Universal non-equilibrium phenomena at submicrometric surfaces and interfaces

Abstract

Abstract. The recent widespread interest in processes occurring at micro and nanometric scales has increased the physical relevance of the surfaces and interfaces constituting system boundaries, both at and far from equilibrium. In the latter case, universal properties occur, such as scale invariance (surface kinetic roughening), surface pattern formation or domain coarsening. However, descriptions of these systems feature limited predictive power when based merely on universality principles. We review examples from Materials Science at nano and submicrometric scales, that underlie the importance of describing growing surfaces by means of (phenomenological) constitutive laws, in order to correctly describe the rich behaviors experimentally found across many different systems. Additionally, this approach provides new generic models that are also of interest in the wider contexts of Pattern Formation and Non-Linear Science.

Self-organized nanopatterning of silicon surfaces by ion beam sputtering

“…In order to see how such an agreement can be obtained, note that continuum equations of the type we are describing apply to the large-scale behavior of the system. As mentioned above, in this limit a great deal of universality frequently occurs [235,195,63]. This means that systems that differ in their microscopic nature may nevertheless display the same large-scale properties.…”

“…MD studies remain typically below 1 ns and 1 mm. With the aim to overcome this and other limitations, it is natural to consider continuum methods, which can probe larger scales in a natural and efficient way [195,196]. In what follows, we will consider this continuum approach with a historical perspective that will allow to appreciate the successive improvements required to reach our present level of understanding of IBS on silicon.…”

Strong anisotropy in surface kinetic roughening: Analysis and experiments

“…This lack of complete knowledge is perhaps one important reason for the relatively moderate experimental impact that this general phenomenon has met, see Ref. 6 and references therein. One such aspect is the phenomenon of anisotropic scaling, namely, when the properties associated with scale invariance in the fluctuations of the surface height change with the substrate direction one is looking along.…”

Strong anisotropy in two-dimensional surfaces with generic scale invariance: Nonlinear effects

“…This characterization might prove useful when invoking universality principles [40,41] in order to put forward a continuum equation for a system featuring SA. To this end, we focus on a number of representative equations, all of which display GSI, and which remained outside the analysis in [30], due to the unavailability of accurate approximations through linear equations for most of the cases.…”