George H. Gilmer

Colorado School of Mines · Department of Mechanical Engineering

Atomistic models are advancing our understanding of crystal growth at an increasing rate, benefiting from rapidly increasing computational power. This chapter discusses Monte Carlo simulations that are focused on fundamental aspects of film deposition on foreign substrates. The simulations demonstrate the influence on film nucleation and growth of...

This article reviews the main theoretical/computational techniques and the experimental characterization methodologies that are used in the quest to investigate the shape, size, composition, and crystallography of metallic nanoparticles. Two morphological regimes are described, one governed by equilibrium thermodynamics, and another in which the sh...

The design and synthesis of shape-directed nanoscale noble metal particles have attracted much attention due to their enhanced catalytic properties and the opportunities to study fundamental aspects of nanoscale systems. As such, numerous methods have been developed to synthesize crystals with tunable shapes, sizes, and facets by adding foreign spe...

Fibrillar collagens, common tissue scaffolds in live organisms, can also self-assemble {\em in vitro} from solution. While previous {\em in vitro} studies showed that the pH and the electrolyte concentration in solution largely control the collagen assembly, the physical reasons why such control could be exerted are still elusive. To address this i...

Vapour-liquid-solid route and its variants are routinely used for scalable synthesis of semiconducting nanowires, yet the fundamental growth processes remain unknown. Here we employ atomic-scale computations based on model potentials to study the stability and growth of gold-catalysed silicon nanowires. Equilibrium studies uncover segregation at th...

Supplementary Figures S1-S6, Supplementary Notes 1 and 2, Supplementary Methods and Supplementary References

The growth dynamics at the droplet-nanowire interface for initial droplet composition XSi=0.48. The animation spans 450 configurations spaced 10 ps apart. The colour scheme is modified to better identify Si atoms nucleating on the truncating facets. Specifically, the atoms nucleating close to the contact line are shaded light blue and the intensity...

As for Supplementary Movie 1, but for XSi=0.463. The animation spans 350 configurations spaced 10 ps apart.

A multi-atom gas bubble-nucleation mechanism has been proposed as part of a predictive fission-gas release model for metallic nuclear fuels. Validation of this mechanism requires experimental measurement of fission-gas bubble-size distributions at well-controlled gas concentrations and temperatures. There are advantages to carrying out such a study...

We have applied a model for lattice and grain boundary diffusion in polycrystalline materials to assess the potential for the use of fission gas release experiments to measure the lattice and grain boundary diffusion coefficients in metallic nuclear fuel materials. Our assessment is that, assuming that grain boundary diffusion in metallic fuels is...

A new atomistic scheme for simulating polycrystalline thin film deposition based on a Monte Carlo approach has been developed. Simulations of polycrystalline aluminum deposition and annealing at different temperatures are presented. The time evolution of the film morphology for those temperatures is discussed. During deposition, columnar growth is...

Monte Carlo simulations of physical and chemical vapor deposition are used to study roughening kinetics of films that grow by nucleation and coalescence of clusters. The effects of interlayer transport, preferential dissociation of molecular precursors and energetic differences between the clusters and the substrate are examined.

The development of future Si device technologies will rely extensively on modeling, requiring truly predictive tools. Here we focus on the front-end processes, during which ion-implantation and annealing create 3-D impurity profiles that determine crucial electrical device parameters. The final configuration is the result of a complex interaction o...

The equilibrium configurations of monolayer films on crystalline substrates have been investigated using molecular dynamics techniques. Misfit dislocation densities are found to differ from those predicted by elasticity theory, because of the more realistic interatomic potential employed in the simulations (Lennard-Jones), and the absence of constr...

We have performed 2D and quasi-3D numerical simulations of physical vapor deposition (PVD) into high aspect ratio trenches and vias used for modern VLSI interconnects. The topographic evolution is modeled using (continuum) level set methods. The level set approach is a powerful computational technique for accurately tracking moving interfaces or bo...

An atomistic model for B implantation, diffusion and clustering is presented. The model embodies the usual mechanism of Si self-interstitial diffusion and B kick-out and also includes the formation of immobile precursors of B clusters prior to the onset of transient enhanced diffusion. These immobile complexes, such as BI2 (a B atom with two Si sel...

