B. H. Cooper

Bio: B. H. Cooper is an academic researcher from Cornell University. The author has contributed to research in topics: Scattering & Ion. The author has an hindex of 18, co-authored 53 publications receiving 1106 citations.

Gibbs-Thomson formula for small island sizes: Corrections for high vapor densities.

Abstract: In this paper we report simulation studies of equilibrium features, namely, circular islands on model surfaces, using Monte Carlo methods. In particular, we are interested in studying the relationship between the density of vapor around a curved island and its curvature. The ``classical'' form of this relationship is the Gibbs-Thomson formula, which assumes that the vapor surrounding the island is an ideal gas. Numerical simulations of a lattice gas model, performed for various sizes of islands, do not fit very well to the Gibbs-Thomson formula. We show how corrections to this form arise at high vapor densities, wherein a knowledge of the exact equation of state (as opposed to the ideal-gas approximation) is necessary to predict this relationship. By exploiting a mapping of the lattice gas to the Ising model, one can compute the corrections to the Gibbs-Thomson formula using high field series expansions. The corrected Gibbs-Thomson formula matches very well with the Monte Carlo data. We also investigate finite size effects on the stability of the islands both theoretically and through simulations. Finally, the simulations are used to study the microscopic origins of the Gibbs-Thomson formula. It is found that smaller islands have a greater adatom detachment rate per unit length of island perimeter. This is principally due to a lower coordination of edge atoms and a greater availability of detachment moves relative to edge moves. A heuristic argument is suggested in which these effects are partially attributed to geometric constraints on the island edge. \textcopyright{} 1996 The American Physical Society.

Decay of isolated surface features driven by the Gibbs-Thomson effect in an analytic model and a simulation

Abstract: A theory based on the thermodynamic Gibbs-Thomson relation is presented that provides the framework for understanding the time evolution of isolated nanoscale features (i.e., islands and pits) on surfaces. Two limiting cases are predicted, in which either diffusion or interface transfer is the limiting process. These cases correspond to similar regimes considered in previous works addressing the Ostwald ripening of ensembles of features. A third possible limiting case is noted for the special geometry of {open_quotes}stacked{close_quotes} islands. In these limiting cases, isolated features are predicted to decay in size with a power-law scaling in time: A{proportional_to}(t{sub 0}{minus}t){sup n}, where A is the area of the feature, t{sub 0} is the time at which the feature disappears, and n=2/3 or 1. The constant of proportionality is related to parameters describing both the kinetic and equilibrium properties of the surface. A continuous-time Monte Carlo simulation is used to test the application of this theory to generic surfaces with atomic scale features. A method is described to obtain macroscopic kinetic parameters describing interfaces in such simulations. Simulation and analytic theory are compared directly, using measurements of the simulation to determine the constants of the analytic theory. Agreement between the two is very goodmore » over a range of surface parameters, suggesting that the analytic theory properly captures the necessary physics. It is anticipated that the simulation will be useful in modeling complex surface geometries often seen in experiments on physical surfaces, for which application of the analytic model is not straightforward. {copyright} {ital 1997} {ital The American Physical Society}« less

Simulations of energetic beam deposition: From picoseconds to seconds

Abstract: We present a method for simulating crystal growth by energetic beam deposition. The method combines a kinetic Monte Carlo simulation for the thermal surface diffusion with a small scale molecular-dynamics simulation of every single deposition event. We have implemented the method using the effective medium theory as a model potential for the atomic interactions, and present simulations for Ag/Ag(111) and Pt/Pt(111) for incoming energies up to 35 eV. The method is capable of following the growth of several monolayers at realistic growth rates of 1 ML per second, correctly accounting for both energy-induced atomic mobility and thermal surface diffusion. We find that the energy influences island and step densities and can induce layer-by-layer growth. We find an optimal energy for layer-by-layer growth (25 eV for Ag), which correlates with where the net impact-induced downward interlayer transport is at a maximum. A high step density is needed for energy-induced layer-by-layer growth, hence the effect dies away at increased temperatures, where thermal surface diffusion reduces the step density. As part of the development of the method, we present molecular-dynamics simulations of single atom-surface collisions on flat parts of the surface and near straight steps, we identify microscopic mechanisms by which the energy influences the growth, and we discuss the nature of the energy-induced atomic mobility.

