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

Montoliu, Carles; Ferrando, N.; Gosálvez, Miguel A.; Cerdá, J.; Colom, R.J.

doi:10.1016/j.cpc.2013.05.016

Cited by 20 publications

(15 citation statements)

References 49 publications

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“…In order to allow for a V ( n) of any complexity, ∂V /∂n l can be calculated numerically with a central difference scheme proposed by Montoliu et al [18] ∂V…”

Section: A Stencil Local Lax Friedrichs Numerical Dissipation Schemementioning

confidence: 99%

“…In contrast, for general etching and growth processes the speed function is not explicitly given. Hence, the dissipation coefficients can be heuristically chosen [17], or a numerical approximation of the derivative of the Hamiltonian is employed, as proposed by Montoliu et al [18]. However, the approximation presented by Montoliu et al requires a numerical calibration parameter which has to be determined for every etching/growth condition.…”

Section: Introductionmentioning

confidence: 99%

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The Level-Set Method for Multi-Material Wet Etching and Non-Planar Selective Epitaxy

et al. 2020

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We present numerical methods to enable accurate and robust level-set based simulation of anisotropic wet etching and non-planar epitaxy for semiconductor fabrication. These fabrication techniques are characterized by highly crystal orientation-dependent etch/growth rates, which lead to non-convex Hamiltonians in their description by the level-set equation. As a consequence, instable surface propagation may emerge, leading to unphysical results. We propose a calibration-free Stencil Lax-Friedrichs scheme and an advanced adaptive time-stepping approach, tailored to the level-set speed functions associated with anisotropic etching and epitaxy. The scheme calculates the numerical dissipation based on information about the local geometry and the nature of the etch rates/growth function, which enables an optimized tradeoff between overly rounding of sharp geometric features and stable surface propagation. Furthermore, we introduce the deposition top layer method, which allows for robust handling of multiple material regions in non-planar epitaxy simulations. Both methods are demonstrated in a prototypical implementation, which is used to validate the capability and accuracy of our approaches. In particular, two-dimensional wet etching and three-dimensional epitaxy simulations are performed and characteristic geometry parameters are compared to the ideally expected values, showing robustness and high accuracy.

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“…In order to allow for a V ( n) of any complexity, ∂V /∂n l can be calculated numerically with a central difference scheme proposed by Montoliu et al [18] ∂V…”

Section: A Stencil Local Lax Friedrichs Numerical Dissipation Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Level-Set Method for Multi-Material Wet Etching and Non-Planar Selective Epitaxy

et al. 2020

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“…The proper amount of dissipation (dissipation parameters) is a still-active research topic. The same method has been used in a recent implementation of the sparse field LS method described in [31,32]. Our approach is based on the ITK (Insight Toolkit) library [55].…”

Section: Simulation Methodsmentioning

confidence: 99%

“…For instance, there are too many parameters in the simulation model (hundreds or even thousands, including removal rates and others), which should be calibrated using experimentally obtained angular dependence of etching velocities. Also, new calibrations are needed each time the experimental conditions are changed, such as the etchant type, concentration and/or temperature, with calibration lasting several hours or even days [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Etching of Uncompensated Convex Corners with Sides along <n10> and <100> in 25 wt% TMAH at 80 °C

et al. 2020

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This paper presents etching of convex corners with sides along <n10> and <100> crystallographic directions in a 25 wt% tetramethylammonium hydroxide (TMAH) water solution at 80 °C. We analyzed parallelograms as the mask patterns for anisotropic wet etching of Si (100). The sides of the parallelograms were designed along <n10> and <100> crystallographic directions (1 < n < 8). The acute corners of islands in the masking layer formed by <n10> and <100> crystallographic directions were smaller than 45°. All the crystallographic planes that appeared during etching in the experiment were determined. We found that the obtained types of 3D silicon shape sustain when n > 2. The convex corners were not distorted during etching. Therefore, no convex corner compensation is necessary. We fabricated three matrices of parallelograms with sides along crystallographic directions <310> and <100> as examples for possible applications. Additionally, the etching of matrices was simulated by the level set method. We obtained a good agreement between experiments and simulations.

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“…However, the CCA method is 1.2 times faster than the LS implementation for the left-hand-side experiment in (f). Although a traditional sequential implementation of both methods shows that the CCA is twice as fast [59], in this study the GPU implementation of the CCA makes use of an octree data structure, which reduces the memory use but adds a relevant overhead to the GPU calculations [24]. The computational cost of our LS implementation is primarily due to the calculation of the spatial derivatives, the local etch rate and the maximum in Eq.…”

Section: Comparison To Experimental Structuresmentioning

confidence: 99%

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

Montoliu

Ferrando

Gosálvez

et al. 2013

J. Micromech. Microeng.

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Abstract.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 than 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 doubleside 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.

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

Cited by 20 publications

References 49 publications

The Level-Set Method for Multi-Material Wet Etching and Non-Planar Selective Epitaxy

The Level-Set Method for Multi-Material Wet Etching and Non-Planar Selective Epitaxy

Etching of Uncompensated Convex Corners with Sides along <n10> and <100> in 25 wt% TMAH at 80 °C

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

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