Néstor Ferrando

Octree-based, GPU implementation of a continuous cellular automaton for the simulation of complex, evolving surfaces

Abstract Presently, dynamic surface-based models are required to contain increasingly larger numbers of points and to propagate them over longer time periods. For large numbers of surface points, the octree data structure can be used as a balance between low memory occupation and relatively rapid access to the stored data. For evolution rules that depend on neighborhood states, extended simulation periods can be obtained by using simplified atomistic propagation models, such as the Cellular Automata (CA). This method, however, has an intrinsic parallel updating nature and the corresponding simulations are highly inefficient when performed on classical Central Processing Units (CPUs), which are designed for the sequential execution of tasks. In this paper, a series of guidelines is presented for the efficient adaptation of octree-based, CA simulations of complex, evolving surfaces into massively parallel computing hardware. A Graphics Processing Unit (GPU) is used as a cost-efficient example of the parallel architectures. For the actual simulations, we consider the surface propagation during anisotropic wet chemical etching of silicon as a computationally challenging process with a wide-spread use in microengineering applications. A continuous CA model that is intrinsically parallel in nature is used for the time evolution. Our study strongly indicates that parallel computations of dynamically evolving surfaces simulated using CA methods are significantly benefited by the incorporation of octrees as support data structures, substantially decreasing the overall computational time and memory usage.

Experimental procurement of the complete 3D etch rate distribution of Si in anisotropic etchants based on vertically micromachined wagon wheel samples

This is part I of a series of two papers dedicated to the presentation of a novel, large throughput, experimental procedure to determine the three-dimensional distribution of the etch rate of silicon in a wide range of anisotropic etchants, including a total of 30 different etching conditions in KOH, KOH+IPA, TMAH and TMAH+Triton solutions at various concentrations and temperatures. The method is based on the use of previously reported, vertically micromachined wagon wheels (WWs) (Wind and Hines 2000 Surf. Sci. 460 21–38; Nguyen and Elwenspoek 2007 J. Electrochem. Soc. 154 D684–91), focusing on speeding up the etch rate extraction process for each WW by combining macrophotography and image processing procedures. The proposed procedure positions the WWs as a realistic alternative to the traditional hemispherical specimen. The obtained, extensive etch rate database is used to perform wet etching simulations of advanced systems, showing good agreement with the experimental counterparts. In part II of this series (Gosalvez et al J. Micromech. Microeng. 21 125008), we provide a theoretical analysis of the etched spoke shapes, a detailed comparison to the etch rates from previous studies and a self-consistency study of the measured etch rates against maximum theoretical values derived from the spoke shape analysis.

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.

Parallelization of the finite-difference time-domain method for room acoustics modelling based on CUDA

Abstract The parallelization of the finite-difference time-domain (FDTD) method for room acoustic simulation using graphic processing units (GPUs) has been subject of study even prior to the introduction of GPGPU (general-purpose computing on GPUs) environments such as the compute unified device architecture (CUDA) from Nvidia. A mature architecture nowadays, CUDA offers enough flexibility and processing power to obtain important performance gains with naively ported serial CPU codes. However, careful implementation of the algorithm and appropriate usage of the different subsystems a GPU offers can lead to even further performance improvements. In this paper, we present a detailed study between different approaches to the parallelization of the FDTD method applied to room acoustics modelling, and we describe several optimization guidelines to improve the computation speed when using single precision and double precision floating point model data, nearly doubling the performance obtained by previously published implementations.

Simulating anisotropic etching of silicon in any etchant: evolutionary algorithm for the calibration of the continuous cellular automaton

An evolutionary algorithm is presented for the automated calibration of the continuous cellular automaton for the simulation of isotropic and anisotropic wet chemical etching of silicon in as many as 31 widely different and technologically relevant etchants, including KOH, KOH+IPA, TMAH and TMAH+Triton, in various concentrations and temperatures. Based on state-of-the-art evolutionary operators, we implement a robust algorithm for the simultaneous optimization of roughly 150 microscopic removal rates based on the minimization of a cost function with four quantitative error measures, including (i) the error between simulated and experimental macroscopic etch rates for numerous surface orientations all over the unit sphere, (ii) the error due to underetching asymmetries and floor corrugation features observed in simulated silicon samples masked using a circular pattern, (iii) the error associated with departures from a step-flow-based hierarchy in the values of the microscopic removal rates, and (iv) the error associated with deviations from a step-flow-based clustering of the microscopic removal rates. For the first time, we present the calibration and successful simulation of two technologically relevant CMOS compatible etchants, namely TMAH and, especially, TMAH+Triton, providing several comparisons between simulated and experimental MEMS structures based on multi-step etching in these etchants.

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

Abstract 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.

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

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.

Faster and exact implementation of the continuous cellular automaton for anisotropic etching simulations

The current success of the continuous cellular automata for the simulation of anisotropic wet chemical etching of silicon in microengineering applications is based on a relatively fast, approximate, constant time stepping implementation (CTS), whose accuracy against the exact algorithm?a computationally slow, variable time stepping implementation (VTS)?has not been previously analyzed in detail. In this study we show that the CTS implementation can generate moderately wrong etch rates and overall etching fronts, thus justifying the presentation of a novel, exact reformulation of the VTS implementation based on a new state variable, referred to as the predicted removal time (PRT), and the use of a self-balanced binary search tree that enables storage and efficient access to the PRT values in each time step in order to quickly remove the corresponding surface atom/s. The proposed PRT method reduces the simulation cost of the exact implementation from to without introducing any model simplifications. This enables more precise simulations (only limited by numerical precision errors) with affordable computational times that are similar to the less precise CTS implementation and even faster for low reactivity systems.

A mixed hardware-software approach to flexible Artificial Neural Network training on FPGA

FPGAs offer a promising platform for the implementation of Artificial Neural Networks (ANNs) and their training, combining the use of custom optimized hardware with low cost and fast development time. However, purely hardware realizations tend to focus on throughput, resorting to restrictions on applicable network topology or low-precision data representation, whereas flexible solutions allowing a wide variation of network parameters and training algorithms are usually restricted to software implementations. This paper proposes a mixed approach, introducing a system-on-chip (SoC) implementation where computations are carried out by a high efficiency neural coprocessor with a large number of parallel processing elements. System flexibility is provided by on-chip software control and the use of floating-point arithmetic, and network parallelism is exploited through replicated logic and application-specific coprocessor architecture, leading to fast training time. Performance results and design limitations and trade-offs are discussed.

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.