Faceting Transition Research Articles

Faceting of local droplet-etched nanoholes in AlGaAs

Nanoholes, drilled in the (001) surface of AlGaAs by local Al droplet etching, are shown to consist of faceted inner walls. The most prominent facets of the inverted pyramidlike nano-sized etch pits are the {111}A and {$1\overline{1}1$}B surfaces, which differ in their atomic surface terminations. In the [110] direction, the {111} facets change to {112} and/or {113}, which are both stepped surfaces with (111)A terraces. Etching-temperature-dependent data indicate that this facet transition seems kinetically hindered up to etch temperatures above 660 \ifmmode^\circ\else\textdegree\fi{}C, at which point the walls along $[1\overline{1}0]$ have already evolved completely towards {$1\overline{1}1$}B facets. The redeposited ring material outside the nanohole develops facets with indices of (115) and higher, thereby forming relatively flat structures. The facets and their indices are unraveled by a combination of atomic force microscopy, scanning electron microscopy, and x-ray diffraction, which is performed on an ensemble as well as on a single hole using nanodiffraction. These results imply that this nanoconfined etching process can be largely understood in a vapor-liquid-solid scheme, which includes the bulk thermodynamics in the Al-Ga-As system, the surface energies of low index facets, and their etch rates and surface terminations.

The stabilization mechanism and size effect of nonpolar-to-polar crystallography facet tailored ZnO nano/micro rods via a top-down strategy.

A simple and efficient top-down strategy, the chemical vapor etching method, is reported for synthesizing corrugated ZnO nano/micro rods (NRs). The stabilization mechanism of this unique nanostructure has been determined through a combination of aberration-corrected field emission scanning electron microscopy, high-resolution transmission electron microscopy, and first-principles calculations. The experimental data are in good agreement with the theoretical calculations, and a remarkable nonpolar-to-polar surface faceting transition is demonstrated. The corrugated-shaped structure results from the remarkable stability of the defect-induced reconstructions (O vacancy, Zn-Zn dimer), which makes the high-index polar {303[combining macron]1} and {101[combining macron]1[combining macron]} planes lower in energy compared to the nonpolar {101[combining macron]0} plane. Based on the results of first-principles surface calculations, a general formula is established to provide an accurate description of the unusual size effect of the length of the corrugated unit vs. the NR diameter, and it also offers direct explanations for certain experimental observations. The present study deepens our atomic-level understanding of the detailed structure and stability of polar surface decorated corrugated ZnO NRs, and points to a viable path towards designing polar-stable wurtzite structures.

Faceting Transition at the Oxide–Metal Interface: (13 13 1) Facets on Cu(110) Induced by Carpet-Like Ceria Overlayer

Structural transitions affect electronic structure of materials and consequently their catalytic properties. We report the observation of faceting of a low index metal surface at an oxide–metal interface in a catalytically relevant system of ceria on Cu(110). We observe formation of (13 13 1) facets on the Cu(110) surface covered by ceria upon annealing above 500 °C. The faceting transition occurs in spite of a weak adsorbate–substrate interaction, which manifests itself in ceria adopting a carpet-like growth mode. We rationalize the surface faceting under such conditions by oxide overlayer-induced modification of the roughening temperature of Cu(110). We describe the carpet-like ceria film in terms of elasticity theory and show that the specific structure of the ceria supported on Cu(13 13 1) can lead to a periodic modulation of the electronic structure of the ceria–copper interface. The reported structural transition indicates that surface faceting of metal can occur at the oxide–metal interface at relatively low temperatures with possible consequences for the catalytic properties of the interface. The oxide overlayer induced faceting transition can be expected to occur for other oxide–metal combinations and, as such, has perspective applications in preparation of functional oxide–metal nanostructures.

