Distribution Of Step Heights Research Articles

Variation of the frictional anisotropy on ventral scales of snakes caused by nanoscale steps

The ventral scales of most snakes feature micron-sized fibril structures with nanoscale steps oriented towards the snake’s tail. We examined these structures by microtribometry as well as atomic force microscopy (AFM) and observed that the nanoscale steps of the micro-fibrils cause a frictional anisotropy, which varies along the snake’s body in dependence of the height of the nanoscale steps. A significant frictional behavior is detected when a sharp AFM tip scans the nanoscale steps up or down. Larger friction peaks appear during upward scans (tail to head direction), while considerably lower peaks are observed for downward scans (head to tail direction). This effect causes a frictional anisotropy on the nanoscale, i.e. friction along the head to tail direction is lower than in the opposite direction. The overall effect increases linearly with the step height of the micro-fibrils. Although the step heights are different for each snake, the general step height distribution along the body of the examined snakes follows a common pattern. The frictional anisotropy, induced by the step height distribution, is largest close to the tail, intermediate in the middle, and lower close to the head. This common distribution of frictional anisotropy suggests that snakes even optimized nanoscale features like the height of micro-fibrils through evolution in order to achieve optimal friction performance for locomotion. Finally, ventral snake scales are replicated by imprinting their micro-fibril structures into a polymer. As the natural prototype, the artificial surface exhibits frictional anisotropy in dependence of the respective step height. This feature is of high interest for the design of tribological surfaces with artificial frictional anisotropy.

Semi-Automated Extraction of the Distribution of Single Defects for nMOS Transistors.

Miniaturization of metal-oxide-semiconductor field effect transistors (MOSFETs) is typically beneficial for their operating characteristics, such as switching speed and power consumption, but at the same time miniaturization also leads to increased variability among nominally identical devices. Adverse effects due to oxide traps in particular become a serious issue for device performance and reliability. While the average number of defects per device is lower for scaled devices, the impact of the oxide defects is significantly more pronounced than in large area transistors. This combination enables the investigation of charge transitions of single defects. In this study, we perform random telegraph noise (RTN) measurements on about 300 devices to statistically characterize oxide defects in a Si/SiO technology. To extract the noise parameters from the measurements, we make use of the Canny edge detector. From the data, we obtain distributions of the step heights of defects, i.e., their impact on the threshold voltage of the devices. Detailed measurements of a subset of the defects further allow us to extract their vertical position in the oxide and their trap level using both analytical estimations and full numerical simulations. Contrary to published literature data, we observe a bimodal distribution of step heights, while the extracted distribution of trap levels agrees well with recent studies.

Structure of the twofold surface of the icosahedral Ag–In–Yb quasicrystal

The structure of the twofold surface of the icosahedral (i-)Ag–In–Yb quasicrystal has been investigated using low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). The LEED confirms that the surface exhibits quasicrystalline long range order with the twofold rotational symmetry expected from the bulk. STM images reveal a step–terrace structure with terrace size comparable to that of the other high symmetry surfaces of the same quasicrystal. The distribution of step heights and high resolution STM images of terraces suggest that the surface terminates at bulk planes that intersect the center of rhombic triacontahedral clusters, the building blocks of the system, as in the case of the threefold and fivefold surfaces of the system. These planes are rich in Yb and In. No facets are observed on the surface, suggesting that the twofold surface is as stable as the other high symmetry surfaces.

Growth of large area monolayer graphene on 3C-SiC and a comparison with other SiC polytypes

Epitaxial graphene growth was performed on the Si-terminated face of 4H-, 6H-, and 3C-SiC substrates by silicon sublimation from SiC in argon atmosphere at a temperature of 2000°C. Graphene surface morphology, thickness and band structure have been assessed by using atomic force microscopy, low-energy electron microscopy, and angle-resolved photoemission spectroscopy, respectively. Differences in the morphology of the graphene layers on different SiC polytypes is related mainly to the minimization of the terrace surface energy during the step bunching process. The uniformity of silicon sublimation is a decisive factor for obtaining large area homogenous graphene. It is also shown that a lower substrate surface roughness results in more uniform step bunching with a lower distribution of step heights and consequently better quality of the grown graphene. Large homogeneous areas of graphene monolayers (over 50×50μm2) have been grown on 3C-SiC (111) substrates. The comparison with the other polytypes suggests a similarity in the surface behaviour of 3C- and 6H-SiC.

