Broad-beam low-energy ion bombardment can lead to the spontaneous formation of nanoscale surface structures, but the dominant mechanisms driving evolution remain controversial. Using coherent x-ray scattering to examine the classic case of ion-beam rippling of ${\mathrm{SiO}}_2$ surfaces, we study the relationship between the average kinetics of ripple formation and the underlying fluctuation dynamics. The early stage growth of fluctuations is well fit with a linear theory formalism employing a viscous relaxation term with full wave-number dependence. In this regime, the x-ray photon correlation spectroscopy two-time correlation function shows distinctive behavior with memory stretching back to the beginning of the bombardment. For a given length scale, correlation times do not grow significantly beyond the characteristic time associated with the early-stage ripple growth. In the late stages of patterning, when the average surface structure on a given length scale is no longer evolving, dynamical processes continue on the surface. Nonlinear processes dominate at long length scales, leading to compressed exponential decay of the speckle correlation functions, while at short length scales the dynamics appears to approach a linear behavior consistent with viscous flow relaxation. This behavior is found to be consistent with simulations of a recent nonlinear growth model. In addition, it is shown that the surface ripple velocity, an important parameter of the ion-driven surface evolution, can be measured with coherent x-ray scattering in conjunction with use of an inhomogeneous ion beam. The change in viewpoint exemplified by this study, from a focus on only average surface kinetics to one incorporating the underlying nanoscale dynamics, is rapidly becoming more widely applicable as new and upgraded x-ray sources with higher coherent flux come online.

• Received 14 January 2019
• Corrected 16 July 2019

DOI:https://doi.org/10.1103/PhysRevB.99.165429