysis of CMUT cell dynamics in arrays. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 60(5), 1016-1024.
• Oguz, H. K., Atalar, A., & Köymen, H. (2013). Equivalent circuit-based analysis of CMUT cell dynamics in arrays. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 60(5), 1016-1024.
• Savoia, A. S., Caliano, G., & Pappalardo, M. (2012). A CMUT probe for medical ultrasonography: from microfabrication to system integration. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 59(6), 1127-1138.
• Song, J., Jung, S., Kim, Y., Cho, K., Kim, B., Lee, S. & Kim, D. (2012, February). Reconfigurable 2D cMUT-ASIC arrays for 3D ultrasound image. In SPIE Medical Imaging (pp. 83201A-83201A). International Society for Optics and Photonics.
• Gurun, G., Tekes, C., Zahorian, J., Xu, T., Satir, S., Karaman, M., ... & Degertekin, F. L. (2014). Single-chip CMUT-on-CMOS front-end system for real-time volumetric IVUS and ICE imaging. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 61(2), 239-250.
• Senturia, S. D. (2007). Microsystem design. Springer Science & Business Media.
• Hung, E. S., & Senturia, S. D. (1999). Extending the travel range of analog-tuned electrostatic actuators. Journal of microelectromechanical systems, 8(4), 497-505.
• Seeger, J. I., & Boser, B. E. (2003). Charge control of parallel-plate, electrostatic actuators and the tip-in instability. Journal of Microelectromechanical systems, 12(5), 656-671.