We present experimental results directed at understanding the growth and structure of metallic barrier layer and interconnect films. Numerical simulation results associated with this experimental work are presented in an accompanying paper in these proceedings. Here, thin films of Al, Ti, Cu and Ta have been grown by magnetron sputtering onto oxidi...

We have mapped out the energy surfaces seen by a single silicon adatom over the Si(100) surface and Si(100) steps, using Molecular Dynamics methods. This identifies the most likely binding sites as well as the activation energies for diffusion over the terraces and steps. We find that only the 5e step with no rebonded atoms is a good sink for adato...

The ability to make highly doped δ-layers in semiconductors depends on the rate of interchange of atoms between layers at the crystal surface. We have simulated molecular beam epitaxy on a silicon (100) surface covered with a monolayer of impurity atoms. The kinetics of impurity segregation to the surface was examined for various growth conditions...

We discuss simulators of the deposition of metal films onto substrates containing vias and trenches. Our Monte Carlo simulations of Al are based on extensive first-principles and molecular dynamics (MD) data for atomic-level energetics and transport rates. We find that surface mobilities are highly anisotropic, and that this has a pronounced influe...

We compare force fields (FF's) that have been used in molecular dynamic (MD) simulations of silica in order to assess their applicability for use in simulating IR-laser damage mitigation. Although pairwise FF's obtained by fitting quantum mechanical calculations such as the BKS and CHIK potentials have been shown to reproduce many of the properties...

We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo (FPKMC) algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions. The FPKMC algorithm presented here is based on the method introduced in Oppelstrup et al. [10] and is implemented in a...

The growth of uniform thin films on foreign substrates is impeded by several morphological instabilities. Hill-and-valley structures are formed and enhanced during sputter deposition where surface height perturbations have an opportunity to grow to large amplitudes. We show via kinetic Monte Carlo (kMC) simulations that while surface roughness can...

The classical terrace-ledge-kink model of crystal growth is widely used to interpret mineral formation in biological and geological systems. A key assumption underlying application of the model is that thermal fluctuations of steps are sufficiently rapid to produce an abundance of kink sites for attachment of growth units. High-resolution in situ a...

We present an efficient method for Monte Carlo simulations of diffusion-reaction processes. Introduced by us in a previous paper [Phys. Rev. Lett. 97, 230602 (2006)], our algorithm skips the traditional small diffusion hops and propagates the diffusing particles over long distances through a sequence of superhops, one particle at a time. By partiti...

We utilize a novel computational approach to model the problem of impurity segregation at grain boundaries in nanophase materials. It is based on a parallel MonteCarlo algorithm that places the impurities according to the local chemical potential for the species, following the thermodynamic driving force for segregation. This technique is combined...

The relation between stress evolution and surface morphology during deposition of sputtered films is examined by combining kinetic Monte Carlo simulations and stress measurements. We find that the surface morphology is susceptible to an instability, which transforms from layer-by-layer growth to the formation of pillarlike columns. The gaps between...

The use of macromolecular scaffolds for hierarchical organization of molecules and materials is a common strategy in living systems that leads to emergent behavior. One characteristic of this strategy is that it generates micron-scale structures from nm-scale building blocks, possessing high-density functionality, defined at angstrom-scales by acti...

The versatility of genetic algorithms for determining the atomic structure of clusters has been well established starting with the seminal article of Deaven and Ho (Physical Review Letters 75, 288, 1995). The genetic algorithm approach has also been extended to spatially periodic structures where it has been recognized that the variation of the num...

In order to provide insight into coarsening mechanisms of pentaerythritol tetranitrate (PETN), we performed kinetic Monte Carlo (KMC) simulations of evaporation from the predominantly exposed (1 1 0) surface. Our KMC simulations show that different surface structures, such as islands and straight step segments, move in very different ways during ev...

We have carried out atomistic simulations of grain-grain collisions for spherical grains of 1.4 and 4 nm radii, with relative velocities of 3.6–6.1 km/s and a number of impact parameters. Since the initial grains are crystallites without any pre-existing defects, grain shattering due to nucleation of cracks was not observed in our simulations. We f...

