Grazing Incidence Fast Atom Diffraction Research Articles

Semiquantum versus quantum methods for grazing-incidence fast-atom diffraction: Influence of the wave-packet size

Semiquantum versus quantum methods for grazing-incidence fast-atom diffraction: Influence of the wave-packet size

Grazing incidence fast atom diffraction: general considerations, semiclassical perturbation theory and experimental implications.

Using semiclassical methods, an analytical approach to describe grazing incidence scattering of fast atoms (GIFAD) from surfaces is described. First, we consider a model with a surface corrugated in the scattering plane, which includes the surface normal and the incidence direction. The treatment uses a realistic, Morse potential, within a perturbation approach, and correctly reproduces the basic GIFAD phenomenology, whereby the scattering is directed primarily in the specular direction. Second, we treat the more general case of scattering from a surface corrugated in two-dimensions. Using time averaging along the direction of fast motion in the incidence direction, we derive a time dependent potential for the GIFAD scattering away from a low index direction. The results correctly describe the observation that diffraction is seen only when the scattering plane is aligned close to a low-index direction in the surface plane. For the case of helium scattering from LiF(001) we demonstrate that the resulting theoretical predictions agree well with experiment and show that the analysis provides new information on the scattering time and the length scale of the interaction. The analysis also gives insights into the validity of the axial surface channeling approximation (ASCA) and shows that within first order perturbation theory, along a low-index direction, the full 3-dimensional problem can be represented accurately by an equivalent 2-dimensional problem with a potential averaged along the third dimension. In contrast, away from low-index directions, the effective 2-dimensional potential in the projectile frame is time-dependent.

Decoherent phonon effects in fast atom-surface scattering

The study of the influence of phonon-mediated processes on grazing-incidence fast atom diffraction (GIFAD) patterns is relevant for the use of GIFAD as a surface analysis technique. In this work, we apply the Phonon-Surface Initial Value Representation (P-SIVR) approximation to investigate lattice vibration effects on GIFAD patterns for the He/LiF(001) system at room temperature. The main features introduced by thermal lattice vibrations in the angular distributions of the scattered helium atoms are analyzed by keeping a fixed impact energy and varying the incidence angle to consider normal energies in the 0.1–3 eV range. In all the cases, thermal fluctuations introduce a wide polar spread that transforms the interference maxima into elongated strips. We found that the log-normal polar widths of the specular and outermost maxima do not depend on the normal energy, as it was experimentally observed. In addition, when the normal energy increases, not only the relative intensities of interference peaks are affected by the crystal vibrations, but also the visibility of the interference structures, which disappear completely for normal energies approximately equal to 3 eV. These findings qualitatively agree with recent experimental data, but the simulated polar widths underestimate the experimentally-derived limit, suggesting that there are other mechanisms, such as inelastic processes involving the net exchange of phonons, that contribute to the polar dispersion of the GIFAD patterns.

Grazing incidence fast atom diffraction in high-pressure conditions

Grazing Incidence Fast Atom Diffraction (GIFAD) is a recent technique for characterizing surface structures and real-time monitoring of thin film growth. Up to now, GIFAD has only been used in Ultra-High-Vacuum conditions, typically in the range of 10−10 to 10−8 mbar, and has therefore only been considered for high vacuum deposition methods like Molecular Beam Epitaxy or very low-pressure Chemical Vapor Deposition (CVD). At pressures exceeding 10−6 mbar, gas phase collisions along the atom beam trajectory not only reduce the mean free path but also degrade the beam coherence length and thus potentially suppress the diffraction signal. In addition, pressures lower than 10−5 mbar are required to maintain a low noise level on the scattered particle detector. In a new configuration, we demonstrate that GIFAD can operate at pressure as high as 10−2 mbar of argon with well-contrasted diffraction patterns. This opens wide avenues for the study of surface reactivity, thin film growth in Magnetron Sputtering Deposition, where electron diffraction is inevitably perturbed by the electromagnetic fields. This High-Pressure version of GIFAD could also be extended to Reactive Pulsed Laser Deposition and many CVD variants.

Comment on "Perturbation theory of scattering for grazing-incidence fast-atom diffraction", by W. Allison, S. Miret-Artés and E. Pollak, Phys. Chem. Chem. Phys., 2022, 24, 15851.