Use of the Thoracolumbar Facet Transition as a Method of Identifying the T12 Segment

Purpose: Evaluate the reliability of the change from the flat, posterolaterally oriented facets of the thoracic segments to the curved, posteromedially oriented facets of the lumbar spine, the “facet transition”, as a marker for the T12 segment and determine if variations in rib number are associated with lumbosacral transitional segments. Materials and methods: 244 patients underwent whole spine CT examinations and the positions of the thoracolumbar facet transition, type of thoracolumbar facet transition (gradual or abrupt), position of the lowest thoracic ribs, and presence or absence of lumbosacral transitional anatomy were recorded. A Fisher Exact Test was used to determine if there was an association between a variant number of ribs and transitional anatomy at the lumbosacral junction. Results: The thoracolumbar facet transition was located at the eighteenth segment in 50/244 (20%), nineteenth segment in 184/244 (75%), and twentieth segment in 10/244 (4%) of cases. The thoracolumbar facet transition was abrupt in 227/244 (93%). The lowest set of ribs was observed at the nineteenth segment in 225/244 (92%), twentieth segment in 11/244 (5%), and eighteenth segment in 8/244 (3%). The lowest fully-formed intervertebral disc was located between the twenty-third and twenty-fourth segments in 9/244 (4%), twenty-fourth and twenty-fifth segments in 216/244 (88%), and twenty-fifth and twenty-sixth segments in 19/244 (8%). Coexistent lumbosacral transitional anatomy was seen in 5/7 (71%) with eleven, 8/11 (73%) with thirteen, and 24/234 (10%) with twelve ribs. There was an association between variant numbers of ribs and coexistent lumbosacral transitional anatomy (p<0.5). Conclusion: The thoracolumbar facet transition is not a reliable method of identifying the T12 segment. There are no known landmarks that reliably identify the lumbar segments. Accurate numbering of the lumbar spine requires counting caudally from C2.

Restricted solid-on-solid growth model with a defect site in a two-dimensional substrate

A restricted solid-on-solid growth model with a defect in the middle of a two-dimensional substrate is studied. A particle is deposited with a probability P at the defect site and with P = 1 at the other sites under a restriction on the local height difference. When P is small, the strength of the defect is strong enough to make a surface facet. For P > Pc, the defect site distorts the surface weakly without producing a facet surface. At P = Pc, the height difference correlation function C(r) shows a power-law behavior C(r) ∼ rδ with δ ≈ 1/2. Other critical exponents near the facet transition are also discussed.

Microstructure Variation in the Arc-Melted Cr-Cr&lt;sub&gt;2&lt;/sub&gt;Nb Hypereutectic Alloy

Microstructure of the arc-melted Cr-20at%Nb alloy solidified in different positions was investigated using optical microscope (OM) and scanning electron microscope (SEM). The results show that fully coupled eutectic was developed at the bottom of the ingot and then the eutectic experienced a columnar to equiaxed transition due to the decrease of G/V ratio (G the thermal gradient and V the solidification rate) with increasing the solidification distance. A novel lamellar structure was observed in the middle side of the arc-melted ingot, which may form by means of the eutectoid reaction of C14-Cr2Nb→C15-Cr2Nb+Crss. With the increase of the solidification distance from the middle side to the top side, the primary Cr2Nb phase underwent a nonfaceted to faceted transition.

On the Morphology of Viral Capsids: Elastic Properties and Buckling Transitions

The morphology of icosahedral viruses ranges from highly spherical to highly faceted, and for some viruses a shape transition occurs during the viral life cycle. This phenomena is predicted from continuum elasticity, via the buckling transition theory by Nelson (Phys. Rev. E 2003, 68, 051910), in which the shape is dependent on the Foppl-von Kármán number (γ), which is a ratio of the two-dimensional Young's modulus (Y) and the bending modulus (κ). However, until now, no direct calculations have been performed on atomic-level capsid structures to test the predictions of the theory. In this study, we employ a previously described multiscale method by May and Brooks (Phys. Rev. Lett. 2011, 106, 188101) to calculate Y and κ for the bacteriophage HK97, which undergoes a spherical to faceted transition during its viral life cycle. We observe a change in γ consistent with the buckling transition theory and also a significant reduction in κ, which facilitates formation of the faceted state. We go on to examine many capsids from the T = 3 and 7 classes using only elastic network models, which allows us to calculate the ratio Y/κ, without the expense of all-atom molecular dynamics. We observe for the T = 7 capsids, there is strong correlation between the shape of the capsid and γ; however, there is no such correlation for the smaller T = 3 viruses.