The atomic structure of the threefold surface of the icosahedral Ag–In–Yb quasicrystal

We report a study of the atomic structure of the threefold icosahedral (i-)Ag–In–Yb quasicrystal surface using scanning tunneling microscopy (STM) and low energy electron diffraction (LEED). The LEED confirms that the surface exhibits quasicrystalline long-range order with the threefold symmetry expected from the bulk. The STM reveals large atomically flat terraces separated by steps of different heights. A comparison of atomically resolved STM images for the terraces and the step-height distribution with the bulk structure of isostructural i-Cd–Yb shows that the terraces are formed at bulk planes intersecting the centers of the rhombic triacontahedral clusters that make up the bulk structure of the system. However, the stability of particular terraces may be influenced by the density of atoms in the interstices (glue atoms that bind the clusters) in the terraces and also by the chemical environment in the underlying atomic plane. The surface exhibits screw dislocations, which is explained in terms of a continuous atomic density along the threefold axis.

Surface structure of niobium-doped potassium tantalateKTa1 − xNbxO3 obtained from helium atom scattering studies

Helium atom scattering experiments have been carried out on the (001) surface ofKTaO3 doped with 6, 10 and 15% Nb, produced by cleaving in situ single crystal samples. Severalphenomena were observed through He atom diffraction measurements, including metastablebehavior immediately after cleaving, reconstruction of a fraction of the surface to (2 × 1) domains after thermally cycling the surface temperatures, and the distribution ofstep heights of terraces at the surface as multiples of the unit cell dimension of ∼ 4 Å. In addition, a large hysteresis effect was found in the⟨100⟩ azimuthin the variation of surface reflectivity with surface temperature; a much smaller hysteresis effect was foundin the ⟨110⟩ azimuth. The hysteresis effects appear for all Nb doping concentrations. Finally, smalloscillations in the specular and Bragg diffraction intensities near the surface temperature80 K were also observed.

Spatial organization in the step‐pool structure of a steep mountain stream (Vogelbach, Switzerland)

Spatial organization in the step‐pool structure of a 1.58 km long section of the Vogelbach, a steep mountain stream (average channel bed slope 0.17 m/m) in the Alpthal basin, Switzerland, is analyzed to evaluate the extent of randomness in the occurrence of steps and to isolate the potential hydraulic and topographic controls on step placement. Statistics of the observed step sequence are compared with those of random sequences generated by permutation from the observed step height distribution. Hydraulic and topographic controls on step placement are analyzed from step length and steepness distributions and relations between mean step properties and step height and channel gradient for both observed and random sequences. Results show that (1) observed step length distributions are statistically significantly different from randomly generated sequences, (2) step steepness is significantly different in observed data because of a positive correlation between mean step length and height and it remains fairly constant for all step sizes, (3) spatial organization in steps does not extend far beyond the nearest step, and (4) the influence of channel gradient on step properties is insignificant and highly variable, indicating that hydraulic rather than topographic controls are dominant for step placement in this stream. Although the Vogelbach is a steep stream on the boundary between a cascading and step‐pool morphology where we would expect randomness to dominate, spatial organization was nevertheless detected in many important aspects of the step‐pool geometry.

Comparison of Surface Structure of Icosahedral Al–Pd–Mn Family Quasi-crystals

We present scanning tunneling microcopy (STM) studies of three different icosahedral (i) quasi-crystals of the same family, namely, i-Al–Cu–Fe, i-Al–Pd–Mn, and i-Al–Cu–Ru. STM images reveal that the fivefold surface of all three quasi-crystals is isostructural. Both step-height distribution and high-resolution images on terraces are consistent in all systems.

