Implementation and evaluation of the Level Set method: towards efficient and accurate simulation of wet etching for microengineering applications

The use of atomistic methods, such as the Continuous Cellular Automaton (CCA), is currently regarded as a computationally efficient and experimentally accurate approach for the simulation of anisotropic etching of various substrates in the manufacture of Micro-electro-mechanical Systems (MEMS). However, when the features of the chemical process are modified, a time-consuming calibration process needs to be used to transform the new macroscopic etch rates into a corresponding set of atomistic rates. Furthermore, changing the substrate requires a labor-intensive effort to reclassify most atomistic neighborhoods. In this context, the Level Set (LS) method provides an alternative approach where the macroscopic forces affecting the front evolution are directly applied at the discrete level, thus avoiding the need for reclassification and/or calibration. Correspondingly, we present a fully-operational Sparse Field Method (SFM) implementation of the LS approach, discussing in detail the algorithm and providing a thorough characterization of the computational cost and simulation accuracy, including a comparison to the performance by the most recent CCA model. We conclude that the SFM implementation achieves similar accuracy as the CCA method with less fluctuations in the etch front and requiring roughly 4 times less memory. Although SFM can be up to 2 times slower than CCA for the simulation of anisotropic etchants, it can also be up to 10 times faster than CCA for isotropic etchants. In addition, we present a parallel, GPU-based implementation (gSFM) and compare it to an optimized, multicore CPU version (cSFM), demonstrating that the SFM algorithm can be successfully parallelized and the simulation times consequently reduced, while keeping the accuracy of the simulations. Although modern multicore CPUs provide an acceptable option, the massively parallel architecture of modern GPUs is more suitable, as reflected by computational times for gSFM up to 7.4 times faster than for cSFM. (c) 2013 Elsevier B.V. All rights reserved.We thank the anonymous reviewers for their valuable comments and suggestions. This work has been supported by the Spanish FPI-MICINN BES-2011-045940 grant and the Ramon y Cajal Fellowship Program by the Spanish Ministry of Science and Innovation. Also, we acknowledge support by the JAE-Doc grant from the Junta para la Ampliacion de Estudios program co-funded by FSE and the Professor Partnership Program by NVIDIA Corporation.Montoliu Álvaro, C.; Ferrando Jódar, N.; Gosalvez, MÁ.; Cerdá Boluda, J.; Colom Palero, RJ. (2013). Implementation and evaluation of the Level Set method: towards efficient and accurate simulation of wet etching for microengineering applications. Computer Physics Communications. 184(10):2299-2309. https://doi.org/10.1016/j.cpc.2013.05.016S229923091841

Semi-implicit representation of sharp features with level sets

The present contribution enriches the nowadays “classical” level set implicit representation of geometries with topological information in order to correctly represent sharp features. For this, sharp features are classified according to their positions within elements of the level set support. Based on this additional information, sub-elements and interface-mesh used in a finite element context for integration and application of boundary conditions are modified to match exactly to the sharp features. In order to analyze evolving geometries, Boolean operations on these semi-implicit representations are derived so that the minimal additional information to represent correctly the new geometry is stored. This approach has been successfully applied to complex two-dimensional geometries. It computes in a robust way numerous Boolean operations and guarantees the precision and the convergence rate of the numerical simulations.Integrating Numerical Simulation and Geometric Design Technology (INSIST

Level set implementation for the simulation of anisotropic etching: application to complex MEMS micromachining

