Magnetron sputter deposition as visualized by Monte Carlo modeling

The Monte Carlo code SIMTRA, simulating the transport of atoms from the source to the substrate during physical vapor deposition (PVD), is used in several case studies to highlight important issues related to thin film sputter deposition. Atom collisions during gas-phase transport affect the energy distribution and the deposition profile of sputtered atoms. The model is compared with published models for the thermalization of sputtered atoms, and some features of this process are discussed. The vacuum chamber design can be easily implemented in the Monte Carlo code, and this possibility is used to discuss the use of shutters and masks, and the influence of the deposition geometry. The code can also be used to predict the composition when combing different sources, segmented targets, and during combinatorial synthesis of thin films. As the details of the transport are described, the velocity and the density of the gas-phase atoms can be calculated which can assist in the interpretation of several spectroscopic techniques such as laser induced fluorescence. Not only the energy loss of the transported atoms, but also their remaining energy upon arrival at the substrate is important as the incident energy strongly influences thin film growth. To illustrate the latter, the model is also used to study the growth of biaxially aligned thin films. The key parameters influencing the level of alignment can easily be retrieved using SIMTRA.     

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.     

Monte Carlo simulation of transport process of the sputtered species in the facing target sputtering technique

In facing target sputtering (FTS) technique two targets facing each other are sputtered simultaneously and the particles are collected in the off axis position. When these two targets constitute two different materials having different sputtering yields, the deposited films show a gradation in composition along the axis parallel to the targets. The process parameters involved, increase the complexity of understanding the composition profile of the deposited films. Here an attempt has been made to simulate the transport behavior of the sputtered species, which leads to the theoretical realization of the variation in composition. The simulation has been performed for SmCo system using the Monte Carlo approach based on the empirical formula proposed by Sigmund and Thompson. The theoretical results have been compared with the experimental results obtained and are explained in detail.     

Tolerance-based process plan evaluation using Monte Carlo simulation

In the discrete part manufacturing industry, engineers develop process plans by selecting appropriate machining processes and production equipment to ensure the quality of finished components. The decisions in process planning are usually made based on personal experience and the verification of process plans is based on physical trial-and-error runs, which is costly and time-consuming. This paper proposes to verify process plans by predicting machining tolerances via Monte Carlo simulation. The basic idea is to use a set of discrete sample points to represent workpiece geometry. The changes of their spatial position are simulated and tracked as the workpiece undergoes a series of machining processes. Virtual inspections are then conducted to determine the dimensional and geometric tolerances of the machined component. Machining tolerance prediction is completed through: (1) manufacturing error synthesis, and (2) error propagation in multiple operations. In this way, engineers can quickly screen alternative process plans, spot the root error causes, and improve their decisions. Therefore, physical trial-and-error runs can be reduced, if not eliminated, resulting in significant savings in both time and costs.     

Procedures of Monte Carlo transport simulation for applications in system engineering

Monte Carlo (MC) simulation is the most promising tool for performing realistic reliability and availability analysis of complex systems. Yet, the efficient use of MC simulation technique is not trivial in large scale applications.This paper considers the two commonly adopted approaches to MC simulation: the direct, component-based approach and the indirect, system-based approach. The mathematical details of the two approaches are worked out in detail, so as to show their probabilistic equivalence. The proper formulation for biasing the simulation is introduced, thus leading to the correct expressions for the statistical weights.Both approaches are applied, in an analog as well as in a biased scheme, to a simple system of the literature and comparisons are made with respect to the computing time and the goodness of the estimate, as measured by the variance of the results.     

Monte Carlo simulation of light transport in tissue: unscattered absorption events

A source of error in the Monte Carlo simulation of the fluence rate in turbid media is the inaccurate recording of unscattered absorption events. The form and magnitude of the error have been studied for Gaussian and uniform beam profiles simulated in cylindrical and Cartesian coordinates. In each case the error decreases as the lateral sampling lattice spacing decreases and is less than 2% of the incident peak irradiance when the beam radius is greater than five lattice spacings. To avoid the error, one may calculate analytically the fluence rate caused by unscattered absorption events.     

