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Spectroscopy with the Low Energy Electron Microscope

  • Rudolf TrompEmail author
Chapter
Part of the Springer Handbooks book series (SHB)

Abstract

Photo electron emission microscopy (PEEM), going back to the earliest days of electron microscopy, and low-energy electron microscopy (LEEM), successfully deployed since the late 1980s, are examples of cathode lens microscopy in which the sample itself is an integral part of the image forming system. While applications have naturally gravitated towards the acquisition of images to elucidate structure and structural evolution, recent years have also seen a rapidly expanding range of spectroscopic capabilities. These address, for example, the occupied and unoccupied electronic band structures of materials, electrical transport in 2-D systems, crystal growth and 2-D strain, inelastic electron energy loss mechanisms, as well as radiation damage in organic materials during low-energy electron irradiation. In this chapter, we discuss applications of these new spectroscopic methods, as well as recent instrumental developments that further expand the potential uses of cathode lens microscopy.

Keywords

Spectroscopy low energy electron microscopy Cathode LENS electron mirror LEEM-IV angle resolved reflected electron spectroscopy potentiometry spot-profile analysis electron energy loss spectroscopy radiation effects electron-volt TEM 
Cathode lens microscopy is one of the earliest forms of electron microscopy, first developed in the early 1930s [11.1, 11.2]. Photo electron emission microscopy ( ) first originated in 1932–1933 [11.3]. However, it was soon overtaken by the transmission electron microscope ( ) [11.4] and later by the scanning electron microscope. Early versions of reflecting microscopes, the precursors of low-energy electron microscopy ( ) saw a similar fate. Indeed, Dennis Gabor wrote [11.5] in his 1948 book The Electron Microscope—Its Development, Present Performance and Future Possibilities:

Such reflecting microscopes, the electronic counterpart of the metallurgical microscope, were up to now rather unsuccessful, and they are not likely to have a great future, the more so, as we possess now in the scanning microscope a fully satisfactory tool for surface investigations.

and furthermore:

The first electrostatic microscope for self-luminous objects was constructed by E. Brüche and H. Johannson, and started operating in 1932, almost simultaneously with the first supermicroscope. In the following, we shall deal only with the second type, not only because of its wider scope and greater general interest, but also because the microscope for self-luminous objects appears to have completed in development, about the year 1936.

Gabor's supermicroscope is now better known as the TEM, and its development has continued unabated for over 80 years, setting a \({\mathrm{50}}\,{\mathrm{pm}}\) resolution record with the aid of spherical and chromatic aberration correction  [11.6]. Self-luminous microscopes (i. e., PEEM) were never quite forgotten, and for some time a commercial instrument was available. Its development was carried forward by Engel et al [11.7], as well as others [11.8]. Mirror electron microscopy saw modest popularity for some time, but its range of applications was rather limited [11.10, 11.9]. A scientific dispute between Lester Germer and Ernst Bauer inspired the latter to take up the construction of the low-energy electron microscope. The first version, beautifully constructed with hand-blown glass, never worked. Undeterred, Bauer persisted in his project, and the first LEEM images saw the light of day in 1985 [11.11]. This result raised considerable interest, and several other groups likewise took on the development of LEEM. Of these early projects, the IBM effort was the first to succeed, and the second operational LEEM instrument came on line in 1992 after a two-year design and construction period [11.12]. Bauer and his group continued developing the instrument, extending it capabilities with energy filtering [11.13] (for PEEM applications) and a spin-polarized electron source [11.14] (for magnetic measurements). These various projects led to a rebirth and acceleration of the cathode lens instrument, deemed dead by Gabor in 1936. The chapters in this book by Ernst Bauer on LEEM, and by Jun Feng and Andreas Scholl on PEEM cover the main aspects of these techniques, as they have been practiced over the last few decades. In this chapter, we will discuss more recent developments, focusing not only on imaging applications, but primarily on various spectroscopic techniques that are becoming increasingly important. In a state-of-the-art cathode LEEM/PEEM instrument (with [11.15, 11.16, 11.17, 11.18, 11.19] or without aberration correction) we have at our disposal not only a microscope, but a broad range of surface analytical techniques that have never before been combined in a single instrument. Of course, there is PEEM imaging with Hg light (\({\leq}{\mathrm{4.9}}\,{\mathrm{eV}}\)), He(1\({\upalpha}\)) (\({\mathrm{21.22}}\,{\mathrm{eV}}\)) and He(2\({\upalpha}\)) (\({\mathrm{40.81}}\,{\mathrm{eV}}\)) radiation, and various laser sources (all in the lab), or with tunable-energy and tunable-polarization synchrotron light. These resources enable not only photon-energy resolved imaging, but also analysis of chemical, magnetic, electronic, and plasmonic structure. Angle-resolved photo electron spectroscopy (ARPES ) [11.20] has long been a mainstay of surface and materials science and is now becoming an integral part of the PEEM repertoire [11.21, 11.22, 11.23]. Cathode-lens-based ARPES is even providing unprecedented time, energy, momentum, and spin resolution.

LEEM started out primarily as an imaging technique, with electron-energy-dependent bright-field and dark-field capabilities. The theory of LEEM/PEEM imaging remained relatively unexplored for a rather long time. The third-order spherical aberration (\(C_{3}\)) and second-rank chromatic aberration (\(C_{\text{c}}\)) coefficients of the uniform electrostatic field between cathode (sample) and anode (front of the objective lens) were derived long ago by Bauer [11.24] and Rempfer [11.25], and their roles in limiting spatial resolution were fairly well understood. However, a direct theoretical link between object and image, similar to the quantitative, wave-based imaging theories for light optics and for TEM, was lacking. A first version of a Fourier-optics theory was put forward by Pang et al, explaining Fresnel fringes observed at step edges on the surface [11.26]. The contrast transfer function method routinely used in TEM theory was then extended to LEEM/PEEM by Kennedy et al [11.27] and Schramm et al [11.28] The latter included not only \(C_{\text{c}}\) and \(C_{3}\), but all significant aberrations up to 5th order (including coma). These higher aberrations of the uniform field were studied theoretically by Tromp et al [11.29]. With the theoretical situation well understood, it also became possible to implement an advanced aberration correction system, based on mirror optics, to correct \(C_{3}\) and \(C_{\text{c}}\). A first practical demonstration of the feasibility of aberration correction, based on a hyperbolic dipole mirror, was given by Rempfer et al [11.15], using an electron optical bench. A more ambitious project was started in Berlin to realize the so-called SMART instrument [11.16], aimed at incorporating spherical and chromatic aberration correction using four-element mirror optics. This highly complex instrument features an achromatic prism array to spatially separate the electron gun, objective lens, mirror corrector, and projector system. It also includes an omega energy filter. It was later realized that a combination of two energy-dispersing prism arrays, arranged in the proper symmetry, could achieve the same goal with much simpler means, leading to two aberration-corrected LEEM/PEEM instruments now commercially available. We will discuss the present status and future opportunities below.

Of course, low-energy electron diffraction ( ) was always available and often used for phase identification. Otherwise, it was mostly an afterthought. With the advent of LEEM-IV [11.30, 11.31] (i. e., LEEM intensity (I) as a function of electron energy (V)—in analogy with traditional LEED-IV), atomic structures can be determined with a few nanometer spatial resolution, even, and in particular, on spatially non-uniform surfaces. A powerful extension of this, angle-resolved reflected electron spectroscopy [11.32, 11.33] ( ), provides momentum and energy-resolved information on the electronic bands of the sample above the vacuum level. Already, ARRES has provided new and important information on unoccupied states in various van der Waals materials. The distribution of the diffracted beam in momentum space has been the basis for spot-profile analysis LEED ( ) since its early development by Martin Henzler [11.34] and Max Lagally [11.35]. With a high spatial coherence length, LEEM-based SPA-LEED has not been used very much, but has much to offer. Layer-by-layer growth of complex oxides was recently studied with an in-situ pulsed laser deposition ( ) system, and such growth can be followed both in real and in reciprocal space, exhibiting strong intensity and width fluctuations of the specular diffracted beam [11.36]. Small shifts and rotations of the diffraction pattern can also be used to quantify lateral strains, as has been beautifully demonstrated for thin graphene layers [11.37]. The energy-dependent features of the LEED-IV curve can also shift as a result of lateral potential variations on the surface and can be used to measure such variations. LEEM-based potentiometry [11.38] is a new method to study charge transport phenomena on surfaces with \({\mathrm{10}}\,{\mathrm{nm}}\) spatial resolution. The LEED-IV curve also allows for structural identification on the same length scale, so that structure and charge transport can be directly correlated.