The use of atomistic methods, such as the continuous cellular automaton (CCA), is currently regarded as an accurate and efficient approach for the simulation of anisotropic etching in the development of micro-electro-mechanical systems (MEMS). However, whenever the targeted etching condition is modified (e. g. by changing the substrate material, etchant type, concentration and/or temperature) this approach requires performing a time-consuming recalibration of the full set of internal atomistic rates defined within the method. Based on the level set (LS) approach as an alternative and using the experimental data directly as input, we present a fully operational simulator that exhibits similar accuracy to the latest CCA models. The proposed simulator is tested by describing a wide range of silicon and quartz MEMS structures obtained in different etchants through complex processes, including double-sided etching as well as different mask patterns during different etching steps and/or simultaneous masking materials on different regions of the substrate. The results demonstrate that the LS method is able to simulate anisotropic etching for complex MEMS processes with similar computational times and accuracy as the atomistic models.This work has been supported by the Spanish FPI-MICINN BES-2011-045940 grant and the Ramon y Cajal Fellowship Program by the Spanish Ministry of Science and Innovation. Also, we acknowledge support by the JAE-Doc grant from the Junta para la Ampliacion de Estudios program co-funded by FSE and the Professor Partnership Program by NVIDIA Corporation.Montoliu, C.; Ferrando Jódar, N.; Gosalvez Ayuso, MA.; Cerdá Boluda, J.; Colom Palero, RJ. (2013). Level set implementation for the simulation of anisotropic etching: application to complex MEMS micromachining. Journal of Micromechanics and Microengineering. 23(7). https://doi.org/10.1088/0960-1317/23/7/075017S237Weirauch, D. F. (1975). Correlation of the anisotropic etching of single−crystal silicon spheres and wafers. Journal of Applied Physics, 46(4), 1478-1483. doi:10.1063/1.321787Seidel, H. (1990). Anisotropic Etching of Crystalline Silicon in Alkaline Solutions. Journal of The Electrochemical Society, 137(11), 3612. doi:10.1149/1.2086277Zielke, D., & Frühauf, J. (1995). Determination of rates for orientation-dependent etching. Sensors and Actuators A: Physical, 48(2), 151-156. doi:10.1016/0924-4247(95)00993-0Wind, R. A., & Hines, M. A. (2000). Macroscopic etch anisotropies and microscopic reaction mechanisms: a micromachined structure for the rapid assay of etchant anisotropy. Surface Science, 460(1-3), 21-38. doi:10.1016/s0039-6028(00)00479-9Gosálvez, M. A., Sato, K., Foster, A. S., Nieminen, R. M., & Tanaka, H. (2007). An atomistic introduction to anisotropic etching. Journal of Micromechanics and Microengineering, 17(4), S1-S26. doi:10.1088/0960-1317/17/4/s01Sato, K., Shikida, M., Matsushima, Y., Yamashiro, T., Asaumi, K., Iriye, Y., & Yamamoto, M. (1998). Characterization of orientation-dependent etching properties of single-crystal silicon: effects of KOH concentration. Sensors and Actuators A: Physical, 64(1), 87-93. doi:10.1016/s0924-4247(97)01658-0Zubel, I., & Kramkowska, M. (2002). The effect of alcohol additives on etching characteristics in KOH solutions. Sensors and Actuators A: Physical, 101(3), 255-261. doi:10.1016/s0924-4247(02)00265-0Charbonnieras, A. R., & Tellier, C. R. (1999). Characterization of the anisotropic chemical attack of {hk0} silicon plates in a T.M.A.H. solution. Sensors and Actuators A: Physical, 77(2), 81-97. doi:10.1016/s0924-4247(99)00020-5Shikida, M., Sato, K., Tokoro, K., & Uchikawa, D. (2000). Differences in anisotropic etching properties of KOH and TMAH solutions. Sensors and Actuators A: Physical, 80(2), 179-188. doi:10.1016/s0924-4247(99)00264-2Gosálvez, M. A., Zubel, I., & Viinikka, E. (2010). Wet Etching of Silicon. Handbook of Silicon Based MEMS Materials and Technologies, 375-407. doi:10.1016/b978-0-8155-1594-4.00024-3Pal, P., Gosalvez, M. A., & Sato, K. (2010). Silicon Micromachining Based on Surfactant-Added Tetramethyl Ammonium Hydroxide: Etching Mechanism and Advanced Applications. Japanese Journal of Applied Physics, 49(5), 056702. doi:10.1143/jjap.49.056702Zubel, I., & Kramkowska, M. (2004). Etch rates and morphology of silicon (h k l) surfaces etched in KOH and KOH saturated with isopropanol solutions. Sensors and Actuators A: Physical, 115(2-3), 549-556. doi:10.1016/j.sna.2003.11.010Fruhauf, J., Trautmann, K., Wittig, J., & Zielke, D. (1993). A simulation tool for orientation dependent etching. Journal of Micromechanics and Microengineering, 3(3), 113-115. doi:10.1088/0960-1317/3/3/004Than, O., & Büttgenbach, S. (1994). Simulation of anisotropic chemical etching of crystalline silicon using a cellular automata model. Sensors and Actuators A: Physical, 45(1), 85-89. doi:10.1016/0924-4247(94)00820-5Camon, H., Gue, A. M., Danel, J. S., & Djafari-Rouhani, M. (1992). Modelling of anisotropic etching in silicon-based sensor application. Sensors and Actuators