Substantial crystalline topology in amorphous silicon

Unveiling Nanoscale Ordering in Amorphous Semiconducting Polymers Using Four-Dimensional Scanning Transmission Electron Microscopy

We present four-dimensional (4D) scanning transmission electron microscopy (STEM) analysis to obtain a high level of detail regarding the nanoscale ordering within largely disordered organic semiconducting polymers. Understanding nanoscale molecular ordering in semiconducting polymers is crucial due to its connection to the materials' important properties. However, acquiring such information in a spatially localized manner has been limited by the lack of a nanoscale experimental probe, weak signal from ordering, and radiation damage to the sample. By collecting nanodiffraction patterns with a high dynamic range pixelated detector, we acquired statistically robust, high signal-to-noise ratio diffraction patterns from semiconducting organic materials, including poly(3-hexylthiophene-2,5-diyl) (P3HT), P3HT/[6,6]-phenyl C61 butyric acid methyl ester, and indacenodithiophene-co-benzothiadiazole (IDTBT), which largely have disordered structures. Real-space images of the ordered domains were reconstructed from the 4D-STEM data set for a variety of scattering vectors and in-plane angles to capture the different molecular stacking distances and their in-plane orientation. These were then analyzed to obtain the average size of the ordered domains within the sample. Such measurements were arranged in a two-dimensional (2D) histogram, which showed a direct relationship between the type and size of molecular ordering. Complementary analyses, such as intensity variance and angular correlation, were applied to obtain ordering and symmetry information. These analyses enabled us to directly characterize the alkyl and π-π stacking of P3HT, as well as the fullerene domains caused by donor segregation in the P3HT sample. Furthermore, the analysis also captured changes in the P3HT domains when the fullerenes are incorporated. Lastly, IDTBT showed a much lesser degree of ordering without much disinclination between the domains within the 2D histogram. The 4D-STEM analysis that we report here unveils new details of molecular ordering that can be used to optimize the properties of this important class of materials.

Clustering characteristic diffraction vectors in 4-D STEM data sets from overlapping structures in nanocrystalline and amorphous materials

We describe a method for identifying and clustering diffraction vectors in four-dimensional (4-D) scanning transmission electron microscopy data to determine characteristic diffraction patterns from overlapping structures in projection. First, the data is convolved with a 4-D kernel, then diffraction vectors are identified and clustered using both density-based clustering and a metric that emphasizes rotational symmetries. The method works well for both crystalline and amorphous samples and in high- and low-dose experiments. A simulated dataset of overlapping aluminum nanocrystals provides performance metrics as a function of Poisson noise and the number of overlapping structures. Experimental data from an aluminum nanocrystal sample shows similar performance. For an amorphous Pd77.5Cu6Si16.5 thin film, experiments measuring glassy structure show strong evidence of 4- and 6-fold symmetry structures. A significant background arises from the diffraction of overlapping structures. Quantifying this background helps to separate contributions from single, rotationally symmetric structures vs. apparent symmetries arising from overlapping structures in projection.

Challenges of Electron Correlation Microscopy on Amorphous Silicon and Amorphous Germanium

Electron correlation microscopy experiments were conducted on amorphous germanium (a-Ge) and amorphous silicon (a-Si) with the goal to study self-diffusion. For this purpose, a series of tilted dark-field images were acquired during in situ heating of the samples in a transmission electron microscope. These experiments show that the measurements are greatly affected by artefacts. Contamination, crystallization, electron beam-induced sputtering, and macroscopic bending of the samples pose major obstacles to the measurements. Other, more subtle experimental artefacts could occur in addition to these which makes interpretations regarding the structural dynamics nearly impossible. The data were nonetheless evaluated to see if some useful information could be extracted. One such result is that the distribution of the characteristic times τKWW, which were obtained from stretched exponential fits to the intensity autocorrelation data, is spatially heterogeneous. This spatial heterogeneity is assumed to be caused by a potential nonergodicity of the materials, the artefacts or an inhomogeneous amorphous structure. Further data processing shows that the characteristic times τKWW are moreover temperature independent, especially for the a-Ge data. It is concluded that the structural rearrangements over time are primarily electron beam-driven and that diffusive dynamics are too slow to be measured at the chosen, experimentally accessible annealing temperatures.