RHEED and STM studies of the pseudo-tenfold surface of theξ′−Al77.5Pd19Mn3.5approximant crystal

The pseudo-tenfold surface of the ${\ensuremath{\xi}}^{\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{Al}}_{77.5}{\mathrm{Pd}}_{19}{\mathrm{Mn}}_{3.5}$ crystal, an approximant of the icosahedral $\mathrm{Al}--\mathrm{Pd}--\mathrm{Mn}$ quasicrystal, is investigated by reflection high-energy electron diffraction (RHEED) and scanning tunneling microscopy. The observed RHEED patterns of the surface after sputtering are found to be consistent with those of a simple cubic lattice with $(1\overline{1}0)$ surface plane. The [001] and [110] axes of the surface plane are oriented along the principal low-index axes of the bulk. The RHEED patterns of the sputter-annealed surface consist of diffraction streaks with periodic spacings expected for the bulk truncated surface. The surface prepared under different preparation methods is found to exhibit different step-height distribution and terrace morphology. A longer annealing yields a high density of shallow pentagonal pits on terraces, separated predominantly by $0.80\text{\ensuremath{-}}\mathrm{nm}$ high steps and occasionally by double steps. In contrast, the surface prepared with shorter annealing time exhibits highly perfect terraces with $0.80\text{\ensuremath{-}}\mathrm{nm}$-high steps and additional unusual steps of heights close to $0.40\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. All step heights observed for both preparation methods are consistent with interlayer spacings of the bulk model.

Structure of the Fivefold Surface of the Icosahedral Al-Cu-Fe Quasicrystal: Experimental Evidence of Bulk Truncations at Larger Interlayer Spacings

Based on scanning tunneling microscopy of the fivefold surface of the icosahedral Al-Cu-Fe quasicrystal and the refined structure model of the isostructural i-Al-Pd-Mn, we present evidence that the surface corresponds to bulk truncations at the positions where blocks of atomic layers are separated by larger interlayer spacings (gaps). Both step-height distribution and high resolution scanning tunneling microscopy images on terraces reveal bulk truncations at larger gaps.

Developments in the analysis of helium atom scattering data: the sequential filtering Lomb periodogram technique

A generalized methodology to analyse lattice-rod scans from helium atom scattering (HAS) has been developed, allowing in situ measurement of interlayer spacing during thin film growth. A Lomb periodogram technique is used to analyse the interference fringes observed in a lattice-rod scan of a stepped crystal surface. The algorithm is ideally suited to the small, unevenly sampled HAS data sets typically collected and has the advantage that the significance of peaks in the resulting frequency distribution can be calculated. We show how the method can be used to assess the significance of each interlayer spacing quantitatively. Using the growth of cobalt on copper(111) as an example, the statistical significance of the surface step height distribution is calculated directly. This paper represents a considerable improvement over existing fast Fourier transform-based methodologies.

Surface Structure of Self-Organized Sapphire (0001) Substrates with Various Inclined Angles

We studied the surface structure of self-organized sapphire (0001) substrates with various inclined angles, using an atomic force microscope (AFM) in UHV. The self-organized surface structure strongly depended on annealing condition, inclined angle and inclined direction. We could successfully produce a highly self-organized step structure by choosing suitable values of these parameters. The surface of the self-organized inclined substrates was characterized by step and terraces. The morphology of step edges depends on the inclined direction of the substrate. In the case of the <11̄00 > inclined direction, the step edges were faceted, and the faceted plane was the {21̄1̄0} plane. On the other hand, in the case of the <112̄0 > inclined direction, the step edges were straight. The distribution of step heights and terrace widths measured from AFM images are presented. The distribution of step heights had peaks corresponding to the unit cell of the sapphire crystal, while the terrace widths followed a normal distribution.

Self-Shadowing Influence on the Reflection from a Random Stepped Surface

The beam reflection from a stepped surface having a stochastic size of steps has been scrutinized using a geometrical optics approach. The coefficient that accounts for the effect of self-shadowing this type of surface is elaborated through auxiliary functions, each of them corresponding to the solution of integro-differential equation. In this paper the exact solution of these equations is constructed for the exponential function of the step height distribution density. In contrast to the earlier investigations this solution is validated for the finite distances between a receiver and a source and a random surface.

