Monte Carlo simulations on large-area deposition of amorphous silicon by hot-wire CVD

Scale-up of hot-wire CVD reactors for commercial production of a-Si:H based solar cells requires understanding of the large-area deposition process. Therefore, the process was simulated using the Direct Simulation Monte Carlo-method (G.A. Bird, Clarendon Press, Oxford (1994)), considering reactions at the filaments, in the gas phase and at the substrate, and in particular large-area deposition by modeling the gas shower and the filament grid, which were found to determine the uniformity and quality of the a-Si:H films (Thin Solid Films 395 (2001) 61; Solar Energy Mater. Solar Cells 73 (2002) 321). The distance between the filament grid and the substrate (d_fil–S) and the distance between the filaments (d_fil) were systematically varied, and the simulation results were compared to experimental results obtained in our large-area deposition system (Thin Solid Films 395 (2001) 61; Solar Energy Mater. Solar Cells 73 (2002) 321). The experimentally obtained optimum filament-to-substrate distance was supported by an optima in the simulated Si₂H₄-concentration. For other species, the existence was confirmed but a definite value for optimum d_fil–S could not be concluded. The simulations also confirmed the influence of the filament geometry on the uniformity as obtained in the experiments.     

Monte Carlo simulations of magnetic properties in multilayers

A Monte Carlo method has been used to simulate Heisenberg multilayer systems (L × L × 4P) consisting of alternating P ferromagnetic layers A and B with antiferromagnetic interface coupling J_AB. Finite-size effects on the specific heat and magnetisation thermal variation for two kinds of boundary conditions at the top and bottom planes are investigated. In particular, our Monte Carlo data evidence that the specific heat exhibits two peaks and a single phase transition occurs at the temperature which corresponds to the location of the high temperature peak (as L → ∞).     

Monte Carlo simulations of very low pressure chemical vapor deposition

Summary Simulation strategies for chemical vapor deposition (CVD) of thin solid films are presented, with emphasis on direct simulation Monte Carlo methods for analyzing and predicting physical phenomena occurring at low pressures and in micron-sized substrate features. The Monte Carlo approach is placed in perspective, relative to standard continuum mechanics-based strategies for modeling of CVD systems. Design issues that may be addressed through the developed methods are exemplified with computations for a new, technologically important CVD process for epitaxy of Si and Si_xGe_1-x alloys. Specifically, radiative heat transfer, rarefied gas-flow characteristics, species separation caused by pressure and thermal diffusion, growth-rate uniformity vs. surface reactivity, and deposition in microscopic features are addressed as parts of the overall CVD reactor-design approach. Process implications of rarefied transport effects unique to very low pressure CVD conditions are described. A new profile evolution technique is also introduced which predicts film topology, as well as the microstructure of the film.     

SiC电子输运的蒙特卡罗模拟

采用了Monte Carlo方法研究了2H-、4H-和6H-SiC的电子输运特性.在模拟中,采用动量弛豫率近似的方法确定散射角,显著压缩散射次数,并用高效的新查表法确定自由飞行时间,相对于阶梯值的自散射方法,完全消除了自散射,大量节省cpu时间.     

Exact calculations of fluid-phase equilibria by Monte Carlo simulation in a new statistical ensemble

A recently proposed method, Monte Carlo simulation in the Gibbs ensemble, allows the prediction of phase equilibria from knowledge of the intermolecular forces. A single computer experiment is required per coexistence point for a system with an arbitrary number of components. The new technique has significant advantages relative to free-energy methods that have been used for phase equilibrium calculations is the past. In this work, a variation of the Gibbs method appropriate for calculations in mixtures with large differences in molecular size is developed. The method is applied for the calculation of high-pressure phase equilibria in two mixtures of simple monatomic fluids, the systems argon-krypton and neon-xenon. Pairwise additive potential functions of the Lennard-Jones type are used to describe the intermolecular interactions. Agreement with experimental results is generally good over a wide range of temperatures and pressures, including the fluid-fluid immiscibility region for the neon-xenon system. Results from the Van der Waals one-fluid theory are compared with experimental data and computer simulation predictions. Agreement is excellent for the mixture with small differences in size (argon-krypton), but the theory fails to describe the coexistence curve for the highly asymmetric system neon-xenon.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Calculations of diffusion in FCC binary alloys using on-the-fly kinetic Monte Carlo

We present a systematic, microscopic approach to diffusion for intermetallic alloys using accelerated molecular dynamics. On-the-fly kinetic Monte Carlo is combined with an efficient saddlepoint search to find the saddlepoints exiting a valley, based on energetics from the embedded atom method. With this technique, we compute the tracer diffusivities, migration energies, short-range order and long-range order as a function of composition and temperature for examples of moderately ordered (Cu₃Au), weakly ordered (Au–Ag) and weakly clustered (Cu–Ni) alloys. We find that away from any critical temperature, the calculations produce reliable results, but when critical behavior dominates the approach is overcome by critical fluctuations.     

