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

TL;DR

This paper extends crater function theory to binary materials, providing a framework to estimate unknown parameters in coupled PDE models of ion bombardment, demonstrated on GaSb with insights into pattern formation mechanisms.

Contribution

It develops a generic framework for parameter estimation in coupled PDE models of ion bombardment for binary materials using molecular dynamics simulations.

Findings

Redistributed atoms dominate the collision cascade in GaSb.

Preferential redistribution appears negligible in this system.

Estimated parameters challenge current pattern formation theories.

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 pattern-forming mechanisms.