Parallelizing a powerful Monte Carlo method for electron beam dose calculations

The Macro Monte Carlo (MMC) method has been developed to improve the speed of traditional Monte Carlo calculations without significant loss in accuracy. MMC runs about one order of magnitude faster for clinically relevant irradiation situations. For routine use in a clinical environment a further speedup is necessary. The MMC code was therefore parallelized and implemented on PowerPC based Parsytec PowerXplorer and GC Power Plus systems. The performance of the parallel code is presented and compared to the sequential implementations on standard hardware platforms. Almost linear speedup is achieved for the parallel sections of the code. Furthermore the performance of the interprocessor communication based on a virtual topology is demonstrated for the two different machine architectures.     

Monte Carlo simulation towards ripple phase modelling

We present a novel approach to analysis of the gel-fluid transition of lipid membrane. The method is based on the Pink's model but in contrast to its standard version the dipole character of the lipid molecules polar part is considered. Moreover, less constrained movement of entire molecules is allowed. Such an approach includes into the model conditions imposed by the adjacent medium such as ionic strength, pH, and other factors affecting biological membranes via the polar part. The results obtained contribute to the explanation of the ripple phase phenomenon.     

Monte Carlo particle modelling of small semiconductor devices

We have at Reading developed a self consistent Monte Carlo particle model for simulation of semiconductor devices, and proved that it is capable of correctly reproducing laboratory measurements. The method consists of following the detailed transport histories of individual carriers. Physical processes such as interaction between the carriers (holes and electrons) and the lattice (various types of phonon scattering), and the imperfections (impurities). Electron-hole pair creation (i.e. in devices interacting with light) and recombination, avalanche effects, trapping and tunnelling have been included in the model. Although the method was first developed with GaAs MESFETs in mind, it has now been generalised to all cubic semiconductors and to any sort of device. As the model reflects the basic physics of semiconductor devices, it can be used to deepen the physical understanding of such devices. It can also be used as a design tool to evaluate novel ideas. These aspects are discussed. This model is aimed at describing devices of geometrical dimensions of the order of, and smaller than the free flight path of the carriers. As no assumptions have been made regarding diffusion or relaxation of the carriers, like in previous models, this model can be used where non-stationary transport becomes dominant. A review of device simulation carried out by us so far has been given.     

单电子器件的仿真

该文介绍了一种利用正统理论与Ｍｏｎｔｅ Ｃａｒｌｏ方法模拟单电子隧空器件的认真程序。该程序可模拟电子通过包含小隧道结、电容和理想电压源的电路的输运过程,利用该程序,对单库仓岛和多库仓同的单电子晶体管（ＳＥＴ）系统进行了模拟。     

Large area mold fabrication for the nanoimprint lithography using electron beam lithography

The mold fabrication is a critical issue for the development of nanoimprint lithography as an effective low-cost and mass production process.This paper describes the fabrication process developed to fabricate the large area nanoimprint molds on the silicon wafers.The optimization of e-beam exposure dose and pattern design is presented.The overlayer process is developed to improve the field stitching accuracy of e-beam exposure,and around 10 nm field stitching accuracy is obtained.By means of the optimizatio...     

电子束光刻三维微结构的模拟仿真

利用电子束光刻技术,在正性光阻上加工三维微结构。为了模拟预测微结构的表面轮廓,需要建立电子束光刻模型。通常有两种方法建立能量沉积模型,获得能量密度分布函数,分别是随机函数方法和近似函数方法。对能量密度分布函数作线性处理,设计加工三维微结构。借助Monte Carlo和元胞自动机综合算法模拟电子束光刻的加工过程,模拟结果与实验结果在很大程度上相一致,说明电子束光刻模型的建立和对能量密度分布函数的线性处理过程是合理的。     

A Monte Carlo study of the primary absorbed energy redistribution in X-ray lithography

The minimum feature size producible by LIGA X-ray lithography is fundamentally limited by the redistribution of primary doses via photoelectrons and the influence of the resulting dose distribution on resist development. Secondary radiation from mask and substrate are well known as source for pattern distortion in deep X-ray lithography. Numerical simulations by means of Monte Carlo simulations using PENELOPE (Salvat et al. in PENELOPE-2008: a code system for Monte Carlo simulation of electron and photon transport. http://www.nea.fr/html/dbprog/penelope-2008.pdf, 2008) are applied to quantify these additional dose values in the resist/substrate interface and the irradiated/shadowed interface. A significant reduction of the additional dose by secondary radiation from the plating base is not observed for Au and Ti layers thicker than 10 nm. The influence of polarized or unpolarized X-rays might be neglected for structure dimensions larger than a few 10 nm. As an example of critical dimension, simulations were used to predict the structure quality of grating structures with a period of 2.4 μm and duty cycle 0.5 in a resist layer of 300 μm.     