Comparison between Monte Carlo and analytical calculation of Clausing functions of cylindrical and conical tubes

In a previous work (J. Vac. Sci. Technol. A 21 (2003) 1452), we calculated the transmission probabilities for cylindrical and conical ducts, solving numerically the Clausing integral equation and integrating the resulting Clausing function. It is also important to obtain the Clausing function itself, because it is proportional to the distribution of molecular collisions with the walls of the system, as we show in this contribution. Besides, the density profile of the gas inside the duct can be calculated using the Clausing function, as shown by Davies and Lucas (J. Phys. D: Appl. Phys. 16 (1983) 1). We have calculated the Clausing functions for different cylindrical and conical ducts using a Monte Carlo simulation method and we have compared these results to the numerical ones, finding a very good agreement, within statistical uncertainties.     

Polymer solutions confined in slit-like pores with attractive walls: An off-lattice Monte Carlo study of static properties and chain dynamics

Summary Using a bead spring model of flexible polymer chains, the density profiles and chain configurational properties of polymer solutions confined between parallel plates were studied. A wide range of density , chain length N, and strength of a short-range attractive wall potential was investigated. Both a temperature T in the good solvent regime (T > , being the Theta temperature where a chain in unconfined bulk three-dimensional solution would behave ideally) and a temperature in the bad solvent regime (T < ) were considered. It is shown that phase separation in a polymer-rich and polymer-poor solution in the slit competes with polymer adsorption at the walls. A qualitative connection to the wetting behavior of semi-infinite polymer solutions is drawn. The acceptance rate for monomer motions was studied for various conditions, and profiles of monomer mobility across the slit were recorded. Also, average chain relaxation times were extracted from the time dependence of mean-square displacements. Although with increasing density the chain radii (at T > ) show a crossover from two-dimensional excluded volume behavior (R_g N² with = 3/4) to ideal random walk behavior ( = 1/2), the relaxation times show effective exponents Z_eff ( N^{Z eff}) that clearly deviate from the Rouse prediction in concentrated confined solutions.     

Full-Band Monte Carlo investigation of hole mobilities in SiGe, SiC and SiGeC alloys

Hole transport properties in relaxed and biaxially strained Si_1-xGe_x, Si_1-yC_y and Si_1-x-yGe_xC_y alloys are investigated using a Full-Band Monte Carlo simulator. Our results allow the extraction of bulk, in-plane and out-of-plane hole drift mobilities. Doping effects in SiGeC alloys are taken into account through an efficient ionized-impurity scattering model. This model is based on inverse momentum relaxation times derived from phase-shift theory.¹ A new alloy scattering model relevant to the case of random ternary alloys is presented. It involves two effective alloy potential parameters, which account for the respective scattering strengths of Ge and C in the crystal lattice. From our mobility results we have derived an analytical hole mobility model which includes dependencies upon doping concentration, doping type, Ge content and C content.     

A family of weak stochastic Newmark methods for simplified and efficient Monte Carlo simulations of oscillators

Engineers are often more concerned with the computation of statistical moments (or mathematical expectations) of the response of stochastically driven dynamical systems than with the determination of path‐wise response histories. With this in perspective, weak stochastic solutions of dynamical systems, modelled as n degrees‐of‐freedom (DOF) mechanical oscillators and driven by additive and/or multiplicative white noise (or, filtered white noise) processes, are considered in this study. While weak stochastic solutions are simpler and quicker to compute than strong (sample path‐wise) solutions, it must be emphasized that sample realizations of weak solutions have no path‐wise similarity with strong solutions. However, the statistical moment of any continuous and sufficiently differentiable deterministic function of the weak stochastic response is ‘close’ to that of the true response (if it exists) within a certain order of a given time step size. Computation of weak response therefore assumes great significance in the context of simulations of stochastically driven dynamical systems (oscillators) of engineering interest. To efficiently generate such weak responses, a novel class of weak stochastic Newmark methods (WSNMs), based on implicit Ito–Taylor expansions of displacement and velocity fields, is proposed. The resulting multiple stochastic integrals (MSIs) in these expansions are replaced by a set of random variables with considerably simpler and discrete probability densities. In fact, yet another simplifying feature of the present strategy is that there is no need to model and compute some of the higher‐level MSIs. Estimates of error orders of these methods in terms of a given time step size are derived and a proof of global convergence provided. Numerical illustrations are provided and compared with exact solutions whenever available to demonstrate the accuracy, simplicity and higher computational speed of WSNMs vis‐à‐vis a few other popularly used stochastic integration schemes as well as the path‐wise versions of the stochastic Newmark scheme. Copyright © 2006 John Wiley & Sons, Ltd.     

