Crater functions for compound materials: A route to parameter estimation in coupled-PDE models of ion bombardment

Abstract

During the ion bombardment of targets containing multiple component species, highly-ordered arrays of nanostructures are sometimes observed. Models incorporating coupled partial differential equations, describing both morphological and chemical evolution, seem to offer the most promise of explaining these observations. However, these models contain many unknown parameters, which must satisfy specific conditions in order to explain observed behavior. The lack of knowledge of these parameters is therefore an important barrier to the comparison of theory with experiment.Here, by adapting the recent theory of "crater functions" to the case of binary materials, we develop a generic framework in which many of the parameters of such models can be estimated using the results of molecular dynamics simulations.As a demonstration, we apply our framework to the recent theory of Bradley and Shipman, for the case of Ar-irradiated GaSb, in which ordered patterns were first observed. In contrast to the requirements therein that sputtered atoms form the dominant component of the collision cascade, and that preferential redistribution play an important stabilizing role, we find instead that the redistributed atoms dominate the collision cascade, and that preferential redistribution appears negligible. Hence, the actual estimated parameters for this system do not seem to satisfy the requirements imposed by current theory, motivating the consideration of other potential patternforming mechanisms.

Self-organized nanopatterning of silicon surfaces by ion beam sputtering

“…Additional results have been obtained, such as the rotation of the ripple pattern for sufficiently glancing incidence angles [191]. More recently, this approach has been also adapted to the case of binary targets [192]. In this work many parameters of the differential equations describing the irradiation of binary materials (see Section 5.2.2) have been estimated.…”

“…Nevertheless, the assumed origin for the necessary morphological instability is still the BH mechanism, which does not seem likely for mono-elemental targets at small incidence angles, as we have seen above. Likewise, MD simulations employing crater functions seem to question the numerical importance of the BH mechanism under such conditions, as shown in [133] and [246] for Ar-irradiated Si and GaSb, respectively. In these works, the parameters controlling the sputtering and the preferential redistributions are estimated and do not satisfy the requirements to induce the ordered pattern formation obtained in the Bradley and Shipman's models.…”

Theory of nanoscale pattern formation produced by oblique-incidence ion bombardment of binary compounds

“…Equation (30) would reduce to the anisotropic Kuramoto-Sivashinsky (AKS) equation if the term φ were removed from its right-hand side. Thus, in our nonlinear equations of motion (30) and (31), the usual AKS equation for the surface height is coupled to the dynamics of the surface composition.…”

“…(30) and (31). We will omit any additional nonlinear terms in the interest of simplicity, and so that the theory reduces to the BS theory for the case of normal-incidence bombardment.…”

“…He finds that phase separation can lead to a narrow band of linearly unstable wavelengths even if the BH effect is negligible. Using molecular dynamics simulations combined with the crater function formalism [29], Norris and his co-workers have also estimated some of the coefficients that appear in the BS equations of motion [30]. Their results seem to show that in the case of GaSb, the BH effect and differential ballistic mass distribution are negligible.…”