Structure of Amorphous Two-Dimensional Materials: Elemental Monolayer Amorphous Carbon versus Binary Monolayer Amorphous Boron Nitride

The structure of amorphous materials has been debated since the 1930s as a binary question: amorphous materials are either Zachariasen continuous random networks (Z-CRNs) or Z-CRNs containing crystallites. It was recently demonstrated, however, that amorphous diamond can be synthesized in either form. Here we address the question of the structure of single-atom-thick amorphous monolayers. We reanalyze the results of prior simulations for amorphous graphene and report kinetic Monte Carlo simulations based on alternative algorithms. We find that crystallite-containing Z-CRN is the favored structure of elemental amorphous graphene, as recently fabricated, whereas the most likely structure of binary monolayer amorphous BN is altogether different than either of the two long-debated options: it is a compositionally disordered "pseudo-CRN" comprising a mix of B-N and noncanonical B-B and N-N bonds and containing "pseudocrystallites", namely, honeycomb regions made of noncanonical hexagons. Implications for other nonelemental 2D and bulk amorphous materials are discussed.

Synthesis of paracrystalline diamond

Solids in nature can be generally classified into crystalline and non-crystalline states^1-7, depending on whether long-range lattice periodicity is present in the material. The differentiation of the two states, however, could face fundamental challenges if the degree of long-range order in crystals is significantly reduced. Here we report a paracrystalline state of diamond that is distinct from either crystalline or amorphous diamond^8-10. The paracrystalline diamond reported in this work, consisting of sub-nanometre-sized paracrystallites that possess a well-defined crystalline medium-range order up to a few atomic shells^4,5,11-13, was synthesized in high-pressure high-temperature conditions (for example, 30 GPa and 1,600 K) employing face-centred cubic C₆₀ as a precursor. The structural characteristics of the paracrystalline diamond were identified through a combination of X-ray diffraction, high-resolution transmission microscopy and advanced molecular dynamics simulation. The formation of paracrystalline diamond is a result of densely distributed nucleation sites developed in compressed C₆₀ as well as pronounced second-nearest-neighbour short-range order in amorphous diamond due to strong sp³ bonding. The discovery of paracrystalline diamond adds an unusual diamond form to the enriched carbon family^14-16, which exhibits distinguishing physical properties and can be furthered exploited to develop new materials. Furthermore, this work reveals the missing link in the length scale between amorphous and crystalline states across the structural landscape, having profound implications for recognizing complex structures arising from amorphous materials.

Correlation symmetry analysis of electron nanodiffraction from amorphous materials

Angular symmetry in diffraction reflects rotational symmetry in the sample. We introduce the angular symmetry coefficient as a method to extract local symmetry information from electron nanodiffraction patterns of amorphous materials. Symmetry coefficients are the average of the angular autocorrelation function at the characteristic angles of a particular rotational symmetry. The symmetry coefficients avoid non-structural features arising from Fourier transformation and Friedel symmetry breakdown that affect the angular power spectrum approach to determining angular symmetries in amorphous nanodiffraction. Both methods require thin samples to avoid overlapping diffraction from clusters of atoms separated in the thickness of the sample, but symmetry coefficients are more forgiving. Electron nanodiffraction experiments on a Pd-based metallic glass sample demonstrate both potentially misleading information in angular power spectrum and the utility of symmetry coefficients.

Unraveling the Unconventional Order of a High-Mobility Indacenodithiophene-Benzothiadiazole Copolymer

A new class of donor-acceptor (D-A) copolymers found to produce high charge carrier mobilities competitive with amorphous silicon (>1 cm² V^-1 s^-1) exhibit the puzzling microstructure of substantial local order, however lacking long-range order and crystallinity previously deemed necessary for achieving high mobility. Here, we demonstrate the application of low-dose transmission electron microscopy to image and quantify the nanoscale and mesoscale organization of an archetypal D-A copolymer across areas comparable to electronic devices (≈9 μm²). The local structure is spatially resolved by mapping the backbone (001) spacing reflection, revealing nanocrystallites of aligned polymer chains throughout nearly the entire film. Analysis of the nanoscale structure of its ordered domains suggests significant short- and medium-range order and preferential grain boundary orientations. Moreover, we provide insights into the rich, interconnected mesoscale organization of this new family of D-A copolymers by analysis of the local orientational spatial autocorrelations.