So far, we have restricted ourselves to elastic electron scattering. But electrons undergo all kinds of inelastic processes, which form the basis for electron energy loss spectroscopy ( ), now an integral part of many TEM and scanning TEM (STEM) instruments [11.39]. Incorporation of an energy filter in a LEEM instrument likewise facilitates EELS experiments in the cathode lens environment, combining EELS with LEEM imaging. Most studies to date have centered on plasmons with loss energies of a few eV, where both the loss peak and its energy and intensity dispersion with momentum can be easily studied. EELS features can also be selected for direct imaging experiments, as demonstrated for Ag nano-islands [11.40, 11.41].

The LEEM instrument routinely delivers a well-controlled electron beam at sub-\({\mathrm{100}}\,{\mathrm{eV}}\) energies with excellent energy resolution and stability, and fine in-plane momentum control. This beam can be used not only for the purposes briefly discussed in the above, but also as a tool to purposely change materials. The use of a LEEM instrument as a resist exposure tool was pioneered in just the last few years [11.42, 11.43]. With such lithographic LEEM we can not only expose thin resist layers to low energy electrons, but using the EELS capability during resist exposure, we can also follow the resist response in real time [11.44].

LEEM experiments are performed by reflecting an electron beam from the surface and measuring the spatial variations of the reflected intensity. However, for sufficiently thin samples, it is also possible to do the experiment in transmission. Electron-volt TEM ( ) is the latest branch on the growing cathode lens tree [11.45], and its feasibility has been demonstrated on few-layer graphene samples suspended on TEM grids [11.46]. The universal electron mean-free path [11.47] plot shows a minimum of about \({\mathrm{1}}\,{\mathrm{nm}}\) at an electron energy of \(\approx{\mathrm{30}}\,{\mathrm{eV}}\). For lower energies, the plot promises a steep increase in mean-free path. At energies below \({\mathrm{10}}\,{\mathrm{eV}}\) the electrons can—in principle—travel tens of nanometers, as few loss processes remain at such low energies. No loss also means no damage, so one may envision a damage-free imaging method for radiation sensitive samples. Graphene monolayers can then be used as a convenient support for delicate samples.

This brief introduction has made it clear that rather than having been completed in development, about the year 1936, cathode lens microscopy is thriving in this new century, with innovations accelerating, not diminishing. Even today we can see a number of new instruments on the horizon that will expand capabilities even further. Gabor invented holography [11.48] and received a well-deserved Nobel Prize for his invention, because he thought the prospect of improving the resolution of the TEM from \({\mathrm{500}}\,{\mathrm{pm}}\) in his day (not being able to see atoms) to \({\mathrm{50}}\,{\mathrm{pm}}\) today (seeing atoms with ease) hopeless. He noted, correctly, that a resolution improvement by a factor of 10 would require a reduction in spherical aberration by a factor of \(\mathrm{10000}\). Indeed, this reduction would take half a century to accomplish [11.6]. Even so, the resolution of the TEM equals about 20 electron wavelengths, which is still very far removed from the diffraction limit. In LEEM, we have realized a record spatial resolution of \(\approx{\mathrm{1.5}}\,{\mathrm{nm}}\) at \({\mathrm{3.5}}\,{\mathrm{eV}}\), i. e., about 2.5 times the electron wavelength. Theory shows that 1 wavelength resolution should be achievable with modest improvements in optics [11.28]. Energy resolution is now on the order of \({\mathrm{100}}\,{\mathrm{meV}}\). A factor 10 improvement is definitely achievable and has already been demonstrated in cathode lens instruments [11.22] optimized for spectroscopic applications. Nanometer resolution EELS capability with \({\mathrm{10}}\,{\mathrm{meV}}\) energy resolution would certainly enable many new experiments. If this is combined with a cryogenic sample environment (\(<{\mathrm{10}}\,{\mathrm{K}}\)) it becomes even more interesting. Several cryo-LEEM instruments are under development and should start delivering first results in the near future. Detector technology is still rather crude, lagging behind the TEM field. Here, some first steps toward direct electron detectors have been made, and large improvements may be expected over the next few years. Today's cathode lens instrument may be comparable to a 1980s TEM: very useful and highly capable, but still open to numerous improvements. It will take dedication, investment, and persistence to make these developments happen. Hopefully, this chapter can provide the necessary inspiration.

11.1 Aspects of the LEEM Instrument

11.1.1 Optical Properties of the Cathode Lens

The cathode lens , at the heart of LEEM/PEEM instruments, distinguishes itself from all other electron microscopes by maintaining a strong electrostatic field between the sample (cathode) and the objective lens (anode). The sample and the front face of the objective lens, spaced at a distance \(L\), are assumed to be flat and accurately parallel to each other, so that the field is uniform. Such a uniform electrostatic field has the remarkable property of forming a virtual image of the sample. If we take the position of the sample as \(Z=-L\) and that of the anode as \(Z=0\), then a virtual image is formed at \(Z=-2L\) (Fig. 11.1a,ba).

Fig. 11.1a,b

Electron path in a uniform electrostatic field (a) without and (b) with anode opening. In (a) a virtual image is formed at \(Z=-2L\) at a magnification of \(M=1\). In (b) the virtual image is shifted to \(Z=-4/3L\), at \(M=2/3\), due to the negative lens effect of the unavoidable opening in the anode. After [11.29]

Since there are no radial components to the field, each sample location is imaged identically, and the magnification of the virtual image equals 1. The aberration coefficients of this image can be obtained analytically. The energy with which the electrons leave the sample is defined as \(E_{0}\), and the additional energy gained as the electrons are accelerated to the anode is defined as \(E\). Thus, when the electrons reach the anode plane, their energy is \(E+E_{0}\). The aberration coefficients relative to this virtual image at energy \(E+E_{0}\) up to fifth order, are then given by [11.29]
$$\begin{aligned}\displaystyle C_{\text{c}}&\displaystyle=-C_{3}=-L\left(\frac{E}{E_{0}}\right)^{1/2},\\ \displaystyle C_{\text{cc}}&\displaystyle=C_{5}=\frac{1}{4}L\left(\frac{E}{E_{0}}\right)^{3/2},\\ \displaystyle C_{\text{3c}}&\displaystyle=-\frac{1}{2}L\left(\frac{E}{E_{0}}\right)^{3/2},\\ \displaystyle C_{\text{c3}}&\displaystyle=-\frac{1}{8}L\left(\frac{E}{E_{0}}\right)^{5/2},\\ \displaystyle C_{\text{3cc}}&\displaystyle=\frac{3}{8}L\left(\frac{E}{E_{0}}\right)^{5/2},\\ \displaystyle C_{\text{c4}}&\displaystyle=\frac{5}{64}L\left(\frac{E}{E_{0}}\right)^{7/2}.\end{aligned}$$
(11.1)

However, this is not the end of the story. The configuration shown in Fig. 11.1a,ba does not allow the electrons to move past the anode, as there is no anode opening. When we do allow for such an opening, the electrostatic field is still approximately uniform close the cathode. However, close to the anode, the effect of the anode opening makes itself felt. The lens action of an aperture with different electrostatic fields on both sides of the opening was first treated by Davisson and Calbick [11.49]. In our case, it acts like a diverging lens with focal length \(f\approx-4L(E+E_{0})/E\). Taking the virtual image at \(Z=-2L\) as the object of this diverging aperture lens, we find that it shifts the virtual image to Z \({\approx}-4L/3\), with a magnification of \(\approx 2/3\) (Fig. 11.1a,bb). As the electrons pass next into the objective lens proper (most often a magnetic lens, but purely electrostatic systems are also in use), this lens sees this second virtual image, at \(Z\approx-4L/3\), with \(M\approx 2/3\) and electron energy \(E+E_{0}\) as its object, and it will transfer this virtual image to a real image plane at some distance along the positive \(z\)-axis. The aperture lens , as well as the objective lens, add their own aberrations to this first real image. It has been shown that the aberrations of the aperture lens are negligible. However, the aberrations of the objective lens are not. Fortunately, they are simply additive to the aberrations of the uniform field [11.50]. If we take the objective lens to be magnetic, then the aberrations in the real image plane can simply be written as \(C_{\text{total}}=C_{\text{e}}+C_{\text{m}}\), where \(C_{\text{e}}\) are the aberrations of the uniform electrostatic field, and \(C_{\text{m}}\) are those of the objective lens. In a typical LEEM instrument, without aberration correction, these aberrations limit the spatial resolution to \(\approx 4{-}8\,{\mathrm{nm}}\), with the lower limit for a cold field emission source (\(\Updelta E\approx{\mathrm{0.25}}\,{\mathrm{eV}}\)), and the upper limit for a \(\mathrm{LaB_{6}}\) source(\(\Updelta E\approx 0.75-{\mathrm{1}}\,{\mathrm{eV}}\)). The larger part of the aberrations, particularly at low electron energies, are due to the electrostatic field and are unavoidable. They cannot be improved by better design or better engineering. Resolution can only be improved beyond this limit by correcting the cathode lens aberrations.

