Kinetic Monte Carlo Scheme Research Articles

Nucleation and growth of atomic layer deposition of HfO2 gate dielectric layers on silicon oxide: a multiscale modelling investigation

We apply our recently developed approach, combining advanced ab initio density functional theory (DFT) methods with a probabilistic kinetic Monte Carlo (KMC) scheme, to quantify the properties of mesoscopic size systems operating in real experimental conditions. The application concerns the investigation of the atomic layer deposition (ALD) of HfO2 film growth on Si(100) surface. We show that the proposed models offer guidance in the optimization of the experimental deposition processes, in terms of OH density on the substrate, optimal growth temperature, pulse durations, and finally growth kinetics.

Kinetic activation-relaxation technique: An off-lattice self-learning kinetic Monte Carlo algorithm

Many materials science phenomena are dominated by activated diffusion processes and occur on time scales that are well beyond the reach of standard molecular-dynamics simulations. Kinetic Monte Carlo (KMC) schemes make it possible to overcome this limitation and achieve experimental time scales. However, most KMC approaches proceed by discretizing the problem in space in order to identify, from the outset, a fixed set of barriers that are used throughout the simulations, limiting the range of problems that can be addressed. Here, we propose a flexible approach---the kinetic activation-relaxation technique ($k$-ART)---which lifts these constraints. Our method is based on an off-lattice, self-learning, on-the-fly identification and evaluation of activation barriers using ART and a topological description of events. Using this method, we demonstrate that elastic deformations are determinant to the diffusion kinetics of vacancies in Si and are responsible for their trapping.

A morphological study of vicinal surface growth based on a hybrid algorithm

A hybrid algorithm that combines a phase-field model and a lattice gas model evolving according to a kinetic Monte-Carlo (KMC) simulation scheme is used to investigate the dynamics of vicinal surface growth during vapor phase epitaxy. The algorithm is computationally far more efficient than pure KMC schemes, and this gain in efficiency does not correspond to a loss in information on the kinetics of individual atoms. We present numerical studies on the temperature dependence of macroscopic properties of the growing surface, evaluating the relevant stochastic processes (attachment, detachment, diffusion and island dynamics) as a function of their rates. We show that the temperature at which step flow is replaced by island nucleation depends on incoming flux, diffusion parameters and interstep distance. Moreover, we validate these finding by comparison to experiments and by analytical investigations.

Combining density functional theory and cluster expansion methods to predict H2 permeance through Pd-based binary alloy membranes

First-principles calculations offer a useful complement to experimental approaches for characterizing hydrogen permeance through dense metal membranes. A challenge in applying these methods to disordered alloys is to make quantitative predictions for the net solubility and diffusivity of interstitial H based on the spatially local information that can be obtained from first-principles calculations. In this study, we used a combination of density functional theory calculations and a cluster expansion method to describe interstitial H in alloys of composition Pd96M4, where M=Ag, Cu, and Rh. The cluster expansion approach highlights the shortcomings of simple lattice models that have been used in the past to study similar systems. We use Sieverts' law to calculate H solubility and a kinetic Monte Carlo scheme to find the diffusivity of H in PdAg, PdCu, and PdRh alloys at a temperature range of 400<or=T<or=1200 K. From these results, we are able to predict the permeability of hydrogen through membranes made from these Pd-based binary alloys.

Simple Surface-Trap-Filling Model for Photoluminescence Blinking Spanning Entire CdSe Quantum Wires

The mechanism for synchronous photoluminescence intensity fluctuations, blinking, spanning entire micrometer-long CdSe quantum wires (Glennon, J. J.; Tang, R.; Buhro, W. E.; Loomis, R. A. Nano Lett. 2007, 7, 3290) is likely different than that commonly cited for semiconductor quantum dots. We present a simple model for the intensity blinking in quantum wires that is based on the dynamic, transient filling of surface-trap sites by photogenerated excitons and the emptying of these occupied trap sites. The model implements a kinetic Monte Carlo scheme and a dynamic photoluminescence quantum yield that depends on the fraction of trap sites filled. When a majority of the surface traps are filled, one-dimensional excitons are formed and a high emission efficiency is realized. Autocorrelation analysis of both experiment and simulation reveal the nonergodic kinetics governing the blinking phenomenon.

Kinetic Monte Carlo simulations of the oscillatory CO oxidation at high pressures: The surface oxide model

The oxidation of CO on metal surfaces is known to exhibit interesting oscillatory behaviour and spatiotemporal patterns. Oscillations arising at high pressures (mbar to atmospheric) are attributed to the “oxide model”, in which the slow oxidation and subsequent reduction of the surface is coupled to the steps of the CO oxidation mechanism. In the present work a mesoscopic skeleton model of this system is formulated in the form of a kinetic Monte Carlo (KMC) scheme which implements the Langmuir–Hinshelwood (LH) mechanism of CO oxidation with additional mechanistic steps taking into account the surface oxide formation. Oscillations in this KMC oxide model are obtained when a different reactivity is attributed to the two phases – metal surface and oxidised surface. The parameter space is explored and the ranges where oscillations are prominent are reported. As a general conclusion of this work, oscillations and clustering of the species are observed within the system’s “reactive” regions when either of the two phases has a considerably higher reactivity than the other. Larger amplitude oscillations are attained when the metal surface is assumed to be more reactive than the oxidised surface.

