Evolutionary continuous cellular automaton for the simulation of wet etching of quartz

Anisotropic wet chemical etching of quartz is a bulk micromachining process for the fabrication of micro-electro-mechanical systems (MEMS), such as resonators and temperature sensors. Despite the success of the continuous cellular automaton for the simulation of wet etching of silicon, the simulation of the same process for quartz has received little attention-especially from an atomistic perspective-resulting in a lack of accurate modeling tools. This paper analyzes the crystallographic structure of the main surface orientations of quartz and proposes a novel classification of the surface atoms as well as an evolutionary algorithm to determine suitable values for the corresponding atomistic removal rates. Not only does the presented evolutionary continuous cellular automaton reproduce the correct macroscopic etch rate distribution for quartz hemispheres, but it is also capable of performing fast and accurate 3D simulations of MEMS structures. This is shown by several comparisons between simulated and experimental results and, in particular, by a detailed, quantitative comparison for an extensive collection of trench profiles. © 2012 IOP Publishing Ltd.We are grateful to D Cheng and K Sato (Nagoya University, Japan) for providing part of the experimental data. We acknowledge support by the JAE-Doc grant form the Junta para la Ampliacion de Estudios program co-funded by FSE, the Ramon y Cajal Fellowship Program by the Spanish Ministry of Science and Innovation, NANO-IKER Project (IE11-304) from the ETORTEK program by the Basque Government and the Professor Partnership Program by NVIDIA Corporation.Ferrando Jódar, N.; Gosalvez Ayuso, MA.; Colom Palero, RJ. (2012). Evolutionary continuous cellular automaton for the simulation of wet etching of quartz. Journal of Micromechanics and Microengineering. 22(2). https://doi.org/10.1088/0960-1317/22/2/025021S222Hida, H., Shikida, M., Fukuzawa, K., Murakami, S., Sato, K., Asaumi, K., … Sato, K. (2008). Fabrication of a quartz tuning-fork probe with a sharp tip for AFM systems. Sensors and Actuators A: Physical, 148(1), 311-318. doi:10.1016/j.sna.2008.08.021Oh, H., Kim, G., Seo, H., Song, Y., Lee, K., & Yang, S. S. (2010). Fabrication of micro-lens array using quartz wet etching and polymer. Sensors and Actuators A: Physical, 164(1-2), 161-167. doi:10.1016/j.sna.2010.10.003Xing, Y., Gosálvez, M. A., & Sato, K. (2007). Step flow-based cellular automaton for the simulation of anisotropic etching of complex MEMS structures. New Journal of Physics, 9(12), 436-436. doi:10.1088/1367-2630/9/12/436Zhou, Z., Huang, Q., Li, W., & Deng, W. (2007). A cellular automaton-based simulator for silicon anisotropic etching processes considering high index planes. Journal of Micromechanics and Microengineering, 17(4), S38-S49. doi:10.1088/0960-1317/17/4/s03Gosalvez, M. A., Yan Xing, & Sato, K. (2008). Analytical Solution of the Continuous Cellular Automaton for Anisotropic Etching. Journal of Microelectromechanical Systems, 17(2), 410-431. doi:10.1109/jmems.2008.916339Zhou, Z., Huang, Q., & Li, W. (2009). Modeling and Simulations of Anisotropic Etching of Silicon in Alkaline Solutions with Experimental Verification. Journal of The Electrochemical Society, 156(2), F29. doi:10.1149/1.3031485Rangsten, P., Hedlund, C., Katardjiev, I. V., & Bäcklund, Y. (1998). Etch rates of crystallographic planes inZ-cut quartz - experiments and simulation. Journal of Micromechanics and Microengineering, 8(1), 1-6. doi:10.1088/0960-1317/8/1/001Tellier, C. R., & Leblois, T. G. (2000). Micromachining of quartz plates: determination of a database by combined stereographic analysis and 3-D simulation of etching shapes. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 47(5), 1204-1216. doi:10.1109/58.869067Hedlund, C., Lindberg, U., Bucht, U., & Soderkvist, J. (1993). Anisotropic etching of Z-cut quartz. Journal of Micromechanics and Microengineering, 3(2), 65-73. doi:10.1088/0960-1317/3/2/006Liang, J., Kohsaka, F., Matsuo, T., & Ueda, T. (2007). Wet Etched High Aspect Ratio Microstructures on Quartz for MEMS Applications. IEEJ Transactions on Sensors and Micromachines, 127(7), 337-342. doi:10.1541/ieejsmas.127.337Gosálvez, M. A., Xing, Y., Sato, K., & Nieminen, R. M. (2009). Discrete and continuous cellular automata for the simulation of propagating surfaces. Sensors and Actuators A: Physical, 155(1), 98-112. doi:10.1016/j.sna.2009.08.012Zhenjun Zhu, & Chang Liu. (2000). Micromachining process simulation using a continuous cellular automata method. Journal of Microelectromechanical Systems, 9(2), 252-261. doi:10.1109/84.846706Gosálvez, M. A., Xing, Y., Sato, K., & Nieminen, R. M. (2008). Atomistic methods for the simulation of evolving surfaces. Journal of Micromechanics and Microengineering, 18(5), 055029. doi:10.1088/0960-1317/18/5/055029Ferrando, N., Gosálvez, M. A., Cerdá, J., Gadea, R., & Sato, K. (2011). Octree-based, GPU implementation of a continuous cellular automaton for the simulation of complex, evolving surfaces. Computer Physics Communications, 182(3), 628-640. doi:10.1016/j.cpc.2010.11.004Mühlenbein, H., & Schlierkamp-Voosen, D. (1993). Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization. Evolutionary Computation, 1(1), 25-49. doi:10.1162/evco.1993.1.1.25Kohsaka, F., Liang, J., Matsuo, T., & Ueda, T. (2007). High Sensitive Tilt Sensor for Quartz Micromachining. IEEJ Transactions on Sensors and Micromachines, 127(10), 431-436. doi:10.1541/ieejsmas.127.43

Full Wave Electromagnetic Analysis And

Progress in MEMS and packaging design has made significant changes in the requirements for modeling tools. In order to design a modern microdevice or interconnect system it is no longer sufficient to limit the analysis to quasielectrostatic modeling due to smaller size and higher operation frequencies of the microdevices. On the other hand, a `full-wave' analysis produces huge systems of equations which require tremendous amounts of computational resources. The method described in this paper is a combination of three-dimensional full-wave coupled RLC electromagnetic analysis and passive Arnoldy based model order reduction algorithm and allows to solve wider range of design problems including miniaturization and high frequency modeling problems