11.1.2 Aberration Correction

Otto Scherzer pointed out already in 1936 that the aberrations of electron optical lenses would limit the resolution of the electron microscope [11.51]. In light optics the aberration correction problem was solved in the early 1880s when Abbe advanced his theory of image formation in the light microscope [11.52]. Positive spherical aberrations of a lens with positive curvature can be offset with negative spherical aberrations of a lens with negative curvature. Chromatic dispersion of one lens element can be offset by a second lens element fabricated from a different glass, with different optical properties. Herzberger's superachromat [11.53] can correct chromatic aberrations across the visible spectrum with just three different materials. However, in electron optics we do not have so many variables to play with. All rotationally symmetric electrostatic or magnetic lenses have positive focal lengths (the aperture lens discussed above is the one exception), and the signs of the aberration coefficients cannot be changed. In 1947 Scherzer offered [11.55] possible solutions:
  1. 1.

    abandon rotational symmetry by the use of multipole elements

     
  2. 2.

    reverse the path of the electrons by use of an electron mirror

     
  3. 3.

    place space charge on or near the optical axis; and

     
  4. 4.

    use time-varying field in combination with a pulsed electron beam.

     
During the decades that followed all of these were tried. In the (S)TEM field, multipole optics in combination with powerful computer control algorithms have proved successful. Mirror optics has been incorporated in LEEM/PEEM instruments and has improved resolution to below \({\mathrm{2}}\,{\mathrm{nm}}\).

Figure 11.2a-c shows ray diagrams [11.54] for light reflecting from a spherical, parabolic, and hyperbolic mirror. Such mirror surfaces can be generated by rotation of a two-dimensional conic section about its axis of symmetry. The conic section is defined by its eccentricity, \({\varepsilon}\), and the curvature at the apex, \({\kappa}\). For a spherical mirror \({\varepsilon}=0\), for a parabolic mirror \({\varepsilon}=1\), and for a hyperbolic mirror \({\varepsilon}> 1\). In Fig. 11.2a-cc we have chosen \({\varepsilon}=\sqrt{2}\). Scaling all dimensions to the curvature at the apex, \({\kappa}\), the lateral displacement of a reflected ray from the optical axis in the paraxial image plane is given by \(\mathrm{d}R=C_{3}y^{3}=(1-{\varepsilon}^{2})y^{3}\), where \(y\) is the lateral displacement of the incident ray parallel to the optical axis. Thus, for \(0<{\varepsilon}<1\), \(C_{3}> 0\); for \({\varepsilon}=1\), \(C_{3}=0\); and for \({\varepsilon}> 1\), \(C_{3}<0\), i. e., both the sign and the magnitude of the spherical aberration coefficient of a mirror can be controlled by its shape. If we were to combine a spherical mirror (\(C_{3}=1\)) with the hyperbolic mirror with \({\varepsilon}=\sqrt{2}\), \(C_{3}=-1\), the sum of the aberration coefficients would be zero, i. e., the spherical mirror can be corrected with the hyperbolic mirror. In light optics the rays undergo specular reflection at the surface of the mirror, and mirrors, therefore, do not suffer from chromatic aberration. This is utilized in Newtonian telescopes. In electron optics, however, electrons do not reflect from the surface of the mirror, but from an equipotential plane in front of the mirror, so that all electrons are reflected, and they are reflected elastically. However, the equipotential plane from which the electron reflects depends on its energy. A faster electron penetrates deeper into the field in front of the electron mirror than a slower electron. And the shape of the equipotential plane will also be slightly different for different energy electrons. Therefore, unlike in light optics, electron mirrors display not only spherical aberration, but also chromatic aberration. This makes it possible, at least in principle, to correct both spherical and chromatic aberration with an electron mirror. Alfred Recknagel showed [11.56] in 1936 that analytical solutions can be found for electron trajectories in a hyperbolic field, and the properties of such fields were further investigated [11.57] by Reinhold Rüdenberg in 1948. After that, almost nothing happened for 40 years, until Gertrude Rempfer (a former co-worker of Rüdenberg) carried out a theoretical investigation [11.58] of the properties of a hyperbolic dipole mirror in 1990, showing that it is capable in principle of correcting both \(C_{\text{c}}\) and \(C_{3}\) of a cathode lens. She demonstrated in 1997 that this is also possible experimentally [11.15].

Fig. 11.2a-c

Ray diagrams for spherical (a), parabolic (b), and hyperbolic (c) mirrors with identical paraxial focal lengths. The eccentricities \(\varepsilon\) as well as the dimensionless spherical aberrations are indicated. Below the parabolic mirror we overlay the shapes of the spherical and hyperbolic mirrors for comparison. The hyperbolic mirror is somewhat flatter. After [11.54]

However, there were still problems. A dipole mirror (containing a ground electrode and a negatively biased mirror electrode that set up the hyperbolic field) has only one adjustable parameter, i. e., the bias voltage applied to the mirror electrode. In a practical microscope, though, we must accomplish three things: first, the mirror must act as transfer lens with an uncorrected image in its input plane and a corrected image in its output plane. For practical reasons, it is convenient to have the input and output planes coincide, i. e., the image is transferred with magnification 1. Since these input and output planes are fixed by the geometry and design of the instrument, the focal length of the mirror must remain at a fixed value. The focal length can be adjusted by the potential applied to the mirror electrode. However, we also want to be able to adjust \(C_{\text{c}}\) and \(C_{3}\) of the mirror, as the aberrations of the cathode lens (as we have seen above) are strongly dependent on the take-off energy \(E_{0}\). With a dipole mirror we have no more adjustable parameters available: after we have adjusted the focal length, \(C_{\text{c}}\) and \(C_{3}\) are fixed and can no longer be changed for changing values of \(E_{0}\). Thus, while a dipole mirror has been implemented successfully in a PEEM instrument in which \(E_{0}\) is essentially fixed and unchanging, it is unsuitable for correction of the general LEEM/PEEM instrument in which \(E_{0}\) changes all the time.

11.1.3 Four-Element Electron Mirrors

As we need to independently control three mirror properties, i. e., focal length, spherical, and chromatic aberration, we need at least three independently adjustable parameters in the mirror optics, i. e., three optical elements with independent bias voltages. The first is the mirror electrode. We may then add two lens-like elements, and finally a ground plane. Such a catadioptric system (combining reflection—catoptrics, and transmission—-dioptrics) was first presented [11.16] in the context of the SMART instrument. Wan et al further explored its properties when designing the corrected PEEM-3 instrument and showed [11.59] that focal length, spherical, and chromatic aberration can indeed be independently controlled. A schematic drawing of their design is shown in Fig. 11.3, with three adjustable voltages \(V_{1}\), \(V_{2}\), and \(V_{3}\).

