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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 submicron 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., Comment: 28 pages, 6 figures

Burton-Cabrera-Frank (BCF) theory has proven to be a versatile framework to relate surface morphology and dynamics during crystal growth to the underlying mechanisms of adatom diffusion and attachment at steps. For an important class of crystal surfaces, including the basal planes of hexagonal close-packed and related systems, the steps in a sequence on a vicinal surface can exhibit properties that alternate from step to step. Here we develop BCF theory for such surfaces, relating observables such as alternating terrace widths as a function of growth conditions to the kinetic coefficients for adatom attachment at steps. We include the effects of step transparency and step-step repulsion. A general solution is obtained for the dynamics of the terrace widths, assuming quasi-steady-state adatom distributions on the terraces. An explicit simplified analytical solution is obtained under widely applicable approximations. From this we obtain expressions for the full-steady-state terrace fraction as a function of growth rate. Fits of the theoretical predictions to recent experimental determinations of the steady-state and dynamics of terrace fractions on GaN (0001) surfaces during organo-metallic vapor phase epitaxy give values of the kinetic coefficients for this system. In Appendices, we also connect a model for diffusion between kinks on steps to the model for diffusion between steps on terraces, which quantitatively relates step transparency to the kinetics of atom attachment at kinks, and consider limiting cases of diffusion-limited, attachment-limited, and mixed kinetics., Comment: 22 pages, 11 fig, 5 tables, 3 appendices, and Supplemental. For clarity, arXiv:2007.05083 was split into two distinct papers focusing on separate subtopics. This paper focuses on developing BCF theory in presence of non-identical step-edges. The other paper arXiv:2010.06166, on the scattering experiments whose interpretations required the extensions to BCF

Miscut surfaces of layered crystals can exhibit a stair-like sequence of terraces having periodic variation in their atomic structure. For hexagonal close-packed and related crystal structures with an {\alpha}{\beta}{\alpha}{\beta} stacking sequence, there have been long-standing questions regarding how the differences in adatom attachment kinetics at the steps separating the terraces affect the fractional coverage of {\alpha} vs. {\beta} termination during crystal growth. To demonstrate how surface X-ray scattering can help address these questions, we develop a general theory for the intensity distributions along crystal truncation rods (CTRs) for miscut surfaces with a combination of two terminations. We consider half-unit-cell-height steps, and variation of the coverages of the terraces above each step. Example calculations are presented for the GaN (0001) surface with various reconstructions. These show which CTR positions are most sensitive to the fractional coverage of the two terminations. We compare the CTR profiles for exactly oriented surfaces to those for vicinal surfaces having a small miscut angle, and investigate the circumstances under which the CTR profile for an exactly oriented surface is equal to the sum of the intensities of the corresponding family of CTRs for a miscut surface., Comment: 15 pages, 15 figures, Supplemental with 9 tables specifying coordinates of the 9 reconstructions examined. v2 has edits for clarity, addition of supplemental. (arXiv admin note: substantial text overlap with arXiv:2007.05083)

Images of the morphology of GaN (0001) surfaces often show half-unit-cell-height steps separating a sequence of terraces having alternating large and small widths. This can be explained by the $\alpha \beta \alpha \beta$ stacking sequence of the wurtzite crystal structure, which results in steps with alternating $A$ and $B$ edge structures for the lowest energy step azimuths, i.e. steps normal to $[0 1 \bar{1} 0]$ type directions. Predicted differences in the adatom attachment kinetics at $A$ and $B$ steps would lead to alternating $\alpha$ and $\beta$ terrace widths. However, because of the difficulty of experimentally identifying which step is $A$ or $B$, it has not been possible to determine the absolute difference in their behavior, e.g. which step has higher adatom attachment rate constants. Here we show that surface X-ray scattering can measure the fraction of $\alpha$ and $\beta$ terraces, and thus unambiguously differentiate the growth dynamics of $A$ and $B$ steps. We first present calculations of the intensity profiles of GaN crystal truncation rods (CTRs) that demonstrate a marked dependence on the $\alpha$ terrace fraction $f_\alpha$. We then present surface X-ray scattering measurements performed \textit{in situ} during homoepitaxial growth on (0001) GaN by vapor phase epitaxy. By analyzing the shapes of the $(1 0 \bar{1} L)$ and $(0 1 \bar{1} L)$ CTRs, we determine that the steady-state $f_\alpha$ increases at higher growth rate, indicating that attachment rate constants are higher at $A$ steps than at $B$ steps. We also observe the dynamics of $f_\alpha$ after growth conditions are changed. The results are analyzed using a Burton-Cabrera-Frank model for a surface with alternating step types, to extract values for the kinetic parameters of $A$ and $B$ steps. These are compared with predictions for GaN (0001)., Comment: 18 pages, 30 figures, 12 tables, 3 appendices. This is long paper to accompany "Do A or B Steps Have Faster Kinetics during Hexagonal Crystal Growth?" by same author list

