Joaquín Cerdá

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.

High-speed data acquisition and digital signal Processing system for PET imaging techniques applied to mammography

This paper is framed into the Positron Emission Mammography (PEM) project, whose aim is to develop an innovative gamma ray sensor for early breast cancer diagnosis. Currently, breast cancer is detected using low-energy X-ray screening. However, functional imaging techniques such as PET/FDG could be employed to detect breast cancer and track disease changes with greater sensitivity. Furthermore, a small and less expensive PET camera can be utilized minimizing main problems of whole body PET. To accomplish these objectives, we are developing a new gamma ray sensor based on a newly released photodetector. However, a dedicated PEM detector requires an adequate data acquisition (DAQ) and processing system. The characterization of gamma events needs a free-running analog-to-digital converter (ADC) with sampling rates of more than 50 Ms/s and must achieve event count rates up to 10 MHz. Moreover, comprehensive data processing must be carried out to obtain event parameters necessary for performing the image reconstruction. A new generation digital signal processor (DSP) has been used to comply with these requirements. This device enables us to manage the DAQ system at up to 80 Ms/s and to execute intensive calculi over the detector signals. This paper describes our designed DAQ and processing architecture whose main features are: very high-speed data conversion, multichannel synchronized acquisition with zero dead time, a digital triggering scheme, and high throughput of data with an extensive optimization of the signal processing algorithms.

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.

Depth of interaction measurement in gamma ray imaging detectors with continuous scintillation crystals

A design for an inexpensive depth of interaction (DOI) detector for gamma rays, suitable for nuclear medical applications, especially positron emission tomography (PET), has been developed, studied by simulations and tested experimentally. The detector consists of a continuous LSO-scintillator of dimensions 42/spl times/42/spl times/10 mm/sup 3/ and a new compact large-area (49/spl times/49 mm/sup 2/) position sensitive photo-multiplier (PSPMT) H8500 from Hamamatsu. Since a continuous crystal is used, the scintillation light distribution is not destroyed and its first 3 moments can be used to determine the energy (0th moment), the centroids along the x- and y-direction (1st moments) and the depth of interaction (DOI), which is strongly correlated to the distributions width and thus its standard deviation (2nd moment). The simultaneous computation of these moments allows a three-dimensional reconstruction of the position of interaction of the /spl gamma/-rays within the scintillating crystal and will be realized by a modified position sensitive proportional (PSP) resistor network. No additional photo detectors or scintillating crystals are needed. According to previous Monte Carlo simulations which estimated the influence of Compton scattering for 511 keV /spl gamma/-rays, the transport of the scintillation light within the detector assembly and also the behavior of the modified PSP resistor network, we expect a spatial resolution of /spl lsim/ 2 mm and a DOI resolution of /spl ap/ 5 mm. The first experimental results presented here yield an intrinsic spatial resolution of /spl lsim/ 1.8 mm and 2.6 mm for the x- and y-direction respectively and a DOI resolution /spl lsim/ 1 cm. Further we measured an energy resolution of 12%-18%.

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.

On the Implementation of a Margolus Neighborhood Cellular Automata on FPGA

Margolus neighborhood is the easiest form of designing Cellular Automata Rules with features such as invertibility or particle conserving. In this paper we propose two different implementations of systems based on this neighborhood: The first one corresponds to a classical RAM-based implementation, while the second, based on concurrent cells, is useful for smaller systems in which time is a critical parameter. This implementation has the feature that the evolution of all the cells in the design is performed in the same clock cycle.

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

Atomistic models are a very valuable simulation tool in the field of material science. Among them are the continuous cellular automata (CCA), which can simulate accurately the process of chemical etching used in micro-electro-mechanical-systems (MEMS) micromachining. Due to the CCA intrinsic atomistic nature, simulation results are obtained in the form of a cloud of points, so data visualization has been usually problematic. When using these models as a part of a computer aided design tool, good data visualization is very important. In this paper, a minimum energy model implemented with the level set (LS) method for improving the visual representation of simulated MEMS is presented. Additionally, the sparse field method has been applied to reduce the high computational cost of the original LS. Finally, some reconstructed surfaces with completely different topologies are presented, proving the effectiveness of our implementation and the fact that it is capable of producing any real surface, flat and smooth ones.