Deterministic and Monte Carlo methods for simulation of plasma‐surface interactions

Rechargeable lithium-ion batteries have been extensively used in mobile communication and portable instruments due to their high volumetric and gravimetric energy density and low self-discharge rate, leading many scientists and engineers to work towards developing lithium-ion batteries with improved performance and longer life.In normal operation, an active solid-electrolyte-interface (SEI) layer forms in the first cycle of charging, due to reactions of lithium and solvent at the active surface (1,2). The SEI layer provides a barrier between the electrolyte and electrode to prevent further reaction while allowing lithium ions to permeate through the SEI layer in order to intercalate into and out of the bulk solid to store and release energy. However, the SEI layer continues to grow under repeated cycling. This growth increases the diffusion resistance of the lithium ions to the bulk active material, and removes cyclable lithium from the system, reducing the efficiency of the battery (1,2). This increased resistance can produce high temperature and can result in thermal runaway (3-5) within the battery. The properties and chemical composition of the SEI layer (active and passive) has been a subject of intense research due to its importance in the safety, capacity fade, and cycle life of Li-ion secondary batteries (6-12). Examination of the growth of the SEI layer as a mechanism for capacity fade has been performed using Kinetic Monte Carlo (KMC) simulations (13). This has provided valuable insight into the growth of the SEI layer and has shown the effects of high rates of charging on SEI layer passivation. These KMC simulations can be used to study the surface heterogeneity of the electrode surface as the passive layer is formed.The KMC model used will be expanded to a 2+1D model which tracks the thickness of the SEI layer over a representative surface of the solid particle. This will give a sense of the heterogeneity that arises in the SEI layer and will be coupled with the pseudo 2D model to simulate full battery operation. The P2D model will be converted from a system of partial differential equations to a system of ordinary differential equations by using reformulation techniques developed for the continuum model (14). The KMC model studies the events that occur in the SEI layer and the particle surface. For example, diffusion of the solvent in the SEI layer is modeled using the KMC approach. The reactions at the active material surface are modeled by considering the relative rate constants and using a random number generator to determine the event which occurs. In contrast, the continuum P2D model explains what happens in the bulk phases, and is deterministic. This coupled model will perform continuum calculations simultaneously with the KMC calculations. As passivation is considered in the KMC model, the capacity of the battery will fade with time, allowing for life time studies to be performed. This will lead to better understanding of the conditions which lead to capacity fade and better operation of lithium-ion batteries. Acknowledgements The authors acknowledge financial support by the National Science Foundation under grant numbers CBET-0828002, CBET-0828123, and CBET-1008692, and the Advanced Research Projects Agency – Energy (ARPA-E), U.S. Department of Energy, under Award Number DE-AR0000275.

Surface reconstruction in reactive dynamics: A kinetic Monte Carlo approach

<p>A Kinetic Monte Carlo (KMC) method was developed to model homoepitaxy and grain boundary propagation on a (111) surface. Barrier energies were calculated using the Nudged Elastic Band (NEB) technique. A recently reported inertial relaxation technique named FIRE (the Fast Inertial Relaxation Engine) was used to relax the NEB images. Both the Lennard-Jones potential and a Sutton-Chen Iridium potential were used and compared. A doubly-refined lattice mesh was developed to incorporate atoms in Face-Centred-Cubic (FCC) and Hexagonal-Close-Packed (HCP) sites as well as atoms in decorated row sites (i.e. supported by 4 atoms). A look-up table was developed to identify hops in the KMC algorithm. The KMC results show that a small difference in energy barriers between FCC and HCP sites on the substrate can cause a substantial bias in the direction of grain boundary propagation. We also investigated the effect of the geometry of the grain boundary on its propagation, as well as the atomistic processes involved in grain boundary propagation and the merger of grain boundaries. Our deposition simulations produced islands with loosely triangular envelopes, where FCC islands are rotated 180° with respect to HCP islands. The results are similar to scanning tunneling microscopy (STM) images of Iridium deposition, although lack of computing power forced us to use a high deposition rate and this caused some differences.</p>

We propose a concurrently coupled hybrid molecular dynamics (MD) and kinetic Monte Carlo (KMC) algorithm to simulate the motion of grain boundaries between fcc and hcp islands during epitaxial growth on a fcc (111) surface. The method combines MD and KMC in an adaptive spatial domain decomposition, so that near the grain boundary, atoms are treated using MD but away from the boundary atoms are simulated by KMC. The method allows the grain boundary to interact with structures that form on spatial scales significantly larger than that of the MD domain but with a negligible increase in computational cost.

