We derive a stochastic nonlinear continuum theory to describe the morphological evolution of amorphous surfaces eroded by ion bombardment. Starting from Sigmund's theory of sputter erosion, we calculate the coefficients appearing in the continuum equation in terms of the physical parameters characterizing the sputtering process. We analyze the morphological features predicted by the continuum theory, comparing them with the experimentally reported morphologies. We show that for short time scales, where the effect of nonlinear terms is negligible, the continuum theory predicts ripple formation. We demonstrate that in addition to relaxation by thermal surface diffusion, the sputtering process can also contribute to the smoothing mechanisms shaping the surface morphology. We explicitly calculate an effective surface diffusion constant characterizing this smoothing effect, and show that it is responsible for the low temperature ripple formation observed in various experiments. At long time scales the nonlinear terms dominate the evolution of the surface morphology. The nonlinear terms lead to the stabilization of the ripple wavelength and we show that, depending on the experimental parameters such as angle of incidence and ion energy, different morphologies can be observed: asymptotically, sputter eroded surfaces could undergo kinetic roughening, or can display novel ordered structures with rotated ripples. Finally, we discuss in detail the existing experimental support for the proposed theory, and uncover novel features of the surface morphology and evolution, that could be directly tested experimentally.

Morphology of Ion-Sputtered Surfaces

pyXPCSviewer, a Python-based graphical user interface that is deployed at beamline 8-ID-I of the Advanced Photon Source for interactive visualization of XPCS results, is introduced. pyXPCSviewer parses rich X-ray photon correlation spectroscopy (XPCS) results into independent PyQt widgets that are both interactive and easy to maintain. pyXPCSviewer is open-source and is open to customization by the XPCS community for ingestion of diversified data structures and inclusion of novel XPCS techniques, both of which are growing demands particularly with the dawn of near-diffraction-limited synchrotron sources and their dedicated XPCS beamlines. 

<i>pyXPCSviewer</i>: an open-source interactive tool for X-ray photon correlation spectroscopy visualization and analysis

Understanding the self-organized ion beam nanopatterning of elemental semiconductors, particularly silicon, is of intrinsic scientific and technological interest. This is the second component of a two-part coherent x-ray scattering and x-ray photon correlation spectroscopy (XPCS) investigation of the kinetics and fluctuation dynamics of nanoscale ripple development on silicon during 1 keV ${\mathrm{Ar}}^{+}$ (part I) and ${\mathrm{Kr}}^{+}$ bombardment at ${65}^{\ensuremath{\circ}}$ polar angle. Here it is found that the ion-enhanced viscous flow relaxation is essentially equal for ${\mathrm{Kr}}^{+}$-induced patterning as previously found for ${\mathrm{Ar}}^{+}$ patterning despite the difference in ion masses. However, the magnitude of the surface curvature-dependent roughening rate in the early-stage kinetics is larger for ${\mathrm{Kr}}^{+}$ than for ${\mathrm{Ar}}^{+}$, consistent with expectations that the heavier ion gives an increased mass redistributive contribution to the initial surface instability. As with the ${\mathrm{Ar}}^{+}$ case, fluctuation dynamics in the late stage show a peak in correlation times at the length scale corresponding to the dominant structural feature on the surface---the ripples. Finally, it is shown that speckle motion during the surface evolution can be analyzed to determine spatial inhomogeneities in erosion rate and ripple velocity. This allows the direction and speed of ripple motion to be measured in a real time experiment. In the present case, ripple motion is found to be into the projected direction of the ion source, in contrast to expectations from an existing sputter erosion driven model with parameters derived from binary collision approximation simulations.

Nanoscale dynamics during self-organized ion beam patterning of Si. I. Ar + bombardment

Solid-phase epitaxy (SPE) and other three-dimensional epitaxial crystallization processes pose challenging structural and chemical characterization problems. The concentration of defects, the spatial distribution of elastic strain, and the chemical state of ions each vary with nanoscale characteristic length scales and depend sensitively on the gas environment and elastic boundary conditions during growth. The lateral or three-dimensional propagation of crystalline interfaces in SPE has nanoscale or submicrometer characteristic distances during typical crystallization times. An in situ synchrotron hard x-ray instrument allows these features to be studied during deposition and crystallization using diffraction, resonant scattering, nanobeam and coherent diffraction imaging, and reflectivity. The instrument incorporates a compact deposition system allowing the use of short-working-distance x-ray focusing optics. Layers are deposited using radio-frequency magnetron sputtering and evaporation sources. The deposition system provides control of the gas atmosphere and sample temperature. The sample is positioned using a stable mechanical design to minimize vibration and drift and employs precise translation stages to enable nanobeam experiments. Results of in situ x-ray characterization of the amorphous thin film deposition process for a SrTiO3/BaTiO3 multilayer illustrate implementation of this instrument.