In this comment we discuss some aspects of Phys. Chem. Chem. Phys., 2022, 24, 15851, by Allison et al., an article intensely motivated by our study of grazing incidence fast atom diffraction (GIFAD) for He-KCl(001) [G. A. Bocan, H. Breiss, S. Szilasi, A. Momeni, M. E. Staicu Casagrande, M. S. Gravielle, E. A. Sánchez and H. Khemliche, Phys. Rev. Lett., 2020, 125, 096101; G. A. Bocan, H. Breiss, S. Szilasi, A. Momeni, M. E. Staicu Casagrande, E. A. Sánchez, M. S. Gravielle and H. Khemliche, Phys. Rev. B, 2021, 104, 235401]. In particular, (a) we show that, contrary to first order perturbation prediction, the surface corrugation is not proportional to the tangent of the rainbow angle and, (b) we analyze whether a Morse-like formula, like the one Allison et al. use, is able to reproduce the atom-surface potential derived from density functional theory (DFT) calculations. In addition, we give some clarifications regarding specific remarks the authors made about our articles.

Elastic and inelastic diffraction of fast neon atoms on a LiF surface.

Grazing incidence fast atom diffraction has mainly been investigated with helium atoms, considered as the best possible choice for surface analysis. This article presents experimental diffraction profiles recorded with neon projectile, between 300 eV and 4 keV kinetic energy with incidence angles θi between 0.3 and 1.5° along three different directions of a LiF(001) crystal surface. These correspond to perpendicular energy ranging from a few meV up to almost 1 eV. A careful analysis of the scattering profile allows us to extract the diffracted intensities even when inelastic effects become so large that most quantum signatures have disappeared. The relevance of this approach is discussed in terms of surface topology.

Reply to the 'Comment on "Perturbation theory of scattering for grazing-incidence fast-atom diffraction"' by G. A. Bocan, H. Breiss, S. Szilasi, A. Momeni, E. M. S. Casagrande, E. A. Sánchez, M. S. Gravielle and H. Khemliche, Phys. Chem. Chem. Phys., 2023, 25, DOI: 10.1039/D3CP02486E.

In this Reply, we show that criticisms of perturbation theory for grazing-incidence fast-atom diffraction (GIFAD) are ill-founded. We show explicitly that our formulation (W. Allison, S. Miret-Artés and E. Pollak, Phys. Chem. Chem. Phys., 2022, 24, 15851) provides a similar precision in describing the observed phenomena as ab initio potentials. Since that is the main criterion to distinguish between methods, it seems reasonable to conclude that the perturbation approach using a Morse-type potential reproduces the essential aspects of the dynamics correctly. In addition we expand on the historical context and summarize the physical insights provided by our methods.

Terrace effects in grazing-incidence fast atom diffraction from a LiF(001) surface

The effect produced by surface defects on grazing-incidence fast atom diffraction (GIFAD) patterns is studied by considering the presence of terraces in a LiF(001) sample. For helium atoms impinging along the $\ensuremath{\langle}110\ensuremath{\rangle}$ direction of the LiF surface, we analyze the influence of a monolayer terrace with its edge oriented parallel or perpendicular to the axial channel. We found that the presence of an outward transverse step introduces a diffuse background above the Laue circle, which displays additional peaked structures. For inward transverse steps, instead, such a background is placed below the Laue circle, showing a much weaker intensity. On the other hand, parallel steps give rise to asymmetric angular distributions, which are completely confined to the Laue circle. Therefore, these theoretical results suggest that GIFAD might be used to characterize terrace defects.

A setup for grazing incidence fast atom diffraction.

We describe a UHV setup for grazing incidence fast atom diffraction (GIFAD) experiments. The overall geometry is simply a source of keV atoms facing an imaging detector. Therefore, it is very similar to the geometry of reflection high energy electron diffraction experiments used to monitor growth at surfaces. Several custom instrumental developments are described making GIFAD operation efficient and straightforward. The difficulties associated with accurately measuring the small scattering angle and the related calibration are carefully analyzed.

Perturbation theory of scattering for grazing-incidence fast-atom diffraction.

Recent grazing-incidence, fast atom diffraction (GIFAD) experiments have highlighted the well known observation that the distance between classical rainbow angles depends on the incident energy. The GIFAD experiments imply an incident vertical scattering angle, facilitating an analytic analysis using classical perturbation theory, which leads to the conclusion that the so called "dynamic corrugation" amplitude, as defined by Bocan et al., Phys. Rev. Lett., 2020 125, 096101 is, within first-order perturbation theory, proportional to the tangent of the rainbow angle. Therefore it provides no further information about the interaction than is gleaned from the rainbow angle and its energy dependence. Perhaps more importantly, the resulting analytic theory reveals how the energy dependence of rainbow angles may be inverted into information on the force field governing the interaction of the incident projectile with the surface.

