Atomistic simulations of deep submicron interconnect metallization

<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 employ a three-dimensional (3D) lattice model based on the kinetic Monte Carlo (KMC) method to study cell self-assembly and cellular aggregate fusion of multicellular aggregate systems. This model is developed to describe and predict time evolution of postprinting morphological structure formation during morphogenesis of tissues or organs in a novel biofabrication process known as bioprinting. In this new technology, live multicellular aggregates are used as the fundamental building blocks, known as the bio-ink, to make tissue or organ constructs via the layer-by-layer deposition technique in biocompatible hydrogels; the printed bio-constructs embedded in the hydrogels are then placed in bioreactors to undergo the fusion process to form the desired functional tissue or organ products. In this paper, we implement the lattice model in an efficient list-based KMC algorithm to simulate the making of a set of tissue/organ constructs in several designer's geometries (a ring, a sheet and a tube), which involves a large number of cells of a single type and various other extracellular matrix materials like agarose etc. We then study the process of cell sorting in fusion of cellular aggregates involving multiple cell types with diverse adhesivities and compatible extracellular hydrogels. The KMC simulations reported in this paper agree qualitatively with the available experimental results. In the meantime, they are also comparable to the results obtained from cellular particle dynamics (CPD) simulations.

Study on formation of step bunching on 6H-SiC (0001) surface by kinetic Monte Carlo method

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.

Simulations of bi-direction pedestrian flow using kinetic Monte Carlo methods

Area-selective growth for patterning and separation of molecules at allocated sites: Designed kinetic Monte Carlo simulation for anisotropic molecules

Two approaches to the modeling of surface kinetics in reactive plasmas are discussed. Coarse‐grained deterministic models incorporate rate balance equations for coverages of surface active sites. They are computationally effective and can be readily coupled to reactor‐scale plasma simulations. In the kinetic Monte Carlo (KMC) approach, the time evolution of a gas‐lattice system consisting of a large number of particles is described. Although being more demanding computationally, KMC algorithms are exact, allow a straightforward description of distributions of surface reactivity and help bridging the gap between simulations on atomic and macroscopic scales. In this paper, theoretical and practical aspects of deterministic and KMC modeling of plasma‐surface interactions are discussed taking O recombination on silica as a model system.

Energetic deposition using filtered cathodic arc plasmas

A multi-scale method for modeling degradation of bioresorbable polyesters

CH3SiCl3 (MTS)-H2-Ar system has been applied to prepare SiC film with chemical vapor deposition (CVD) method in this paper. For three facets of SiC film, some significant influence on growth rate, surface roughness, thickness and relative density brought by MTS consistency has been mainly discussed with kinetic monte carlo (KMC) method. The simulation results show that there is a certain scale for mol ratio of H2 to MTS (H2/MTS) with different deposition temperature. When MTS consistency increases, growth rate and surface roughness of three facets all increase, which manifests approximate linearity relationship. Thickness of three facets also increases while increasing trend of three facets thickness is different obviously. Although relative density of three facets all increases, increasing trend shows a little difference with MTS consistency increasing.

In the paper, we focus on atom diffusion behavior in Ni-based superalloys, which have important applications in the aero-industry. Specifically, the expressions of the key physical parameter – transition rate (jump rate) in the diffusion can be given from the diffusion theory in solids and the kinetic Monte Carlo (KMC) method, respectively. The transition rate controls the diffusion process and is directly related to the energy of vacancy formation and the energy of migration of atom from density functional theory (DFT). Moreover, from the KMC calculations, the diffusion coefficients for Ni and Al atoms in the γ phase (Ni matrix) and the γʹ phase (intermetallic compound Ni3Al) of the superalloy have been obtained. We propose a strategy of time stepping to deal with the multi-time scale issues. In addition, the influence of temperature and Al concentration on diffusion in dilute alloys is also reported.

Research on KMC-based evolution simulation of dust particles in virtual campus environment

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.

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.

This report presents an accelerated kinetic Monte Carlo (KMC) method to compute the diffusivity of hydrogen in hcp metals and alloys, considering both thermally activated hopping and quantum tunneling. The acceleration is achieved by replacing regular KMC jumps in trapping energy basins formed by neighboring tetrahedral interstitial sites, with analytical solutions for basin exiting time and probability. Parameterized by density functional theory (DFT) calculations, the accelerated KMC method is shown to be capable of efficiently calculating hydrogen diffusivity in α-Zr and Zircaloy, without altering the kinetics of long-range diffusion. Above room temperature, hydrogen diffusion in α-Zr and Zircaloy is dominated by thermal hopping, with negligible contribution from quantum tunneling. The diffusivity predicted by this DFT + KMC approach agrees well with that from previous independent experiments and theories, without using any data fitting. The diffusivity along <c> is found to be slightly higher than that along <a>, with the anisotropy saturated at about 1.20 at high temperatures, resolving contradictory results in previous experiments. Demonstrated using hydrogen diffusion in α-Zr, the same method can be extended for on-lattice diffusion in hcp metals, or systems with similar trapping basins.