Instrument for in situ hard x-ray nanobeam characterization during epitaxial crystallization and materials transformations.

Here, we demonstrate an experimental proof of concept for nanofocused x-ray photon correlation spectroscopy, a technique sensitive to nanoscale fluctuations present in a broad range of systems. The experiment, performed at the NanoMAX beamline at MAX IV, uses a novel event-based x-ray detector to capture nanoparticle structural dynamics with microsecond resolution. By varying the nanobeam size from σ=88 nm to σ=2.5μm, we quantify the effect of the nanofocus on the small-angle scattering lineshape and on the diffusion coefficients obtained from nano-XPCS. We observe that the use of nanobeams leads to a multifold increase in speckle contrast, which greatly improves the experimental signal-to-noise ratio, quantified from the two-time intensity correlation functions. We conclude that it is possible to account for influence of the high beam divergence on the lineshape and measured dynamics by including a convolution with the nanobeam profile in the model.Received 17 December 2021Revised 19 May 2022Accepted 16 June 2022DOI:https://doi.org/10.1103/PhysRevResearch.4.L032012Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsNanoparticlesSynchrotron radiation & free-electron lasersTechniquesCoherent X-ray scatteringX-ray photon correlation spectroscopyCondensed Matter, Materials & Applied PhysicsPolymers & Soft Matter 

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Nanofocused x-ray photon correlation spectroscopy

Investigating the relationship between structure and dynamical processes is a central goal in condensed matter physics. Perhaps the most noted relationship between the two is the phenomenon of de Gennes narrowing, in which relaxation times in liquids are proportional to the scattering structure factor. Here, a similar relationship is discovered during the self-organized ion-beam nanopatterning of silicon using coherent x-ray scattering. However, in contrast to the exponential relaxation of fluctuations in classic de Gennes narrowing, the dynamic surface exhibits a wide range of behaviors as a function of the length scale, with a compressed exponential relaxation at lengths corresponding to the dominant structural motif---self-organized nanoscale ripples. These behaviors are reproduced in simulations of a nonlinear model describing the surface evolution. We suggest that the compressed exponential behavior observed here is due to the morphological persistence of the self-organized surface ripple patterns which form and evolve during ion-beam nanopatterning.

de Gennes Narrowing and Relationship between Structure and Dynamics in Self-Organized Ion-Beam Nanopatterning.

Pulsed laser deposition (PLD) is widely used to grow epitaxial thin films of quantum materials. Here, we use in situ x-ray scattering to study homoepitaxy of ${\mathrm{SrTiO}}_{3}$ by energetic deposition (e-PLD) versus PLD thermalized by a He background gas (th-PLD). Energetic PLD suppresses the lateral growth of two-dimensional islands, which suggests that particles with kinetic energies of $\ensuremath{\sim}100$ eV break up smaller islands. Fast interlayer transport occurs for th-PLD as well as e-PLD, implying a process operating on submicrosecond time scales for incident particles with kinetic energies below 10 eV.

Fast nonthermal processes in pulsed laser deposition

Normal-incidence 1-keV ${\mathrm{Ar}}^{+}$ ion bombardment leads to amorphization and ultrasmoothing of Ge at room temperature, but at elevated temperatures the Ge surface remains crystalline and is unstable to the formation of self-organized nanoscale patterns of ordered pyramid-shaped pits. The physical phenomenon distinguishing the high-temperature patterning from room-temperature ultrasmoothing is believed to be a surface instability due to the Ehrlich-Schwoebel barrier for diffusing vacancies and adatoms, which is not present on the amorphous material. This real-time grazing-incidence small-angle x-ray scattering study compares smoothing of a prepatterned Ge sample at room temperature with patterning of an initially flat Ge sample at an elevated temperature. In both experiments, when the nanoscale structures are relatively small in height, the average kinetics can be explained by a linear theory. The linear theory coefficients, indicating surface stability or instability, were extracted for both experiments. A comparison between the two measurements allows estimation of the contribution of the Ehrlich-Schwoebel barrier to the self-organized formation of ordered nanoscale patterns on crystalline Ge surfaces.

Xiaozhi Zhang

Papers

de Gennes Narrowing and Relationship between Structure and Dynamics in Self-Organized Ion-Beam Nanopatterning.

Nanoscale dynamics during self-organized ion beam patterning of Si. I. Ar + bombardment

Fast nonthermal processes in pulsed laser deposition

Measurement of Ehrlich-Schwoebel barrier contribution to the self-organized formation of ordered surface patterns on Ge(001)