Fig. 11.3

Four-element electron mirror with adjustable voltages \(V_{1}\), \(V_{2}\), and \(V_{3}\). Both spherical and chromatic aberrations can be corrected at fixed focal length with this simple optical element. After [11.54]

\(C_{\text{c}}\) depends mostly on \(V_{1}\) and \(C_{3}\) mostly on \(V_{3}-V_{2}\), while mirror focusing is adjusted by \(V_{2}\). These dependencies are highly non-linear. Figure 11.4a shows the measured focusing voltage, \(V_{2}\), as a function of \(V_{3}-V_{2}\) and \(V_{1}\) for the electron mirror system installed in the IBM/SPECS developed AC-LEEM instrument [11.17, 11.18]. The data points were obtained on three different instruments installed at IBM, BESSY, and Leiden University. The solid lines are theoretical predictions, obtained with Munro's electron optics software [11.60]. In the experiments, the absolute value of \(V_{1}\) was adjusted to obtain the best agreement with the theory. For the IBM instrument, for example, this required a \({\mathrm{10}}\,{\mathrm{V}}\) offset on an absolute voltage of \(-{\mathrm{16200}}\) to \(-{\mathrm{16800}}\,{\mathrm{V}}\) applied to the mirror electrode. Figure 11.4a shows that the first-order imaging properties of the electron mirror are in excellent agreement with theory. Therefore, we can be confident that the higher-order properties, in particular \(C_{\text{c}}\) and \(C_{3}\), also agree with theoretical predictions. Experimentally, we find that this is indeed the case. Figure 11.4b shows theoretical optimum resolutions in PEEM and LEEM as a function of the contrast aperture cutoff angle (at magnification 1) for non-aberration corrected (nac) and aberration corrected (ac) conditions. Aberration correction strongly improves resolution, while at the same time improving transmission (the square of the optimum aperture angle).

Fig. 11.4

(a) First-order properties of the mirror shown in Fig. 11.3 measured on three different microscopes. \(V_{1}\) changes from \(-{\mathrm{1200}}\,{\mathrm{V}}\) for the upper curve to \(-{\mathrm{1800}}\,{\mathrm{V}}\) for the lower curve, in steps of \({\mathrm{100}}\,{\mathrm{V}}\). Voltages are shown relative the beam potential of \(-{\mathrm{15000}}\,{\mathrm{V}}\) (Adapted from [11.18]). (b) Resolution versus aperture angle for uncorrected (nac) and corrected (ac) LEEM/PEEM instruments under a variety of imaging conditions. The points below \({\mathrm{2}}\,{\mathrm{mrad}}\) are for PEEM, above \({\mathrm{2}}\,{\mathrm{mrad}}\) for LEEM. Aberration correction provides a large gain in resolution in all cases. Adapted from [11.28], with permission from Elsevier

While this shows that the leading aberrations of the cathode lens can be corrected, the practical problem of how to perform that correction in practice remains. Before the doctor prescribes a set of eyeglasses to correct our vision, the imaging properties of our uncorrected eyes must first be measured. In (S)TEM, the automated measurement of spherical aberration is highly developed. Basically, image properties are monitored as the angle of incidence of the electron beam is varied, and the aperture angle within which the imaging properties remain unchanged is maximized. A (S)TEM \(C_{3}\) corrector can have up to 80 adjustable current supplies to control not only the primary aberration but also a long list of higher-order and parasitic aberrations, and the full system must be optimized to obtain the best performance. This complex, non-linear problem is handled by a powerful computer system and algorithm that measures and corrects the system iteratively. If correction of \(C_{\text{c}}\) is also required, the task becomes even more complex, as electrostatic multipole elements are now added to the correction system. Most (S)TEMs today incorporate only \(C_{3}\) correction, although \(C_{\text{c}}\) correction has been demonstrated in a few instruments.

In LEEM/PEEM on the other hand, the energy with which the electrons leave the sample, \(E_{0}\), changes frequently, and the aberration coefficients of the electrostatic field depend strongly on \(E_{0}\) (11.1). As we add the aberrations of the objective lens, and of all the additional lens elements between the objective lens and the electron mirror to the aberrations of the uniform field, the final values of \(C_{\text{c}}\) and \(C_{3}\) to be corrected by the electron mirror do not have the same functional dependence on \(E_{0}\), complicating our task even further. On the other hand, setting the aberrations of the electron mirror at fixed focal length requires the adjustment of only three voltages, much less than the number of adjustments made in a (S)TEM corrector. Over the last 5 years methods have been developed to characterize the LEEM/PEEM instrument without excessive experimental effort. Once the system is properly characterized, the electron mirror can automatically follow changes in \(E_{0}\) in real time. Nonetheless, considerable skill is required on the part of the instrument operator to obtain optimum results [11.19, 11.50, 11.61].

11.1.4 Adjustable Achromats

One may even ask what it means for the microscope to be corrected when the aberrations of the cathode lens change rapidly with electron energy. Here, an analogy with light optics is useful. The simplest chromatically corrected system is the achromat, invented in 1730 by Chester Moore Hall. It uses two optical elements made from different glasses (crown and flint) to obtain a combined lens with the same focal length at two different wavelengths. Later improvements include the apochromat (1763, Peter Dollond), which corrects at three wavelengths, and the superachromat [11.53] (1963, Maximilian Herzberger), which corrects over the full visible range. The apochromat and the superachromat require three optical elements, with three different kinds of glass (simultaneous correction of spherical aberration requires many more lens elements). In a corrected LEEM/PEEM system, we combine two optical elements: cathode lens and electron mirror, and we may, therefore, expect the system to behave like the 1730 achromat, as is indeed the case [11.62, 11.63].

Fig. 11.5

Defocus curves for a LEEM/PEEM system corrected at 2.5 (solid line), 10 (dotted), and 30 (dashed) eV, with added defocus of 2 (solid line), 8 (dotted) and 15 (dashed) \(\mathrm{{\upmu}m}\). These quasi-parabolic figures are very similar to light-optical achromats. After [11.62]

Figure 11.5 shows defocus curves calculated as a function of take-off energy \(E_{0}\), for three cases. The solid (dotted, dashed) curve is for a system with \(C_{\text{c}}\) corrected for \(E_{0}=2.5\) (10, 30), eV with an added positive defocus of 2 (8, 15) \(\mathrm{{\upmu}m}\). The symbols are the results of numerical ray tracing calculations, while the lines are given by analytical theory, taking into account the energy dependence of the aberrations of both the cathode lens and the electron mirror. Although usually neglected, it turns out that the chromatic dispersion of the electron mirror is significant and must also be taken into account. The curves in Fig. 11.5 look very similar to defocus curves of two-element achromats in light optics, with zero defocus at two energies/wavelengths. However, unlike a light-optical achromat, we find that the electron-mirror-based achromat is adjustable. First, we can adjust the electron energy at which we correct the cathode lens (2.5, 10, and \({\mathrm{30}}\,{\mathrm{eV}}\) in Fig. 11.5). Second, we can adjust the defocus that we then add. The purpose of this added defocus is to broaden the usable energy range, by bringing a portion of the defocus curve to positive values. For instance, the dashed line in Fig. 11.5 spans an energy range from about 8 to \({\mathrm{62}}\,{\mathrm{eV}}\) within a maximum defocus range of \({\pm}{\mathrm{15}}\,{\mathrm{{\upmu}m}}\). Even with this enormously wide energy range, the system can deliver a spatial resolution of \(11{-}14\,{\mathrm{nm}}\) in a PEEM experiment. If the experiment requires a narrower energy window, the added defocus can be reduced. For instance, the dotted curve is optimized for a window of \(2{-}20\,{\mathrm{eV}}\), i. e., the secondary electron peak for a typical soft x-ray illuminated sample. For this case, resolution of \(7{-}10\,{\mathrm{nm}}\) is possible. For the solid line, we have a window from \(1{-}5\,{\mathrm{eV}}\), with a spatial resolution of \(3{-}4\,{\mathrm{nm}}\). Note that in all these cases, the microscope is nominally corrected at the center energy, i. e., the peak of the achromat curves in Fig. 11.5. The choice of this energy sets the overall width of the curve: narrow for very low energies, and broadening with energy. By adding an adjustable defocus, we can then choose how much of this window will be used in the given experiments, and hence the spatial resolution that can then be achieved. Importantly, the system can be optimized for any given experiment.