A: Physical, 33(1-2), 103-105. doi:10.1016/0924-4247(92)80237-wGosalvez, M. ., Nieminen, R. ., Kilpinen, P., Haimi, E., & Lindroos, V. (2001). Anisotropic wet chemical etching of crystalline silicon: atomistic Monte-Carlo simulations and experiments. Applied Surface Science, 178(1-4), 7-26. doi:10.1016/s0169-4332(01)00233-1Zhenjun Zhu, & Chang Liu. (2000). Micromachining process simulation using a continuous cellular automata method. Journal of Microelectromechanical Systems, 9(2), 252-261. doi:10.1109/84.846706Gosalvez, 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.2008.916339Ferrando, N., Gosálvez, M. A., Cerdá, J., Gadea, R., & Sato, K. (2011). Faster and exact implementation of the continuous cellular automaton for anisotropic etching simulations. Journal of Micromechanics and Microengineering, 21(2), 025021. doi:10.1088/0960-1317/21/2/025021Ferrando, 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.2010.11.004Moktadir, Z., & Camon, H. (1997). Monte Carlo simulation of anisotropic etching of silicon: investigation of surface properties. Modelling and Simulation in Materials Science and Engineering, 5(5), 481-488. doi:10.1088/0965-0393/5/5/004Flidr, J., Huang, Y.-C., & Hines, M. A. (1999). An atomistic mechanism for the production of two- and three-dimensional etch hillocks on Si(111) surfaces. The Journal of Chemical Physics, 111(15), 6970-6981. doi:10.1063/1.479990Gos lvez, M. A., & Nieminen, R. M. (2003). Surface morphology during anisotropic wet chemical etching of crystalline silicon. New Journal of Physics, 5, 100-100. doi:10.1088/1367-2630/5/1/400Xing, Y., Gosálvez, M. A., Sato, K., Tian, M., & Yi, H. (2012). Evolutionary determination of kinetic Monte Carlo rates for the simulation of evolving surfaces in anisotropic etching of silicon. Journal of Micromechanics and Microengineering, 22(8), 085020. doi:10.1088/0960-1317/22/8/085020Xing, Y., Gosálvez, M. A., Sato, K., & Yi, H. (2009). Orientation-dependent surface morphology of crystalline silicon during anisotropic etching using a continuous cellular automaton. Journal of Micromechanics and Microengineering, 20(1), 015019. doi:10.1088/0960-1317/20/1/015019Zhou, 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/s03Gosálvez, 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.2009.08.012Ferrando, N., Gosálvez, M. A., & Colóm, R. J. (2012). Evolutionary continuous cellular automaton for the simulation of wet etching of quartz. Journal of Micromechanics and Microengineering, 22(2), 025021. doi:10.1088/0960-1317/22/2/025021Osher, S., & Sethian, J. A. (1988). Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics, 79(1), 12-49. doi:10.1016/0021-9991(88)90002-2Adalsteinsson, D., & Sethian, J. A. (1995). A Level Set Approach to a Unified Model for Etching, Deposition, and Lithography I: Algorithms and Two-Dimensional Simulations. Journal of Computational Physics, 120(1), 128-144. doi:10.1006/jcph.1995.1153Adalsteinsson, D., & Sethian, J. A. (1995). A Level Set Approach to a Unified Model for Etching, Deposition, and Lithography II: Three-Dimensional Simulations. Journal of Computational Physics, 122(2), 348-366. doi:10.1006/jcph.1995.1221Adalsteinsson, D., & Sethian, J. A. (1997). A Level Set Approach to a Unified Model for Etching, Deposition, and Lithography. Journal of Computational Physics, 138(1), 193-223. doi:10.1006/jcph.1997.5817Ertl, O., & Selberherr, S. (2009). A fast level set framework for large three-dimensional topography simulations. Computer Physics Communications, 180(8), 1242-1250. doi:10.1016/j.cpc.2009.02.002Ertl, O., & Selberherr, S. (2010). Three-dimensional level set based Bosch process simulations using ray tracing for flux calculation. Microelectronic Engineering, 87(1), 20-29. doi:10.1016/j.mee.2009.05.011Burzynski, T., & Papini, M. (2010). Level set methods for the modelling of surface evolution in the abrasive jet micromachining of features used in MEMS and microfluidic devices. Journal of Micromechanics and Microengineering, 20(8), 085004. doi:10.1088/0960-1317/20/8/085004Radjenović, B., Lee, J. K., & Radmilović-Radjenović, M. (2006). Sparse field level set method for non-convex Hamiltonians in 3D plasma etching profile simulations. Computer Physics Communications, 174(2), 127-132. doi:10.1016/j.cpc.2005.09.010Radjenović, B., Radmilović-Radjenović, M., & Mitrić, M. (2006). Nonconvex Hamiltonians in three dimensional level set simulations of the wet etching of silicon. Applied Physics Letters, 89(21), 213102. doi:10.1063/1.2388860Branislav, R., & Marija, R.