X-Ray Scattering Study of the Surface Morphology of Au(111) during Ar + Ion Irradiation

Abstract: Using real-time x-ray scattering to measure the surface morphology of Au(111) during sputter erosion with 500 eV Ar ions, we observe three distinct regimes: three-dimensional rough erosion at 20–60 ±C, quasi-layer-by-layer removal at 120–220 ±C, and step retraction above 270 ±C. Sputtering at 20–60 ±C leads to pattern formation with a characteristic spacing between features. The average separation l between features increases with time t, consistent with a power law l , t0.2760.02. The observations are consistent with the predictions of a continuum model for deposition which includes an EhrlichSchwoebel barrier to the interlayer diffusion of surface defects. [S0031-9007(98)06122-5]

Kinetic Monte Carlo molecular dynamics investigations of hyperthermal copper deposition on Cu(111)

Abstract: Detailed kinetic Monte Carlo--molecular dynamics (KMC-MD) simulations of hyperthermal energy (10--100 eV) copper homoepitaxy reveal a reentrant layer-by-layer growth mode at low temperatures (50 K) and reasonable fluxes (1 ML/s. where ML stands for monolayer). This growth mode is the result of atoms with hyperthermal kinetic energies becoming inserted into islands when the impact site is near a step edge. The yield for atomic insertion as calculated with molecular dynamics near (111) step edges reaches a maximum near 18 eV. KMC-MD simulations of growing films find a minimum in the rms roughness as a function of energy near 25 eV. We find that the rms roughness saturates just beyond 0.5 ML of coverage in films grown with energies greater than 25 eV due to the onset of adatom-vacancy formation near 20 eV. Adatom-vacancy pairs increase the island nuclei density and the step-edge density, which increase the number of sites available to insert atoms. Smoothest growth in this regime is achieved by maximizing island and step-edge densities, which consequently reverses the traditional roles of temperature and flux: low temperatures and high fluxes produce the smoothest surfaces in these films. Dramatic increases in island densities are found to persist at room temperature, where island densities increase an order of magnitude from 20 to 150 eV.

Collective and single particle diffusion on surfaces

Abstract: We review in this article the current theoretical understanding of collective and single particle diffusion on surfaces and how it relates to the existing experimental data. We begin with a brief survey of the experimental techniques that have been employed for the measurement of the surface diffusion coefficients. This is followed by a section on the basic concepts involved in this field. In particular, we wish to clarify the relation between jump or exchange motion on microscopic length scales, and the diffusion coefficients which can be defined properly only in the long length and time scales. The central role in this is played by the memory effects. We also discuss the concept of diffusion under nonequilibrium conditions. In the third section, a variety of different theoretical approaches that have been employed in studying surface diffusion such as first principles calculations, transition state theory, the Langevin equation, Monte Carlo and molecular dynamics simulations, and path integral formalism...

Making waves: Kinetic processes controlling surface evolution during low energy ion sputtering

Abstract: When collimated beams of low energy ions are used to bombard materials, the surface often develops a periodic pattern or “ripple” structure. Different types of patterns are observed to develop under different conditions, with characteristic features that depend on the substrate material, the ion beam parameters, and the processing conditions. Because the patterns develop spontaneously, without applying any external mask or template, their formation is the expression of a dynamic balance among fundamental surface kinetic processes, e.g., erosion of material from the surface, ion-induced defect creation, and defect-mediated evolution of the surface morphology. In recent years, a comprehensive picture of the different kinetic mechanisms that control the different types of patterns that form has begun to emerge. In this article, we provide a review of different mechanisms that have been proposed and how they fit together in terms of the kinetic regimes in which they dominate. These are grouped into regions of behavior dominated by the directionality of the ion beam, the crystallinity of the surface, the barriers to surface roughening, and nonlinear effects. In sections devoted to each type of behavior, we relate experimental observations of patterning in these regimes to predictions of continuum models and to computer simulations. A comparison between theory and experiment is used to highlight strengths and weaknesses in our understanding. We also discuss the patterning behavior that falls outside the scope of the current understanding and opportunities for advancement.