Comparison of Experimental STEM Conditions for Fluctuation Electron Microscopy

Variable-resolution fluctuation electron microscopy (VR-FEM) data from measurements on amorphous silicon and PdNiP have been obtained at varying experimental conditions. Measurements have been conducted at identical total electron dose and with an identical electron dose normalized to the respective probe size. STEM probes of different sizes have been created by variation of the semi-convergence angle or by defocus. The results show that defocus yields a reduced normalized variance compared to data from probes created by convergence angle variation. Moreover, the trend of the normalized variance upon probe size variation differs between the two methods. Beam coherence, which affects FEM data, has been analyzed theoretically using geometrical optics on a multi-lens setup and linked to the illumination conditions. Fits to several experimental beam profiles support our geometrical optics theory regarding probe coherence. The normalized variance can be further optimized if one determines the optimal exposure time for the nanobeam diffraction patterns.

Detection of Ring and Adatom Defects in Activated Disordered Carbon via Fluctuation Nanobeam Electron Diffraction

How the structure of disordered porous carbons evolves during their activation is particularly poorly understood. This problem endures primarily because of a lack of high-resolution 3D techniques for the characterization of amorphous and highly disordered structure. To address this, the measurement of the 3D pair-angle distribution function using nanodiffraction patterns from high-energy electrons is demonstrated. These rich multiatom correlations are measured for a disordered carbon and they clearly show the structural evolution during activation. They provide previously inaccessible bond-angle information and direct evidence for the presence of ring and adatom defects. An increase in the short-range order and the number of fivefold ring defects with activation are observed, indicating stress relaxation by increasing curvature. These observations support models of disordered porous carbons based on curved graphene networks and explain how large amounts of free volume can be created with surprisingly small changes in the average ratios of tetrahedral to graphitic bonding.

Disorder by design: A data-driven approach to amorphous semiconductors without total-energy functionals

X-ray diffraction, Amorphous silicon, Multi-objective optimization, Monte Carlo methods. This paper addresses a difficult inverse problem that involves the reconstruction of a three-dimensional model of tetrahedral amorphous semiconductors via inversion of diffraction data. By posing the material-structure determination as a multiobjective optimization program, it has been shown that the problem can be solved accurately using a few structural constraints, but no total-energy functionals/forces, which describe the local chemistry of amorphous networks. The approach yields highly realistic models of amorphous silicon, with no or only a few coordination defects (≤1%), a narrow bond-angle distribution of width 9-11.5°, and an electronic gap of 0.8-1.4 eV. These data-driven information-based models have been found to produce electronic and vibrational properties of a-Si that match accurately with experimental data and rival that of the Wooten-Winer-Weaire models. The study confirms the effectiveness of a multiobjective optimization approach to the structural determination of complex materials, and resolves a long-standing dispute concerning the uniqueness of a model of tetrahedral amorphous semiconductors obtained via inversion of diffraction data.

Pressure-driven phase transitions and reduction of dimensionality in 2D silicon nanosheets

In-situ high-pressure synchrotron X-ray powder diffraction studies up to 21 GPa of CVD-grown silicon 2D-nanosheets establish that the structural phase transitions depend on size and shape. For sizes between 9.3(7) nm and 15.2(8) nm we observe an irreversible phase transition sequence from I (cubic) → II (tetragonal) → V (hexagonal) during pressure increase and during decompression below 8 GPa the emergence of an X-ray amorphous phase. High-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) and atomic force microscopy (AFM) images of this X-ray amorphous phase reveal the formation of significant numbers of 1D nanowires with aspect ratios > 10, which are twinned and grow along the <111> direction. We discovered a reduction of dimensionality under pressure from a 2D morphology to a 1D wire in a material with a diamond structure. MD simulations indicate the reduction of thermal conductivity in such nanowires.

