Back illuminated photo emission electron microscopy (BIPEEM).

A new, complementary technique based on Photo Emission Electron Microscopy (PEEM) is demonstrated. In contrast to PEEM, the sample is placed on a transparent substrate and is illuminated from the back side while electrons are collected from the other (front) side. In this paper, the working principle of this technique, coined back-illuminated PEEM (BIPEEM), is described. In BIPEEM, the electron intensity is strongly thickness-dependent. This dependence can be described by a simple model which contains the optical attenuation length and the electron mean free path. Electrons forming an image in BIPEEM hence carry information of the inner part of the sample, as well as of the surface, as we demonstrate experimentally.

Low-Energy Electron Irradiation Damage in Few-Monolayer Pentacene Films.

Crystalline films of pentacene molecules, two to four monolayers in thickness, are grown via in situ sublimation on silicon substrates in the ultrahigh vacuum chamber of a low-energy electron microscope. It is observed that the diffraction pattern of the pentacene layers fades upon irradiation with low-energy electrons. The damage cross section is found to increase by more than an order of magnitude for electron energies from 0 to 10 eV and by another order of magnitude from 10 to 40 eV. Close to 0 eV, damage is virtually nil. Creation of chemically reactive atomic centers after electron attachment or impact ionization is thought to trigger chemical reactions between neighboring molecules that gradually transform the layer into a disordered carbon nanomembrane. Additionally, diminishing spectroscopic features related to the unoccupied band structure of the layers, accompanied by loss of definition in real-space images, and an increase in the background intensity of diffraction images during irradiation point to chemical changes and formation of a disordered layer.

Quantitative analysis of spectroscopic low energy electron microscopy data: High-dynamic range imaging, drift correction and cluster analysis.

For many complex materials systems, low-energy electron microscopy (LEEM) offers detailed insights into morphology and crystallography by naturally combining real-space and reciprocal-space information. Its unique strength, however, is that all measurements can easily be performed energy-dependently. Consequently, one should treat LEEM measurements as multi-dimensional, spectroscopic datasets rather than as images to fully harvest this potential. Here we describe a measurement and data analysis approach to obtain such quantitative spectroscopic LEEM datasets with high lateral resolution. The employed detector correction and adjustment techniques enable measurement of true reflectivity values over four orders of magnitudes of intensity. Moreover, we show a drift correction algorithm, tailored for LEEM datasets with inverting contrast, that yields sub-pixel accuracy without special computational demands. Finally, we apply dimension reduction techniques to summarize the key spectroscopic features of datasets with hundreds of images into two single images that can easily be presented and interpreted intuitively. We use cluster analysis to automatically identify different materials within the field of view and to calculate average spectra per material. We demonstrate these methods by analyzing bright-field and dark-field datasets of few-layer graphene grown on silicon carbide and provide a high-performance Python implementation.

Nonuniversal Transverse Electron Mean Free Path through Few-layer Graphene.

In contrast to the in-plane transport electron mean-free path in graphene, the transverse mean-free path has received little attention and is often assumed to follow the "universal" mean-free path (MFP) curve broadly adopted in surface and interface science. Here we directly measure transverse electron scattering through graphene from 0 to 25 eV above the vacuum level both in reflection using low energy electron microscopy and in transmission using electronvolt transmission electron microscopy. From these data, we obtain quantitative MFPs for both elastic and inelastic scattering. Even at the lowest energies, the total MFP is just a few graphene layers and the elastic MFP oscillates with graphene layer number, both refuting the universal curve. A full theoretical calculation taking the graphene band structure into consideration agrees well with experiment, while the key experimental results are reproduced even by a simple optical toy model.

Measuring chromatic aberration in LEEM/PEEM.

Measurement of chromatic aberration in a Low Energy Electron Microscope (LEEM) or Photo Electron Emission Microscope (PEEM) is necessary for quantitative image interpretation, and for accurate correction of chromatic aberration in an aberration-corrected instrument. While methods have been developed for measuring the spherical aberration coefficient, C3, measuring the chromatic aberration coefficient, Cc, remains a more difficult task. Here a novel method is introduced to simplify such measurements. The viability and accuracy is demonstrated using detailed electron-optical ray-tracing calculations. Experimental results show that the method is easily reduced to practice.

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.

Charge Catastrophe and Dielectric Breakdown During Exposure of Organic Thin Films to Low-Energy Electron Radiation.