Performance comparison of controllers acting on a batch pulp digester using Monte Carlo modelling

Finding a suitable control structure for any process usually involves comparing the performance of different possible control structures and choosing one which best satisfies chosen criteria. It is desirable to do this performance comparison off-line, as installation of a sub-optimal controller will cost both time and money.Monte Carlo modelling provides a well documented method of evaluating the statistical properties of stochastic systems. Applied to control system design, Monte Carlo modelling can incorporate detailed process models and accurate estimates of input distributions to give an accurate estimate of the effect of different control strategies on the system.In this study, Monte Carlo modelling was used to compare three candidate controllers in order to determine the best controller in terms of two criteria, namely variance reduction and setpoint tracking. The modelling technique yielded results that could be interpreted without difficulty, showing one controller to be clearly superior to the others according to these criteria. These results can be used to implement the best controller without expensive trial and error procedures.In situ experiments on an operational digester correlated well with the simulation results, showing the best controller to reduce variance by 43% and reduce the mean error by 90% when compared to the controller currently in use.It is shown that Monte Carlo modelling is a viable technique for controller performance analysis on highly nonlinear processes, due to the increasing availability of powerful computing systems.     

极性电介质极化规律的蒙特卡罗模拟研究

使用蒙特卡罗方法模拟了极性电介质的极化现象,结果显示:系统达到平衡态后,倾向于电场方向的分子数增多,逆着电场方向的分子数减少,每个分子电矩的取向仍不断发生变化;电场越强,沿电场方向的分子数越多,电极化强度越大,电极化强度与场强成线性关系;场强不变时,温度越高,分子电矩取向越杂乱,电极化强度越小,说明电介质的极化率和介电常量随温度升高而减小。我们还对20℃、1 atm条件下CH₃Cl、HBr、HCl、CH₃Br、CH₃I、CH₃F、C₂H₅Cl、C₂H₃Cl 8种气体的相对介电常量作了估算,估算值和相应的实验值符合得较好,说明本文的模拟方法可较好地用来估算电介质气体的相对介电常量。     

Fast and accurate X-ray lithography simulation enabled by using Monte Carlo method. New version of DoseSim: a software dedicated to deep X-ray lithography (LIGA)

This paper presents the recent development of a simulation tool for deep X-ray lithography. The simulation tool named DoseSim (Meyer et al. in Rev Sci Instrum 74(2):1113–1119, 2003) is a graphical user interface, working under Windows, specially dedicated to the necessary requirements of X-ray lithography setting at a synchrotron. The previous version included the computation of synchrotron radiation from bending magnets, the effects of the optical properties of materials, single mirror and the necessary parameters for the resist exposure. New functionalities, including among others, the exposure time calculation, the insertion of a double mirror, secondary effects (Fresnel diffraction, dose deposited under the absorber) have been added. Also, DoseSim includes traceability concerning the database and calculations used, and de facto the results obtained. Furthermore, Monte Carlo calculations using the PENetration and Energy LOss of Positrons and Electrons (PENELOPE) (Salvat et al.in OECD/NEA Data Bank, France, NEA N°6416, http://www.nea.fr/lists/penelope.html, 2008) code of the spatial distribution of the dose deposited by an X-ray beam in a resist are used. The PENELOPE results (simulations were done mono-energetically for a large range of energy) are the basis of the DoseSim routines for the calculations of the absorbed dose behind the absorber, and at the interface resist/seed layer/substrate. Example of calculations will be discussed along with the effects on dose from different seed layers and substrates.     