Atomistic simulations of grain-grain collisions have been carried out for spherical grains of 1.4 and 4 nm radii with relative velocities of 3.6--6.1 km/s and a number of random impact parameters. Since the initial grains are crystallites without any pre-existing defects, grain shattering due to nucleation of cracks was not observed in our simulati...

IntroductionThe Kinetic SOS ModelSimple Theories for the Dynamics of Crystal GrowthNucleation Theory of Crystal GrowthThe Surface at Equilibrium and the Roughening TransitionDynamics of the Roughening TransitionSpiral Growth and the Influence of Line DefectsImpuritiesFinal Remarks

We study sputtering by 100 eV deuterium irradiation on deuterated amorphous carbon layers at 300 K using molecular dynamics (MD) simulations. Two main results are reported here. First, a special mechanism for carbon release—additional to and distinct from the standard definitions for physical and chemical sputtering of carbon by hydrogen isotopes—h...

We unveil a principally new Monte Carlo algorithm for simulations of multiple diffusing particles of finite dimensions that coalesce or annihilate on collisions. The algorithm is derived from the theory of first-passage processes and a time-dependent Green's function formalism. The new method circumvents the need for long and tedious diffusion hops...

The lack of detailed knowledge of internal process conditions remains a key challenge in magnetron sputtering, both for chamber design and for process development. Fundamental information such as the pressure and temperature distribution of the sputter gas, and the energies and arrival angles of the sputtered atoms and other energetic species is of...

We present a novel Monte Carlo algorithm for N diffusing finite particles that react on collisions. Using the theory of first-passage processes and time dependent Green's functions, we break the difficult N-body problem into independent single- and two-body propagations circumventing numerous diffusion hops used in standard Monte Carlo simulations....

We discuss recent experimental and theoretical results on ultrafast materials dynamics. Intense, femtosecond lasers can deposit energy in a time that is short compared with relaxation processes and can generate extremely large carrier densities that drive bond softening, nonthermal melting, and ablation. In particular, we present optical experiment...

Starting from an accurate inter-atomic potential we develop a simple scheme of generating an ``on-lattice''molecular potential of short range, which is then incorporated into a lattice Monte Carlo code for simulating size and shape evolution of nanocrystallites. As a specific example, we test such a procedure on the morphological evolution of a mol...

The interaction of edge plasma with material surfaces raises key issues for the viability of the international thermonuclear reactor (ITER) and future fusion reactors, including heat-flux limits, net material erosion and impurity production. After exposure of the graphite divertor plates to the plasma in a fusion device, an amorphous C/H layer form...

We apply a hybrid Monte Carlo-molecular dynamics code to the study of grain boundary motion upon annealing of pure Cu and Cu with low concentrations of Fe. The hybrid simulations account for segregation and precipitation of the low solubility Fe, together with curvature-driven grain boundary motion. Grain boundaries in two different systems, a Sigm...

Low-temperature crystal growth techniques can deposit silicon films with impurity concentration orders of magnitude above their bulk solubility limits. First-principles calculations were performed of the energies (relative to the bulk) of single substitutional carbon, germanium, boron, and arsenic atoms at several positions within a thin (100) slab...

We present an extensive first-principles study of the pressure dependence of the formation enthalpies of all the know vacancy and self-interstitial configurations in silicon, in each charge state from -2 through +2. The neutral vacancy is found to have a formation volume that varies markedly with pressure, leading to a remarkably large negative val...

Monte Carlo (MC) is a very general computational technique that can be used to carry out sampling of distributions. Random numbers are employed in the sampling, and often in other parts of the code. One definition of MC based on common usage in the literature is, any calculation that involves significant applications of random numbers. Historical a...

A set of simulation models is under development to describe impurity production and transport, especially hydrocarbons, in tokamaks. The set is designed for use with either a developing kinetic code (see adjacent papers) or a fluid code for the main hydrogenic fuel ions and electrons. Three regions are treated: surface sputtering, near-surface tran...