In each of these three examples, the ratio of the energy window over which the achromat is used (\(\Updelta E\)) to the nominal energy over which the instrument is corrected, \(E_{\text{c}}\), is significantly larger than 1, i. e., \(\Updelta E/E_{\text{c}}> 1\). This is very different from the case of a chromatically corrected (S)TEM, in which \(\Updelta E\) is on the order of a \(0.3{-}30\,{\mathrm{eV}}\) or so, for a beam energy of \(30{-}300\,{\mathrm{keV}}\), so \(\Updelta E/E_{c}=E-3{-}E-6\). So, while in (S)TEM it is straightforward to define the meaning of corrected, in cathode lens microscopy it is always a matter of degree, in particular for PEEM experiments where the electron energy distributions are usually very broad. In LEEM, with an energy width of \({\mathrm{0.25}}\,{\mathrm{eV}}\) (cold field emission) or \({\mathrm{0.75}}\,{\mathrm{eV}}\) (\(\mathrm{LaB_{6}}\) source), the situation is simpler, but \(\Updelta E/E_{\text{c}}\) is still a few orders of magnitude larger than in (S)TEM.

11.1.5 Stability and Accuracy

The stability of the electron-optical state of a corrected instrument has been the subject of considerable debate. We may go back to Gabor's remark that in order to correct the resolution of the TEM by a factor 10, the spherical aberration of the objective lens had to be reduced by a factor \(\mathrm{10000}\), as the spatial resolution of the TEM, \({\delta}\), is proportional to \(C_{3}^{1/4}\). This also implies that the derivative of \({\delta}\) with respect to \(C_{3}\), that is, the sensitivity of \({\delta}\) to small variations in \(C_{3}\), varies with \(C_{3}^{-3/4}\), diverging as \(C_{3}^{1/4}\) approaches zero. Figure 11.6 shows the resolution for a LEEM instrument as a function of \(C_{3}\), for three different degrees of \(C_{\text{c}}\) correction (0, 50, and \({\mathrm{100}}\%\) correction) [11.64]. The horizontal axis runs from \(-1\) (\({\mathrm{100}}\%\) overcorrected) to 0 (exactly corrected) to \(+1\) (uncorrected). Figure 11.6 was calculated using the contrast transfer function method, taking into account all significant aberrations up to fifth order [11.28]. The resolution improves around \(C_{3}=0\), as expected, and is more complete with more complete chromatic correction. This highlights that both spherical and chromatic aberration correction are important. However, also with increased \(C_{\text{c}}\) correction we find a deep cusp near \(C_{3}=0\), following the green \(C_{3}^{1/4}\) line closely. The optimally corrected state of the system is located at the bottom of the cusp near \(C_{\text{c}}=C_{3}=0\). Small variations in \(C_{3}\) rapidly take the system out of the narrow minimum, negatively affection resolution. For chromatic aberration, the resolution varies with \(C_{\text{c}}^{1/2}\), and is, therefore, not quite as sensitive to small changes in \(C_{\text{c}}\).

Fig. 11.6

Resolution versus the normalized value of \(C_{3}\), for different settings of \(C_{\text{c}}\) (\({\mathrm{100}}\%\), uncorrected; \({\mathrm{0}}\%\), fully corrected). Start energy \(E_{0}={\mathrm{10}}\,{\mathrm{eV}}\), \(\Updelta E_{0}={\mathrm{0.25}}\,{\mathrm{eV}}\). The dotted line shows a \(C_{3}^{1/4}\) dependence of resolution on \(C_{3}\), as predicted by simple geometric theory. Adapted with permission from [11.64]. Copyright 2012 the American Physical Society

There are two implications. First, the system must be corrected with high accuracy. Naively, one might think that a reduction of \(C_{3}\) by \({\mathrm{90}}\%\) already gives us most of the improvement, but this is not true. A \({\mathrm{90}}\%\) reduction in \(C_{3}\) improves the resolution by only a factor 0.56, i. e., not even half of the optimum improvement. So, the system must be corrected with high accuracy for optimum performance. The fact that the best LEEM resolution obtained to date is \(\approx{\mathrm{1.5}}\,{\mathrm{nm}}\) suggests that we have not yet succeeded in obtaining sufficient accuracy. Second, the divergence of the sensitivity of the resolution upon small changes of the aberration coefficients in the vicinity of the optimally corrected state also implies that this state is intrinsically unstable. Indeed, extensive experiments in aberration-corrected TEM instruments [11.65] have shown that the optimally corrected state can only be maintained for short times (tens of seconds to several minutes). That is, even if we place the microscope in the corrected state with high accuracy, it is not likely to stay there for very long, as small fluctuations in power supplies, defocus conditions, sample drift, etc., will quickly take it out of the optimally corrected state again. This sounds dire. However, if we are willing to operate in the vicinity of the optimally corrected state, we can still obtain a very significant improvement in resolution with much better long-term stability. We may not obtain the optimum improvement, but we will still obtain a very worthwhile and robust improvement. In our experience, obtaining \({\mathrm{2}}\,{\mathrm{nm}}\) resolution or better in a corrected LEEM instrument is routine.

We conclude this section by noting that aberration correction in cathode lens microscopy has advanced from an experiment in its own right to a technique with practical use and applications. We will see some of these applications in the sections that follow. That said, aberration correction has not seen the tremendous uptake in LEEM/PEEM as in (S)TEM. Ease-of-use and instrument stability must be further improved, and the true resolution limit, well below \({\mathrm{1}}\,{\mathrm{nm}}\), must still be achieved. There is, however, no doubt that both of these goals can be achieved.

11.1.6 The LEEM/PEEM Instrument

Having looked at two key components of the modern LEEM instrument, i. e., the cathode objective lens and the aberration correcting electron mirror , it is now time to see how these two come together in a full instrument.

Fig. 11.7a,b

IBM LEEM/PEEM without (a) and with (b) electron-mirror aberration corrector. A modular design approach allows (a) to be converted into (b) by inserting the correction optics. The yellow squares around the MPAs show the symmetric locations of the diffraction entrance/exit planes. Adapted from [11.17], with permission from Elsevier

Figure 11.7a,b shows schematic diagrams of the IBM-developed LEEM/PEEM instrument without [11.66] (a) and with (b) aberration correction optics [11.17]. Starting with the uncorrected instrument (a), a cold field emission gun at the top of the instrument generates an electron beam with a typical energy of \({\mathrm{15}}\,{\mathrm{keV}}\). A gun lens and a condenser lens focus the electron beam in the entrance plane of a magnetic prism array ( ), which deflects the electron beam by a \(90^{\circ}\) angle towards the objective lens. The MPA, in spite of its planar geometry with both inner and outer deflection fields, behaves like a round lens. The gun cross-over placed on the entrance side is imaged with unit magnification on the exit side. There, the beam encounters first a transfer lens and then the cathode objective lens . The transfer lens re-images the beam cross-over in the backfocal plane of the objective lens, so that the sample is illuminated with a parallel beam of electrons. The sample is held at a potential close to that of the electron source, so that the electrons interact with the sample with an adjustable energy in the 0–few \({\mathrm{100}}\,{\mathrm{eV}}\) range. After reflection from the sample and re-acceleration to \({\mathrm{15}}\,{\mathrm{keV}}\), the electrons once again enter the objective lens. A diffraction pattern is formed in the backfocal plane, and a real-space image at a further distance. The transfer lens now relays the diffraction plane to the entrance plane of the MPA, and the real-space image to the geometric center of the MPA. The combination of objective lens and transfer lens ensure that locations of both image and diffraction planes can be controlled with high accuracy. Next, the MPA deflects the electron beam by another \(90^{\circ}\), into the projector system. The MPA places the diffraction plane at the center of P1, while P1 also sees an image at the geometric center of the MPA. A contrast aperture at the center of P1 is used to select a suitable diffracted beam for forming a real-space image. In Fig. 11.7a,ba P2 is not excited, and the remaining lens system forms a real-space image of the sample onto the detector. When P2 is excited to a suitable value, the diffraction plane is imaged onto the detector. The total magnification of the system is controlled by the relative excitations of P3, P4A, and P4B.