Shape deviations in masks for optical structures produced by electron beam lithography

E-beam lithography is a well-known technology used in the structuring of resist for mask fabrication. In the LIGA process E-beam lithography is used to fabricate the first X-ray mask. Due to the high precision of X-ray lithography patterning errors and defects are transformed into the several hundred micrometers thick resist structures. The side walls of these high-aspect-ratio structures are often used as optical mirrors, for which very good surface properties are essential. Deviations in the shape of the side walls even far below the wavelength of the used light lead to spurious strayed or misguided light. For grating microspectrometers the requirements are particularly stringent. The width of the grating teeth does not only have to be precise, but also the grating teeth have to be positioned accurately along the entire grating width. Using LIGA microspectrometers as an example, deviations in masks and LIGA-structured side walls were studied and subsequent correlations made with the corresponding e-beam writing pattern.     

利用电子束曝光系统制作高深宽比图形的研究

为了加工具有高深宽比的器件,采用能量连续递减近似模型,运用蒙特卡罗方法分析高能电子束曝光领域的电子散射轨迹及背散射电子对曝光分辨力的影响,探讨了制作高深宽比图形的工艺条件。计算机模拟结果与实验结果吻合得很好,表明在其它实验条件不变的情况下,较高的加速电压能提高图形的高深宽比,提供了制作高深宽比图形的一种方法。     

热场发射电子枪在电子束光刻机中的应用研究

介绍了电子枪的分类与特点,重点介绍了热场发射电子枪的原理、结构、特点及在电子束光刻机中的应用。阐述了电子束光刻机束流与电子枪提取极电流之间关系,并分析了热场发射电子枪各个参数对提取极电流的影响。研究了热场发射电子枪的调校对电子束光刻工艺的影响,并通过实验得出束斑与束流的关系。最后通过调整电子枪参数,制备了不同的光刻图形,满足了不同的光刻工艺要求,验证了分析的结论。     

FPGA acceleration of a quantum Monte Carlo application

Quantum Monte Carlo methods enable us to determine the ground-state properties of atomic or molecular clusters. Here, we present a reconfigurable computing architecture using Field Programmable Gate Arrays (FPGAs) to accelerate two computationally intensive kernels of a Quantum Monte Carlo (QMC) application applied to N-body systems. We focus on two key kernels of the QMC application: acceleration of potential energy and wave function calculations. We compare the performance of our application on two reconfigurable platforms. Firstly, we use a dual-processor 2.4 GHz Intel Xeon augmented with two reconfigurable development boards consisting of Xilinx Virtex-II Pro FPGAs. Using this platform, we achieve a speedup of 3× over a software-only implementation. Following this, the chemistry application is ported to the Cray XD1 supercomputer equipped with Xilinx Virtex-II Pro and Virtex-4 FPGAs. The hardware-accelerated application on one node of the high performance system equipped with a single Virtex-4 FPGA yields a speedup of approximately 25× over the serial reference code running on one node of the dual-processor dual-core 2.2 GHz AMD Opteron. This speedup is mainly attributed to the use of pipelining, the use of fixed-point arithmetic for all calculations and the fine-grained parallelism using FPGAs. We can further enhance the performance by operating multiple instances of our design in parallel.     

A computer program for a Monte Carlo analysis of sensitivity in equations of environmental modelling obtained from experimental data

In the construction of mathematical models from experimental data, it is possible to determine equations that model relations using several methodologies [Un nuevo algoritmo para la modelización de sistemas altamente estructurados (2000); Env. Model. Software 15 (2000) 461; Guide to Statistics 1,2 (1999); Regression models (1999); Ecosystems and Sustainable Development II (1999)]. These methodologies build equations that are in line with the experimental data and they analyse a dimension of adjustment and a dimension of error or distance between the experimental data and the data that is produced by the model. There are studies of sensitivity of the sample of data, as found by Bolado and Alonso [Proceedings SAMO 2001]. The authors consider that it is useful to obtain new parameters that relate the sensitivity of the equations to the variations that are produced by the experimental data. This will allow the selection of the model according to new criteria.On the one hand, the authors present a theoretical study of sensitivity of the models according to different points of view. On the other hand, they discuss a computing algorithm that allows the analysis of sensitivity (and stability) of the mathematical equations, which are built from any methodology. An interface has been incorporated into this algorithm to allow a graphic visualisation of the effects that are produced when modifications of the model are carried out.     