Monte Carlo simulation of intermixed layer formed by ion beam enhanced deposition

A Monte Carlo simulation code SIBL has been used to simulate the intermixed layer formed during ion beam enhanced deposition (IBED). Depending on the simple collision cascade mixing model, the relations between the shape of the intermixed layer and the ion energy, the atomic arrival ratio and the incident angle have been investigated. A semi-empirical expression has been established, which is in agreement with Sigmund's analytical expression, indicating a quadratic dependence of the thickness of the intermixed layer on the ion fluence and the total elastic energy deposited in the interface region.     

Assessment of sensitivities and uncertainties in Monte Carlo particle transport calculations for neutron spectrometry

Monte Carlo particle transport (MCPT) calculations are increasingly used in neutron metrology and especially in neutron spectrometry for the numerical simulation of measurements based on computational models for the underlying experiment. Sensitivities express the dependence of results on input data and uncertainties are a measure of the dispersion of calculated or measured values. The knowledge of sensitivities is instrumental for physical understanding and a possible optimisation of computational models and/or the experiments. The assessment of uncertainties is necessary to state the degree of belief in results and to objectively validate calculations by measurements. Methods used in MCPT calculations which assess sensitivities of the computational model and propagate uncertainties associated with input data are discussed. The technique most often used is demonstrated by a simple example.     

Direct simulation Monte Carlo modeling of metal vapor flows in application to thin film deposition

Thin films of metal for electronics, nano/microelectromechanical systems and optical coatings are often prepared by various vacuum deposition techniques. Modeling such metal vapor flows using methods such as the direct simulation Monte Carlo (DSMC) can aid in the design and analysis of deposition systems and accelerate development of films with desired properties. The determination of suitable variable hard sphere (VHS) molecular model parameters for DSMC simulations using measured growth rate distribution is demonstrated with aluminum vapor as an example. Axisymmetric DSMC simulations using a VHS model corresponding to a reference diameter of 0.8 nm and a viscosity-temperature exponent of 1 are shown to agree well with available experimental data. The model is then used in two-dimensional DSMC simulations to study the interaction of plumes from multiple sources. An expression for substrate mass flux assuming no interaction between sources agrees well with DSMC simulations for a mass flow rate of 0.1 g/min corresponding to a Knudsen number (Kn) of about 0.1. The non-additive interaction of plumes at a higher flow rate of 1 g/min corresponding to a Kn of about 0.01 results in a higher mass flux non-uniformity in the DSMC simulations which is not captured by the simplified analytical expression.     

A Monte Carlo simulation of silicon nitride thin film microstructure in ultraviolet localized-chemical vapor deposition

Microstructural changes of surfaces and bulk of a SiN: H were investigated at the atomic level by a simulator. The simulator is based on a solid-on-solid type model for ultraviolet localized-chemical vapor deposition. The calculations consider the well-defined photolysis products adsorbed at atomic sites. Incorporation of main species is enabled by a Monte Carlo-Metropolis simulation technique. Photodeposition rates are obtained using bond dissociation energies. In this manner, the dependence of root-mean-square deviation of surface roughness and bulk porosity on operating conditions can be predicted. Photonucleation and photodeposition with a UV low pressure mercury lamp at low pressure and temperature were simulated onto indium phosphide substrate.     

Monte Carlo simulations of the Galileo energetic particle detector

Monte Carlo radiation transport studies have been performed for the Galileo spacecraft energetic particle detector (EPD) in order to study its response to energetic electrons and protons. Three-dimensional Monte Carlo radiation transport codes, MCNP version 4B (for electrons) and MCNPX version 2.2.3 (for protons), were used throughout the study. The results are presented in the form of “geometric factors” for the high-energy channels studied in this paper: B1, DC2, and DC3 for electrons and B0, DC0, and DC1 for protons. The geometric factor is the energy-dependent detector response function that relates the incident particle fluxes to instrument count rates. The trend of actual data measured by the EPD was successfully reproduced using the geometric factors obtained in this study.     