Studies of Self-Organized Steps and Terraces in inclined SrTiO3 (001) Substrate by Atomic Force Microscopy

Features of self-organized steps and terraces present in SrTiO3 (001) substrates with various inclined angles (α) have been investigated by atomic force microscopy (AFM). The details of the shape of step edges, the direction of the straight step edges, the distribution of step heights and terrace widths are described. The existence of various step heights such as single, double and triple heights are observed in the self-organized substrates. The surface after the self-organization conserves the same ratio of the step height and terrace width as that before the self-organization. The features of the self-organized steps and terraces, as well as the relative amount of step interaction energy required to influence the formation of the self-organized surface structure are discussed theoretically.

Characterization of epitaxial rubidium films with helium-atom scattering

The growth of thin rubidium films on a nickel(001) substrate has been investigated for coverages of between one and six monolayers using helium-atom scattering (HAS). Two different growth modes were found by monitoring the specular reflectivity during deposition which, at 50 K, displayed oscillations indicating layer-by-layer growth, whereas at 90 K the onset of step flow is observed. Information concerning the morphology of the film surface and the Debye–Waller factor was obtained by measuring the intensity of the specularly scattered helium beam as a function of the incident energy. The experiments showed that, for beam energies between 9 and 66 meV, the Debye–Waller factor is proportional to Δ k 2 z , with Δ k z denoting the perpendicular momentum transfer to the surface. The average terrace width of the annealed films was measured to be of the same order as that of the substrate, which is larger than 230 Å. The step height distribution was found to depend on the preparation process: annealing the rubidium film reduces the density of monatomic rubidium steps, whereas the height modulation induced by steps on the nickel substrate remains unchanged and can be observed up to a film thickness of six monolayers. The Debye temperature of the film surface has been determined at various stages of film preparation and for various coverages. In the case of annealed films it was found to decrease from 96 K to 62 K as the coverage was raised from 1.3 to 6.1 monolayers.

Scale invariance and dynamical correlations in growth models of molecular beam epitaxy.

Dynamical scaling behavior of the kinetic roughening phenomena in (1+1)- and (2+1)-dimensional models of molecular beam epitaxy (MBE) is studied using kinetic Monte Carlo simulations mostly within the solid-on-solid lattice gas approximation. We relate the simulation results of our finite temperature stochastic Monte Carlo algorithm, which employs local-configuration-dependent thermally activated Arrhenius diffusion, to those obtained from simpler manifestly nonequilibrium dynamical growth models involving instantaneous relaxation. The extracted critical exponents for kinetic roughening are found to be temperature dependent due to finite size and crossover effects, and in particular, the growth (\ensuremath{\beta}) and roughness (\ensuremath{\alpha}) exponents decrease with increasing temperature as diffusion noise becomes stronger relative to the deposition noise. We find strong evidence for anomalous dynamic scaling, with global and local scaling behaviors being substantially different in 1 + 1 dimensions. Remarkably, the anomalous roughness exponent \ensuremath{\alpha}\ensuremath{'} (=\ensuremath{\alpha} in the usual dynamic scaling situation) defining the spatial scaling in the height-height correlation function is found to be approximately a temperature-independent constant (\ensuremath{\approxeq}0.6--0.7 in 1 + 1 dimensions) in all our models, including the Arrhenius-activated diffusion model.An associated significant result is the marked up-down (h\ensuremath{\rightarrow}-h) asymmetry in our simulated growth morphologies, clearly indicating the presence of nonlinear microscopically irreversible processes dominating local growth features. We study in some detail the recently suggested connection between height fluctuations in MBE growth models and intermittent fluctuations in fluid turbulence by numerically calculating the multiaffine dynamic scaling behavior of higher moments of the height correlation functions and by obtaining the stretched exponential behavior of the step-height distribution functions in our growth models. We critically analyze our growth rules to comment on possible coarse-grained continuum descriptions that could qualitatively account for our MBE simulation results. \textcopyright{} 1996 The American Physical Society.