Direct determination of structural heterogeneity in metallic glasses using four-dimensional scanning transmission electron microscopy

We report the first direct quantification of the structural heterogeneity in metallic glasses using intensity variance and angular correlation analyses of the 4-dimensional (4-D) scanning transmission electron microscopy (STEM) data. We demonstrate that the real-space reconstruction and analyses of the 4-D nanodiffraction data acquired using a pixelated fast STEM detector enables quantitative determination of the details of local structural heterogeneity, including the type, size, volume fraction and spatial distribution of local ordering at the nano- to meso-scale, beyond the limits of the previous measurements using conventional detectors. We show that different types of local ordering are present in Zr₅₅Co₂₅Al₂₀ glass, leading to a high degree of structural heterogeneity, with the total volume of locally ordered regions making up to ∼14% of the entire volume. These findings are significant, as the structure-property relationship in metallic glasses and other amorphous materials has been difficult to establish because of the lack of detailed structural information from experiments.

Favored local structures in amorphous colloidal packings measured by microbeam X-ray diffraction

Local structure and symmetry are keys to understanding how a material is formed and the properties it subsequently exhibits. This applies to both crystals and amorphous and glassy materials. In the case of amorphous materials, strong links between processing and history, structure and properties have yet to be made because measuring amorphous structure remains a significant challenge. Here, we demonstrate a method to quantify proportions of the bond-orientational order of nearest neighbor clusters [Steinhardt, et al. (1983) Phys Rev B 28:784-805] in colloidal packings by statistically analyzing the angular correlations in an ensemble of scanning transmission microbeam small-angle X-ray scattering (μSAXS) patterns. We show that local order can be modulated by tuning the potential between monodisperse, spherical colloidal silica particles using salt and surfactant additives and that more pronounced order is obtained by centrifugation than sedimentation. The order in the centrifuged glasses reflects the ground state order in the dispersion at lower packing fractions. This diffraction-based method can be applied to amorphous systems across decades in length scale to connect structure to behavior in disordered systems with a range of particle interactions.

Fluctuation microscopy analysis of amorphous silicon models

Using computer-generated models we discuss the use of fluctuation electron microscopy (FEM) to identify the structure of amorphous silicon. We show that a combination of variable resolution FEM to measure the correlation length, with correlograph analysis to obtain the structural motif, can pin down structural correlations. We introduce the method of correlograph variance as a promising means of independently measuring the volume fraction of a paracrystalline composite. From comparisons with published data, we affirm that only a composite material of paracrystalline and continuous random network that is substantially paracrystalline could explain the existing experimental data, and point the way to more precise measurements on amorphous semiconductors. The results are of general interest for other classes of disordered materials.

Orientational order of liquids and glasses via fluctuation diffraction

Liquids, glasses and other amorphous matter lack long-range order, which makes them notoriously difficult to study. Local atomic order is partially revealed by measuring the distribution of pairwise atomic distances, but this measurement is insensitive to orientational order and unable to provide a complete picture of diverse amorphous phenomena, such as supercooling and the glass transition. Fluctuation scattering with electrons and X-rays is able provide this orientational sensitivity, but it is difficult to obtain clear structural interpretations of fluctuation data. Here we show that the interpretation of fluctuation diffraction data can be simplified by converting it into a real-space angular distribution function. We calculate this function from simulated diffraction of amorphous nickel, generated with a classical molecular dynamics simulation of the quenching of a high temperature liquid state. We compare the results of the amorphous case to the initial liquid state and to the ideal f.c.c. lattice structure of nickel. We show that the extracted angular distributions are rich in information about orientational order and bond angles. The diffraction fluctuations are potentially measurable with electron sources and also with the brightest X-ray sources, like X-ray free-electron lasers.

