Kinetic Monte Carlo Code Research Articles

Development of a Versatile Kinetic Monte Carlo Code to Simulate Physical Processes in Thin Film Nucleation and Growth

Thin film development and nanoscale oxidation studies have been of great interest recent years. Nucleation rate theory[1‐3] has been successfully used to describe metal heteroepitaxy [4] and qualitatively explained the initial stage of oxidation behavior[5]. To further quantitative understanding of these nano‐scale processes and the morphology evolution in general gas‐metal reactions and thin film development, a powerful simulation tool is urgently needed. The Thin Film Oxidation (TFOx) model is an atomistic Kinetic Monte Carlo (KMC) model, which has been developed of this purpose. The TFOx model includes all of the relevant microscopic processes in thin film growth. It simulates various steps and phenomenon during thin film development, which includes deposition, decomposition, adatom diffusion, nucleation, adatom desorption, island growth and et.al. TFOx has a large amount of input parameters compared to other KMC models to assure the realistic and accuracy, which also makes itself a versatile tool of studying the thin film development. Some application of TFOx in simulating the Cu (100) oxidation behavior will also be discussed in this paper.

A study on mutual interaction between atomistic and macroscopic phenomena during electrochemical processes using coupled finite difference – kinetic Monte Carlo model: Application to potential step test in simple copper sulfate bath

A novel method is used to link a 2D kinetic Monte Carlo code to a 1D finite difference code to construct a more realistic and efficient tool for simulating various electrochemical processes. This multiscale model is able to simulate the long-scale mass transfer of electroactive species in bath along with electrode surface phenomena at atomic scale simultaneously. An embedded atom method (EAM) has been used to evaluate the barrier energies of diffusion and redox reactions on electrode surface. The FD code provides the ion concentration on OHP for KMC code, while the KMC code provides the surface activity and rate constants of redox reactions as an input data for FD code. The electrochemical deposition and dissolution of copper has been simulated by both FD-KMC and simple FD code and the results have been compared. The differences between the results of these two approaches could be explained by considering the variation of surface electrochemical properties during electrochemical processes which has been ignored by simple FD code. These properties are strongly dependent on the surface morphology. The results show that the fractal properties and the morphology of the electrode surface are a function of applied potential.

Role of Trapping Impurities on He Desorption and Clustering in Irradiated α-Fe [PowerPoint Submission

AbstractIt is well-known that impurities affect the migration of intrinsic point defects in metals. For instance, carbon is a common impurity in Fe that significantly retards diffusion of vacancies. Under fusion irradiation conditions, high levels of He are produced by transmutation reactions. This element strongly interacts with vacancies produced during irradiation and agglomerate into stable He-vacancy clusters that can deteriorate the mechanical properties of the material. A physically-based model accounting for the interactions between He, point defects (interstitials and vacancies) and trapping impurities is therefore necessary to understand and predict damage evolution in Fe.We have used a multi-scale approach to predict the evolution of He in the presence of impurities in irradiated Fe. Density Functional Theory (DFT) calculations were performed to investigate the migration mechanisms and to determine the activation energies of the different atomistic processes. The influence of impurities - such as carbon - on the binding energies of small He-vacancy clusters was also studied. Using the information obtained by DFT a physically-based model was developed and implemented in a kinetic Monte Carlo (kMC) code to follow the evolution of He in Fe. In addition, a model based on the rate theory (RT) was developed in order to achieve larger simulation times and volumes. Results obtained with this model, which is based on a mean field approximation are compared to those obtained with kMC. Using this multiscale approach, the simulation results are used to interpret the different stages of thermal He desorption experiments and to determine the predominant migration mechanism. The influence of impurities which affect the diffusion of point defects or modify the binding energies of He-vacancy type clusters is also studied.