Scanning tunneling microscope study of GaAs(001) surfaces grown by migration enhanced epitaxy

We report an investigation of the morphology of p-type GaAs(001) surfaces using scanning tunneling microscopy (STM). The substrates were prepared using two methods: migration enhanced epitaxy (MEE) and standard molecular-beam epitaxy (MBE). The STM measurements were performed ex situ using As decapping. Analysis indicates that the overall step density of the MEE samples decreases as the growth temperature is increased. Nominally flat samples grown at 300 °C exhibited step densities of 10.5 steps/1000 Å along [110] dropping to 2.5 steps at 580 °C. MEE samples exhibited a lower step density than MBE samples. However as-grown surfaces exhibited a larger distribution of step heights. Annealing the samples reduced the step height distribution exposing fewer atomic layers. Samples grown by MEE at 580 °C and annealed for 2 min displayed the lowest step density and the narrowest step height distribution. All samples displayed an anisotropic step density. We found a ratio of A-type to B-type steps of between 2 and 3 which directly reflects the difference in the incorporation energy at steps. The aspect ratio increased slightly with growth temperature. We found a similar aspect ratio on samples grown by MBE. This indicates that anisotropic growth during MEE, like MBE, is dominated by incorporation kinetics. MEE samples grown at 580 °C and capped immediately following growth exhibited a number of ‘‘holes’’ in the surface. The holes could be eliminated by annealing the surface prior to quenching.

Observation of kinetically controlled monolayer step height distribution at normal and inverted interfaces in ultrathin GaAs/AlxGa1−xAs quantum wells

We report on comparative photoluminescence (PL) studies of GaAs/Al0.33Ga0.67As single quantum well structures grown via molecular beam epitaxy under identical growth conditions employing (a) customary practice of no growth interruption and (b) growth interruption. The growth conditions themselves are chosen to be near optimum, as determined from the growth kinetics exemplified by the reflection high-energy electron diffraction intensity dynamics. Results show PL lines with fine structure and widths among the narrowest ever reported for 28.3 and 56.6 Å wells. The fine structure is indicative of kinetically controlled interfaces with a predominant step height of one atomic layer and the linewidths a first measurement of intrinsic alloy disorder scattering.

Diffraction from surfaces with randomly distributed steps

A closed-form solution is obtained for the angular distribution of intensity in diffraction from a surface on which the terrace size distribution is given by the geometric distribution, i.e. a surface in which the occurrence of steps is random. Several distributions of step heights that are integral multiples of the monatomic step height are considered. It is shown that a random occurrence of monatomic steps will cause some multiatomic steps. If a very broad distribution of step heights is assumed, the beam width no longer oscillates with energy but approaches a constant value except at the characteristic energies of zero width. Comparisons are made with a previous model and with measurements on GaAs(110).

The study of crystal growth with the electron microscope V. The crystal growth ofn-pentacontanol-1

The crystal growth ofn-pentacontanol-1, C50H101OH, from a series of polar and non-polar solvents has been studied to obtain further information about the effect of molecular association on growth-step height. The solvents used were petroleum ether, benzene, xylene, amyl acetate, dioxan,n- andiso-propyl alcohols,n-butyl alcohol and amyl alcohol. In general, crystals grown from polar solvents showed monomolecular growth steps, and crystals grown from non-polar solvents showed a high proportion of bimolecular growth steps with some monomolecular growth steps. These results support the idea that step height is determined by the size of the associated group of molecules in solution. Alcohol solvents, although polar, gave results which did not conform to the general distribution of step heights for polar solvents. A suggested explanation is offered by the complex association possible when both solute and solvent are themselves alcohols. Twin growth occurs more extensively from non-polar solvents than from polar solvents. Habit modification was observed in crystallization from alcohols, and this was related to the residual water content of the solvent. In aqueous alcohols reproducible crystals showing modified growth habit could be obtained. Polytypism has been observed in one crystal out of the many hundreds examined. This crystal did not show cross-lacing of the growth-step pattern. Conversely, a crystal showing a cross-laced pattern was encountered which was not a polytype. These two results show that the detection of cross-laced growth steps cannot be taken as adequate proof of polytypism. In this investigation a unique crystal, composed of two independent helical monomolecular interleaving layers, has been encountered.