Physical mechanisms affecting critical angle for nanopatterning in irradiated thin films: I. A composite model

Abstract

Ion-beam irradiation of an amorphizable material such as Si or Ge may lead to spontaneous pattern formation, rather than flat surfaces, for irradiation beyond some critical angle against the surface normal. It is observed experimentally that this critical angle varies according to many factors, including beam energy, ion species and target material. In this first part of a set of papers, we consider a composite model of stress-free strain and isotropic swelling with a generalized treatment of stress modification along idealized ion tracks. We obtain a highly-general linear stability result with a careful treatment of arbitrary depth-dependence profiles for each of the stress-free strain-rate tensor, a source of deviatoric stress modification, and isotropic swelling, a source of isotropic stress. We compare our theoretical results with experimental measurements of angle-dependent deviatoric and isotropic stresses for 250eV Ar+ on Si. Our analysis suggests that the presence of angle-independent isotropic stress and the relationship between the amorphous-crystalline and free interfaces may be strong contributors to critical angle selection, while the influence of inhomogeneous stress modification is seemingly non-existent in the idealized case of diagonally-translated interface and stress generated entirely along a thin, down-beam ion track. We also consider an opposing idealization: that of interfaces defined by vertical translation, with stress modification along the vertical regardless of beam orientation. The unacceptable variability in predictions resulting from these two idealizations, both of which have appeared in recent analyses, prompts modeling refinements discussed in subsequent papers in this set. These refinements include the relationship between interfaces and a more sophisticated treatment of the inhomogeneous stress field.