Energetics and dynamics of Cu(001)-c(2×2)Cl steps

The energetics of the step faceting transition of Cu(001) [copper (001) surface] upon Cl (chloride) adsorption in contact with HCl (hydrogen chloride) solution is modeled in terms of a solid-on-solid model that incorporates both nearest-neighbor and next-nearest-neighbor interactions. It is shown that faceting of the closed packed [110] Cu(001) steps into step segments oriented along [010] directions of the Cu(001)-c(2×2)Cl can be explained by a strongly repulsive interaction between next-nearest-neighbor Cl atoms in the c(2×2) adlayer. The dynamics of kink motion along the [010]-oriented steps of the Cl-covered Cu(001) surface via attachment/detachment is studied with scanning tunneling microscopy. At some kink sites local dissolution takes place, whereas at other kink sites growth occurs. After correcting for the net local dissolution (or growth) process the kinks perform a one-dimensional random walk along the [010] oriented step segments.

Self-organized nanoscale pattern formation on vicinal Si(111) surfaces via a two-stage faceting transition.

We demonstrate a self-organized pattern formation on vicinal Si(111) surfaces that are miscut toward the [2;11] direction. All the patterns, consisting of a periodic array of alternating (7 x 7) reconstructed terraces and step-bunched facets, have the same periodicity and facet structure, independent of the miscut angle, while the width of the facets increases linearly with miscut angle. We attribute such unique pattern formation to a surface faceting transition that involves two transition stages: the first stage forms a stress-domain structure defining the universal periodicity; the second stage forms the low-energy facets controlling the facet width.

Pattern Formation via a Two-Step Faceting Transition on Vicinal Si(111) Surfaces

AbstractWe demonstrate a self-organized pattern formation on vicinal Si(111) surfaces that are miscut toward the [211] direction. All the patterns, consisting of a periodic array of alternating (7×7) reconstructed terraces and step-bunched facets, have the same periodicity and facet structure, independent of the miscut angle; while the width of the facets increases linearly with miscut angle. We attribute such unique pattern formation to a surface faceting transition that involves two transition steps: the first step forms a stress-domain structure defining the universal periodicity; the second step forms the low-energy facets controlling the facet width.

Martensitic relief formation on an electropolished Ni-37 at.% Al (001) surface by diffuse X-ray scattering under grazing angles

Abstract The development of a martensitic relief on an electropolished (001) surface of a Ni-37 at.% Al crystal was studied in a high-resolution, in-situ experiment by diffuse X-ray reflectivity using synchrotron radiation. A one-dimensional detector was used to monitor the distribution of the reflected intensity in the scattering plane as a function of temperature between 300 and 270 K. The presence of surface precursor effects with second-order (continuous) character was found far above the phase transition, whereas the discontinuous surface morphology change from nanoscopic roughness to macroscopic relief occurred within a temperature interval of less than 1 K. We observed three stages in the relief formation, which were followed with a temperature resolution of 0.1 K: (1) enhancement of the Fresnel transmission (Yoneda) peak by more than a factor of three on cooling from 272.5 to 272.0 K, reflecting a changing surface height-height correlation function that heralds the build-up of the martensitic relief; (2) reduction of the Yoneda peak intensity by more than two orders of magnitude with simultaneous appearance of a second peak, indicative of an intermediate faceting transition; and (3) suppression of the Yoneda peaks and development of a diffuse, featureless signal due to extensive surface roughening. The observed scattering patterns were reversible on heating. Resistivity measurements from the same sample suggest that surface relief represents only the final stage of the bulk transformation, preceded by non-equilibrium, intermediate stages without surface tilts.

