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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)

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

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

Using in situ grazing-incidence x-ray scattering, we have measured the diffuse scattering from islands that form during layer-by-layer growth of GaN by metal-organic vapor phase epitaxy on the (1010) m-plane surface. The diffuse scattering is extended in the (0001) in-plane direction in reciprocal space, indicating a strong anisotropy with islands elongated along [1 $\overline{2}$ 10] and closely spaced along [0001]. This is confirmed by atomic force microscopy of a quenched sample. Islands were characterized as a function of growth rate G and temperature. The island spacing along [0001] observed during the growth of the first monolayer obeys a power-law dependence on growth rate G$^{-n}$, with an exponent $n = 0.25 \pm 0.02$. Results are in agreement with recent kinetic Monte Carlo simulations, indicating that elongated islands result from the dominant anisotropy in step edge energy and not from surface diffusion anisotropy. The observed power-law exponent can be explained using a simple steady-state model, which gives n = 1/4., Comment: 4 pages, 5 figures, ancillary material includes Supplement material (pdf) of 4 pages, 5 figures with details of analysis

The surface orientation can have profound effects on the atomic-scale processes of crystal growth, and is essential to such technologies as GaN-based light-emitting diodes and high-power electronics. We investigate the dependence of homoepitaxial growth mechanisms on the surface orientation of a hexagonal crystal using kinetic Monte Carlo simulations. To model GaN metal-organic vapor phase epitaxy, in which N species are supplied in excess, only Ga atoms on a hexagonal close-packed (HCP) lattice are considered. The results are thus potentially applicable to any HCP material. Growth behaviors on c-plane ${(0 0 0 1)}$ and m-plane ${(0 1 \overline{1} 0)}$ surfaces are compared. We present a reciprocal space analysis of the surface morphology, which allows extraction of growth mode boundaries and direct comparison with surface X-ray diffraction experiments. For each orientation we map the boundaries between 3-dimensional, layer-by-layer, and step flow growth modes as a function of temperature and growth rate. Two models for surface diffusion are used, which produce different effective Ehrlich-Schwoebel step-edge barriers, and different adatom diffusion anisotropies on m-plane surfaces. Simulation results in agreement with observed GaN island morphologies and growth mode boundaries are obtained. These indicate that anisotropy of step edge energy, rather than adatom diffusion, is responsible for the elongated islands observed on m-plane surfaces. Island nucleation spacing obeys a power-law dependence on growth rate, with exponents of -0.24 and -0.29 for m- and c-plane, respectively., Comment: 30 pages, 40 figures

Memristive switching devices, candidates for resistive random access memory technology, have been shown to switch off through a progression of states with quantized conductance and subsequent non-integer conductance (in terms of conductance quantum $G_0$). We have performed calculations based on density functional theory to model the switching process for a Pt-HfO$_2$-Pt structure, involving the movement of one or two oxygen atoms. Oxygen atoms moving within a conductive oxygen vacancy filament act as tunneling barriers, and partition the filament into weakly coupled quantum wells. We show that the low-bias conductance decreases exponentially when one oxygen atom moves away from interface. Our results demonstrate the high sensitivity of the device conductance to the position of oxygen atoms.

Reversible resistive switching between high-resistance and low-resistance states in metal-oxide-metal heterostructures makes them very interesting for applications in random access memories. While recent experimental work has shown that inserting a metallic "oxygen scavenger layer" between the positive electrode and oxide improves device performance, the fundamental understanding of how the scavenger layer modifies heterostructure properties is lacking. We use density functional theory to calculate thermodynamic properties and conductance of TiN/HfO$_2$/TiN heterostructures with and without Ta scavenger layer. First, we show that Ta insertion lowers the formation energy of low-resistance states. Second, while the Ta scavenger layer reduces the Schottky barrier height in the high-resistance state by modifying the interface charge at the oxide-electrode interface, the heterostructure maintains a high resistance ratio between high- and low-resistance states. Finally, we show that the low-bias conductance of device on-states becomes much less sensitive to the spatial distribution of oxygen removed from the HfO$_2$ in the presence of the Ta layer. By providing fundamental understanding of the observed improvements with scavenger layers, we open a path to engineer interfaces with oxygen scavenger layers to control and enhance device performance. In turn, this may enable the realization of a non-volatile low-power memory technology with concomitant reduction in energy consumption by consumer electronics and significant benefits to society., Comment: 9 pages, 10 figures

High purity niobium (Nb), subjected to the processing methods used in the fabrication of superconducting RF cavities, displays micron-sized surface patches containing excess carbon. High-resolution transmission electron microscopy and electron energy-loss spectroscopy measurements are presented which reveal the presence of nanoscale NbC coherent precipitates in such regions. Raman backscatter spectroscopy on similar surface regions exhibit spectra consistent with the literature results on bulk NbC but with significantly enhanced two-phonon scattering. The unprecedented strength and sharpness of the two-phonon signal has prompted a theoretical analysis, using density functional theory (DFT), of phonon modes in NbC for two different interface models of the coherent precipitate. One model leads to overall compressive strain and a comparison to ab-initio calculations of phonon dispersion curves under uniform compression of the NbC shows that the measured two-phonon peaks are linked directly to phonon anomalies arising from strong electron-phonon interaction. Another model of the extended interface between Nb and NbC, studied by DFT, gives insight into the frequency shifts of the acoustic and optical mode density of states measured by first order Raman. The exact origin of the stronger two-phonon response is not known at present but it suggests the possibility of enhanced electron-phonon coupling in transition metal carbides under strain found either in the bulk NbC inclusions or at their interfaces with Nb metal. Preliminary tunneling studies using a point contact method show some energy gaps larger than expected for bulk NbC., Comment: Phys. Rev. B, accepted

Understanding electronic properties of sub-stoichiometric phases of titanium oxide such as Magn\'eli phase Ti4O7 is crucial in designing and modeling resistive switching devices. Here we present our study on Magn\'eli phase Ti4O7 together with rutile TiO2 and Ti2O3 using density functional theory methods with atomic-orbital-based self-interaction correction (ASIC). We predict a new antiferromagnetic ground state in the low temperature phase (or LT phase), and we explain energy difference with a competing antiferromagnetic state using a Heisenberg model. The predicted energy ordering of these states in the LT phase is calculated to be robust in a wide range of modeled isotropic strain. We have also investigated the dependence of the electronic structures of the Ti-O phases on stoichiometry. The splitting of titanium t2g orbitals is enhanced with increasing oxygen deficiency as Ti-O is reduced. The electronic properties of all these phases can be reasonably well described by applying ASIC with a standard value for transition metal oxides of the empirical parameter {\alpha} of 0.5 representing the magnitude of the applied self-interaction correction.

We investigate transport properties of ultrananocrystalline diamond films for a broad range of temperatures. Addition of nitrogen during plasma-assisted growth increases the conductivity of ultrananocrystalline diamond films by several orders of magnitude. We show that films produced at low concentration of nitrogen in the plasma are very resistive and electron transport occurs via a variable range hopping mechanism while in films produced at high nitrogen concentration the electron states become delocalized and the transport properties of ultrananocrystalline diamond films can be described using the Boltzmann formalism. We discuss the critical concentration of carriers at which the metal to insulator transition in ultrananocrystalline diamond films occurs and compare our results with available experimental data., Comment: 5 pages, 3 figures