-R. (2010). Level set simulations of the anisotropic wet etching process for device fabrication in nanotechnologies. Hemijska industrija, 64(2), 93-97. doi:10.2298/hemind100205008rRadjenović, B., Radmilović-Radjenović, M., & Mitrić, M. (2010). Level Set Approach to Anisotropic Wet Etching of Silicon. Sensors, 10(5), 4950-4967. doi:10.3390/s100504950Radjenović, B., & Radmilović-Radjenović, M. (2011). Three-Dimensional Simulations of the Anisotropic Etching Profile Evolution for Producing Nanoscale Devices. Acta Physica Polonica A, 119(3), 447-450. doi:10.12693/aphyspola.119.447Crandall, M. G., & Lions, P.-L. (1984). Two approximations of solutions of Hamilton-Jacobi equations. Mathematics of Computation, 43(167), 1-1. doi:10.1090/s0025-5718-1984-0744921-8Whitaker, R. T. (1998). International Journal of Computer Vision, 29(3), 203-231. doi:10.1023/a:1008036829907Gomes, J., & Faugeras, O. (2000). Reconciling Distance Functions and Level Sets. Journal of Visual Communication and Image Representation, 11(2), 209-223. doi:10.1006/jvci.1999.0439Fukuzawa, K., Terada, S., Shikida, M., Amakawa, H., Zhang, H., & Mitsuya, Y. (2007). Mechanical design and force calibration of dual-axis micromechanical probe for friction force microscopy. Journal of Applied Physics, 101(3), 034308. doi:10.1063/1.2434825Schröpfer, G., Labachelerie, M. de, Ballandras, S., & Blind, P. (1998). Collective wet etching of a 3D monolithic silicon seismic mass system. Journal of Micromechanics and Microengineering, 8(2), 77-79. doi:10.1088/0960-1317/8/2/008Wilke, N., Reed, M. L., & Morrissey, A. (2006). The evolution from convex corner undercut towards microneedle formation: theory and experimental verification. Journal of Micromechanics and Microengineering, 16(4), 808-814. doi:10.1088/0960-1317/16/4/018Liang, 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.127.337Hida, 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.2008.08.02

Study, Modelling and Implementation of the Level Set Method Used in Micromachining Processes

[EN] The main topic of the present thesis is the improvement of fabrication processes simulation by means of the Level Set (LS) method. The LS is a mathematical approach used for evolving fronts according to a motion defined by certain laws. The main advantage of this method is that the front is embedded inside a higher dimensional function such that updating this function instead of directly the front itself enables a trivial handling of complex situations like the splitting or coalescing of multiple fronts. In particular, this document is focused on wet and dry etching processes, which are widely used in the micromachining process of Micro-Electro-Mechanical Systems (MEMS). A MEMS is a system formed by mechanical elements, sensors, actuators, and electronics. These devices have gained a lot of popularity in last decades and are employed in several industry fields such as automotive security, motion sensors, and smartphones. Wet etching process consists in removing selectively substrate material (e.g. silicon or quartz) with a liquid solution in order to form a certain structure. This is a complex process since the result of a particular experiment depends on many factors, such as crystallographic structure of the material, etchant solution or its temperature. Similarly, dry etching processes are used for removing substrate material, however, gaseous substances are employed in the etching stage. In both cases, the usage of a simulator capable of predicting accurately the result of a certain experiment would imply a significant reduction of design time and costs. There exist a few LS-based wet etching simulators but they have many limitations and they have never been validated with real experiments. On the other hand, atomistic models are currently considered the most advanced simulators. Nevertheless, atomistic simulators present some drawbacks like the requirement of a prior calibration process in order to use the experimental data. Additionally, a lot of effort must be invested to create an atomistic model for simulating the etching process of substrate materials with different atomistic structures. Furthermore, the final result is always formed by unconnected atoms, which makes difficult a proper visualization and understanding of complex structures, thus, usually an additional visualization technique must be employed. For its part, dry etching simulators usually employ an explicit representation technique to evolve the surface being etched according to etching models. This strategy can produce unrealistic results, specially in complex situations like the interaction of multiple surfaces. Despite some