Nanoscale kinetics and dynamics during Ar+ patterning of SiO2

Abstract

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 SiO2 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 wavenumber dependence. In this regime, the x-ray photon correlation spectroscopy (XPCS) two-time correlation function shows novel 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 the anisotropic Kuramoto-Sivashinsky equation. 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.

X-Ray Photon Correlation Spectroscopy with Coherent Nanobeams: A Numerical Study

“…However, for systems that use 'mesoscopic' real space simulations to describe their properties, very large matrices (or a high density of points in real space) may be necessary to extract portions of these simulations with enough number of points and calculate the expected scattered signal when using a nanobeam. Ion eroded surface or growth simulations are a good example of such systems [59][60][61], and have also been investigated with conventional XPCS [19,20,61]. Simulations of real systems must undoubtedly go beyond archetypal simulations.…”

“…The field of application of XPCS has originally developed around the investigation of equilibrium dynamics of meso-scale particle assemblies as colloids, gels and polymers [2,15] studied with small angle scattering geometry (SAXS) and it has later extended towards out-of-equilibrium systems, such as complex fluids and rheology [17,18] or ageing in self-organised systems [19,20]. The access to increased coherent flux has opened the field to include atomic fluctuations or diffusion in hard-condensed matter systems, such as ageing and phase transitions in metallic glasses [6,21], diffusion in alloys [22][23][24], order-disorder fluctuations in crystals close to phase transitions [25] and even flow and diffusion of "phase discontinuities" as defects in thin metal films [26] (see also [8] and references therein).…”

de Gennes Narrowing and the Relationship Between Structure and Dynamics in Self-Organized Ion Beam Nanopatterning

“…The ripple structure coarsens with time, but at a very slow rate so that the correlation peaks remain well within the detector window throughout the experiment. For our purposes here, this is an important difference with previous XPCS studies of ion beam nanopatterning of GaSb [11] and SiO 2 [12]. It's known that the ripples move across the surface during continued bombardment and that, at late times, the sinusoidal ripples develop into asymmetric sawtooth structures [13][14][15][16], which creates asymmetry in the scattering between positive and negative q || [8,17].…”

20 µs-resolved high-throughput X-ray photon correlation spectroscopy on a 500k pixel detector enabled by data-management workflow

“…Many of these applications are summarized in recent reviews (Leheny, 2012;Shpyrko, 2014;Sinha et al, 2014;Madsen et al, 2016;Sandy et al, 2018). Partially driven by XPCS-applicable area detectors with increasingly high frame rates (Trapani et al, 2018;Zhang et al, 2020Zhang et al, , 2018Zinn et al, 2018;Pennicard et al, 2018;Redford et al, 2018;Maj et al, 2020;Allahgholi et al, 2019;Poikela et al, 2014) but also by emerging near-diffraction-limited storage rings (DLSRs) (Eriksson et al, 2014), a growing area of interest is XPCS applied to rapidly fluctuating and often weakly scattering soft materials (Vodnala et al, 2018;Mö ller et al, 2019;Chung et al, 2019;Zhang et al, 2019;Dallari et al, 2020;Nigro et al, 2020;Frenzel et al, 2019;Yavitt et al, 2020).…”

“…Area detectors allow multiple intensity-time series to be measured simultaneously, improving the equilibrium g 2 SNR by (N p ) 1/2 , while also providing concurrent measurements of the Q dependence of g 2 , thereby improving the efficiency of measurements. In the case of two-time measurements where the dynamics evolve over time (Fluerasu et al, 2005;Madsen et al, 2010;Das et al, 2019;Mokhtarzadeh et al, 2019;Hoshino et al, 2020;Jain et al, 2020), the SNR does not improve by increasing N f since the correlation is calculated between two frames, making the large N p provided by an area detector the only way to maintain the SNR of the correlation without sacrificing the time resolution indicated by t e .…”