R. Mark Bradley

Theory of ripple topography induced by ion bombardment

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

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.

Phase field model of surface electromigration in single crystal metal thin films

Abstract A phase field model is developed for numerically studying the time evolution of insulating voids in a current-carrying single crystal metal thin film. In our model, we include the effects of surface electromigration, surface self-diffusion and current crowding in the fully nonlinear regime. A continuously varying scalar order parameter is used to describe the metal and void “phases” within the wire in this phase field formulation. The time evolution of the metal–void interface is given by two partial differential equations: one embodying the conserved dynamics of the order parameter and the other a modified Laplace’s equation for the electrical potential. We also carry out detailed asymptotic analysis to verify that our phase field formulation faithfully represents the surface electromigration problem.

Stability of a circular void in a passivated, current‐carrying metal film

We perform a linear stability analysis of a preexisting circular void in a passivated current‐carrying metal thin film. We introduce small perturbations to the shape of a circular void and study the time evolution of these perturbations in two cases. In the first case, we take only current crowding and surface electromigration into account and find that the void relaxes to a nontrivial steady state in which there are slitlike projections from an otherwise circular void. The relaxation time needed to approach this steady state is also calculated. We then include the effect of surface self‐diffusion in our analysis and find that the steady state is a circular void drifting with constant speed. Our calculations indicate that a circular void whose radius is small compared to the line width is stable with respect to small perturbations of its shape in the presence of current crowding, surface electromigration, and surface self‐diffusion.

THEORY OF IMPROVED RESOLUTION IN DEPTH PROFILING WITH SAMPLE ROTATION

We advance a theory that explains why sample rotation during depth profiling leads to a dramatic improvement in depth resolution. When the sample is rotated, the smoothing effects of viscous flow and surface self‐diffusion can prevail over the roughening effect of the curvature‐dependent sputter yield and generate a smooth surface. If the sample is not rotated initially and the depth resolution declines, we predict that subsequent rotation leads to improved resolution. This phenomenon has already been observed experimentally.

Summary Abstract: Theory of thin‐film orientation by ion bombardment during deposition

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Crater function approach to ion-induced nanoscale pattern formation: Craters for flat surfaces are insufficient

In the crater function approach to the erosion of a solid surface by a broad ion beam, the average crater produced by the impact of an ion is used to compute the constant coefficients in the continuum equation of motion for the surface. We extend the crater function formalism so that it includes the dependence of the crater on the curvature of the surface at the point of impact. We then demonstrate that our formalism yields the correct coefficients for the Sigmund model of ion sputtering if terms up to second order in the spatial derivatives are retained. In contrast, if the curvature dependence of the crater is neglected, the coefficients can deviate substantially from their exact values. Our results show that accurately estimating the coefficients using craters obtained from molecular dynamics simulations will require significantly more computational power than was previously thought.

Anomalous patterns and nearly defect-free ripples produced by bombarding silicon and germanium with a beam of gold ions

We demonstrate that surface ripples with an exceptionally high degree of order can develop when germanium is bombarded with a broad beam of gold ions. In contrast, if silicon is sputtered with an Au− beam, patches of ripples with two distinct wave vectors can emerge. These types of order can be understood if the coupling between the surface morphology and composition is taken into account.

Highly ordered nanoscale surface ripples produced by ion bombardment of binary compounds

Nanoscale surface ripples generated by oblique-incidence ion bombardment of a solid are generally full of defects, and this has prevented the widespread adoption of ion bombardment as a nanofabrication tool. We advance a theory that predicts that remarkably defect-free ripples can be produced by ion bombardment of a binary material if the ion species, energy and angle of incidence are appropriately chosen. This high degree of order results from the coupling between the surface height and composition, and cannot be achieved by bombarding an elemental material.

Exact nonstationary solutions to the mean-field equations of motion for two-component Bose–Einstein condensates in periodic potentials

We study the dynamics of two-component Bose–Einstein condensates in periodic potentials in one dimension. Elliptic potentials which have the sinusoidal optical potential as a special case are considered. We construct exact nonstationary solutions to the mean-field equations of motion. Among the solutions are two types of temporally periodic solutions—in one type there are condensate oscillations between neighbouring potential wells, while in the other the condensates oscillate from side to side within the wells. Our numerical studies of the stability of these solutions suggest the existence of one-parameter families of stable nonstationary solutions.