The MPA has another special property that we must consider. As the electrons traverse a deflecting field, the exact angle of deflection (nominally \(90^{\circ}\)) depends on the electron energy. The dispersion in the diffraction plane (location of the contrast aperture in P1) amounts to \(\approx{\mathrm{6}}\,{\mathrm{{\upmu}m/eV}}\). While this number appears small, we will see later that this chromatic dispersion enables the use of the MPA as a convenient in-line energy filter with an energy resolution at \({\mathrm{15}}\,{\mathrm{keV}}\) of \({\mathrm{160}}\,{\mathrm{meV}}\). By symmetry, the image at the center of the MPA is dispersion free and is, therefore, not blurred by this dispersion [11.17, 11.18].

Figure 11.7a,bb shows the additional optics required to add aberration correction to the system. It uses all the components seen in Fig. 11.7a,ba, plus an additional optical module that contains a second MPA, an electrostatic transfer lens between MPA1 and MPA2, transfer lenses M2 and M3, and the four-element electron mirror [11.15, 11.16] (represented schematically). The electrostatic transfer lens, located in the exit plane of MPA1, transfers the image from the center of MPA1 to the center of MPA2. In combination with MPA2, it also cancels the chromatic dispersion of the electron beam as it enters the mirror branch. The diffraction plane is at the center of M2, which places the image plane at the center of M3. M3 then places the diffraction plane at the reflection plane of the electron mirror, so that the mirror acts on the image plane only. After reflection, a corrected image is formed at the center of M3, the diffraction plane returns to the center of M2, and an image is once again placed at the center of MPA2, which deflects the beam into the projection column. This design is highly modular, and makes extensive use of symmetries to reduce and eliminate higher-order aberrations from the imaging system.

The diagrams do not show the locations of various stigmators and XY deflectors needed to align, adjust, and correct the lowest-order parasitic aberrations in the system. The number of such elements is kept to a strict minimum, so that each alignment aid fulfills one and only one function, considerably easing instrument setup.

Other instruments use MPAs with a \(60^{\circ}\) deflection [11.67] or less [11.68], but the MPAs serve the same purpose: to spatially separate incident and reflected electron beams, both in the sample and corrector branches of the microscope. Smaller deflection angles lead to smaller chromatic dispersion, which, depending on the design philosophy, is either an advantage or a disadvantage. An MPA with \(90^{\circ}\) deflection has sufficient dispersion so that it can be used as a convenient and effective in-line electron energy filter, without any additional hardware (and associated alignment) requirements. Energy filtering in \(60^{\circ}\) instruments is done exclusively with additional energy filters placed in the projector system of the microscope [11.13].

In the following sections, we will turn to different operating modes and applications of the LEEM instrument, with an emphasis on novel spectroscopic techniques.

11.2 LEEM-IV

Low-energy electron diffraction ( ) is one of the oldest techniques to study the structure of surfaces, albeit preceded by optical studies, notably ellipsometry [11.69]. In fact, the wave nature of the electron was first demonstrated [11.70] by diffraction of low-energy electrons from a nickel crystal by Davisson and Germer in 1927. Lester Germer continued these LEED studies over the decades that followed, and developed the display-type LEED system [11.71] around 1960 (following a 1934 suggestion [11.72] by W. Ehrenberg). Diffraction of high-energy electrons was demonstrated, also in 1927, by G.P. Thompson [11.73], soon followed by the successful development of TEM in the early 1930s. Although in the early 1930s Ernst Ruska and his collaborators were apparently unaware [11.74] of the wave nature of the electron, it did not matter much, as the electron wave length is so much smaller than the wavelength of visible light. That said, Ruska was relieved when he calculated a typical electron wavelength and found how small it is. The development from LEED to LEEM would take much longer and was not fully accomplished [11.11] until 1985. In its most common bright-field imaging form the LEEM image shows the spatial distribution of the intensity of the (\(0,0\)) LEED beam at normal incidence. The variation of the (\(0,0\)) LEED beam with electron energy is often referred to as the (\(0,0\)) LEED-IV (intensity-voltage) curve, and in a standard, non-imaging LEED experiment this intensity is averaged over the area illuminated by the electron beam. If we now acquire a LEEM image as a function of the landing energy, we obtain a LEED-IV curve in each pixel of the LEEM image. Hence, such a mode of data acquisition [11.30, 11.31] is referred to as LEEM-IV. The resulting data set is a cube of (\(x,y,E_{0}\)) voxels. The spatial resolution of the LEEM-IV data is not limited by the size of the illuminating electron beam but by the (energy-dependent) spatial resolution of the LEEM instrument. Of course, if the sample is spatially uniform, this dataset contains no more information than the spatially averaged LEED-IV curve. However, on samples that are not uniform, the data contain much additional information. The LEED-IV curve can be used in a fingerprinting fashion, to distinguish one surface structure from another, or it can be used to obtain the detailed atomic structure of a surface, by comparison of experimental LEED-IV data with theoretically calculated LEED-IV curves. The structure of the surface is then varied in theory until optimum agreement with experiment has been obtained. The smallest area over which this is possible is limited by the spatial resolution of the microscope, i. e., \({\mathrm{2}}\,{\mathrm{nm}}\) in an aberration-corrected LEEM instrument. Most of the surface structures known today, with accurate atomic positions, were determined by such LEED-IV analysis [11.75].

11.2.1 Fingerprinting

The simplest form of LEEM-IV experiments is to take several given structures and obtain the LEEM-IV data for these different structures (fingerprints). If we then have a sample that contains several of these structures side-by-side, the fingerprint spectra can be used to identify each of them and map their spatial distribution.

Figure 11.8 shows LEED-IV curves obtained by Schmid et al [11.76] on a Pt(001) surface covered with varying amount of CO and O. Fingerprint LEED-IV curves were obtained for surfaces that were covered either with CO or with O alone. As CO and O are co-adsorbed at \({\mathrm{250}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\) this will lead to catalytic oxidation of CO and desorption of \(\mathrm{CO_{2}}\). The reaction is spatially highly non-uniform, giving rise to spatiotemporal reaction fronts that sweep across the surface. LEED-IV curves were obtained in the vicinity of these reaction fronts. The local CO and O coverages were then obtained by fitting the LEED-IV curves for areas of unknown composition by a linear combination of the CO and O only LEED-IV curves. The implicit assumption is that the O and CO-covered areas are sufficiently large (i. e., larger than electron beam coherence length), so that their contributions to the LEED-IV curve can be added incoherently. It is not clear whether this assumption is justified, and in general this will certainly not apply.

Fig. 11.8

IV curves for Pt(001) with different adsorbates. (a) Clean surface; (b) 0.6 monolayer O, (\(5{\times}5\)) superstructure; (c) \(<0.65\) ML CO, (\(\sqrt{2}{\times}\sqrt{2}\))R45 superstructure;(d) 0.67 ML CO, (\(\sqrt{2}{\times 3}\sqrt{2}\))R45 superstructure; (e) 0.75 ML CO, c(\(4{\times}2\)) superstructure. After [11.76]

11.2.2 Atomic Structure

LEED-IV-based atomic structure determination has a long and distinguished history. In LEEM-IV, we obtain a LEED-IV curve in every pixel of the image, and in principle we can use these LEED-IV curves to determine the atomic structure in each pixel of the image. That this can indeed be done was first demonstrated by Hannon et al [11.30] for thin Pd films deposited on a Cu(001) substrate at \({\mathrm{200}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\). Figure 11.9 shows a \({\mathrm{13.1}}\,{\mathrm{eV}}\) bright field LEEM image after depositing 0.6 monolayers (ML) of Pd. Immediately striking is the extreme non-homogeneity of the resulting surface and the lack of sharp boundaries as the contrast changes from dark to bright. It is clear even from a casual inspection of this image that atomic steps play an important role in the surface incorporation of Pd.

Fig. 11.9

Image of Cu(001) surface after deposition of 0.6 ML Pd. \(E_{0}={\mathrm{13.1}}\,{\mathrm{eV}}\), \({\mathrm{200}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\). Adapted with permission from [11.30]. Copyright 2006 the American Physical Society

Figure 11.10c shows a similar image at \({\mathrm{20.1}}\,{\mathrm{eV}}\), while Fig. 11.10a shows LEED-IV curves obtained inside the square box in Fig. 11.10c as a function of the amount of Pd deposited. While there are changes throughout the IV curves, most obvious is the strong increase of the peak intensity at \({\mathrm{20}}\,{\mathrm{eV}}\) with increasing Pd coverage. To fit these experimental data, LEED-IV curves were calculated for trial structures in which the Pd concentrations in the first three atomic layers of the crystal, \(c_{1}\), \(c_{2}\), and \(c_{3}\), were used as parameters.