The stacking sequence of hexagonal close-packed and related crystals typically results in steps on vicinal {0001} surfaces that have alternating A and B structures with different growth kinetics. However, because it is difficult to experimentally identify which step has the A or B structure, it has not been possible to determine which has faster adatom attachment kinetics. Here we show that in situ microbeam surface X-ray scattering can determine whether A or B steps have faster kinetics under specific growth conditions. We demonstrate this for organo-metallic vapor phase epitaxy of (0001) GaN. X-ray measurements performed during growth find that the average width of terraces above A steps increases with growth rate, indicating that attachment rate constants are higher for A steps, in contrast to most predictions. Our results have direct implications for understanding the atomic-scale mechanisms of GaN growth and can be applied to a wide variety of related crystals., Comment: Main paper: 11 pages, 8 figures; Supplemental: 8 pages, 12 figures. Version 3 is similar to v2, with additional edits to text and figures for clarity. In-depth descriptions of BCF (growth) model extended to alternating steps and CTR (scattering) analysis can be found at arXiv:2010.09575 and arXiv:2010.06166 (admin note: substantial text overlap with arXiv:2007.05083)

We present proof-of-concept imaging measurements of a polycrystalline material that integrate the elements of conventional high-energy X-ray diffraction microscopy with coherent diffraction imaging techniques, and that can enable in-situ strain-sensitive imaging of lattice structure in ensembles of deeply embedded crystals over five decades of length scale upon full realization. Such multi-scale imaging capabilities are critical to addressing important questions in a variety of research areas such as materials science and engineering, chemistry, and solid state physics. Towards this eventual goal, the following key aspects are demonstrated: 1) high-energy Bragg coherent diffraction imaging (HE-BCDI) of sub-micron-scale crystallites at 52 keV at current third-generation synchrotron light sources, 2) HE-BCDI performed in conjunction with far-field high-energy diffraction microscopy (ff-HEDM) on the grains of a polycrystalline sample in an smoothly integrated manner, and 3) the orientation information of an ensemble of grains obtained via ff-HEDM used to perform complementary HE-BCDI on multiple Bragg reflections of a single targeted grain. These steps lay the foundation for integration of HE-BCDI, which typically provides a spatial resolution tens of nanometers, into a broad suite of well-established HEDM methods, extending HEDM beyond the few-micrometer resolution bound and into the nanoscale, and positioning the approach to take full advantage of the orders-of-magnitude improvement of X-ray coherence expected at fourth generation light sources presently being built and commissioned worldwide., Comment: 11 pages, 7 figures

Understanding surface dynamics during epitaxial film growth is key to growing high quality materials with controllable properties. X-ray photon correlation spectroscopy (XPCS) using coherent x-rays opens new opportunities for in situ observation of atomic-scale fluctuation dynamics during crystal growth. Here, we present the first XPCS measurements of 2D island dynamics during homoepitaxial growth in the layer-by-layer mode. Analysis of the results using two-time correlations reveals a new phenomenon - a memory effect in island nucleation sites on successive crystal layers. Simulations indicate that this persistence in the island arrangements arises from communication between islands on different layers via adatoms. With the worldwide advent of new coherent x-ray sources, the XPCS methods pioneered here will be widely applicable to atomic-scale processes on surfaces., Comment: 13 page, 5 figures, also note additional supplementary document of 10 pages, 7 figures

In anticipation of the increased use of coherent x-ray methods and the need to upgrade beamlines to match improved source quality, we have characterized the coherence properties of the x-rays delivered by beamline 12ID-D at the Advanced Photon Source. We compare the measured x-ray divergence, beam size, brightness, and coherent flux at energies up to 26 keV to the calculated values from the undulator source, and evaluate the effects of beamline optics such as a mirror, monochromator, and compound refractive lenses. Diffraction patterns from slits as a function of slit width are analyzed using wave propagation theory to obtain the beam divergence and thus coherence length. Imaging of the source using a compound refractive lens was found to be the most accurate method for determining the vertical divergence. While the brightness and coherent flux obtained without a monochromator ("pink beam") agree well with those calculated for the source, those measured with the monochromator were a factor of 3 to 6 lower than the source, primarily because of vertical divergence introduced by the monochromator. The methods we describe should be widely applicable for measuring the x-ray coherence properties of synchrotron beamlines., Comment: 14 pages, 14 figures