The effects of exposure to ionizing radiation are central in many areas of science and technology, including medicine and biology. Absorption of UV and soft-x-ray photons releases photoelectrons, followed by a cascade of lower energy secondary electrons with energies down to 0 eV. While these low energy electrons give rise to most chemical and physical changes, their interactions with soft materials are not well studied or understood. Here, we use a low energy electron microscope to expose thin organic resist films to electrons in the range 0-50 eV, and to analyze the energy distribution of electrons returned to the vacuum. We observe surface charging that depends strongly and nonlinearly on electron energy and electron beam current, abruptly switching sign during exposure. Charging can even be sufficiently severe to induce dielectric breakdown across the film. We provide a simple but comprehensive theoretical description of these phenomena, identifying the presence of a cusp catastrophe to explain the sudden switching phenomena seen in the experiments. Surprisingly, the films undergo changes at all incident electron energies, starting at ∼0 eV.

Low-Energy Electron Potentiometry: Contactless Imaging of Charge Transport on the Nanoscale.

Charge transport measurements form an essential tool in condensed matter physics. The usual approach is to contact a sample by two or four probes, measure the resistance and derive the resistivity, assuming homogeneity within the sample. A more thorough understanding, however, requires knowledge of local resistivity variations. Spatially resolved information is particularly important when studying novel materials like topological insulators, where the current is localized at the edges, or quasi-two-dimensional (2D) systems, where small-scale variations can determine global properties. Here, we demonstrate a new method to determine spatially-resolved voltage maps of current-carrying samples. This technique is based on low-energy electron microscopy (LEEM) and is therefore quick and non-invasive. It makes use of resonance-induced contrast, which strongly depends on the local potential. We demonstrate our method using single to triple layer graphene. However, it is straightforwardly extendable to other quasi-2D systems, most prominently to the upcoming class of layered van der Waals materials.

An adjustable electron achromat for cathode lens microscopy.

Chromatic aberration correction in light optics began with the invention of a two-color-corrected achromatic crown/flint lens doublet by Chester Moore Hall in 1730. Such color correction is necessary because any single glass shows dispersion (i.e. its index of refraction changes with wavelength), which can be counteracted by combining different glasses with different dispersions. In cathode lens microscopes (such as Photo Electron Emission Microscopy - PEEM) we encounter a similar situation, where the chromatic aberration coefficient of the cathode lens shows strong dispersion, i.e. depends (non-linearly) on the energy with which the electrons leave the sample. Here I show how a cathode lens in combination with an electron mirror can be configured as an adjustable electron achromat. The lens/mirror combination can be corrected at two electron energies by balancing the settings of the electron mirror against the settings of the cathode lens. The achromat can be adjusted to deliver optimum performance, depending on the requirements of a specific experiment. Going beyond the achromat, an apochromat would improve resolution and transmission by a very significant margin. I discuss the requirements and outlook for such a system, which for now remains a wish waiting for fulfilment.

Catadioptric aberration correction in cathode lens microscopy.

In this paper I briefly review the use of electrostatic electron mirrors to correct the aberrations of the cathode lens objective lens in low energy electron microscope (LEEM) and photo electron emission microscope (PEEM) instruments. These catadioptric systems, combining electrostatic lens elements with a reflecting mirror, offer a compact solution, allowing simultaneous and independent correction of both spherical and chromatic aberrations. A comparison with catadioptric systems in light optics informs our understanding of the working principles behind aberration correction with electron mirrors, and may point the way to further improvements in the latter. With additional developments in detector technology, 1 nm spatial resolution in LEEM appears to be within reach.

A versatile ultra high vacuum sample stage with six degrees of freedom.

We describe the design and practical realization of a versatile sample stage with six degrees of freedom. The stage was designed for use in a Low Energy Electron Microscope, but its basic design features will be useful for numerous other applications. The degrees of freedom are X, Y, and Z, two tilts, and azimuth. All motions are actuated in an ultrahigh vacuum base pressure environment by piezoelectric transducers with integrated position sensors. The sample can be load-locked. During observation, the sample is held at a potential of -15 kV, at temperatures between room temperature and 1500 °C, and in background gas pressures up to 1 × 10(-4) Torr.

Characterization of the cathode objective lens by Real-Space Microspot Low Energy Electron Diffraction.

Measurement of the geometric aberrations of the cathode objective lens is a key step in setting up a high quality C(c) and C3 corrected state in state-of-the-art aberration corrected instruments. In addition to Cc and C3, elimination of sample tilt and astigmatism is necessary for optimum imaging conditions. In transmission electron microscopy (TEM), the use of Zemlin tableaux has become the method of choice for measuring geometric aberrations, while Scanning TEM relies on the use of the ronchigram to assess the properties of the contrast transfer function. These techniques are not applicable to cathode lens instruments such as a low energy electron microscope. Instead, we propose to utilize Microspot Low Energy Electron Diffraction (LEED) with an illumination area on the order of 0.1 µm, where the image locations of the diffracted beams are observed in the Gaussian image plane. This Real-Space MicroLEED (RS-µLEED) pattern is the first derivative of the aberration function with respect to the angle of the diffracted beams. Thus, the geometric distortions observed in the RS-µLEED pattern are a direct measure of the relevant geometric aberrations.