Grazing incidence fast atom diffraction, similarities and differences with thermal energy atom scattering (TEAS).

Grazing incidence fast atom diffraction (GIFAD) at surfaces has made rapid progress and has established itself as a surface analysis tool where effective energy E⊥ of the motion towards the surface is in the same range as that in thermal energy atom scattering (TEAS). To better compare the properties of both techniques, we use the diffraction patterns of helium and neon atoms impinging on a LiF (001) surface as a model system. E-Scan, θ-scan, and φ-scan are presented where the primary beam energy E is varied between a few hundred eV up to five keV, the angle of incidence θi between 0.2 and 2° and the azimuthal angle φi around 360°. The resulting diffraction charts are analyzed in terms of high and low values of effective energy E⊥. The former provides high resolution at the positions of the surface atoms and the attached repulsive interaction potentials while the second is sensitive to the attractive forces towards the surface. The recent progress of inelastic diffraction is briefly presented.

Thermal effects on helium scattering from LiF(001) at grazing incidence

Grazing-incidence fast atom diffraction (GIFAD) is an exceptionally sensitive method for surface analysis, which can be applied not only at room temperature but also at higher temperatures. In this work we use the He-LiF(001) system as a benchmark to study the influence of temperature on GIFAD patterns from insulator surfaces. Our theoretical description is based on the phonon-surface initial value representation (P0-SIVR) approximation, which is a semiquantum approach that includes the phonon contribution to the elastic scattering. Within the P0-SIVR approach the main features introduced by thermal lattice vibrations on the angular distributions of scattered projectiles are investigated as a function of the crystal temperature. We found that azimuthal and polar spectra are strongly affected by thermal fluctuations, which modify the relative intensities and the polar spread of the interference structures. These findings are relevant for the use of GIFAD in surface research. Moreover, the present results are contrasted with available experimental data at room temperature.

Phonon contribution to grazing incidence fast atom diffraction

SynopsisWe address the effect of lattice vibrations of the crystal on grazing incidence fast atom diffraction (GIFAD) from insulator surfaces. To describe the phonon contribution to GIFAD we introduce a semi-quantum method, named Phonon-Surface Initial Value Representation (P-SIVR), which represents the surface with a harmonic crystal model, while the scattering process is given by the Surface Initial Value Representation approach including phonon excitations. P-SIVR results for Ne/LiF(001) are compared with other theoretical methods and available experiments.

Fast atom interaction with surfaces at grazing incidence: classical and quantum scattering applied to thin film growth

SynopsisCharacterization of solid surfaces with heavy particles has mainly relied on the use of ions at energies from keV to MeV. Although atomic diffraction at thermal energies has been known since 1930 and became popular in the 1970’s as a powerful surface characterization technique, it is nowadays rather confidential. Unexpectedly, diffraction with atoms in the keV range has also been observed despite the tininess of the de Broglie wavelength. Grazing Incidence Fast Atom Diffraction (GIF AD) has now become mature and allows the real-time analysis, during the growth, of the most fragile layers.

Phonon contribution in grazing-incidence fast atom diffraction from insulator surfaces

We study the effect of crystal lattice vibrations on grazing-incidence fast atom diffraction (GIFAD) from insulator surfaces. To describe the phonon contribution to GIFAD we introduce a semiquantum method named phonon-surface initial value representation (P-SIVR), which represents the surface with a harmonic-crystal model, while the scattering process is described by means of the surface initial value representation approach, including phonon excitations. Expressions for the partial scattering probabilities involving zero- and one-phonon exchange are derived. In particular, the P-SIVR approach for zero-phonon scattering is applied to study the influence of thermal lattice vibrations on GIFAD patterns for Ne/LiF(001) at room temperature. It is found that the thermal lattice fluctuations introduce a polar-angle spread into the projectile distributions, which can affect the relative intensities of the interference maxima, even giving rise to interference subpatterns depending on the incidence conditions. Present results are in agreement with the available experiments.

Coherence-Length Effects in Fast Atom Diffraction at Grazing Incidence

Coherence properties of projectiles, found relevant in ion-atom collisions, are investigated by analyzing the influence of the degree of coherence of the atomic beam on interference patterns produced by grazing-incidence fast-atom diffraction (GIFAD or FAD). The transverse coherence length of the projectiles, which depends on the incidence conditions and the collimating setup, determines the overall characteristics of GIFAD distributions. We show that for atoms scattered from a LiF(001) surface after a given collimation, we can modify the interference signatures of the angular spectra by varying the total impact energy, while keeping the normal energy as a constant. Also, the role played by the geometry of the collimating aperture is analyzed, comparing results for square and circular openings. Furthermore, we study the spot-beam effect, which is due to different focus points of the impinging particles. We show that when a region narrower than a single crystallographic channel is coherently illuminated by the atomic beam, the spot-beam contribution strongly affects the visibility of the interference structures, contributing to the gradual quantum-classical transition of the projectile distributions.