Faceting and stress of missing-row reconstructed transition-metal (110) surfaces

We present ab initio total energy and stress calculations for the unreconstructed and $(2\ifmmode\times\else\texttimes\fi{}1)$--missing-row reconstructed Ir (110) and Rh (110) surfaces. We then use those results to set up a model rationalizing the $(2\ifmmode\times\else\texttimes\fi{}1)$ reconstruction as a faceting transition to a long-wavelength--corrugated (111)-like surface. Next, we discuss the qualitative extension of such model to a general $n\ifmmode\times\else\texttimes\fi{}1$ reconstruction, using ab initio results, elasticity theory, and classical dynamics simulations for Al (110). Remarkably, despite the severe inherent limitations of the model, the $3\ifmmode\times\else\texttimes\fi{}1$ structure is found to be the most stable for Ir. Finally, we use the stress density to analyze the stress increase upon reconstruction, and find it to be due to a changed balance of tensile and compressive contributions in the near-surface region, which closely matches previous interpretations of the reconstruction mechanism. We conclude that, as for the (100) surface, the reconstruction basically originates from the strong relativistic contraction effects on the electronic structure of end-of-series $5d$ metals.

Spatially Resolved Optical Characterization of AlGaAs Layers Grown on Patterned Substrates

We have applied micro-photoluminescence (PL) spectroscopy to scan the Al concentration and the well width of an undoped GaAs/AlGaAs single quantum well (QW) and micro-Raman spectroscopy to scan the carrier concentration of a Si-doped AlGaAs layer along (100)/(111)A/(100) facet transitions. The QW and the doped layer were grown by MBE on patterned GaAs substrates exhibiting (100) ridges and (100) grooves separated by 5 μm wide (111)A facets. The width of the GaAs QW, obtained from the spectral position of the QW PL, decreases from 10 nm on the (100) planes to 8 nm on the (111)A facet. The Al concentration, derived from the spectral position of the AlGaAs-barrier PL, varies between 23.5 and 29.5% along the facet transition. The type and concentration of charge carriers, deduced from the spectral position and line shape of the coupled plasmon–LO-phonon modes varies from n = 1.8 × 1018 cm—3 on the (100) planes to n < 4 × 1017 cm—3 or p-type on the (111)A facet.

Spatially resolved characterization of material composition and free carrier concentration by micro-Raman spectroscopy at surface selectively grown layers

Micro-Raman spectroscopy has been utilized to determine the local material composition of an In x Ga 1− x As layer and the local free-charge-carrier concentration of a Si-doped InP layer grown on patterned InP(1 0 0) substrates. The layers exhibited 8 or 11 μm long {1 1 1}A and {1 1 1}B facets delimited by (1 0 0) planes. The In concentration x in the In x Ga 1− x As layer has been derived from the Raman shift of the GaAs-like LO phonon. Line scans along (1 0 0)/{1 1 1}A/(1 0 0) and (1 0 0)/{1 1 1}B/(1 0 0) facet transitions reveal a distinct drop of x over more than 0.1 at the (1 0 0)/{1 1 1} transitions. In the Si-doped InP layer the density n of free electrons has been obtained from the Raman shift of the coupled plasmon–LO–phonon mode. A line scan along a (1 0 0)/(1 1 1)A/(1 0 0) facet transition shows a decrease of n from 1.4×10 18 cm −3 on the (1 0 0) surface to 0.5×10 18 cm −3 on the (1 1 1)A facet.

Growth of 4He-Crystals at mK-Temperatures

Liquid-solid interface of 4 He has been investigated down to mK-temperatures using an optical interferometer in combination with a sensitive pressure gauge. The c- facets with 5–100 screw dislocations/cm 2 grew with spiral growth which can be understood by including inertial terms and localization of steps to the standard theory. Crystals without screw dislocations revealed two novel growth mechanisms. At growth rates > 1 nm/s, these high-quality crystals grew in a burst-like manner, creating abruptly 200–2000 new atomic-layers. At rates below 0.5 nm/s, the c- facet revealed slow, continuous growth. Studies of a- facets yielded a velocity vs. pressure dependence which can be explained by spiral growth. The shape of the c- facet was monitored down to 2 mK without any evidence of the freezing of kinks. Pressure measurements down to our minimum temperature did not show any anomalies connected with the supersolid transition. Indications of new faceting transitions were not observed down to 2 mK.