Structure and dynamics in network-forming materials

The study of the structure and dynamics of network-forming materials is reviewed. Experimental techniques used to extract key structural information are briefly considered. Strategies for building simulation models, based on both targeting key (experimentally-accessible) materials and on systematically controlling key model parameters, are discussed. As an example of the first class of materials, a key target system, SiO₂, is used to highlight how the changing structure with applied pressure can be effectively modelled (in three dimensions) and used to link to both experimental results and simple structural models. As an example of the second class the topology of networks of tetrahedra in the MX₂ stoichiometry are controlled using a single model parameter linked to the M-X-M bond angles. The evolution of ordering on multiple length-scales is observed as are the links between the static structure and key dynamical properties. The isomorphous relationship between the structures of amorphous Si and SiO₂ is discussed as are the similarities and differences in the phase diagrams, the latter linked to potential polyamorphic and 'anomalous' (e.g. density maxima) behaviour. Links to both two-dimensional structures for C, Si and Ge and near-two-dimensional bilayers of SiO₂ are discussed. Emerging low-dimensional structures in low temperature molten carbonates are also uncovered.

Calculation of Projected Bond-Orientational Order Parameters to Quantify Local Symmetries from Transmission Diffraction Data

The bond-orientational order parameters introduced by Steinhardt et al. [Phys. Rev. B 28, 784 (1983)] have been an invaluable measurement tool for assessing short-range order in disordered, close-packed assemblies of particles in which the particle positions are known. In many glassy systems the measurement of particle position is not possible or limited (field of view, thickness, resolution) and the bond-orientational order parameters cannot be measured, or adequately sampled. Here we calculate a set of rotationally averaged, projected bond-orientational order parameters that reflect the symmetries of close-packed particle clusters when projected onto a plane. We show by simulation that these parameters are unique fingerprints that can be directly compared to angular correlations in limited-volume, transmission geometry, diffraction patterns from close-packed glassy assemblies.

Detection of an ordered-structure fraction in amorphous silicon

Amorphous silicon (a-Si) films were prepared by radio frequency magnetron sputtering. Spectroscopic ellipsometry (SE) was utilized to detect an ordered-structure fraction in a-Si. The SE analysis of a-Si films with different thicknesses (7.0–140.0 nm) demonstrates that no more than 2.81% of medium-range order exists in the samples, and interestingly, there is a thickness dependence of optical constants for a-Si in the range of 1.5–5.0 eV.

Speckle Suppression by Decoherence in Fluctuation Electron Microscopy

We compare experimental fluctuation electron microscopy (FEM) speckle data with electron diffraction simulations for thin amorphous carbon and silicon samples. We find that the experimental speckle intensity variance is generally more than an order of magnitude lower than kinematical scattering theory predicts for spatially coherent illumination. We hypothesize that decoherence, which randomizes the phase relationship between scattered waves, is responsible for the anomaly. Specifically, displacement decoherence can contribute strongly to speckle suppression, particularly at higher beam energies. Displacement decoherence arises when the local structure is rearranged significantly by interactions with the beam during the exposure. Such motions cause diffraction speckle to twinkle, some of it at observable time scales. We also find that the continuous random network model of amorphous silicon can explain the experimental variance data if displacement decoherence and multiple scattering is included in the modeling. This may resolve the longstanding discrepancy between X-ray and electron diffraction studies of radial distribution functions, and conclusions reached from previous FEM studies. Decoherence likely affects all quantitative electron imaging and diffraction studies. It likely contributes to the so-called Stobbs factor, where high-resolution atomic-column image intensities are anomalously lower than predicted by a similar factor to that observed here.

Interferometric Diffraction from Amorphous Double Films

We explore the interference fringes that arise in diffraction patterns from double-layer amorphous samples where there is a substantial separation, up to about a micron, between two overlapping thin films. This interferometric diffraction geometry, where both waves have interacted with the specimen, reveals phase gradients within microdiffraction patterns. The rapid fading of the observed fringes as the magnitude of the diffraction vector increases confirms that displacement decoherence is strong in high-energy electron scattering from amorphous samples. The fading of fringes with increasing layer separation indicates an effective illumination coherence length of about 225 nm, which is consistent with the value of 270 nm expected for the heated Schottky field emitter source. A small reduction in measured coherence length is expected because of the additional energy spread induced in the beam after it passes through the first layer.

Interpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimens

The interpretation of angular symmetries in electron nanodiffraction patterns from thin amorphous specimens is examined. It is found that in general there are odd symmetries in experimental electron nanodiffraction patterns. Using simulation, it is demonstrated that this effect can be attributed to dynamical scattering, rather than other divergences from the ideal experimental conditions such as probe-forming lens aberrations and camera noise. The departure of opposing diffracted intensities from Friedel's law in the phase grating formalism is calculated using a general structure factor for disordered materials. On the basis of this, a simple correction procedure is suggested to recover the kinematical angular symmetries, and thus readily interpretable information that reflects the symmetries of the original projected object. This correction is numerically tested using both the phase object and multislice calculations, and is demonstrated to fully recover all the kinematical diffracted symmetries from a simulated atomic model of a metallic glass.

Quantitative fluctuation electron microscopy in the STEM: methods to identify, avoid, and correct for artifacts

Fluctuation electron microscopy can reveal the nanoscale order in amorphous materials via the statistical variance in the scattering intensity as a function of position, scattering vector, and resolution. However, several sources of experimental artifacts can seriously affect the magnitude of the variance peaks. The use of a scanning transmission electron microscope for data collection affords a convenient means to check whether artifacts are present. As nanodiffraction patterns are collected in serial, any spatial or temporal dependence of the scattering intensity across the series can easily be detected. We present examples of the major types of artifact and methods to correct the data or to avoid the problem experimentally. We also re-cast the statistical formalism used to identify sources of noise in view of the present results. The present work provides a basis on which to perform fluctuation electron microscopy with a high level of reliability and confidence in the quantitative magnitude of the data.

Nanocrystallite model for amorphous calcium carbonate

Amorphous calcium carbonate phases, either synthesized artificially or generated biogenically, can be identified from broadened peaks in X-ray or electron diffraction profiles. It is conceivable that randomly oriented nanocrystals, approximately 1 nm in size, could give rise to coherent diffraction profiles that are characterized as amorphous. The coherent diffraction profiles for 200 keV electrons, as might be used in an electron microscope, and Cu Kα X-rays were calculated for needle-shaped calcite crystals bounded by \{ {11\overline 21}\} facets and rhomb-shaped crystals bounded by \{ {10\overline 14} \} facets. Crystals of about 1.0 nm in size gave a profile that is consistent with the X-ray measurements of amorphous calcium carbonate. The relative intensity of high-angle broadened peaks and changes in the IR spectrum are best explained by disorder in the nanocrystallites. The presence of randomly oriented nanocrystallites also explains the lack of optical birefringence.

Liquid-liquid phase transition in quasi-two-dimensional supercooled silicon

Anomalies of the local structural order in quasi-two-dimensional liquid silicon upon cooling are investigated. Results show that the appearance of the left subpeak in pair correlation functions is the signature of the liquid-liquid phase transition (LLPT). The structural origin of the LLPT is the formation of a crystal-like ordered structure with a short-range scale, which in turn forms the local well-organized paracrystalline region. Unlike in the bulk liquid silicon, the stages of the LLPT and liquid-solid phase transition (LSPT) in the quasi-two-dimensional liquid silicon do not overlap. The crystal-like ordered structures formed in the LLPT are precursors which are prepared for the subsequent LSPT. Also observed was a strong interconnection between the local well-organized paracrystalline region and the transition from the typical metal to the semimetal in the two-dimensional silicon. This study will aid in better understanding of the essential phase change in two-dimensional liquid silicon.

Detecting orientational order in model systems by X-ray cross-correlation methods

The results of a computational X-ray cross-correlation analysis (XCCA) study on two-dimensional polygonal model structures are presented. This article shows how to detect and identify the orientational order of such systems, demonstrates how to eliminate the influence of the `computational box' on the XCCA results and develops new correlation functions that reflect the sample's orientational order only. For this purpose, the dependence of the correlation functions on the number of polygonal clusters and scattering vector magnitudeqis studied for various types of polygons, including mixtures of polygons and randomly placed particles. An order parameter that describes the orientational order within the sample is defined. Finally, the influence of detector noise and nonplanar wavefronts on the XCCA data is determined, both of which appear to affect the results significantly and have thus to be considered in real experiments.

