arXiv subjects

Carol Thompson

Publications and source records attributed to Carol Thompson.

9 recordsLinked to original sources

arXiv2021

Crystal Truncation Rods from Miscut Surfaces with Alternating Terminations

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 αβαβ 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 α vs. β 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.

cond-mat.mtrl-sci↗

arXiv2021

In Situ Microbeam Surface X-ray Scattering Reveals Alternating Step Kinetics During Crystal Growth

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.

cond-mat.mtrl-sci↗

arXiv2020

Burton-Cabrera-Frank theory for surfaces with alternating step types

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.

cond-mat.mtrl-sci↗

arXiv2020

Dynamics of Atomic Steps on GaN (0001) during Vapor Phase Epitaxy

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 $αβαβ$ 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 $α$ and $β$ 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 $α$ and $β$ 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 $α$ terrace fraction $f_α$. 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 $f_α$ 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 $f_α$ 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).

cond-mat.mtrl-sci↗

arXiv2018

Persistence of Island Arrangements During Layer-by-Layer Growth Revealed Using Coherent X-rays

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.

cond-mat.mtrl-sci↗

arXiv2018

Characterization of the X-ray Coherence Properties of an Undulator Beamline at the Advanced Photon Source

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.

physics.acc-ph↗

arXiv2017

Island dynamics and anisotropy during vapor phase epitaxy of m-plane GaN

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.

cond-mat.mtrl-sci↗

arXiv2017

An instrument for advanced in situ x-ray studies of metal-organic vapor phase epitaxy of III-nitrides

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.

cond-mat.mtrl-sci↗

arXiv2016

Kinetic Monte Carlo simulations of GaN homoepitaxy on c- and m-plane surfaces

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.

cond-mat.mtrl-sci↗