Fourier optics of image formation in aberration-corrected LEEM.

We present the extended Fourier Optics (FO) approach for modeling image formation in aberration-corrected low energy electron microscopy (ac-LEEM). The FO formalism is also generalized for image simulations of one or two-dimensional objects in ac and uncorrected (nac) LEEM. A comparison is made of the extended FO approach presented here and the extended contrast transfer function (CTF) approach for ac-LEEM that was developed earlier. The mathematically rigorous extended FO approach gains an advantage under conditions, particularly defocus, that partial coherence of the illumination may compromise the validity of the approximate CTF intensity calculation. The drawback of the FO approach compared to the CTF approach, which is its slow computational speed, is mitigated partly here by the implementation of a multi-core, multi-threading programming architecture. This work broadens our capabilities to understand the origins of LEEM image contrast and to perform quantitative evaluation of contrast observed in an image focal series.

High throughput scanning µLEED imaging of surface structural heterogeneity: Defective graphene on Cu(111).

Micro-low energy electron diffraction (µLEED) is frequently used in conjunction with low energy electron microscopy (LEEM) to learn about local surface structural features in small selected areas. Scanning µLEED measurements performed with a very small electron beam (250 nm) can provide precise quantitative information about structural variations with high spatial resolution. We have developed the Source Extraction and Photometry (SEP) - Spot Profile Analysis (SPA) tool for evaluating scanning µLEED data with high throughput. The capability to automate diffraction peak identification with SEP-SPA opens up the possibility to investigate systems with complex diffraction patterns in which diffraction peak positions vary rapidly for small lateral displacements on the surface. The application of this tool to evaluate scanning µLEED data obtained for defective graphene on Cu(111) demonstrates its capabilities. A rich rotational domain structure is observed in which a majority of the graphene is co-aligned with the Cu(111) substrate and the significant remainder comprises domains with large rotations and small sizes that are comparable to the small beam size.

Comparing Fourier optics and contrast transfer function modeling of image formation in low energy electron microscopy.

A theoretical understanding of image formation in cathode lens microscopy can facilitate image interpretation. We compare Fourier Optics (FO) and Contrast Transfer Function (CTF) approaches that were recently adapted from other realms of microscopy to model image formation in low energy electron microscopy (LEEM). Although these two approaches incorporate imaging errors from several sources similarly, they differ in the way that the image intensity is calculated. The simplification that is used in the CTF calculation advantageously leads to its computational efficiency. However, we find that lens aberrations, and spatial and temporal coherence may affect the validity of the CTF approach to model LEEM image formation under certain conditions. In particular, these effects depend strongly on the nature of the object being imaged and also become more pronounced with increasing defocus. While the use of the CTF approach appears to be justified for objects that are routinely imaged with LEEM, comparison of theory to experimental observations of a focal image series for rippled, suspended graphene reveals one example where FO works, but CTF does not. This work alerts us to potential pitfalls and guides the effective use of FO and CTF approaches. It also lays the foundation for quantitative image evaluation using these methods.

Defocus in cathode lens instruments.

Accurately measuring defocus in cathode lens instruments (Low Energy Electron Microscopy - LEEM, and Photo Electron Emission Microscopy - PEEM) is a pre-requisite for quantitative image analysis using Fourier Optics (FO) or Contrast Transfer Function (CTF) image simulations. In particular, one must establish a quantitative relation between lens excitation and image defocus. One way to accomplish this is the Real-Space Microspot LEED method, making use of the accurately known angles of diffracted electron beams, and the defocus-dependent shifts of their corresponding real-space images. However, this only works if a sufficiently large number of diffracted beams is available for the sample under investigation. An alternative is to shift the sample along the optical axis by a known distance, and measure the change in objective lens excitation required to re-focus the image. We analytically derive the relation between sample shift and defocus, and apply our results to the measurement and analysis of achromats in an aberration-corrected LEEM instrument.

Probing buried magnetic interface structure with the quantum size effect in spin-dependent electron reflectivity.

The quantum size effect (QSE) in electron reflectivity from Fe thin films grown on a W(110) surface precovered with a two monolayer Cu film has been investigated using spin polarized low energy electron microscopy. Spin-dependent QSE-induced oscillations in the reflected intensity occur with energy and film thickness. The series of intensity peaks that is observed identifies spin-dependent quantum well resonances in the Fe film that are sensitive to electronic band structure and details of the buried interface. Information about the spin-dependent unoccupied bands of the Fe film in the ΓΝ direction normal to the film plane is obtained by analyzing the observed quantum well resonance conditions. The spin-split bands that are determined are uniformly shifted downward by 1.7 eV compared to bulk-like bands determined previously in Fe films on a bare W(110) substrate by the same method. Evidence is also obtained that the buried interface that defines the thin film quantum well boundary is located one layer above the W(110) surface. These results suggest that the Cu layer in direct contact with the substrate remains largely intact, but the weakly-bound second Cu layer mixes or segregates freely.