Fig. 11.10

(a) LEED-IV curves (obtained from LEEM-IV data cube) averaged over the rectangle as shown in (c). Blue lines are fits to the data (see text). (b) Pd concentrations in the first three layers of the crystal versus deposition time. Adapted with permission from [11.30]. Copyright 2006 the American Physical Society

The best fits are shown in Fig. 11.10a (blue lines), and Fig. 11.10b shows the best-fit values for these concentrations as a function of deposition time. Surprisingly, the amount of Pd in the outermost atomic layer is near zero throughout the entire deposition sequence, with most of the Pd atoms going into the second layer. Figure 11.11a shows concentration data along a line crossing an atomic step, obtained by fitting the LEEM-IV data, after deposition of 0.4 ML of Pd. The Pd concentration in the first layer is low at all locations. The third layer concentration is high on the upper terrace near the atomic step but decays with distance to the step, while the second layer concentration is high everywhere, except on the upper terrace near the step. Not only do these data tell us where the Pd atoms go, they also suggest why. Clearly, Pd atoms prefer to reside in the second layer, and they can get there easily: to the right of the atomic step in Fig. 11.11, on the lower terrace, virtually all Pd atoms are in the 2nd layer, and none in the third. Thus, Pd atoms replace second layer Cu atoms, expelling these Cu atoms to the surface, where they diffuse and attach to the atomic step, which then advances during growth. However, when Pd atoms are already in the second layer, and get overgrown by this advancing atomic step, they become third-layer Pd atoms and can no longer diffuse. This simple physical picture can be used in a Monte Carlo simulation of the growth process (solid black lines Fig. 11.11a). The high quality of the LEEM-IV fits in Fig. 11.10a gives high confidence in the accuracy of the results. Figure 11.11b shows maps of the Pd concentration in the first three layers of the crystal in the vicinity of an atomic step. Again, the first layer is practically devoid of Pd. In layer 2 we see a dip near the atomic step, and in layer 3 a peak, in agreement with Fig. 11.11a. To obtain the maps in Fig. 11.11b, a LEED-IV fit was obtained for each pixel in the image.

Fig. 11.11

(a) Pd concentrations across an atomic step after deposition of 0.4 ML of Pd. At the start of growth the step is located at position 0. Black lines give the results of Monte Carlo simulations of the first and second layer Pd concentrations. (b) Best-fit maps of Pd concentration in layers 1, 2, and 3. After [11.30]

Another example concerns the growth of thin graphene layers on a polycrystalline Ni(111) sample [11.41, 11.77]. Figure 11.12a shows a \({\mathrm{10}}\,{\mathrm{eV}}\) bright-field LEEM image of such a sample, in which we find both bright and dark areas. LEED-IV curves from areas A and B are shown in Fig. 11.12b, as well as a LEED-IV curve obtained on clean Ni(111) (black lines). Again, LEED-IV curves were calculated for a number of trial structures. For the clean surface, the best fit is obtained for a bulk-terminated surface (brown line). In the area marked A in Fig. 11.12a, the surface is covered with a single graphene layer, where the hexagons of the graphene lattice are placed above the Ni atoms in the second layer of the crystal. The area marked B is covered with two atomic layers of graphene. Now there is a choice in the stacking of these layers, either so-called AA, or AB (i. e., Bernal) stacking. Theoretical IV curves are shown for both of these possibilities, and best agreement is found for Bernal stacking.

Fig. 11.12

(a) Bright field LEEM image of graphene grown on polycrystalline Ni(111). (b) Measured (thin black line) and calculated (brown lines) IV curves for clean and graphene covered Ni(111). The atomic geometry for one layer of graphene is shown in the inset. (c) EELS data for regions A (one layer of graphene) and B (two layers of graphene) in (a). \({\pi}\) and \({\sigma}+{\pi}\) plasmon losses are seen in region B. Reprinted (adapted) with permission from [11.41]. Copyright 2010 the American Chemical Society

These structural studies were augmented with in-situ LEEM-EELS studies, where the inelastic energy loss spectra were recorded on these same areas, as shown in Fig. 11.12c. On the A area, the EELS spectrum is devoid of structure, but on the B areas pronounced \({\pi}\) and \({\sigma}+{\pi}\) plasmon losses are seen. One might have expected to see these plasmon losses in the monolayer graphene A areas also. However, the interaction of the Ni d-electrons with the first graphene layer is very strong, disrupting the graphene band structure and killing the plasmon excitations. The second layer graphene, however, in area B is decoupled from the Ni substrate by the underlying graphene in the first layer. The plasmon losses are restored in the second layer, and observed experimentally. Detailed first-principles band structure calculations and subsequent calculations of the electron loss function are in good agreement with the data [11.41]. The use of EELS in the LEEM instrument will be discussed in more detail in Sect. 11.6.

11.2.3 Layer Counting

Van der Waals materials  [11.78] such as graphene, hexagonal boron nitride (hBN), and the broad class of metal-chalcogenides are the subject of numerous studies, thanks to their promising electronic, optical, and magnetic properties, particularly in samples that consist of a single, or a few atomic/molecular layers. Knowing how many layers are present in a given sample is essential in understanding and fine-tuning its properties. In some cases, it is possible to count layers by purely optical means, but such methods have only limited lateral resolution. LEEM-IV measurements enable layer counting for such layered systems, as was first demonstrated by Hibino et al [11.79]

Fig. 11.13a-d

LEEM images for multilayer graphene grown in SiC(0001) at (a) 2.5, (b) 3.5, (c) 4.5, and (d) 5.5 eV electron energy. From [11.79], published under CC-BY 4.0 license

Figure 11.13a-d shows LEEM images of a 4H-SiC(0001) sample after heating to \({\mathrm{1450}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\), leading to the formation of epitaxial graphene films with variable layer thicknesses. The images, taken at 2.5, 3.5, 4.5, and \({\mathrm{5.5}}\,{\mathrm{eV}}\) show different contrasts depending on electron energy and film thickness. As the electron energy is scanned and a LEEM-IV dataset acquired, LEED-IV data can be extracted from the data for each area labeled A–H in Fig. 11.13a-d. Such LEED-IV data are shown in Fig. 11.14. While for energies above \(\approx{\mathrm{8}}\,{\mathrm{eV}}\) the IV curves look almost identical, in the range from \(0{-}8\,{\mathrm{eV}}\) there are strong differences. The bottom curve, for area A, shows only one deep minimum at \(\approx{\mathrm{2.5}}\,{\mathrm{eV}}\). Thus, area A is dark in Fig. 11.13a-da. At the same energy, area B has a maximum, surrounded by two minima. Thus, area B is bright in Fig. 11.13a-da but dark in Fig. 11.13a-dc. Going from area A to H in Fig. 11.14, we notice the addition of one additional minimum with each new curve.

Fig. 11.14

LEEM-IV curves obtained in locations A–H in Fig. 11.13a-d. From [11.79], published under CC-BY 4.0 license

The number of minima is directly related to the number of layers of graphene. If we have two layers of graphene, electronic structure calculations [11.79, 11.80] show that there is an electronic state located between the two graphene layers: a so-called interlayer state , unoccupied and above the vacuum level. When the incident electron beam energy coincides with the energy of this interlayer state, it is resonantly transmitted through the graphene layer, and reflectivity is low [11.79, 11.80]. Thus, area A has one such interlayer state, formed between the first and second graphene layers formed on the SiC substrate. (The first layer, like the first graphene layer formed on Ni(111) discussed above, has a strong interaction with the SiC substrate and is often referred to as the buffer layer). When a third layer is added, there will be an additional interlayer state between the second and third layers, which couples to the interlayer state between the first and second layer. This coupling gives rise to a splitting of the energies of the two interlayer states, as expected in a simple tight-binding model, giving rise to the two minima for curve B. This process repeats with the addition of each layer, so that the number of minima in the LEED-IV curves is a direct measure for the number of graphene layers in the film.

