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Analysis of Thermal Damping in Si Based Torsional Micromirrors

Authors: M. R. Baiju, R. Resmi


The thermal damping of a dynamic vibrating micromirror is an important factor affecting the design of MEMS based actuator systems. In the development process of new micromirror systems, assessing the extent of energy loss due to thermal damping accurately and predicting the performance of the system is very essential. In this paper, the depth of the thermal penetration layer at different eigenfrequencies and the temperature variation distributions surrounding a vibrating micromirror is analyzed. The thermal penetration depth corresponds to the thermal boundary layer in which energy is lost which is a measure of the thermal damping is found out. The energy is mainly dissipated in the thermal boundary layer and thickness of the layer is an important parameter. The detailed thermoacoustics is used to model the air domain surrounding the micromirror. The thickness of the boundary layer, temperature variations and thermal power dissipation are analyzed for a Si based torsional mode micromirror. It is found that thermal penetration depth decreases with eigenfrequency and hence operating the micromirror at higher frequencies is essential for reducing thermal damping. The temperature variations and thermal power dissipations at different eigenfrequencies are also analyzed. Both frequency-response and eigenfrequency analyses are done using COMSOL Multiphysics software.

Keywords: Eigen frequency analysis, micromirrors, thermal damping, thermoacoustic interactions

Digital Object Identifier (DOI):

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[1] Olav Solgard, Asif A. Godil, Roger T. Howe, Luke P. Lee, Yves-Alain Peter, Hanes Zappe, “Optical MEMS: From micromirrors to complex systems,” Journal of Micro Electro Mechanical Systems, vol. 23, no.3, June 2014.
[2] R. Sulima and S. Wiak, “Modeling of vertical electrostatic comb-drive for scanning micromirrors,” Int. J. Comput. Math. Electr. Electron.Eng., vol. 27, no. 4, pp. 780–787, 2008.
[3] Xingguo Xiong and Hanyu Xie, “MEMS dual-mode electrostatically actuated micromirror,” Proceedings of Zone 1 Conference of the American Society for Engineering Education (ASEE Zone 1), 2014.
[4] David A. Ditmars and George T. Furukawa “Detection and Damping of Thermal-Acoustic Oscillationsi n Low-temperature Measurements” Journal of Research of the National Bureau of Standards-C. Engineering and Instrumentation, Vol. 69C, No. I, January-March 1965.
[5] Srikar Vengallatore, “Analysis of thermoelastic damping in laminated composite micromechanical beam resonators”, J. Micromech. Microeng. 2398-2404,2005.
[6] Minikes A, Bucher I and Avivi G, “Damping of a microresonator torsion mirror in rarefied gas ambient,” J Micromech Microengg 15:1762–1769K., 2005.
[7] Hamid Moeenfard, Mohammad Taghi Ahmadian, and Anooshiravan Farshidianfar, “Modeling squeezed film air damping in torsional micromirrors using extended Kantorovich method lateral shift,” Meccanica, 48:791–805, 2013.
[8] Tilmans H A C, “Equivalent circuit representation of electromechanical transducers: Lumped-parameter systems, J. Micromech. Microeng. 6 157–76, 1996.
[9] C. Zener, “Internal friction in solids II: General theory of thermoelastic internal friction,” Phys. Rev., vol. 53, no. 1, pp. 90–99, Jan.
[10] T.V. Roszhart, “The effect of thermoelastic internal friction on the Q of micromachined silicon resonators”, Tech. Dig. Solid-State Sens. Actuator Workshop, Hilton Head, SC, 13-16, 1990.
[11] H. Tijdeman "Energy Dissipation in Thin Air Layers” ISMA 21 Conference on Noise and vibration Engineering, WB 26/TM 1582, 1996.
[12] T. Veijola, A. Pursula and P. Raback, “Surface extension model for MEMS squeezed-film dampers” in Proc. DTIP’05, pp. 235, 2005.
[13] R. Lifshitz and M. L. Roukes, “Thermoelastic damping in micro- and nanomechanical systems”, Physical review B, Vol. 6, No 8, Feb. 2000, 5600-5609, 2000.
[14] Yusuke Kawai, Jin-Hyeok Kim, “Parametrically Actuated Resonant Micromirror Using Stiffness Tunable Torsional Springs” Sensors and Materials, Vol.28 No.2131-139, 2016.
[15] M. Gologanu, C.G. Bostan, V. Avramescu, O. Buiu, “Damping Effects in MEMS Resonators”, Sensors and Wireless Lab Bucharest (SWLB), IEEE Conference, pp: 67-74,2012.