Spin polarized low energy electron microscopy of quantum well resonances in Fe films on the Cu-covered W(110) surface.

Spin polarized low energy electron microscopy has been used to investigate the quantum size effect (QSE) in electron reflectivity from Fe films grown on a pseudomorphic Cu layer on a W(110) surface. Intensity oscillations caused by the QSE as functions of Fe film thickness and incident electron energy identify quantum well resonance conditions in the film. Evaluation of these intensity oscillations using the phase accumulation model provides information on the unoccupied spin polarized band structure in the Fe film above the vacuum level. We also find evidence that the presence of the non-magnetic Cu layer shifts spin polarized quantum well resonances in the Fe layer uniformly downward in energy by 1.1eV compared to Fe/W(110) films without an interface Cu layer, suggesting that the Cu layer gives a small degree of control over the quantum well resonances.

LEEM image phase contrast of MnAs stripes.

Low energy electron microscopy (LEEM) imaging of strained MnAs layers epitaxially grown on GaAs(001) reveals striped contrast features that become more pronounced and vary systematically in width with increasing defocus, but that are completely absent in focus. Weaker subsidiary fringe-like features are observed along the stripe lengths, while asymmetric contrast reversal occurs between under-focus and over-focus conditions. A Fourier optics calculation is performed that demonstrates that these unusual observations can be attributed to a phase contrast mechanism between the hexagonal α phase and orthorhombic ß phase regions of the MnAs film, which self-organize into a periodic stripe array with ridge-groove morphology. The unequal widths of the α and ß phase regions are determined accurately from the through focus series, while the height variation in this system can also be determined in principle from the energy dependence of contrast.

Superdiffusive motion of the Pb wetting layer on the Si(111) surface.

Mass transport in the Pb wetting layer on the Si(111) surface is investigated by observing nonequilibrium coverage profile evolution with low energy electron microscopy and microlow energy electron diffraction. Equilibration of an initial coverage step profile occurs by the exchange of mass between oppositely directed steep coverage gradients that each move with unperturbed shape. The bifurcation of the initial profile, the shape of the profile between the two moving edges, and the time dependence of equilibration are all at odds with expectations for classical diffusion behavior. These observations signal a very unusual coverage dependence of diffusion or may even reveal an exceptional collective superdiffusive mechanism.

Low energy electron microscopy and photoemission electron microscopy investigation of graphene.

Low energy electron microscopy (LEEM) and photoemission electron microscopy (PEEM) are two powerful techniques for the investigation of surfaces, thin films and surface supported nanostructures. In this review, we examine the contributions of these microscopy techniques to our understanding of graphene in recent years. These contributions have been made in studies of graphene on various metal and SiC surfaces and free-standing graphene. We discuss how the real-time imaging capability of LEEM facilitates a deeper understanding of the mechanisms of dynamic processes, such as growth and intercalation. Numerous examples also demonstrate how imaging and the various available complementary measurement capabilities, such as selected area or micro low energy electron diffraction (µLEED) and micro angle resolved photoelectron spectroscopy (µARPES), allow the investigation of local properties in spatially inhomogeneous graphene samples.

A Contrast Transfer Function approach for image calculations in standard and aberration-corrected LEEM and PEEM.

We introduce an extended Contrast Transfer Function (CTF) approach for the calculation of image formation in low energy electron microscopy (LEEM) and photo electron emission microscopy (PEEM). This approach considers aberrations up to fifth order, appropriate for image formation in state-of-the-art aberration-corrected LEEM and PEEM. We derive Scherzer defocus values for both weak and strong phase objects, as well as for pure amplitude objects, in non-aberration-corrected and aberration-corrected LEEM. Using the extended CTF formalism, we calculate contrast and resolution of one-dimensional and two-dimensional pure phase, pure amplitude, and mixed phase and amplitude objects. PEEM imaging is treated by adapting this approach to the case of incoherent imaging. Based on these calculations, we show that the ultimate resolution in aberration-corrected LEEM is about 0.5 nm, and in aberration-corrected PEEM about 3.5 nm. The aperture sizes required to achieve these ultimate resolutions are precisely determined with the CTF method. The formalism discussed here is also relevant to imaging with high resolution transmission electron microscopy.

Trends in low energy electron microscopy.