Faster simulations of step bunching during anisotropic etching: formation of zigzag structures on Si(1 1 0)

We propose that the formation of zigzag structures on Si(1 1 0) during anisotropic etching is mainly a result of the formation of inhomogeneous regions in the etchant due to diffusion phenomena. In the same way as the presence of these etchant inhomogeneities results in step bunches on miscut (1 1 1) surfaces, it results in zigzags on the (1 1 0) surface. To support this proposal, we present an incremental activity monitoring (IAM) method for the simulation of step bunching using a kinetic Monte Carlo scheme. For stepped (1 1 1) surfaces, comparison with a previous step density monitoring (SDM) method shows that IAM is typically faster by one order of magnitude and is well suited for the simulation of step bunching. By applying IAM to (1 1 0), the formation of zigzag structures can be simulated, strongly suggesting that the morphology of this surface is dominated by the formation of inhomogeneous regions close to the surface in the etchant phase.

Physisorption Kinetics in Carbon Nanotube Bundles

The kinetics of gas uptake on different regions of carbon nanotube bundles is investigated by means of a kinetic Monte Carlo scheme. A lattice-gas description is used to model the adsorption of particles on a one-dimensional chain of sites under two types of dynamics: (a) external kinetics, in which the chain is on the bundle's external surface directly exposed to the gas, and (b) pore-like kinetics, expected to occur inside the tubes and interstitial channels, where adsorption occurs via gas diffusion from the ends. From the time evolution of the coverage at a fixed temperature, equilibration times are obtained as a function of chemical potential (or amount adsorbed). The equilibration time of the external phase decreases linearly as the coverage increases toward monolayer completion; the rate at which this occurs strongly depends on the ratio between the binding energy and the temperature. Because of this dependence, unexpectedly long waiting times can be observed for very low coverages in systems with...

Modeling the release of proteins from degrading crosslinked dextran microspheres using kinetic Monte Carlo simulations

To optimize and predict the release of proteins from biodegradable microspheres based on crosslinked dextran, a fundamental understanding of the mechanisms controlling their release is necessary. For that purpose, a mathematical model has been developed to describe the release of proteins from these hydrogel-based microspheres. A kinetic Monte Carlo scheme for the degradation of a small domain inside the microsphere was developed. The results from this were used in a second kinetic Monte Carlo scheme to model the diffusion and the subsequent release of proteins. The only processes included in this model are diffusion and degradation. The general effects of diffusion, crosslink density, protein loading, and clustering of proteins on the release were investigated. The model crosslink density ( X model) and the model diffusivity ( D model) were fitted to experimental release data of BSA monomer from hydroxyethyl methacrylated dextran (dex-HEMA) microspheres. By using the experimental release curves of liposomes and BSA monomer, it was found that (1) the model crosslink density ( X model) scales with the hydrodynamic diameter ( d h) as d h 1.64 and (2) the diffusivity of the protein ( D model) scales approximately with 1 / d h (Stokes–Einstein). Using these scaling relations, quantitative predictions of the release curves of BSA dimer, immunoglobulin G and human growth hormone were possible. In conclusion, this model may play an important role in the optimization, understanding and prediction of the release of various proteins from degradable hydrogels.

Kinetic approach to the cluster liquid-gas transition

The liquid-gas transition in free atomic clusters is investigated theoretically based on simple unimolecular rate theories and assuming sequential evaporations. A kinetic Monte Carlo scheme is used to compute the time-dependent properties of clusters undergoing multiple dissociations, and two possible definitions of the boiling point are proposed, relying on the cluster or gas temperature. This numerical approach is supported by molecular dynamics simulations of clusters made of sodium atoms or C60 molecules, as well as simplified rate equation.

A hybrid scheme for simulating epitaxial growth

This article continues the development of a hybrid scheme for simulating epitaxial growth that combines the Burton–Cabrera–Frank (BCF) model with kinetic Monte-Carlo (KMC) simulation. This is the first implementation of the scheme for “2+1” dimensional growth. Other improvements over an earlier version include the use of a more conventional KMC model and some refinement in the handling of the boundary condition between the KMC and continuum regions. The method is used to examine unstable step-flow with direct comparison to KMC simulations. The results are extremely good with respect to computational speed and reveal effects due to fluctuations to a much greater extent than the BCF model alone. This method will be especially useful in scenarios with widely separated steps and high adatom densities, as these are situations that cannot be easily simulated with KMC due to increased computational cost. The hybrid method is extremely flexible and can be coupled interchangeably to any KMC scheme.

