Application of the level set method for the visual representation of continuous cellular automata oriented to anisotropic wet etching

References

• D. Adalsteinsson, J. A. Sethian, A fast level set method for propagating interfaces, J. Comput. Phys. 118 (1994), pp. 269–277 doi: 10.1006/jcph.1995.1098
   Web of Science ®Google Scholar
• D. Adalsteinsson, J. A. Sethian, A level set approach to a unified model for etching, deposition, and lithography i: Algorithms and two-dimensional simulations, J. Comput. Phys. 120 (1995), pp. 128–144 doi: 10.1006/jcph.1995.1153
   Web of Science ®Google Scholar
• D. Adalsteinsson, J. A. Sethian, A level set approach to a unified model for etching, deposition, and lithography ii: Three-dimensional simulations, J. Comput. Phys. 122 (1995), pp. 348–366 doi: 10.1006/jcph.1995.1221
   Web of Science ®Google Scholar
• D. Adalsteinsson, J. A. Sethian, A level set approach to a unified model for etching, deposition, and lithography iii: Redeposition, reemission, surface diffusion, and complex simulations, J. Comput. Phys. 138 (1997), pp. 193–223 doi: 10.1006/jcph.1997.5817
   Web of Science ®Google Scholar
• R. Allegre, R. Chaine, S. Akkouche, A flexible framework for surface reconstruction from large point sets, Comput. Graph. 31 (2007), pp. 190–204 doi: 10.1016/j.cag.2006.11.013
   Web of Science ®Google Scholar
• N. Amenta, M. Bern, D. Eppstein, The crust and the beta-skeleton: Combinatorial curve reconstruction, Graph. Models Image Process. 60 (1998), pp. 125–135 doi: 10.1006/gmip.1998.0465
   Google Scholar
• N. Amenta, M. Bern, and M. Kamvysselis, A New Voronoi-based Surface Reconstruction Algorithm, Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’98, ACM, Orlando, FL, 1998, pp. 415–421.
   Google Scholar
• K. Asaumi, Y. Iriye, K. Sato, Anisotropic-Etching Process Simulation System Microcad Analyzing Complete 3d Etching Profiles of Single Crystal SiliconNagoya, Japan (1997), pp. 412–417 IEEE Micro Electro Mechanical Systems
   Google Scholar
• S. Buttgenbach, O. Than, Suzana: A 3d Cad Tool for Anisotropically Etched Silicon MicrostructuresParis, France (1996), pp. 454–458 Proceedings of ED&TC ’96
   Google Scholar
• H. Camon, A. M. Gue, J. S. Daniel, M. Djafari-Rouhani, Modelling of anisotropic etching in silicon-based sensor application, Sens. Actuators A 33 (1992), pp. 103–105 doi: 10.1016/0924-4247(92)80237-W
   Web of Science ®Google Scholar
• J.C. Carr, R.K. Beatson, B.C. McCallum, W.R. Fright, T.J. McLennan, and T.J. Mitchell, Smooth Surface Reconstruction from Noisy Range Data, Proceedings of the 1st International Conference on Computer Graphics and Interactive Techniques in Australasia and South East Asia, GRAPHITE ’03, Melbourne, Australia, ACM, New York, 2003, pp. 119–126. Available at http://doi.acm.org/10.1145/604471.604495
   Google Scholar
• R. Courant, K. Friedrichs, H. Lewy, Über die partiellen differenzengleichungen der mathematischen physik, Math. Ann. 100 (1928), pp. 32–74 doi: 10.1007/BF01448839
   Web of Science ®Google Scholar
• H. Edelsbrunner, Shape Reconstruction with Delaunay ComplexSpringer-VerlagCampinas, Brazil (1998), pp. 119–132 Proceedings of the Third Latin American Symposium on Theoretical Informatics, LATIN ’98
   Google Scholar
• N. Ferrando, M. A. Gosálvez, J. Cerdá, R. Gadea, K. Sato, Faster and exact implementation of the continuous cellular automaton for anisotropic etching simulations, J. Micromech. Microeng. 21 (2011)
   Web of Science ®Google Scholar