Atomistic simulations in Si processing: Bridging the gap between atoms and experiments

With devices shrinking to nanometric scale, process simulation tools have to shift from continuum models to an atomistic description of the material. However, the limited sizes and time scales accessible for detailed atomistic techniques usually lead to the difficult task of relating the information obtained from simulations to experimental data. The solution consists of the use of a hierarchical simulation scheme: more fundamental techniques are employed to extract parameters and models that are then feed into less detailed simulators which allow direct comparison with experiments. This scheme will be illustrated with the modeling of the amorphization and recrystallization of Si, which has been defined as a key challenge in the last edition of the International Technology Roadmap for Semiconductors. The model is based on the bond defect or IV pair, which is used as the building block of the amorphous phase. The properties of this defect have been studied using ab initio methods and classical molecular dynamics techniques. It is shown that the recombination of this defect depends on the surrounding bond defects, which accounts for the cooperative nature of the amorphization and recrystallization processes. The implementation of this model in a kinetic Monte Carlo code allows extracting data directly comparable with experiments. This approach provides physical insight on the amorphization and recrystallization mechanisms and a tool for the optimization of solid-phase epitaxial-related processes.

Robust nonlinear feedback–feedforward control of a coupled kinetic Monte Carlo–finite difference simulation

Robust nonlinear feedforward–feedback controllers are designed for a multiscale system that dynamically couples kinetic Monte Carlo (KMC) and finite difference (FD) simulation codes. The coupled codes simulate the copper electrodeposition process for manufacturing on-chip copper interconnects in electronic devices. The control objective is to regulate the current density subject to the condition that the steady-state fluctuation of the overpotential remains bounded within ±0.01 V. The controller designs incorporate a low-order stochastic model that captures the input–output behavior of the coupled KMC–FD code. The controllers achieve the objectives and the closed-loop responses implemented on the low-order model and the coupled KMC–FD code match well within stochastic variations. The nonlinear feedforward control reduces the rise time of the controller response while the feedback control ensures robustness in the presence of model uncertainty.

Multiscale simulations of copper electrodeposition onto a resistive substrate

During the initial stages of copper electrodeposition onto a thin seed layer, a nonuniform potential distribution arises, resulting in local variations in growth rate and deposit morphology. Early stages of morphology evolution during copper electrodeposition are of practical importance but have not been well studied. Here, a new multiscale approach is developed for numerical simulation of the effect of a macroscopic potential distribution along a seed layer on microscopic local roughness evolution. The key contribution is a generic method for coupling multiple computer codes, and the demonstration of its use. The macroscopic code passes the local potential at ten points along the seed layer to ten kinetic Monte Carlo codes, each of which simulates additive-free copper electrodeposition and roughness evolution on an initially flat surface. Periodically, each Monte Carlo code computes the local film thickness and passes it back to the resistance code, which updates the potential distribution for the next iteration. Results are obtained for a wide range of parameter space including both constant-potential and constant-current operation. A confirmation procedure was developed to verify that the multiscale approach (using small Monte Carlo simulation domains with periodic boundary conditions) does not significantly alter the physical accuracy of the simulations.

Coarse-Grained Kinetic Monte Carlo Simulation of Copper Electrodeposition with Additives

A (2+1)D kinetic Monte Carlo (KMC) code was developed for coarse-grained as well as atomic-scale simulations that require detailed consideration of complex surface-reaction mechanisms associated with electrodeposition of copper in the presence of additives. The physical system chosen for simulation is similar to that used by the microelectronics industry to fabricate on-chip interconnects, where additives are used to tailor shape evolution. Although economically significant, such systems are often designed in an empirical manner that would be greatly enhanced by improved understanding of the additive mechanism gained through simulations. By comparing simulated results at atomic as well as coarse-grained scales with theoretical results obtained analytically for various limiting cases of behavior, the validity of the KMC code was tested. It was found that the surface roughness at a specified length scale can be accurately simulated by using a coarse-grained KMC code with lattice spacing of 1/10 or smaller than that of the specified length scale—a result that is particularly useful for comparing experimental data on surface roughness with numerical simulations. For second-order homogeneous surface reactions, it is shown that the KMC-simulated surface coverage approaches the analytical surface coverage as surface mixing is increased by increasing the surface diffusion rate. The results verified the numerical accuracy and the reduced computational cost of the coarse-grained KMC approach for simulating complex chemical and electrochemical mechanisms.