Characteristics of angular cross correlations studied by light scattering from two-dimensional microsphere films

Recently the analysis of scattering patterns by angular cross-correlation analysis (CCA) was introduced to reveal the orientational order in disordered samples with special focus to future applications on x-ray free-electron laser facilities. We apply this CCA approach to ultra-small-angle light-scattering data obtained from two-dimensional monolayers of microspheres. The films were studied in addition by optical microscopy. This combined approach allows to calculate the cross-correlations of the scattering patterns, characterized by the orientational correlation function Ψ(l)(q), as well as to obtain the real-space structure of the monolayers. We show that CCA is sensitive to the orientational order of monolayers formed by the microspheres which are not directly visible from the scattering patterns. By mixing microspheres of different radii the sizes of ordered monolayer domains is reduced. For these samples it is shown that Ψ(l)(q) quantitatively describes the degree of hexagonal order of the two-dimensional films. The experimental CCA results are compared with calculations based on the microscopy images. Both techniques show qualitatively similar features. Differences can be attributed to the wave-front distortion of the laser beam in the experiment. This effect is discussed by investigating the effect of different wave fronts on the cross-correlation analysis results. The so-determined characteristics of the cross-correlation analysis will be also relevant for future x-ray-based studies.

The importance of averaging to interpret electron correlographs of disordered materials

The development of effective new tools for structural characterization of disordered materials and systems is becoming increasingly important as such tools provide the key to understanding, and ultimately controlling, their properties. The relatively novel technique of correlograph analysis (i.e., the approach of calculating angular autocorrelations within diffraction patterns) promises unique advantages for probing the local symmetries of disordered structures. Because correlograph analysis examines a component of the high-order four-body correlation function, it is more sensitive to medium-range ordering than conventional diffraction methods. As a follow-up of our previous publication, where we studied thin samples of sputtered amorphous silicon, we describe here the practical experimental method and common systematic errors of electron correlograph analysis. Using both experimental data and numerical simulations, we demonstrate that reliable structural information about the sample can only be extracted from the mean correlograph averaged over a sufficient number of individual results.

A journey from order to disorder - atom by atom transformation from graphene to a 2D carbon glass

One of the most interesting questions in solid state theory is the structure of glass, which has eluded researchers since the early 1900's. Since then, two competing models, the random network theory and the crystallite theory, have both gathered experimental support. Here, we present a direct, atomic-level structural analysis during a crystal-to-glass transformation, including all intermediate stages. We introduce disorder on a 2D crystal, graphene, gradually, utilizing the electron beam of a transmission electron microscope, which allows us to capture the atomic structure at each step. The change from a crystal to a glass happens suddenly, and at a surprisingly early stage. Right after the transition, the disorder manifests as a vitreous network separating individual crystallites, similar to the modern version of the crystallite theory. However, upon increasing disorder, the vitreous areas grow on the expense of the crystallites and the structure turns into a random network. Thereby, our results show that, at least in the case of a 2D structure, both of the models can be correct, and can even describe the same material at different degrees of disorder.

Quantifying nanoscale order in amorphous materials via scattering covariance in fluctuation electron microscopy

Fluctuation Transmission Electron Microscopy (FTEM) has a unique ability to probe topological order on the 1-3 nm length scale in diffraction amorphous materials. However, extracting a quantitative description of the order has been challenging. We report that the FTEM covariance, computed at two non-degenerate Bragg reflections, is able to distinguish different regimes of size vs. volume fraction of order. The covariance analysis is general and does not require a material-specific atomistic model. We use a Monte-Carlo approach to compute different regimes of covariance, based on the probability of exciting multiple Bragg reflections when a STEM nanobeam interacts with a volume containing ordered regions in an amorphous matrix. We perform experimental analysis on several sputtered amorphous thin films including a-Si, nitrogen-alloyed GeTe and Ge₂Sb₂Te₅. The samples contain a wide variety of ordered states. Comparison of experimental data with the covariance simulation reveals different regimes of nanoscale topological order.

Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor

We report the results of highly sensitive transmission X-ray scattering measurements performed at the Advanced Photon Source, Argonne National Laboratory, on nearly fully dense high-purity amorphous-silicon (a-Si) samples for the purpose of determining their degree of hyperuniformity. A perfectly hyperuniform structure has complete suppression of infinite-wavelength density fluctuations, or, equivalently, the structure factor S(q→0) = 0; the smaller the value of S(0), the higher the degree of hyperuniformity. Annealing was observed to increase the degree of hyperuniformity in a-Si where we found S(0) = 0.0075 (±0.0005), which is significantly below the computationally determined lower bound recently suggested by de Graff and Thorpe [de Graff AMR, Thorpe MF (2010) Acta Crystallogr A 66(Pt 1):22-31] based on studies of continuous random network models, but consistent with the recently proposed nearly hyperuniform network picture of a-Si. Increasing hyperuniformity is correlated with narrowing of the first diffraction peak and extension of the range of oscillations in the pair distribution function.

Systematic mapping of icosahedral short-range order in a melt-spun Zr36Cu64 metallic glass

By analyzing the angular correlations in scanning electron nanodiffraction patterns from a melt-spun Zr(36)Cu(64) glass, the dominant local order was identified as icosahedral clusters. Mapping the extent of this icosahedral short-range order demonstrates that the medium-range order in this material is consistent with a face-sharing or interpenetrating configuration. These conclusions support results from atomistic modeling and a structural basis for the glass formability of this system.

Examination of a polycrystalline thin-film model to explore the relation between probe size and structural correlation length in fluctuation electron microscopy

We examine simulated electron microdiffraction patterns from models of thin polycrystalline silicon. The models are made by a Voronoi tessellation of random points in a box. The Voronoi domains are randomly selected to contain either a randomly-oriented cubic crystalline grain or a region of continuous random network material. The microdiffraction simulations from coherent probes of different widths are computed at the ideal kinematical limit, ignoring inelastic and multiple scattering. By examining the normalized intensity variance that is obtained in fluctuation electron microscopy experiments, we confirm that intensity fluctuations increase monotonically with the percentage of crystalline grains in the material. However, anomalously high variance is observed for models that have 100% crystalline grains with no imperfections. We confirm that the reduced normalized variance, V(k,R) - 1, that is associated with four-body correlations at scattering vector k, varies inversely with specimen thickness. Further, for probe sizes R larger than the mean grain size, we confirm that the reduced normalized variance obeys the predicted form given by Gibson et al. [Ultramicroscopy, 83, 169-178 (2000)] for the kinematical coherent scattering limit.

Focused-ion-beam-inflicted surface amorphization and gallium implantation--new insights and removal by focused-electron-beam-induced etching

Recently focused-electron-beam-induced etching of silicon using molecular chlorine (Cl(2)-FEBIE) has been developed as a reliable and reproducible process capable of damage-free, maskless and resistless removal of silicon. As any electron-beam-induced processing is considered non-destructive and implantation-free due to the absence of ion bombardment this approach is also a potential method for removing focused-ion-beam (FIB)-inflicted crystal damage and ion implantation. We show that Cl(2)-FEBIE is capable of removing FIB-induced amorphization and gallium ion implantation after processing of surfaces with a focused ion beam. TEM analysis proves that the method Cl(2)-FEBIE is non-destructive and therefore retains crystallinity. It is shown that Cl(2)-FEBIE of amorphous silicon when compared to crystalline silicon can be up to 25 times faster, depending on the degree of amorphization. Also, using this method it has become possible for the first time to directly investigate damage caused by FIB exposure in a top-down view utilizing a localized chemical reaction, i.e. without the need for TEM sample preparation. We show that gallium fluences above 4 × 10(15) cm(-2) result in altered material resulting from FIB-induced processes down to a depth of ∼ 250 nm. With increasing gallium fluences, due to a significant gallium concentration close beneath the surface, removal of the topmost layer by Cl(2)-FEBIE becomes difficult, indicating that gallium serves as an etch stop for Cl(2)-FEBIE.