• N. Ferrando, M. A. Gosalvez, J. Cerda, R. Gadea, K. Sato, Octree-based, GPU implementation of a continuous cellular automaton for the simulation of complex, evolving surfaces, Comput. Phys. Commun. 182 (2011), pp. 628–640 doi: 10.1016/j.cpc.2010.11.004
   Web of Science ®Google Scholar
• J. Gomes, O. Faugeras, Reconciling distance functions and level sets, J. Vis. Commun. Image Represent. 11 (1999), pp. 209–223 doi: 10.1006/jvci.1999.0439
   Web of Science ®Google Scholar
• M. A. Gosalvez, Y. Xing, K. Sato, Analytical solution of the continuous cellular automaton for anisotropic etching, J. Micromech. Syst. 17 (2008), pp. 410–431 doi: 10.1109/JMEMS.2008.916339
   Web of Science ®Google Scholar
• M. A. Gosalvez, R. M. Nieminen, P. Kilpinen, E. Haimi, V. Lindroos, Anisotropic wet chemical etching of crystalline silicon: Atomistic Monte-Carlo simulations and experiments, Appl. Surface Sci. 178 (2001), pp. 7–26 doi: 10.1016/S0169-4332(01)00233-1
   Web of Science ®Google Scholar
• M. A. Gosalvez, K. Sato, A. S. Foster, R. M. Nieminen, H. Tanaka, An atomistic introduction to anisotropic etching, J. Micromech. Microeng. 17 (2007), pp. S1–S26 doi: 10.1088/0960-1317/17/4/S01
   Google Scholar
• M. A. Gosálvez, P. Pal, N. Ferrando, H. Hida, K. Sato, Experimental procurement of the complete 3d etch rate distribution of Si in anisotropic etchants based on vertically micromachined wagon wheel samples, J. Micromech. Microeng. 21 (2011)
   Web of Science ®Google Scholar
• M. A. Gosalvez, N. Ferrando, Y. Xing, P. Pal, K. Sato, J. Cerda, R. Gadea, Simulating anisotropic etching of silicon in any etchant: Evolutionary algorithm for the calibration of the continuous cellular automaton, J. Micromech. Microeng. 21 (2011)
   Web of Science ®Google Scholar
• H. Gouraud, Continuous shading of curved surfaces, IEEE Trans. Comput. C-20 (1971), pp. 623–629 doi: 10.1109/T-C.1971.223313
   Web of Science ®Google Scholar
• H. Hoppe, T. DeRose, T. Duchamp, M. Halstead, H. Jin, J. McDonald, J. Schweitzer, and W. Stuetzle, Piecewise Smooth Surface Reconstruction, Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’94, ACM, New York, 1994, pp. 295–302. Available at http://doi.acm.org/10.1145/192161.192233
   Google Scholar
• T. Hubbard, E. K. Antonsson, Cellular automata modeling in MEMS design, Sens. Mater. 9 (1997), pp. 437–448
   Web of Science ®Google Scholar
• IntelliSense-Corp., Intellietch Web Page, 2010. Available at http://www.intellisensesoftware.com/modules/IntelliEtch.html
   Google Scholar
• G. S. Jian, D. Peng, Weighted eno schemes for Hamilton–Jacobi equations, SIAM J. Sci. Comput. 21 (1997), pp. 2126–2143 doi: 10.1137/S106482759732455X
   Web of Science ®Google Scholar
• A.E. Lefohn, J.E. Cates, and R.T. Whitaker, Interactive GPU-based Level Sets for 3d Segmentation, Proceedings of Medical Image Computing and Computer Assisted Intervention, Montréal, Canada, 2003, pp. 564–572.
   Google Scholar
• H. Liu, X. Wang, and W. Qiang, Implicit Surface Reconstruction from 3D Scattered Points based on Variational Level Set Method, in 2nd International Symposium on Systems and Control in Aerospace and Astronautics, 2008, ISSCAA 008, Shenzhen, China, December 2008, pp. 1–5.
   Google Scholar
• W. E. Lorensen, H. E. Cline, Marching cubes: A high resolution 3d surface construction algorithm, Comput. Graph. 21(4) (1987), pp. 163–169 doi: 10.1145/37402.37422
   Google Scholar
• R. Mencl and H. Muller, Graph-based surface reconstruction using structures in scattered point sets, Proceedings of the Computer Graphics International, Hannover, Germany, June 1998, pp. 298 –311.