Kinetic effects are important in the boundary plasma because the mean-free-path is often larger than the connection length, while the radial width of trapped particle orbits is similar in width to the H-mode pedestal. We are developing a hydrogen and electron continuum gyro-kinetic model of the boundary plasma over a region extending from inside th...

In this paper we discuss atomistic Monte Carlo simulations of thin film microstructure evolution. We discuss physical vapor deposition, and are primarily concerned with the nucleation and coalescence of three-dimensional islands and their effect on film morphology. We discuss some fundamental issues associated with thin film formation, together wit...

No abstract prepared.

It is known that atoms being deposited onto a substrate can be manipulated using laser beams before deposition and form periodic structures [1]. This effect is due to interaction of induced dipole moments of atoms with the standing wave of the laser beams. More recently, periodic pattern formation after deposition caused by anisotropic diffusion du...

We present results of modeling and simulation of sputter-deposited thin films used for barrier and seed layers for the metalization stage of integrated circuits. We employ a continuum model in conjunction with the level set method for simulating the motion of the interface. An important physical input in our code is the angular distribution of the...

The authors have discussed computer models of crystal surfaces and the transport of material by diffusion along these surfaces. Phase transitions involving changes in the surface structure have been described together with their influence on the diffusion process. Neither surface roughening nor the formation of a quasi-liquid layer produced an anom...

We have combined experiments and atomistic modeling in order to better understand the growth and structure of metal films deposited onto sidewalls of trenches and vias. Using x-ray reflectance, atomic force microscopy, and high-resolution transmission electron microscopy to characterize the microstructure and morphology of Ta films grown by magnetr...

An atomistic Monte Carlo code to simulate the deposition and annealing of three-dimensional polycrystalline thin films is presented. Atoms impinge on the substrate with selected angular distributions, and grains are nucleated with different crystalline orientations, defined by the tilt and rotation angles. Grain boundaries appear naturally when the...

We propose an atomistic model to describe the evolution of the damage generated by irradiation in Si, going from isolated point defects to the formation of continuous amorphous layers. The elementary units used to reproduce the defective zones are Si interstitials, vacancies and the bond defect, which is a local distortion of the Si lattice without...

We propose an atomistic model to describe the damage generation during ion irradiation in Si and its evolution upon anneal. We have included new features to the classical models used to describe damage in crystalline Si, that allow us to extend the atomistic approach to the modeling of continuous amorphous layers. The elementary units to describe t...

Targets to study high-energy density physics and inertial confinement fusion processes have very specific and precise tolerances that are pushing the state-of-the-art in mesoscale microsculpting technology. A significant effort is required in order to advance the capabilities to make these targets with very challenging geometries. Ultrashort pulsed...

A transmission electron microscope capable of identifying individual atoms or defects in a crystal lattice has much to offer materials scientists. It has now been used to study the early stages of nanocluster nucleation and growth in semiconductors.

We show that surface evolution resulting from the deposition of discrete particles is intrinsically different from that produced by continuum processes. The atomistic effects have major consequences, even when observed at macroscopic length scales. We have elucidated some of the atomistic effects by comparing: (i) numerical simulations of thin film...

Carbon often appears in Si in concentrations above its solubility. In this article, we propose a comprehensive model that, taking diffusion and clustering into account, is able to reproduce a variety of experimental results. Simulations have been performed by implementing this model in a Monte-Carlo atomistic simulator. The initial path for cluster...

In order to investigate the nature of defects produced by ion irradiation through a heterostructure, a silicon-on-insulator substrate with a buried SiO2 layer at a depth of ∼1.5 μm was irradiated. The implantation was done using 2 MeV 28Si+ ions in the dose range of 0.2–1×1016 cm−2. The subsequent defect analysis was performed using the Au labeling...

In this paper, we describe an implementation of grain boundary migration in the atomistic simulator of thin film deposition (ADEPT), and apply the simulator to study effects of the grain boundary migration on texture evolution. In the implementation, atoms are classified into two categories: those belong to a single grain and those at grain boundar...