The potential energy surface of an atomic or molecular system can be transformed into a set of catchment basins for the local minima. Monte Carlo methods can be applied to explore the resulting landscape and search for the global potential minimum or calculate thermodynamic and dynamic properties. For example, the kinetic Monte Carlo (KMC) approach has been used to study the structure and dynamics of a supercooled binary Lennard‐Jones liquid, which is a popular model glass former. The KMC technique allows us to explore the potential energy surface without suffering an exponential slowing down at low temperature. In agreement with previous studies we observe a distinct change in behaviour close to the dynamical transition temperature of mode‐coupling theory. Below this temperature the number of different local minima visited by the system for the same number of KMC steps decreases by more than an order of magnitude. The mean number of atoms involved in each jump between local minima and the average distance they move also decreases significantly, and new features appear in the partial structure factor. At higher temperature the probability distribution for the magnitude of the atomic displacement per KMC step exhibits an exponential decay, which is only weakly temperature dependent.

In this paper, we report our theoretical investigation on boron diffusion in silicon posterior to PAI (pre-amorphization implant) process in an effort to understand the physical mechanism for forming a shallow and abrupt junction. We performed numerical calculation for examining the characteristics of silicon atoms as a candidate for PAI species. Our KMC (Kinetic Monte Carlo) simulation revealed that PAI process helps to get a shallower junction than the case of PAI-free boron implantation and that Si-PAI process produces more amount of interstitial and vacancy which results in the reduction of so-called boron transient enhanced diffusion (TED). In addition, we made a comparison between Si-PAI and Ge-PAI in terms of the generation dynamics of defects and the effect on the subsequent diffusion of boron. Our KMC study on the interstitial distribution revealed that Si-PAI produces more interstitials than Ge-PAI whilst Ge-PAI help interstitials move further up toward the surface than Si-PAI during the subsequent annealing process.

Unspoken aspects of chain shuttling reactions: Patterning the molecular landscape of olefin multi-block copolymers

This study introduces a novel kinetic Monte Carlo (KMC) simulation package which models H-ZSM-5 crystals across experimentally relevant time and length scales to understand the role of transport during arene interconversion reactions (~100 reactions). This small subset of the methanol-to-hydrocarbon (MTH) network was previously modeled using periodic, dispersion-corrected density functional theory (DFT) to determine activation barriers and reaction energies for these KMC methods. Transport of arene molecules through the straight and sinusoidal channels of MFI was modeled as site-hopping and the DFT-calculated barriers are incorporated into the KMC model to account for mass-transport limitations. Barriers of different arene molecules trend well with their effective radii, and species with a smaller effective radii diffusive more readily. A previously published maximum rate analysis of arene interconversion pathways—previously validated by experimental data—is compared to a diffusion-free KMC model to confirm the accuracy of this KMC package. The temperature and pressure dependencies of rates obtained from KMC agree well with those of maximum rate analysis on the diffusion-free model, demonstrating that KMC effectively predicts rates as well as maximum rate analysis methods commonly used in kinetic applications of DFT. Arene interconversion pathways were also analyzed on KMC models incorporating diffusion to and from interior crystal sites. These simulations suggest that large species, such as hexamethylbenzene, become trapped at 10–20% of sites, thus causing site deactivation by limiting diffusion through MFI channels and lowering overall rates of product formation. Benzene diffusion barriers are artificially varied from 20–200 kJ mol−1 and rates of benzene methylation decrease by 4-fold with diffusion barriers greater than 80 kJ mol−1; this suggests that species with diffusion barriers greater than 80 kJ mol−1 (such as penta- and hexamethylbenzene) will likely become trapped at interior sites and ultimately cause catalyst deactivation. This study serves as a proof-of-concept for a novel KMC package that expedites kinetic analysis of complex reaction pathways and introduces mass-transport limitations which are not commonly accounted for in kinetic DFT studies. This KMC package can predict the behavior of diffusion-limited species, such as penta- and hexamethylbenzene, and the mechanisms by which they are formed and eventually lead to catalyst deactivation.

A kinetic Monte Carlo (KMC) numerical approach was used to investigate initial stages of kinetically controlled nucleation and growth on electrodes. Deposition, surface diffusion, nucleation, and growth were simulated for a pristine system consisting of metal ions in solution adjacent to a face-centered-cubic (fcc) surface that is initially configured with a series of parallel, monatomic step edges. Simulations were carried out with an atomic-scale, solid-on-solid KMC algorithm, in which the deposited atoms occupied the sites of a fcc lattice. One series of simulations was carried out for metal deposition onto a substrate of the same metal. The results were characterized according to a dimensionless quantity, Λ, that represented the ratio of the rate of surface diffusion to the rate of deposition. It was found for large values of Λ that the deposit grew at the monatomic step edges, whereas for small values of Λ the step edges played no role in the nucleation of islands. A second series of simulations was carried out for deposition onto a foreign substrate. The growth modes associated with various combinations of system parameters was explored.