models that use implicit representation have been published, they have never been directly compared with real experiments and computational performance of the implementations have not been properly analysed. The commented limitations are addressed in the various chapters of the present thesis, producing the following contributions: - An efficient LS implementation in order to improve the visual representation of atomistic wet etching simulators. This implementation produces continuous surfaces from atomistic results. - Definition of a new LS-based model which can directly use experimental data of many etchant solutions (such as KOH, TMAH, NH4HF2, and IPA and Triton additives) to simulate wet etching processes of various substrate materials (e.g. silicon and quartz). - Validation of the developed wet etching simulator by comparing it to experimental and atomistic simulator results. - Implementation of a LS-based tool which evolves the surface being etched according to dry etching models in order to enable the simulation of complex processes. This implementation is also validated experimentally. - Acceleration of the developed wet and dry etching simulators by using Graphics Processing Units (GPUs).[ES] El tema principal de la presente tesis consiste en mejorar la simulación de los procesos de fabricación utilizando el método Level Set (LS). El LS es una técnica matemática utilizada para la evolución de frentes según un movimiento definido por unas leyes. La principal ventaja de este método es que el frente está embebido dentro de una función definida en una dimensión superior. Actualizar dicha función en lugar del propio frente permite tratar de forma trivial situaciones complejas como la separación o la colisión de diversos frentes. En concreto, este documento se centra en los procesos de atacado húmedo y seco, los cuales son ampliamente utilizados en el proceso de fabricación de Sistemas Micro-Electro-Mecánicos (MEMS, de sus siglas en inglés). Un MEMS es un sistema formado por elementos mecánicos, sensores, actuadores y electrónica. Estos dispositivos hoy en día son utilizados en muchos campos de la industria como la seguridad automovilística, sensores de movimiento y teléfonos inteligentes. El proceso de atacado húmedo consiste en eliminar de forma selectiva el material del sustrato (por ejemplo, silicio o cuarzo) con una solución líquida con el fin de formar una estructura específica. Éste es un proceso complejo pues el resultado depende de muchos factores, tales como la estructura cristalográfica del material, la solución atacante o su temperatura. De forma similar, los procesos de atacado seco son utilizados para eliminar el material del sustrato, sin embargo, se utilizan sustancias gaseosas en la fase de atacado. En ambos casos, la utilización de un simulador capaz de predecir de forma precisa el resultado de un experimento concreto implicaría una reducción significativa del tiempo de diseño y de los costes. Existen unos pocos simuladores del proceso de atacado húmedo basados en el método LS, no obstante tienen muchas limitaciones y nunca han sido validados con experimentos reales. Por otro lado, los simuladores atomísticos son hoy en día considerados los simuladores más avanzados pero tienen algunos inconvenientes como la necesidad de un proceso de calibración previo para poder utilizar los datos experimentales. Además, debe invertirse mucho esfuerzo para crear un modelo atomístico para la simulación de materiales de sustrato con distintas estructuras atomísticas. Asimismo, el resultado final siempre está formado por átomos inconexos que dificultan una correcta visualización y un correcto entendimiento de aquellas estructuras complejas, por tanto, normalmente debe emplearse una técnica adicional para la visualización de dichos resultados. Por su parte, los simuladores del proceso de atacado seco normalmente utilizan técnicas de representación explícita para evolucionar, según los modelos de atacado, la superficie que está siendo atacada. Esta técnica puede producir resultados poco realistas, sobre todo en situaciones complejas como la interacción de múltiples superficies. A pesar de que unos pocos modelos son capaces de solventar estos problemas, nunca han sido comparados con experimentos reales ni el rendimiento computacional de las correspondientes implementaciones ha sido adecuadamente analizado. Las expuestas limitaciones son abordadas en la presente tesis y se han producido las siguientes contribuciones: - Implementación eficiente del método LS para mejorar la representación visual de los simuladores atomísticos del