Optimization and stability of the contrast transfer function in aberration-corrected electron microscopy.

The Contrast Transfer Function (CTF) describes the manner in which the electron microscope modifies the object exit wave function as a result of objective lens aberrations. For optimum resolution in C3-corrected microscopes it is well established that a small negative value of C3, offset by positive values of C5 and defocus C1 results in the most optimal instrument resolution, and optimization of the CTF has been the subject of several studies. Here we describe a simple design procedure for the CTF that results in a most even transfer of information below the resolution limit. We address not only the resolution of the instrument, but also the stability of the CTF in the presence of small disturbances in C1 and C3. We show that resolution can be traded for stability in a rational and transparent fashion. These topics are discussed quantitatively for both weak-phase and strong-phase (or amplitude) objects. The results apply equally to instruments at high electron energy (TEM) and at very low electron energy (LEEM), as the basic optical properties of the imaging lenses are essentially identical.

A new aberration-corrected, energy-filtered LEEM/PEEM instrument II. Operation and results.

In Part I we described a new design for an aberration-corrected Low Energy Electron Microscope (LEEM) and Photo Electron Emission Microscope (PEEM) equipped with an in-line electron energy filter. The chromatic and spherical aberrations of the objective lens are corrected with an electrostatic electron mirror that provides independent control of the chromatic and spherical aberration coefficients Cc and C3, as well as the mirror focal length. In this Part II we discuss details of microscope operation, how the microscope is set up in a systematic fashion, and we present typical results.

Intrinsic instability of aberration-corrected electron microscopes.

Aberration-corrected microscopes with subatomic resolution will impact broad areas of science and technology. However, the experimentally observed lifetime of the corrected state is just a few minutes. Here we show that the corrected state is intrinsically unstable; the higher its quality, the more unstable it is. Analyzing the contrast transfer function near optimum correction, we define an "instability budget" which allows a rational trade-off between resolution and stability. Unless control systems are developed to overcome these challenges, intrinsic instability poses a fundamental limit to the resolution practically achievable in the electron microscope.

Selected-area diffraction and spectroscopy in LEEM and PEEM.

This paper addresses the effects of spherical and chromatic aberration of the objective lens, as well as chromatic dispersion of magnetic prism arrays, on the ability to perform selected area Low Energy Electron Diffraction, as well as (Angle Resolved) Photo Electron Spectroscopy experiments in today's advanced cathode lens microscopy instruments.

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.

Aberrations of the cathode objective lens up to fifth order.

In this paper we discuss a topic that was close to Prof. Gertrude Rempfer s interests for many years. On this occasion of her 100th birthday, we remember and honor Gertrude for her many outstanding contributions, and for the inspiring example that she set. We derive theoretical expressions for the aberration coefficients of the uniform electrostatic field up to 5th order and compare these with raytracing calculations for the cathode lens used in Low Energy Electron Microscopy and Photo Electron Emission Microscopy experiments. These higher order aberration coefficients are of interest for aberration corrected experiments in which chromatic (C(c)) and spherical (C3) aberrations of the microscope are set to zero. The theoretical predictions are in good agreement with the results of raytracing. Calculations of image resolution using the Contrast Transfer Function method show that sub-nanometer resolution is achievable in an aberration corrected LEEM system.

Direct measurement of the growth mode of graphene on SiC(0001) and SiC(0001¯).

We have determined the growth mode of graphene on SiC(0001) and SiC(0001¯) using ultrathin, isotopically labeled Si(13)C "marker layers" grown epitaxially on the Si(12)C surfaces. Few-layer graphene overlayers were formed via thermal decomposition at elevated temperature. For both surface terminations (Si face and C face), we find that the (13)C is located mainly in the outermost graphene layers, indicating that, during decomposition, new graphene layers form underneath existing ones.

Atomic-scale transport in epitaxial graphene.

The high carrier mobility of graphene is key to its applications, and understanding the factors that limit mobility is essential for future devices. Yet, despite significant progress, mobilities in excess of the 2×10(5) cm(2) V(-1) s(-1) demonstrated in free-standing graphene films have not been duplicated in conventional graphene devices fabricated on substrates. Understanding the origins of this degradation is perhaps the main challenge facing graphene device research. Experiments that probe carrier scattering in devices are often indirect, relying on the predictions of a specific model for scattering, such as random charged impurities in the substrate. Here, we describe model-independent, atomic-scale transport measurements that show that scattering at two key defects--surface steps and changes in layer thickness--seriously degrades transport in epitaxial graphene films on SiC. These measurements demonstrate the strong impact of atomic-scale substrate features on graphene performance.