Low energy electron microscopy (LEEM) and spin polarized LEEM (SPLEEM) are two powerful in situ techniques for the study of surfaces, thin films and other surface-supported nanostructures. Their real-time imaging and complementary diffraction capabilities allow the study of structure, morphology, magnetism and dynamic processes with high spatial and temporal resolution. Progress in methods, instrumentation and understanding of novel contrast mechanisms that derive from the wave nature and spin degree of freedom of the electron continue to advance applications of LEEM and SPLEEM in these areas and beyond. We review here the basic imaging principles and recent developments that demonstrate the current capabilities of these techniques and suggest potential future directions.

Fourier optics of image formation in LEEM.

A Fourier optics calculation of image formation in low energy electron microscopy (LEEM) is presented. The adaptation of the existing theory for transmission electron microscopy to the treatment of LEEM and other forms of cathode lens electron microscopy is explained. The calculation incorporates imaging errors that are caused by the objective lens (aberrations), contrast aperture (diffraction), imperfect source characteristics, and voltage and current instabilities. It is used to evaluate the appearance of image features that arise from phase objects such as surface steps and amplitude objects that produce what is alternatively called amplitude, reflectivity or diffraction contrast in LEEM. This formalism can be used after appropriate modification to treat image formation in other emission microscopies. Implications for image formation in the latest aberration-corrected instruments are also discussed.

Anomalous mass transport in the Pb wetting layer on the Si(111) surface.

The temporal evolution of nonequilibrium coverage profiles in the Pb wetting layer on the Si(111) surface is studied using low energy electron microscopy. The initial coverage step profile propagates rapidly at a constant velocity with an unperturbed shape. A model is proposed that attributes this nonclassical equilibration behavior to the diffusion of thermally generated adatoms on top of the wetting layer. This model can account for the observed convectionlike mass transport, as well as its dramatic dependence on Pb coverage. Such anomalous mass transport is believed to facilitate the remarkably efficient self-organization of uniform Pb quantum island height on the Si(111) surface that was observed previously.

Spin-dependent Fabry-Pérot interference from a Cu thin film grown on fcc Co(001).

Spin-dependent electron reflection from a Cu thin film grown on Co/Cu(001) was investigated using spin-polarized low-energy electron microscopy (SPLEEM). Fabry-Pe rot type interference was observed and is explained using the phase accumulation model. SPLEEM images of the Cu overlayer reveal magnetic domains in the Co underlayer, with the domain contrast oscillating with electron energy and Cu film thickness. This behavior is attributed to the spin-dependent electron reflectivity at the Cu/Co interface which leads to spin-dependent Fabry-Pe rot electron interference in the Cu film.

Ultrathin chromium oxide films on the W(100) surface.

Ultrathin chromium oxide films were prepared on a W(100) surface under ultrahigh-vacuum conditions and investigated in situ by X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy, and low-energy electron diffraction. The results show that, at Cr coverage of less than 1 monolayer, CrO2 is formed by oxidizing pre-deposited Cr at 300-320 K in approximately 10(-7) mbar oxygen. However, an increase of temperature causes formation of Cr2O3. At Cr coverage above 1 monolayer, only Cr2O3 is detected.

Kinetic limitations in electronic growth of Ag films on Fe(100).

Quantum well (QW) resonances are identified in Ag films on an Fe(100) surface and are used in low energy electron microscopy to monitor film morphology during annealing and growth. We find that Ag films thermally decompose to thicknesses that are stabilized by QW states at the Gamma point. Novel growth morphologies are also observed that highlight the competition between kinetic limitations and the QW state energetics that promote electronic growth. These combined observations help to explain the unusual bifurcation mode of thermal decomposition that was reported previously for this system.

Layer spacings in coherently strained epitaxial metal films.

Laterally resolved measurements of the quantum size effect (QSE) in electron reflectivity are made with low energy electron microscopy on coherently strained Ag films on a W(110) surface. The evolution of the total film thickness with increasing number of atomic layers is determined accurately by dynamical theory analysis of the QSE features. Combined with a model of layer spacings obtained from first-principles calculations, this provides for a novel approach to determine the buried interface layer spacing, which is inaccessible to other methods.

Surface diffusion anomaly near a substrate phase transition: H on W(100).

Using a linear optical diffraction method, we have experimentally studied the long predicted diffusion anomalous behavior for H/W(100) near the reconstructive phase transition of the W(100) substrate. This anomaly manifests itself in the form of a strong dip in the diffusion coefficient D at the transition temperature T(C). We interpret the strong reduction of D as a result of the diverging friction damping near the transition. The finite dip in D instead of a vanishing D at T(C) also demonstrates the importance of the non-Markovian (memory) deviation from the simple instantaneous damping picture.