In this paper we discuss methods to obtain high dopant concentrations during processing of Si devices. The possibility of increasing the solubility of B in Si by misfit stress is investigated. The enthalpy of B atoms is calculated, with and without stress, using density functional theory. A second approach, the trapping of excess dopant atoms durin...

We performed a theoretical investigation on the properties of iron–acceptor impurity pairs (Fe–A, with A=B , Al, Ga, and In) in silicon. The calculations were performed within the framework of an ionic model, including elastic and electrostatic interactions. In contrast to the conventional point charge ionic model, our model includes a correction t...

Measurements of the binding energy (Eb) of vacancies to vacancy clusters formed in silicon following high-energy ion implantation are reported. Vacancy clusters were created by 2 MeV, 2×1015 cm−2 dose Si implant and annealing. To prevent recombination of the excess vacancies (Vex) with interstitials from the implant damage near the projected range...

Using molecular-dynamics simulation techniques, we have investigated the role that point defects and interstitial-vacancy complexes have on the silicon amorphization process. We have observed that accumulation of interstitial-vacancy complexes in concentrations of 25% and above lead to homogeneous amorphization. However, we have determined the basi...

We discuss atomistic simulations of ion implantation and annealing of Si over a wide range of ion dose and substrate temperatures. The DADOS Monte Carlo model has been extended to include the formation of amorphous regions, and this allows simulations of dopant diffusion at high doses. As the dose of ions increases, the amorphous regions formed by...

Metallization is the back end of the integrated-circuit (IC) fabrication process where the transistor interconnections are formed. Figure 1 shows the metallized part of a static random-access memory chip. Metal lines for electrical connections (Al and Cu) in Si devices are deposited as blanket films and then etched or polished away to define the co...

This letter contains some calculations of the thermodynamic properties of lattice model interfaces. The work is compared with that reported recently by Hunt and Gale (see abstr. A16653 of 1974). Their results are shown to be greatly influenced by their restrictive limitation of the interface width.

A Monte Carlo dopant diffusion simulation program has been developed which includes charged species, Fermi-level effects on drift-diffusion and clustering reactions. An algorithm that determines variable time steps was improved to account for all the Fermi-level dependent quantities, such as different charge states of point-defects, pairs and compl...

We discuss atomistic simulations of ion implantation and annealing of Si over a wide range of ion dose and substrate temperatures. The DADOS Monte Carlo model has been extended to include the formation of amorphous regions, and this allows simulations of dopant diffusion at high doses. As the dose of ions increases, a continuous amorphous layer may...

We have performed two-dimensional (2D) and three-dimensional (3D) (axisymmetric) numerical simulations of physical vapor deposition into high aspect ratio trenches and vias used for modern very large-scale integration interconnects. The topographic evolution is modeled using (continuum) level set methods. The level set approach is a powerful comput...

In this paper, we review the principles and the applications of an atomistic simulator for thin film deposition (ADEPT), which is a hybrid of classical molecular dynamics and lattice Monte Carlo methods. Molecular dynamics is used to study details of the atomic movement, whereas lattice Monte Carlo method is used to simulate the long time evolution...

Simulation of front-end processing is a critical component of integrated-circuit (IC) technology development. Today's electronics are so small that characterization of their material parameters is very difficult and expensive. Simulation is often the only effective tool for exploring the lateral and vertical doping profiles of a modern device at th...

Monte Carlo models of crystal growth have contributed to the theoretical understanding of thin film deposition, and are now becoming available as tools to assist in device fabrication. Because they combine efficient computation and atomic-level detail, these models can be applied to a large number of crystallization phenomena. They have played a ce...

Kinetic Monte Carlo (KMC) atomistic process simulations mimic the jumps and interactions of individual atoms, based on jump rates derived from ab initio calculations or experiments. By only following ‘defect’ atoms (unlike molecular dynamics), KMC can simulate the typical long annealing times (seconds to hours) used in materials processing. Thus, i...

The properties of thin films grown by sputtering are sensitive to the conditions in the deposition chamber. In particular, the Ar pressure affects the kinetic energies of Ar atoms and sputtered particles as they impinge on the growing film. In this talk, we present kinetic Monte Carlo simulations of thin film deposition which include these energeti...