   Google Scholar
• C. Oblonsek, N. Guid, A fast surface-based procedure for object reconstruction from 3d scattered points, Comput. Vis. Image Underst. 69 (1998), pp. 185–195 doi: 10.1006/cviu.1997.0584
   Web of Science ®Google Scholar
• S. Osher, J. A. Sethian, Fronts propagating with curvature dependent speed: Algorithms based on Hamilton–Jacobi formulations, J. Comput. Phys. 79 (1988), pp. 12–49 doi: 10.1016/0021-9991(88)90002-2
   Web of Science ®Google Scholar
• P. Pal, K. Sato, Various shapes of silicon freestanding microfluidic channels and microstructures in one-step lithography, J. Micromech. Microeng. 19(5) (2004)
   Google Scholar
• M. Roberts, J. Packer, M. Costa-Sousa, and J.R. Mitchell, A Work-efficient gpu Algorithm for Level Set Segmentation, Proceedings of the Conference on High Performance Graphics, Saarbrüken, Germany, 2010, pp. 123–132.
   Google Scholar
• F. Santosa, A level set approach for inverse problems involving obstacles, ESAIM: Control Optim. Calc. Var. 1 (1996), pp. 17–33 doi: 10.1051/cocv:1996101
   Google Scholar
• G. Schröpfer, M. de Labachelerie, S. Ballandras, P. Blind, Collective wet etching of a 3d monolithic silicon seismic mass system, J. Micromech. Microeng. 8 (1998), pp. 77–79 doi: 10.1088/0960-1317/8/2/008
   Web of Science ®Google Scholar
• J. A. Sethian, M. Popovici, Fast marching methods applied to computation of seismic travel times, Geophysics 64 (1999), p. 2. doi: 10.1190/1.1444558
   Web of Science ®Google Scholar
• M. Shikida, M. Ando, Y. Ishihara, T. Ando, K. Sato, K. Asaumi, Non-photolithographic pattern transfer for fabricating pen-shaped microneedle structures, J. Micromec. Microeng. 14 (2004), pp. 1462–1467 doi: 10.1088/0960-1317/14/11/005
   Web of Science ®Google Scholar
• O. Than, S. Buttgenbach, Simulation of anisotropic chemical etching crystalline silicon using a cellular automata model, Sens. Actuators A 45 (1994), pp. 85–88 doi: 10.1016/0924-4247(94)00820-5
   Web of Science ®Google Scholar
• R. T. Whitaker, A level-set approach to 3d reconstruction from range data, Int. J. Comput. Vis. 29 (1998), pp. 203–231 doi: 10.1023/A:1008036829907
   Web of Science ®Google Scholar
• R. A. Wind, H. Jones, M. A. Hines, Macroscopic etch anisotropies and microscopic reaction mechanisms: A micromachined structure for the rapid assay of etchant anisotropy, Surface Sci. 460 (2000), pp. 21–38 doi: 10.1016/S0039-6028(00)00479-9
   Web of Science ®Google Scholar
• H.K. Zhao, S. Osher, and R. Fedkiw, Fast Surface Reconstruction Using the Level Set Method, Proceedings of the IEEE Workshop on Variational and Level Set Methods in Computer Vision, Vancouver, Canada, 2001, pp. 194–201.
   Google Scholar
• H. K. Zhao, S. Osher, B. Merriman, M. Kang, Implicit and non-parametric shape reconstruction from unorganized data using a variational level set method, Comput. Vis. Image Underst. 80 (2000), pp. 295–319 doi: 10.1006/cviu.2000.0875
   Web of Science ®Google Scholar
• Z. Zhu, C. Liu, Micromachining process simulation using a continuous cellular automata method, J. Micromech. Syst. 9 (2000), pp. 252–261 doi: 10.1109/84.846706
   Google Scholar
• I. Zubel, M. Kramkowska, The effect of alcohol additives on etching characteristics in KOH solutions, Sens. Actuators A 101 (2002), pp. 255–261 doi: 10.1016/S0924-4247(02)00265-0
   Web of Science ®Google Scholar
• I. Zubel, M. Kramkowska, Etch rates and morphology of silicon (h k l) surfaces etched in KOHand KOH saturated with isopropanol solutions, Sens. Actuators A 115 (2004), pp. 549–556 doi: 10.1016/j.sna.2003.11.010
   Web of Science ®Google Scholar