proceso de atacado húmedo. - Definición de un nuevo modelo basado en el LS que pueda usar directamente los datos experimentales de muchos atacantes para simular el proceso de atacado húmedo de diversos materiales de sustrato. - Validación del simulador comparándolo con resultados experimentales y con los de simuladores atomísticos. - Implementación de una herramienta basada en el método LS que evolucione la superficie que está siendo atacada según los modelos de atacado seco para habilitar la simulación de procesos comple[CA] El tema principal de la present tesi consisteix en millorar la simulació de processos de fabricació mitjançant el mètode Level Set (LS). El LS és una tècnica matemàtica utilitzada per a l'evolució de fronts segons un moviment definit per unes lleis en concret. El principal avantatge d'aquest mètode és que el front està embegut dins d'una funció definida en una dimensió superior. D'aquesta forma, actualitzar la dita funció en lloc del propi front, permet tractar de forma trivial situacions complexes com la separació o la col·lisió de diversos fronts. En concret, aquest document es centra en els processos d'atacat humit i sec, els quals són àmpliament utilitzats en el procés de fabricació de Sistemes Micro-Electro-Mecànics (MEMS, de les sigles en anglès). Un MEMS és un sistema format per elements mecànics, sensors, actuadors i electrònica. Aquests dispositius han guanyat molta popularitat en les últimes dècades i són utilitzats en molts camps de la indústria, com la seguretat automobilística, sensors de moviment i telèfons intel·ligents. El procés d'atacat humit consisteix en eliminar de forma selectiva el material del substrat (per exemple, silici o quars) amb una solució líquida, amb la finalitat de formar una estructura específica. Aquest és un procés complex ja que el resultat de un determinat experiment depèn de molts factors, com l'estructura cristal·logràfica del material, la solució atacant o la seva temperatura. De manera similar, els processos d'atacat sec son utilitzats per a eliminar el material del substrat, no obstant, s'utilitzen substàncies gasoses en la fase d'atacat. En ambdós casos, la utilització d'un simulador capaç de predir de forma precisa el resultat d'un experiment en concret implicaria una reducció significativa del temps de disseny i dels costos. Existeixen uns pocs simuladors del procés d'atacat humit basats en el mètode LS, no obstant tenen moltes limitacions i mai han sigut validats amb experiments reals. Per la seva part, els simuladors atomístics tenen alguns inconvenients com la necessitat d'un procés de calibratge previ per a poder utilitzar les dades experimentals. A més, deu invertir-se molt d'esforç per crear un model atomístic per a la simulació de materials de substrat amb diferents estructures atomístiques. Així mateix, el resultat final sempre està format per àtoms inconnexos que dificulten una correcta visualització i un correcte enteniment d'aquelles estructures complexes, per tant, normalment deu emprar-se una tècnica addicional per a la visualització d'aquests resultats. D'altra banda, els simuladors del procés d'atacat sec normalment utilitzen tècniques de representació explícita per evolucionar, segons els models d'atacat, la superfície que està sent atacada. Aquesta tècnica pot introduir resultats poc realistes, sobretot en situacions complexes com per exemple la interacció de múltiples superfícies. A pesar que uns pocs models son capaços de resoldre aquests problemes, mai han sigut comparats amb experiments reals ni tampoc el rendiment computacional de les corresponents implementacions ha sigut adequadament analitzat. Les exposades limitacions son abordades en els diferents capítols de la present tesi i s'han produït les següents contribucions: - Implementació eficient del mètode LS per millorar la representació visual dels simuladors atomístics del procés d'atacat humit. - Definició d'un nou model basat en el mètode LS que puga utilitzar directament les dades experimentals de molts atacants per a simular el procés d'atacat humit de diversos materials de substrat. - Validació del simulador d'atacat humit desenvolupat comparant-lo amb resultats experimentals i amb els de simuladors atomístics. - Implementació d'una ferramenta basada en el mètode LS que evolucione la superfície que està sent atacada segons els models d'atacat sec per, d'aquesta forma, habilitar la simulació de processoMontoliu Álvaro, C. (2015). Study, Modelling and Implementation of the Level Set Method Used in Micromachining Processes [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/58609TESI