Microscopic description of the irradiation-induced amorphization in silicon.

We have investigated the atomistic mechanism behind the irradiation-induced amorphization in Si using molecular dynamics simulation techniques. The microscopic description of the process is based on the defect known as bond defect or IV pair. IV pairs recombine very fast when isolated, but if they interact to each other they survive longer times and thus accumulate giving rise to amorphization. This fact accounts for the superlinear behavior of the accumulated damage with dose and the different activation energies for recrystallization observed in the experiments. The molecular dynamics results have been used to define an atomistic model for amorphization and recrystallization which has been implemented in a kinetic Monte Carlo code. The model is able to reproduce quantitatively the dependence of the critical crystal-amorphous transition on the irradiation parameters.

Simulation of ion-irradiation stimulated Ge nanocluster formation in gate oxides containing GeO 2

Process simulations were performed for a novel fabrication technique of Ge nanoclusters (NCs) located in the thin gate oxide of a MOS field effect transistor, which will be applied in non-volatile random access memories (nvRAMs). The simulations start from a thin GeO 2 layer buried in the gate oxide, which might be produced by heteroepitaxy of a thin Ge layer in (0 0 1)Si followed by a special oxidation of Si and Ge avoiding Ge segregation. The present process simulations predict that the recently reported transformation of such a GeO 2 layer into Ge NCs by thermal annealing can be accelerated by ion irradiation. It is even more important that under ion irradiation the chemical reduction of GeO 2 should be achieved at lower process temperature. The limiting mechanism of the transformation of GeO 2 into Ge NCs during thermal annealing is shown to be thermally activated detachment of Si monomers from the Si/SiO 2 interface into SiO 2. Thus, ion beam mixing of Si into SiO 2 stimulates the Ge NC formation. The process simulations were performed by a specifically adapted and extended multicomponent kinetic Monte Carlo code.

Particle in cell simulations of low pressuresmall radius positive column discharges

Improved positive column simulation techniques are needed because ofthe non-local nature of typical low-pressure discharges used for lighting. Ina local model, the power balance between Joule heating and collisionallosses must hold for each volume element of the discharge separately while anon-local model requires only a global power balance. The departurefrom locality increases as either gas density ng or radius R isdecreased. Despite this, most current fluorescent lamp software is based onthe local concept. We present a non-local kinetic particle-in-cell Monte Carlocollisions (PIC-MCC) code to simulate low-pressure, small-radius, positivecolumn discharges. This code is also compared to a non-local fluid code, anon-local kinetic Monte Carlo code and to experimental data. The PIC-MCC codemade the least approximations and assumptions and was accurate and stable overa wider parameter regime than the other codes. Also, 1d3v PIC-MCC simulationspeeds are quite competitive even on moderate workstations. Finally, weanalyse the PIC-MCC simulation results in detail, especially the power balanceand the radial electron kinetic energy flux Hr(r). We found that for lowngR< 1×1015 cm-2, the electron kinetic energy flux is directed radiallyoutward while for higher ngR, it is directed radially inward except rightnear the wall.

Modeling RNA folding paths with pseudoknots: application to hepatitis delta virus ribozyme.

A quantitative understanding of nucleic acid hybridization is essential to many aspects of biotechnology, such as DNA microarrays, as well as to the structure and folding kinetics of RNA. However, predictions of nucleic acid secondary structures have long been impeded by the presence of helices interior to loops, so-called pseudoknots, which impose complex three-dimensional conformational constraints. In this paper we compute the pseudoknot free energies analytically in terms of known standard parameters, and we show how the results can be included in a kinetic Monte Carlo code to follow the succession of secondary structures during quenched or sequential folding. For the hepatitis delta virus ribozyme, we predict several nonnative stems on the folding path, characterize a kinetically trapped state, interpret several experimentally characterized mutations in terms of the folding path, and suggest how hybridization with other parts of the genome inactivates the newly formed ribozyme.