蒙特卡洛法在膜簧碟簧生产中的优化

 在膜片弹簧或碟形弹簧大批量生产过程中，弹簧压紧力偏差的增大由弹簧的锥角内径和外径的加工误差
造成．正确计算最佳的厚度可使弹簧压紧力偏差最小．列举了一些在不同修正条件下的计算方程式，引入蒙特卡洛
法并得到了计算方程式的结果． 结果是比较满意的，证明了蒙特卡洛法在膜簧和碟簧生产中的实用性．     

Monte Carlo方法的精度分析及其在算术平均亚洲期权定价中的应用

本文讨论了Monte Carlo(MC)方法的精度分析及其在算术平均亚洲期权定价中的应用.首先,我们对MC方法的精度做了分析,讨论了两种依分布收敛到标准正态分布的情况(即对样本均值用标准差和标准误差进行标准化).接下来对于三种MC方法(即Crude MC、Antithetic MC和Control MC)的精度及标准(误)差做了进一步的分析.然后,再介绍了MC方法在计算亚洲期权价格中的应用.最后,由算术平均亚洲看涨期权价格的数值模拟结果得到如下结论:两种模拟成功的频率都接近于理论概率;在对样本均值进行标准化为标准正态分布时,用标准差比用标准误差更好.     

Atomistic modeling of defect diffusion and interdiffusion in SiGe heterostructures

In this work we present models and simulation results for diffusion in strained SiGe heterostructures. Our approach makes a comprehensive, physically-based, treatment of defect and dopant diffusion, self-diffusion (of Si and Ge) and interdiffusion, including some effects inherent to heterostructures. The models have been implemented in the DADOS code, within the framework of the atomistic kinetic Monte Carlo approach. The parameter set has been calibrated in the whole composition range, from silicon to germanium, both for relaxed and strained conditions, and an illustrative set of experiments has been simulated.     

An overview of spatial microscopic and accelerated kinetic Monte Carlo methods

The microscopic spatial kinetic Monte Carlo (KMC) method has been employed extensively in materials modeling. In this review paper, we focus on different traditional and multiscale KMC algorithms, challenges associated with their implementation, and methods developed to overcome these challenges. In the first part of the paper, we compare the implementation and computational cost of the null-event and rejection-free microscopic KMC algorithms. A firmer and more general foundation of the null-event KMC algorithm is presented. Statistical equivalence between the null-event and rejection-free KMC algorithms is also demonstrated. Implementation and efficiency of various search and update algorithms, which are at the heart of all spatial KMC simulations, are outlined and compared via numerical examples. In the second half of the paper, we review various spatial and temporal multiscale KMC methods, namely, the coarse-grained Monte Carlo (CGMC), the stochastic singular perturbation approximation, and the τ-leap methods, introduced recently to overcome the disparity of length and time scales and the one-at-a time execution of events. The concepts of the CGMC and the τ-leap methods, stochastic closures, multigrid methods, error associated with coarse-graining, a posteriori error estimates for generating spatially adaptive coarse-grained lattices, and computational speed-up upon coarse-graining are illustrated through simple examples from crystal growth, defect dynamics, adsorption–desorption, surface diffusion, and phase transitions.     

Monte Carlo and molecular dynamics simulation of argon clusters andn-alkanes in the confined regions of zeolites

Geometry and energy of argon clusters confined in zeolite NaCaA are compared with those of free clusters. Results indicate the possible existence of magic numbers among the confined clusters. Spectra obtained from instantaneous normal mode analysis of free and confined clusters give a larger percentage of imaginary frequencies for the latter indicating that the confined cluster atoms populate the saddle points of the potential energy surface significantly. The variation of the percentage of imaginary frequencies with temperature during melting is akin to the variation of other properties. It is shown that confined clusters might exhibit inverse surface melting, unlike medium-to-large-sized free clusters that exhibit surface melting. Configurational-bias Monte Carlo (CBMC) simulations ofn-alkanes in zeolites Y and A are reported. CBMC method gives reliable estimates of the properties relating to the conformation of molecules. Changes in the conformational properties ofn-butane and other longern-alkanes such asn-hexane andn-heptane when they are confined in different zeolites are presented. The changes in the conformational properties ofn-butane andn-hexane with temperature and concentration is discussed. In general, in zeolite Y as well as A, there is significant enhancement of thegauche population as compared to the pure unconfined fluid. Contribution No. 1260 from the Solid State and Structural Chemistry Unit     

Least-squares analysis of data with uncertainty in x and y: A Monte Carlo methods comparison

The least-squares analysis of data with error in x and y is generally thought to yield best results when the quantity minimized is the sum of the properly weighted squared residuals in x and in y. As an alternative to this “total variance” (TV) method, “effective variance” (EV) methods convert the uncertainty in x into an effective contribution to that in y, and though easier to use are considered to be less reliable. There are at least two EV methods, differing in how the weights are treated in the optimization. One of these is identical to the TV method for fits to a straight line. The formal differences among these methods are clarified, and Monte Carlo simulations are used to examine the statistical properties of each on the widely used straight-line model of York, a quadratic variation on this, Orear's hyperbolic model, a nonlinear binding (Langmuir) model, and Wentworth's kinetics model. The simulations confirm that the EV and TV methods are statistically equivalent in the limit of small data error, where they yield unbiased, normally distributed parameter estimates, with standard errors correctly predicted by the a priori covariance matrix. With increasing data error, these properties fail to hold; and the TV method is not always statistically best. Nonetheless, the method differences should seldom be of practical significance, since they are likely to be small compared with uncertainties from incomplete information about the data error in x and y.