We report the results of x-ray scattering studies of AlN on c-plane sapphire during reactive radiofrequency magnetron sputtering. The sensitivity of in situ x-ray measurements allowed us to follow the structural evolution of strain and roughness from initial nucleation layers to fullyrelaxed AlN films. A growth rate transient was observed, consistent with the initial formation of non-coalesced islands with significant oxygen incorporation from the substrate. Following island coalescence, a steady state growth rate was seen with a continuous shift of the c and a lattice parameters towards the relaxed bulk values as growth progressed, with films reaching a fully relaxed state at thicknesses of about 30 nm., Comment: 5 pages, 4 figures

We describe an instrument that exploits the ongoing revolution in synchrotron sources, optics, and detectors to enable in situ studies of metal-organic vapor phase epitaxy (MOVPE) growth of III-nitride materials using coherent x-ray methods. The system includes high-resolution positioning of the sample and detector including full rotations, an x-ray transparent chamber wall for incident and diffracted beam access over a wide angular range, and minimal thermal sample motion, giving the sub-micron positional stability and reproducibility needed for coherent x-ray studies. The instrument enables surface x-ray photon correlation spectroscopy, microbeam diffraction, and coherent diffraction imaging of atomic-scale surface and film structure and dynamics during growth, to provide fundamental understanding of MOVPE processes., Comment: 13 pages, 13 figures, published in RSI v2 revision, clarified several points for reader from suggestions of referees, fixed typo Please cite paper as : G. Ju, et al., Review of Scientific Instruments 88, 035113 (2017)

Dynamical phase separation during a solid-solid phase transition poses a challenge for understanding the fundamental processes in correlated materials. Critical information underlying a phase transition, such as localized phase competition, is difficult to reveal by measurements that are spatially averaged over many phase separated regions. The ability to simultaneously track the spatial and temporal evolution of such systems is essential to understanding mesoscopic processes during a phase transition. Using state-of-the-art time-resolved hard x-ray diffraction microscopy, we directly visualize the structural phase progression in a VO2 film upon photoexcitation. Following a homogenous in-plane optical excitation, the phase transformation is initiated at discrete sites and completed by the growth of one lattice structure into the other, instead of a simultaneous isotropic lattice symmetry change. The time-dependent x-ray diffraction spatial maps show that the in-plane phase progression in laser-superheated VO2 is via a displacive lattice transformation as a result of relaxation from an excited monoclinic phase into a rutile phase. The speed of the phase front progression is quantitatively measured, and is faster than the process driven by in-plane thermal diffusion but slower than the sound speed in VO2. The direct visualization of localized structural changes in the time domain opens a new avenue to study mesoscopic processes in driven systems.

Thermodynamic theory is developed for the ferroelectric phase transition of an ultrathin film in equilibrium with a chemical environment that supplies ionic species to compensate its surface. Equations of state and free energy expressions are developed based on Landau-Ginzburg-Devonshire theory, using electrochemical equilibria to provide ionic compensation boundary conditions. Calculations are presented for a monodomain PbTiO$_3$ (001) film coherently strained to SrTiO$_3$ with its exposed surface and its electronically conducting bottom electrode in equilibrium with a controlled oxygen partial pressure. The stability and metastability boundaries of phases of different polarization are determined as a function of temperature, oxygen partial pressure, and film thickness. Phase diagrams showing polarization and internal electric field are presented. At temperatures below a thickness-dependent Curie point, high or low oxygen partial pressure stabilizes positive or negative polarization, respectively. Results are compared to the standard cases of electronic compensation controlled by either an applied voltage or charge across two electrodes. Ionic surface compensation through chemical equilibrium with an environment introduces new features into the phase diagram. In ultrathin films, a stable non-polar phase can occur between the positive and negative polar phases when varying the external chemical potential at fixed temperature, under conditions where charged surface species are not present in sufficient concentration to stabilize a polar phase., Comment: 53 pages, 24 figures