Simulation of damage production and accumulation in vanadium

Energetic atoms which have been knocked-off their lattice sites by neutron or ion irradiation leave a trail of vacancies and interstitials in their wake. Most of these defects recombine with their opposites within their own collision cascade. Some fraction, however, escape to become freely migrating defects (FMD) in the bulk of the material. The interaction of FMD with the microstructure has long been linked to changes in the macroscopic properties of materials under irradiation. We calculate the fraction of FMD in pure vanadium for a wide range of temperatures and primary knock-on atom (PKA) energies. The collision cascade database is obtained from molecular dynamics (MD) simulations with an embedded atom method (EAM) potential. The actual FMD calculation is carried out by a kinetic Monte Carlo (kMC) code with a set of parameters extracted either from the experimental literature or from MD simulations. Annealing each individual cascade at different temperatures allows the mobile species to escape and account for FMD. We also analyze damage accumulation in a specimen irradiated at low dose rate in the presence of impurities. At the temperature studied, beginning of stage V, we observe that only vacancies are free to move whereas most interstitials are stopped by impurities. We also analyze the role of impurities on damage accumulation and on the concentration of mobile defects.

A lattice kinetic Monte Carlo code for the description of vacancy diffusion and self-organization in Si

We have investigated the mechanism driving void evolution in crystalline Si by means of 'on lattice' kinetic Monte Carlo (MC) simulations. The implementation of an efficient algorithm allowed us to compare, on a macroscopic time scale, the predictions of simulation codes using three different binding models. We demonstrate that the use of a modified Ising model, taking also into account second neighbour interaction, results in a MC code embodying the main physical features on vacancy (V) interaction, derived by Tight Binding Molecular Dynamics (TBMD) simulations. In particular the dependence of cluster stability and reactivity on size and geometrical configuration can be efficiently taken into account. We have found that, when this model is used, the ripening process is also driven by the migration of small V clusters, and not only by free Vs as predicted by less refined models. This feature strongly modifies the kinetics of growth and the basic mechanism of void ripening.

Annealing Kinetics of Single Displacement Cascades in Ni: An Atomic Scale Computer Simulation

AbstractIn order to describe the long term evolution of the defects produced by a displacement cascade, Molecular dynamics (MD) and Kinetic Monte Carlo (KMC) methods are employed. Using an empirical Ni interatomic potential in MD, the damage resulting from primary knock-on atom (PKA) energies up to 30 keV has been simulated. The annealing kinetics and the fraction of freely migrating defects (FMD) are determined for each single displacement cascade, by a KMC code which is based on a set of parameters extracted mainly from MD simulations. It allows an atomistic study of the evolution of the initial damage over a time scale up to lOOs and the determination of the fraction of the defects that escape the KMC box, compared to those obtained by MD, as function of temperature and PKA energy. It has been found that this fraction depends strongly on the temperature but reaches a saturation value above stage V.

Kinetic Monte Carlo Annealing Simulation of Damage Produced by Cascades in Alpha-Iron

AbstractThe mobile defects created in displacement cascades can either interact within the cascade region or undergo long-range diffusion in the crystal. The kinetic Monte Carlo code ALSOME has been used in the present work to carry out annealing simulations of electron irradiation and single cascades with energy in the range of 2 to 40 keV in α-Fe as a function of temperature. Isochronal annealing of electron irradiation shows a temperature-dependence of the recovery stages that is reasonably close to experiment, but Stage I is controlled by the rotation energy of the &lt;110&gt; dumbbell to the &lt;111&gt; crowdion. The annealing of single cascades has demonstrated that nearly 60% of SIAs formed in the primary state of cascade damage escape from the cascade at temperatures above stage I. Most of the escaping SlAs are in clusters, for only 10% of them are mono-interstitials. Although the number of escaping defects increases with increasing cascade energy, the relative fraction is almost constant for the recoil energies considered. The results are compared with those for copper obtained using the same code [1].