Efficient kinetic Monte Carlo simulation

Divide-Conquer-Recombine Kinetic Monte Carlo Simulations of Electron Transfer in the Extracellular Redox Network of Shewanella oneidensis MR-1

Damascene approaches are widely used for creating microelectronic interconnects. Successful implementation of the process is reliant upon the deposition of a refractory metal or metal nitride liner coating. It functions as a diffusion barrier layer to suppress transport of subsequently deposited interconnect metals into the surrounding dielectric. The development of vapor-phase processes for the deposition of uniform thickness liner layers has been problematic. Flux collimation and energetic deposition approaches have been attempted with mixed results as the feature size is decreased. Here, a modified kinetic Monte Carlo (KMC) method has been used to explore the physical vapor deposition of liner coatings. To incorporate the many effects associated with energetic metal fluxes, the results of molecular dynamics calculations of incident atom reflection, resputtering, surface biased diffusion, and athermal relaxations have been introduced into the KMC algorithm. The method has been applied to investigate the effects of the incidence flux’s angular distribution and kinetic energy upon the liner coating coverage. It has been found that trench step coverage uniformity increases with increasing atom kinetic energy above a threshold energy value of 20 eV. Atom resputtering/reflection are found to be the most important mechanisms responsible for improvements in the step coverage. Sputtering of already deposited material is found to be the most important mechanism for transporting the flux to the most difficult to coat lower sidewall region of a trench. Energetic deposition processes that activate these mechanisms are therefore preferred. The simulations reveal the existence of an optimal incident angular distribution to maximize coverage uniformity. For a flux with a kinetic energy of 70 eV, a cosine angular distribution within the collimation angle of ±15°–25° provided the best balance of direct and resputtered/reflected fluxes to maximize coating uniformity.

The current contribution proposes a multi-scale bridging modeling approach for the dissolution of crystals to connect the atomistic scale to the (sub-) micro-scale. This is demonstrated in the example of dissolution of portlandite, as a relatively simple benchmarking example for cementitious materials. Moreover, dissolution kinetics is also important for other industrial processes, e.g., acid gas absorption and pH control. In this work, the biased molecular dynamics (metadynamics) coupled with reactive force field is employed to calculate the reaction path as a free energy surface of calcium dissolution at 298 K in water from the different crystal facets of portlandite. It is also explained why the reactivity of the (010), (100), and (10) crystal facet is higher compared to the (001) facet. In addition, the influence of neighboring Ca crystal sites arrangements on the atomistic dissolution rates is explained as necessary scenarios for the upscaling. The calculated rate constants of all atomistic reaction scenarios provided an input catalog ready to be used in an upscaling kinetic Monte Carlo (KMC) approach.

This Perspective discusses the physics, implementation and findings of Kinetic Monte Carlo (KMC) models applied to organic photovoltaic devices (OPVs). It is shown that KMC models can relate morphology and energy levels on the nano-scale to geminate and non-geminate recombination, charge transport, charge injection and charge extraction measured in macro-scale OPVs. In particular, KMC investigations probing the circumstances under which geminate recombination is, and is not, a significant loss mechanism in OPVs are reviewed. Furthermore, the mechanisms which yield non-geminate (bimolecular) recombination in OPVs that is both slower than the predictions of Langevin, and charge density dependent, are discussed. It is also shown how KMC models can predict average mobility, as well as spatial heterogeneity and temporal dispersion around this average value in disordered bulk heterojunctions. Finally, it is shown how KMC can be used to quantify the effect of non-ideal electrodes, interlayers and surface wetting layers on OPV performance.

In the suspension plasma spray, nanosized particles are suspended in a liquid and the suspension is injected into the plasma to deposit coatings. The structure of the highly branched solid aggregates has significant influence on the microstructure and performance of the coating. In this paper, we investigate the formation of branched nanoparticle aggregates resulting from the evaporation of nanofluid droplets. A kinetic Monte Carlo (KMC) approach is used to simulate the drying process of a nanofluid droplet in a circular domain. It is found that the two-dimensional lattice-gas-based Monte Carlo model can describe the self-assembly of nanoparticles into a highly branched solid aggregate. The results reveal that the fingering contact line instabilities can emerge under a given condition and force the formation of a branched nanoparticle structure. The results also show that the initial chemical potential of boundary and the rate of chemical potential change have significant influence on the resulting patterns and the finger number.