Simulation of nanoscale patterns yielded by ion bombardment of solid surfaces

Pearson, Daniel A., author
Bradley, Mark, advisor
Buchanan, Kristen, committee member
Gelfand, Martin, committee member
Shipman, Patrick, committee member
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This thesis includes numerical investigations into two topics of self-organized topographies produced on solid surfaces that are bombarded with a broad ion beam. The first topic is the formation of terraces. When a surface is bombarded at relatively large angles of incidence, the surface often develops facets that are characterized by large regions of nearly constant gradient in height, which are called terraces. The second topic is related to the observation that when the surface of a nominally flat binary material is bombarded with a broad, normally-incident ion beam, disordered hexagonal arrays of nanodots can form. Shipman and Bradley have derived equations of motion that govern the coupled dynamics of the height and composition of such a surface [P. D. Shipman and R. M. Bradley, Phys. Rev. B 84, 085420 (2011)]. We investigate the influence of initial conditions on the hexagonal order yielded by integration of those equations of motion. In our work on terrace formation, we introduce a model that includes an improved approximation to the sputter yield and that produces a terraced surface morphology at long times for a wide range of parameter values. Numerical integrations of our equation of motion reveal that the terraces coarsen for a finite amount of time after which the coarsening is interrupted, just as observed experimentally. We also show that the terrace propagation direction can reverse as the amplitude of the surface disturbance grows. This highlights the important role higher order nonlinearities play in determining the propagation velocity at high fluences. We study the nanoscale terraced topographies that arise when a solid surface is bombarded with a broad ion beam that has a relatively high angle of incidence θ. Our simulations establish that the surfaces exhibit interrupted coarsening, i.e., the characteristic width and height of the surface disturbance grow for a time but ultimately asymptote to finite values as the fully terraced state develops. In addition, as θ is reduced, the surface can undergo a transition from a terraced morphology that changes little with time as it propagates over the surface to an unterraced state that appears to exhibit spatiotemporal chaos. For different ranges of the parameters, our equation of motion produces terraced topographies that are remarkably similar to those seen in various experiments, including pyramidal structures that are elongated along the projected beam direction and isolated lenticular depressions. For our study of the influence of prepatterning surfaces governed by the Bradley-Shipman equations, the initial conditions studied are hexagonal and sinusoidal templates, straight scratches and nominally flat surfaces. Our simulations indicate that each of the prepatterned surfaces can lead to marked improvements in the hexagonal order compared to what is obtained from the nominally flat surfaces. For the hexagonal and sinusoidal templates with amplitude approximately equal to one hundredth of the amplitude of the pattern obtained at late times, the greatest improvement in order is obtained if the initial wavelength is approximately equal to or double the linearly selected wavelength. Our simulations of sinusoidal templates demonstrate that increasing the amplitude of the template can improve the effectiveness of templates with longer wavelengths. Scratches enhance the hexagonal order in their vicinity if their width is close to or less than the linearly selected wavelength. Our results suggest that prepatterning a binary material can dramatically increase the hexagonal order achieved at large ion fluences.
2018 Spring.
Includes bibliographical references.
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