Anisotropic surface diffusion at crystal facet transitions during localized GaInAsP growth by MOMBE

Localized grown InP/GaInAs(P) heterostructure ridges by selective area metalorganic molecular beam epitaxy (MOMBE) are investigated concerning the surface diffusion. The structures have different crystal facets at the semiconductor mask transition area. The surface diffusion processes between these simultaneously growing facets are a function of the step density, which is preset by the selected substrate misorientations. The anisotropic surface diffusion in the direction of the group V terminated surface steps determines the lateral facet growth and leads to a fine oscillating surface corrugation on the ridge surface only near the step upwards oriented facet transition. A simulation of this anisotropic surface corrugation by a deterministic nonlinear partial differential equation of a one dimensional diffusion model for the selective area growth in MOMBE presents a good agreement with the measured corrugation depth and periods.

Spatially resolved Raman investigation of Si-doped GaAs layers on patterned GaAs(100) substrates grown by molecular beam epitaxy

Local carrier transport properties of Si-doped GaAs layers on ridge structures exhibiting (111)A and (111)B sidewalls are investigated. The layers were grown by molecular beam epitaxy at different substrate temperatures and As/Ga flux ratios. Using spatially resolved Raman spectroscopy we determine the type and density of free charge carriers (≥ 5 × 10 17 cm −3) in the grown layers on the different index facets from an analysis of the coupled plasmon-longitudinal optical-phonon mode which was calibrated against Hall standards. We demonstrate that on the (100) and (111)B facets the regrown layers are n-type and on the (111)A facets p- or n-type depending on the growth conditions. Line scans of the carrier density show that the (100)/(111)A/(100) facet transition forms a graded lateral n-p-n junction. Spatially resolved photoluminescence measurements confirm our findings.

Vicinal Surfaces and the Calogero-Sutherland Model.

A miscut (vicinal) crystal surface can be regarded as an array of meandering but non-crossing steps. Interactions between the steps are shown to induce a faceting transition of the surface between a homogeneous Luttinger liquid state and a low-temperature regime consisting of local step clusters in coexistence with ideal facets. This morphological transition is governed by a hitherto neglected critical line of the well-known Calogero-Sutherland model. Its exact solution yields expressions for measurable quantities that compare favorably with recent experiments on Si surfaces.

High-temperature scanning tunneling microscopy study of the Li/Si(111) surface

A study of the topographical changes of Li/Si(111) during annealing has been conducted using a high-temperature scanning tunneling microscope. Depending on the Li coverage and postdeposition annealing temperature the surface exhibited a variety of structures replacing the initial (7×7) reconstruction during in situ investigations. In addition to the previously observed (3×1) structure a coexistence phase with domains of (n×n) (n=5,7,9), a (4×4) structure, and a faceting transition were imaged. Distinct differences were noticed on the Li/Si(111)-(3×1) surface compared to the corresponding Na structure. Moreover, the dynamic properties of the morphological transformations were revealed by a high-temperature scanning tunneling microscope.

Terrace growth in partially melt-regrown EuBa2Cu3 ? high-T c superconductors

An SEM and STM study was made of terrace formation in partial melt-regrown EuBa2Cu3O7−δ. Terraces form above 920°C, well below the bulk melting temperature (1075±10°C). The terrace formation is accompanied by significant grain growth, possibly triggered by a “surface-melting” transition. Melting occurs in a layer a few monolayers thick, and the highly mobile layers reconstruct into terraced form due to a faceting transition. The terrace growth can be reproduced by a theoretical faceting model. The STM also reveals a finer-scale sinusoidal modulation of the surface, of unknown origin.