Spot-beam effect in grazing atom-surface collisions: from quantum to classical

Grazing incidence fast atom diffraction (GIFAD) is a sensitive tool for surface analysis, which strongly relies on the quantum coherence of the incident beam. In this article we study the spot-beam effect, due to contributions coming from different positions of the focus point of the incident particles, which affects the coherence of GIFAD spectra. We show that the influence of the spot-beam effect on GIFAD patterns depends on the width of the surface area that is coherently lighted by the atomic beam. While for extended illuminations the spot-beam contribution plays a minor role, when a narrow surface area is coherently lighted, the spot-beam effect allows projectiles to explore different zones of a single crystallographic channel, bringing to light intra-channel interference structures. In this last case the spot-beam effect gives also rise to a non-coherent background, which deteriorates the visibility of the interference structures. We found that by varying the impact energy, while keeping the same collimating setup, it is possible to switch gradually from quantum to classical projectile distributions. Present results are compared with available experimental data, making evident that the inclusion of focusing effects is necessary for the proper theoretical description of the experimental spectra.

GIFAD for He/KCl(001). Structure in the pattern for 〈110〉 incidence as a measure of the projectile-cation interaction

Abstract In this article we address grazing incidence fast atom diffraction (GIFAD) for the He/KCl(001) system, for which a systematic experimental study was recently reported [E. Meyer, Ph.D dissertation, Humboldt-Universitat, Berlin, Germany, 2015]. Our theoretical model is built from a projectile-surface interaction obtained from Density Functional Theory (DFT) calculations and the Surface Initial-Value Representation (SIVR), which is a semi-quantum approach to describe the scattering process. For incidence along the 〈 100 〉 and 〈 110 〉 directions, we present and discuss the main features of our interaction potential, the dependence of the rainbow angle with the impact energy normal to the surface, and the simulated GIFAD patterns, which reproduce the main aspects of the reported experimental charts. The features of the diffraction charts for He/KCl(001) are related to the averaged equipotential curves of the system and a comparison is established with the case of He/LiF(001). The marked differences observed for 〈 110 〉 incidence are explained as due to the much larger size of the K+ ion relative to that of Li+.

Ultrafast Crystallization Dynamics at an Organic-Inorganic Interface Revealed in Real Time by Grazing Incidence Fast Atom Diffraction.

The poor structural properties of organic-inorganic interfaces and their variability represent the main cause of device under-performance. Understanding and controlling the development of these properties in real time has been a difficult experimental challenge. Using a recent technique based on grazing incidence fast atom diffraction (GIFAD), we were able to directly observe during deposition structural transitions in a perylene monolayer on Ag(110). Crystallization from the liquid phase occurs into two distinct structures with drastically different dynamics. Transition to the most compact packing occurs by self-organization only after a second layer has started to build up; subsequent incorporation of molecules from second to first layer triggers an ultrafast crystallization on a macroscopic sale. The final compact crystalline structure shows a long-range order and superior stability, which opens good perspectives for producing in a controlled manner highly ordered hybrid interfaces for photovoltaics and molecular electronics.

Fast interaction of atoms with crystal surfaces: coherent lighting

Quantum coherence of incident waves results essential for the observation of interference patterns in grazing incidence fast atom diffraction (FAD). In this work we investigate the influence of the impact energy and projectile mass on the transversal length of the surface area that is coherently illuminated by the atomic beam, after passing through a collimating aperture. Such a transversal coherence length controls the general features of the interference structures, being here derived by means of the Van Cittert-Zernike theorem. The coherence length is then used to build the initial coherent wave packet within the Surface Initial Value Representation (SIVR) approximation. The SIVR approach is applied to fast He and Ne atoms impinging grazingly on a LiF(001) surface along a low-indexed crystallographic direction. We found that with the same collimating setup, by varying the impact energy we would be able to control the interference mechanism that prevails in FAD patterns, switching between inter-cell and unit-cell interferences. These findings are relevant to use FAD spectra adequately as a surface analysis tool, as well as to choose the appropriate collimating scheme for the observation of interference effects in a given collision system.