Monte Carlo modelling of energy deposition in trabecular bone

This study includes the design and testing of a program that creates quadric-based geometric models of the trabecular region, designed specifically for use with the 2005 version of the Monte Carlo radiation transport code PENELOPE. Our model was tested, by comparison with published data, in two aspects: the distributions of path lengths throughout the geometry and absorbed fraction values from the monoenergetic emission of electrons from within our geometry. In both comparisons, our results show a close agreement with published methods.     

Monte Carlo simulation of light scattering from magnetic fluids asa function of the particle chain width

Light scattering from a magnetic fluid in a strong magnetic field is simulated in this article on the basis of the Monte Carlo method, where the scattering effects of the anisotropic chains formed under the influence of the magnetic field play the most important role in scattering the incident light. The distribution of the widths of the chains is believed to follow a normal distribution pattern in a given area [W_min, W_max] where (W_min and W_max are the minimum and maximum widths of the chains in the sample, respectively. The simulated curve is compared with that based on the experimental results obtained under the same conditions and the two agree well. The influences of both the expectation and the deviation of the distribution which the widths of the chains follow on light scattering are also simulated, respectively, and conclusions are drawn     

Limitations in the PHOTON Monte Carlo gamma transport code

Three Monte Carlo gamma transport codes, MCNP, EGS, PHOTON, differ in the degree of difficulty in implementing them for calculation and in the requirements for the input file. Differences in the results were discovered when evaluating the same case using these three transport codes. These differences that are energy dependent are presented here.     

A Monte Carlo solution of transport equations

A local method is developed for solving partial differential transport equations. The method is local in the sense that the value of the unknown solution of these equations can be calculated at arbitrary space and time coordinates directly rather than extracting its value from the field solution as done when using current numerical methods for solution. The proposed method is based on an analogy between the partial differential operator of transport equations and the infinitesimal generator of Itô processes, the Itô formula, the Dynkin formula, and Monte Carlo simulation. The method can be applied to solve transport problems with Dirichlet and Neumann boundary conditions. The solution of transport problems with Neumann boundary conditions is less simple because it requires the use of reflected Brownian motion and Itô processes.     

Monte Carlo simulation of model spin systems

In this paper, applications of the Monte Carlo technique to estimate the static and dynamic properties of model spin systems are discussed. Finite-size effects and choice of boundary conditions in simulating different types of real systems are outlined. Various applications of the Monte Carlo simulations to one-, two- and three-dimensional Ising models and Heisenberg models are dealt with in some detail. Recent applications of the Monte Carlo method to spin glass systems and to estimate renormalisation group critical exponents are reviewed. Communication No. 19 from the Solid State Structural Chemistry Unit.     

Monte Carlo simulation of low density flows

The necessity for adopting a kinetic-theoretical approach to obtain aerodynamic characteristics in low density flow past space vehicles is highlighted in this paper; it is shown how long-standing difficulties in theoretically handling such flows can be circumvented by adopting a Monte Carlo technique. The principles underlying the technique are briefly described, and are first illustrated by applying the technique to the evaluation of the drag of cylinders and cones in collisionless flow. The Markoff process underlying the Monte Carlo simulation of the full Boltzmann equation with collisions is then described in detail. Instead of the time-counter strategy of Bird, a theoretically sounder ‘Random Collision Number’ (RCN) strategy has been adopted in the present simulation. In this strategy the number of collisions in each time-step in the computation is a random number drawn from an appropriate distribution. Computer programs using this strategy have been developed for calculating aerodynamic characteristics like drag and heat transfer for a cone in the transition regime between free molecule and continuum flow. The results obtained from these programs show that both time-counter and RCN strategies require almost the same computer time.