Nonthermal transport of small sorbates in zeolites: Chaotic dynamics and long jumps

In some molecular systems, the dominant driving force for transport is not thermal noise from lattice vibration or other sources, but low-dimensional deterministic chaos. We consider this deterministic transport for an example of diffusion of methane sorbate in zeolite AlPO4-5. In this system, the chaotic motion of the sorbate is due to nonlinear coupling between its longitudinal and azimuthal degrees of freedom. Assuming ergodicity of the sorbate motion, we develop a quantitative RRKM-type theory for the sorbate transport. The theoretical predictions for the escape rate of the sorbate from the zeolite cage are in good agreement with molecular dynamics simulations. We observe that, in addition to ergodic mixing of the sorbate degrees of freedom when the sorbate is trapped inside a zeolite cage, long ballistic flights are an important aspect of the sorbate dynamics. We investigate the complicated interplay between the ergodic trapping and the multisite flights, where the ergodicity assumption breaks down, with a kinetic Monte Carlo scheme which offers a diffusivity estimate that includes contribution from ballistic flights.

Monte Carlo Simulation of the Topology and Conformational Behavior of Hyperbranched Molecules: Pd-Diimine-Catalyzed Polyethylene

A kinetic Monte Carlo model was developed to simulate the polymerization of ethylene with palladium-α-diimine catalyst wherein hyperbranched molecules are formed through a chain-walking mechanism. The total degree of branching and the distribution of short branches obtained with the model agree well with reported 13 C NMR experimental results. Different chain topologies were generated by varying the probability of chain walking, P n , which controls the competition between chain-walking and monomer insertion. Molecular Monte Carlo simulations were subsequently conducted to study the conformations of isolated molecules (created by the kinetic Monte Carlo scheme) to relate molecular shape and topology, Our results provide evidence that the topology varies from predominantly linear with many short branches at low P w to a densely branched,globular structure at high P w . In contrast to experimental observations, our results for the molecular weight (N) dependence of the radius of gyration (R g N') indicate that the branching topology has an effect on this relation, i.e., high-P w molecules have a smaller scaling exponent v. The simulated N-dependence of the second virial coefficient exhibits a similar behavior. We also discnss the unusual conformational behavior of highly branched polymers obtained when P w → 1.

Collective surface diffusion: n-fold way kinetic Monte Carlo simulation

Collective surface diffusion of strongly interacting particles is simulated on the basis of an $n$-fold way kinetic Monte Carlo scheme. The coverage dependence of the jump and tracer diffusion coefficients is calculated for one- and two-dimensional lattice gases at very low (subcritical) temperatures. Results are compared with exact analytical ones and Monte Carlo simulations using the standard Metropolis algorithm. The method proves to be highly reliable to investigate surface diffusion at subcritical temperatures where phase coexistence in the adlayer occurs.

Traveling through potential energy landscapes of disordered materials: The activation-relaxation technique

A detailed description of the activation-relaxation technique (ART) is presented. This method defines events in the configurational energy landscape of disordered materials such as amorphous semiconductors, glasses and polymers, in a two-step process: first, a configuration is activated from a local minimum to a nearby saddle point; next, the configuration is relaxed to a new minimum; this allows for jumps over energy barriers much higher than what can be reached with standard techniques. Such events can serve as basic steps in equilibrium and kinetic Monte Carlo schemes.

Morphologies of diamond films from atomic-scale simulations of chemical vapor deposition

The growth of {110}- and {111}-oriented diamond films under typical chemical vapor deposition (CVD) conditions was simulated on the atomic scale. The films are represented in three dimensions by diamond cubic crystal lattices, and thus the effects of surface atomic structure and film morphology are built into the model. The temporal evolution of the films during growth is accomplished by a kinetic Monte Carlo scheme parameterized by conventional surface chemical reaction-rate coefficients. Growth on {110}:H and {111}:H surfaces was simulated in atmospheres containing H, H2, CH3 and various partial pressures of C2H2. Film growth rates and morphologies are found to depend strongly on the presence of C2H2 at the surface. Under typical growth conditions, film growth rates agree well with experiment and other modeling studies, and the film morphologies are atomically rough. However, growth of {110} and {111} films in C2H2-deficient environments is found to be controlled by the nucleation of diamond clusters on smooth faces, and growth rates are very low under these conditions. This is because the initiation of a monolayer on smooth {110} and {111} facets requires the bonding of two and three adsorbed C atoms, respectively. Since a single C2H2 molecule contributes two C atoms when it is chemisorbed, the presence of C2H2 is important to {110} and especially {111} growth. The {111} films grow by the flow of atomic-height steps at triangular islands on the surface and are atomically smooth when the partial pressure of C2H2 is very low. The {110} films grow by one-dimensional step flow in the atomic “troughs” of the {110}-terminated diamond cubic surface, and become corrugated into {111} microfacets.