Stochastic DAG scheduling using a Monte Carlo approach

In heterogeneous computing systems, there is a need for solutions that can cope with the unavoidable uncertainty in individual task execution times, when scheduling DAGs. When such uncertainties occur, static DAG scheduling approaches may suffer, and some rescheduling may be necessary. Assuming that the uncertainty in task execution times is modelled in a stochastic manner, we may be able to use this information to improve static DAG scheduling considerably. In this paper, a novel DAG scheduling approach is proposed to solve this stochastic scheduling problem, based on a Monte Carlo method. The approach is built on the top of a classic static DAG scheduling heuristic and evaluated through extensive simulation. Empirical results show that a significant improvement of average application performance can be achieved by the proposed approach at a reasonable execution time cost.     

Parallel Monte Carlo Driver (PMCD)—a software package for Monte Carlo simulations in parallel

Thanks to the dramatic decrease of computer costs and the no less dramatic increase in those same computer's capabilities and also thanks to the availability of specific free software and libraries that allow the set up of small parallel computation installations the scientific community is now in a position where parallel computation is within easy reach even to moderately budgeted research groups. The software package PMCD (Parallel Monte Carlo Driver) was developed to drive the Monte Carlo simulation of a wide range of user supplied models in parallel computation environments. The typical Monte Carlo simulation involves using a software implementation of a function to repeatedly generate function values. Typically these software implementations were developed for sequential runs. Our driver was developed to enable the run in parallel of the Monte Carlo simulation, with minimum changes to the original code that implements the function of interest to the researcher. In this communication we present the main goals and characteristics of our software, together with a simple study its expected performance. Monte Carlo simulations are informally classified as “embarrassingly parallel”, meaning that the gains in parallelizing a Monte Carlo run should be close to ideal, i.e. with speed ups close to linear. In this paper our simple study shows that without compromising the easiness of use and implementation, one can get performances very close to the ideal.     

A Monte Carlo study of back-scattered gamma radiation from a broad beam normally incident on an infinitely thick slab

The method presented in this paper is an application of the Monte Carlo technique employed in calculating reflected radiation from a broad beam of gamma radiation normally incident on a plane and smooth surface. The reflecting medium is infinitely thick and homogeneous. It should be noted that the results of the calculation are almost 100 per cent accurate for thicknesses over 20 mean free paths ^? “Mean free path” is the length of travel of a particle in a medium before it collides with a particle of the medium. and for engineering purposes are useful between 10 and 20 mean free paths within a few per cent of accuracy.

The incident radiation considered here is mono-energetic. In case of a spectrum of energies of the incident radiation the beam first has to be lumped in discrete energy bins and for each bin the mean energy must be evaluated, after which each is used as a mono-energetic radiation.

In order to be able to reuse calculated values without repetition of the computer work it is planned to perform calculations for energies from 0.5 Mev to 10 Mev in 0.5 Mev energy increments and to print the results as a set of tables.

The purpose of this paper is to serve as a practical introduction into the Monte Carlo technique by use of a relatively simple geometry showing a way toward solution of more complicated problems.     

Polynomial expansion Monte Carlo study of frustrated itinerant electron systems: Application to a spin-ice type Kondo lattice model on a pyrochlore lattice

We present the benchmark of the polynomial expansion Monte Carlo method to a Kondo lattice model with classical localized spins on a geometrically frustrated lattice. The method enables us to reduce the calculation amount by using the Chebyshev polynomial expansion of the density of states compared to a conventional Monte Carlo technique based on the exact diagonalization of the fermion Hamiltonian matrix. Further reduction is brought about by a real-space truncation of the vector–matrix operations. We apply the method to the model with spin-ice type Ising spins on a three-dimensional pyrochlore lattice and carefully examine the convergence in terms of the order of polynomials and the truncation distance. We find that, in a wide range of electron density at a relatively weak Kondo coupling compared to the noninteracting bandwidth, the results by the polynomial expansion method show good convergence to those by the conventional method within reasonable numbers of polynomials. This enables us to study the systems up to 4×8³=2048$4\times 8^3=2048$ sites, while the previous study by the conventional method was limited to 4×4³=256$4\times 4^3=256$ sites. On the other hand, the real-space truncation is not helpful in reducing the calculation amount for the system sizes that we reached, as the sufficient convergence is obtained when most of the sites are involved within the truncation distance. The necessary truncation distance, however, appears not to show significant system size dependence, suggesting that the truncation method becomes efficient for larger system sizes.