R. Mark Bradley

Bio: R. Mark Bradley is an academic researcher from Colorado State University. The author has contributed to research in topics: Sputtering & Ion beam. The author has an hindex of 23, co-authored 81 publications receiving 2718 citations.

Theory of ripple topography induced by ion bombardment

Abstract: When an amorphous solid is etched by an off‐normal incidence ion beam, a ripple topography often results. A theory explaining the origin of these waves is presented. For incidence angles close to the normal, we find that the ripple wave vector is parallel to the surface component of the beam direction, provided that longitudinal straggling of the beam is not too large. The ripple orientation is rotated by 90° when the beam is close to grazing incidence. The wavelength given by the theory varies as λ∼( f T)−1/2 exp(−ΔE/2kBT) for high temperatures T and low fluxes f, where ΔE is the activation energy for surface self‐diffusion. The predicted magnitude of the wavelength is in reasonable accord with experiments in this regime.

Theory of thin‐film orientation by ion bombardment during deposition

Abstract: We study the development of orientational order in thin films grown with off‐normal incidence ion bombardment during deposition. The overall orientational order in our model results from the dependence of the sputtering yield on grain orientation. We demonstrate that the degree of orientational order at the surface of a thick film grows slowly with increasing ion flux until, at a critical value of the flux, it begins to rise more steeply and then saturates at its maximum value. The time needed to approach the thick‐film limit displays a peak as the ion flux is varied. We compare our work with the experimental results of Yu et al. [Appl. Phys. Lett. 47, 932 (1985)] and use our results to show how the deposition technique can be optimized.

Spontaneous pattern formation induced by ion bombardment of binary compounds.

Abstract: A theory is developed that explains the genesis of the strikingly regular hexagonal arrays of nanoscale mounds that can form when a flat surface of a binary compound is subjected to normal-incidence ion bombardment. We find that the species with the higher sputter yield is concentrated at the peaks of the nanodots and that hysteretic switching between the flat and the hexagonally ordered state can occur as the sample temperature is varied. Surface ripples are predicted to emerge for a certain range of the parameters.

Diffusion in a two-dimensional channel with curved midline and varying width: reduction to an effective one-dimensional description.

Abstract: Diffusion in a narrow two-dimensional channel with a midline that need not be straight and a width that may vary is reduced to an effective one-dimensional equation of motion. This equation takes the form of the Fick-Jacobs equation with a spatially varying effective diffusivity. The effective diffusivity includes a contribution that comes from the slope of the midline as well as the usual term stemming from variations in the channel width along the length of the channel. Our derivation of our equation of motion is completely rigorous and is based on an asymptotic expansion in a small dimensionless parameter that characterizes the channel width. For a channel that has a straight midline or wall, our equation of motion reduces to Zwanzig's equation [R. Zwanzig, J. Phys. Chem. 96, 3926 (1992)]. Our derivation therefore provides a rigorous proof of the validity of the latter equation. Finally, the equation of motion is solved analytically for channels with curved midline and constant width.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Abstract: to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Phase-Field Models for Microstructure Evolution

Abstract: ■ Abstract The phase-field method has recently emerged as a powerful computational approach to modeling and predicting mesoscale morphological and microstructure evolution in materials. It describes a microstructure using a set of conserved and nonconserved field variables that are continuous across the interfacial regions. The temporal and spatial evolution of the field variables is governed by the Cahn-Hilliard nonlinear diffusion equation and the Allen-Cahn relaxation equation. With the fundamental thermodynamic and kinetic information as the input, the phase-field method is able to predict the evolution of arbitrary morphologies and complex microstructures without explicitly tracking the positions of interfaces. This paper briefly reviews the recent advances in developing phase-field models for various materials processes including solidification, solid-state structural phase transformations, grain growth and coarsening, domain evolution in thin films, pattern formation on surfaces, dislocation microstructures, crack propagation, and electromigration.

Microstructural evolution during film growth

Abstract: Atomic-scale control and manipulation of the microstructure of polycrystalline thin films during kinetically limited low-temperature deposition, crucial for a broad range of industrial applications, has been a leading goal of materials science during the past decades. Here, we review the present understanding of film growth processes—nucleation, coalescence, competitive grain growth, and recrystallization—and their role in microstructural evolution as a function of deposition variables including temperature, the presence of reactive species, and the use of low-energy ion irradiation during growth.

Formation of Ordered Nanoscale Semiconductor Dots by Ion Sputtering.

Abstract: A formation process for semiconductor quantum dots based on a surface instability induced by ion sputtering under normal incidence is presented. Crystalline dots 35 nanometers in diameter and arranged in a regular hexagonal lattice were produced on gallium antimonide surfaces. The formation mechanism relies on a natural self-organization mechanism that occurs during the erosion of surfaces, which is based on the interplay between roughening induced by ion sputtering and smoothing due to surface diffusion.