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. 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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

Fluctuations During Anisotropic Etching: Local Recalibration and Application to Si{110}

Based on the previous studies of the etch rate of crystalline silicon in alkaline etchants, we stress the fact that the etch rates can noticeably differ between different research groups. This affects the prediction of the etch front, since the simulators typically use experimental data gathered in one laboratory. Considering the most efficient and accurate simulator currently available for the description of anisotropic etching, namely the continuous cellular automaton (CCA), any such variation in the experimental etch rates requires a time-consuming calibration procedure in order to adjust the atomistic removal rates internally used by the method. Since normally it is possible to directly compare the experimental and simulated etch fronts - without actual knowledge of the variations in the macroscopic etch rates - here we propose a local recalibration procedure by which the atomistic removal rates of a few atoms are modified, thus recovering most features of the experimental fronts in the simulated counterparts. As an application, we evaluate for the first time the ability of the CCA to describe wet etching on Si{110}, focusing on a large collection of wet etched structures including cavities and mesas at different stages of the etching process, obtaining excellent agreement between experiment and simulation