Fig. 11.15

(a) LEEM image of multilayer hBN. IV curves for the different marked areas are shown in (b). Adapted from [11.33]

This works not only for graphene, but also for hBN [11.33]. Figure 11.15a shows a LEEM image at \({\mathrm{3.7}}\,{\mathrm{eV}}\), for a sample consisting of several layers of hBN. Figure 11.15b shows LEED-IV curves for the differently colored circles in Fig. 11.15a, again showing progressive addition of minima as the number of layers increases one by one. We can see the progression most easily by noting that the minimum for two layers coincides with a maximum for three layers, and the maximum for three layers corresponds to a minimum for four layers, etc. However, for four layers, we also see that the lower minimum is just at the mirror-mode/LEEM threshold, i. e., just at the vacuum level. For five layers, the first minimum has now completely shifted below the vacuum level and is no longer visible. Yet again, the minima for the four-layer IV curve coincide with maxima in the five-layer IV curve, so that we can still confidently count the number of layers. Eventually, the minima and maxima merge and can no longer be resolved, as the electronic system evolves from a few-layer system to a bulk material. Similar results were obtained for thin hBN layers grown on Ni foils [11.81]. For WSe\({}_{2}\) films on graphene a combined experimental and theoretical study [11.82] was made by Sergio de la Barrera et al In this case, the IV curves still carry a signature of layer thickness, but not nearly as distinct as for the graphene and hBN cases, and a comparison with detailed band structure and electron reflectivity calculations becomes a necessity.

Intensity oscillations as a function of thickness are also observed in thin (epitaxial) metal films on a variety of substrates. In these systems, quantum well states  [11.83] result from a Fabry–Pérot-like interference of the electrons between the surface of the epitaxial film and the interface to the underlying substrate. Such quantum well oscillations are discussed in the chapter by Ernst Bauer in this volume and will not be further discussed here.

11.3 ARPES and ARRES

11.3.1 ARPES

Angle-resolved photo electron spectroscopy (ARPES ) was developed in the early 1970s, with the advent of synchrotron radiation, as the premiere technique to study the electronic band structure of solids [11.20]. Photo-electrons, emitted by illumination of the sample with photons of energy \(h{\nu}\), are analyzed both in energy and emission angle. Due to refraction of the emitted electrons at the solid–vacuum interface, the normal momentum of the electrons is not conserved upon emission, but the momentum parallel to the surface is conserved. When electron energy relative to the Fermi level is plotted versus in-plane momentum, the resulting bandstructure plots, showing the dispersion of the electron states in the solid with momentum, can be compared with theoretical band structure calculations. Over the years, both energy and momentum resolution have steadily improved, and ARPES has turned into a highly refined technique, critical to the understanding of electronic, chemical, and (with the addition of spin detection) magnetic properties of a wide range of materials.

In a cathode lens instrument operated in PEEM mode, we also have access to the energy and momentum distributions of the emitted photoelectrons. Due to the strong electrostatic field between the sample and the objective lens, all photoelectrons are extracted and enter into the objective lens. The backfocal plane of the cathode lens contains a direct representation of the photo electron in-plane momentum distribution. With the addition of a suitable energy filter to separate electrons of different energies, the PEEM instrument can be used as an ARPES tool. Energy and momentum resolution are not as high as with a dedicated ARPES instrument, but still sufficient to be useful in many situations. Of course, the PEEM instrument is also a microscope, and by placing a selected area aperture in a suitable image plane, ARPES data can be obtained on sample areas as small as \({\mathrm{1}}\,{\mathrm{{\upmu}m}}\), which is extremely useful for inhomogeneous samples [11.21].

Energy filters can take different forms. In the instrument first developed by Lee Veneklasen [11.13] and later commercialized by Elmitec [11.67], a retarding electrostatic hemispherical analyzer was added to the projection system of the LEEM/PEEM instrument. For such a hemisphere, with a deflection angle of \(180^{\circ}\), the dispersion is given by \(D=2R/E\), where \(R\) is the deflection radius and \(E\) the pass energy of the electrons (i. e., the energy of the electrons as they pass through the hemisphere). Dispersion increases as \(E\) decreases, so it is common practice to decelerate the electrons inside the hemispherical analyzer. The SMART instrument [11.16] followed a similar approach, i. e., adding an electron spectrometer to the projection system of the microscope. In this case, the choice was made for a magnetic omega-type energy filter [11.16, 11.39], passing the electrons without deceleration. Other systems, such as the Scienta/Omicron NanoESCA instrument [11.85], use a double hemispherical analyzer, canceling some of the spectrometer aberrations, for use in both ARPES and core-level spectroscopy experiments.

Another option is to implement an in-line energy filter , i. e., use the magnetic prism array already present in a LEEM/PEEM instrument as an energy filter [11.86], without addition of any further electron optical components. The magnetic prism array has a real-space image at its center and diffraction planes located symmetrically on both the entrance and exit sides (Fig. 11.7a,b). If the distance between the diffraction plane and the edge of the magnetic prism array is \(S\), and the deflection radius inside the prism array is \(R\), then the dispersion is given by \(D=(R+S)/2E\). For the same deflection radius \(R\), the dispersion of a hemispherical analyzer at a given energy \(E\) is about twice as large as for a magnetic prism array with \(90^{\circ}\) deflection. This is reasonable, as the deflection angle in a hemispherical analyzer is twice as large.

Figure 11.16 shows experimental band structures measured [11.84] using the NSLS instrument of exfoliated bilayer, trilayer, and bulk \(\mathrm{MoS_{2}}\), respectively. The NSLS instrument [11.67] uses a retarding hemispherical analyzer, and the energy spectra are obtained by scanning the pass energy through the analyzer and recording a (\(k_{x},k_{y}\)) plane for each pass energy. Cuts along a given momentum direction (as in Fig. 11.16) are then constructed after the complete dataset has been acquired.

Fig. 11.16

Synchrotron ARPES data of exfoliated bilayer (a), trilayer (b), and bulk (c) \(\mathrm{MoS_{2}}\). Data obtained with a hemispherical analyzer in the projection column of the LEEM/PEEM instrument. Reprinted with permission from [11.84]. Copyright 2013 the American Physical Society

For comparison, Fig. 11.17 shows experimental bandmaps obtained on epitaxial graphene on SiC, measured with an in-line energy filter at the Advanced Light Source. Figure 11.17a is a Hg-PEEM image of a sample containing several layer thicknesses of graphene: buffer layer, buffer \(+\) monolayer, and buffer \(+\) bilayer. A K-\({\Upgamma}\)-K (\(k_{x},E\)) slice (obtained with a single, fixed entrance slit position) is shown in Fig. 11.17b for a selected region containing monolayer graphene, while Fig. 11.17c shows a K-M-K (\(k_{x},E\)) slice for bilayer graphene. If a contrast aperture is placed at the Dirac point (the brown circle in Fig. 11.17c) a real-space image can be formed with just these electrons (Fig. 11.17d). We now have a real-space image of a specific (\(k_{x},k_{y},E\)) feature in the reciprocal-space band structure of the thin film. Figures 11.17b,c were obtained for two specific, but fixed entrance slit positions, taking two different cuts through the first Brillouin zone. We can also obtain such (\(k_{x},E\)) slices, while \(k_{y}\) is scanned from slice to slice. When a full 3-D dataset has been obtained (\(k_{x},k_{y}\)), planes at different binding energies can be constructed from the data, as shown in Fig. 11.17e. Comparing Figs. 11.16 and 11.17 we find that the two types of spectrometers obtain the data in a different acquisition order, but in the end, the datasets obtained contain identical information.

Fig. 11.17

(a) Hg PEEM image of multilayer graphene on SiC(0001). (b) K-\({\Upgamma}\)-K electron spectra obtained inside the brown circle in (a) (monolayer graphene). (c) K-M-K electron spectra obtained in the black circle in (a) (mostly bilayer graphene); (d) dark-field PEEM image obtained using electrons at the Dirac point in (c). (e) Selected-energy (\(k_{x},k_{y}\)) planes for monolayer graphene. Data obtained using the \(90^{\circ}\) deflection MPA as an in-line energy filter. Courtesy of D. Schwartz, S. Ulstrup, R. Koch, C.M. Jozwiak, A. Bostwick, and E. Rotenberg

Clearly, both types of energy filters can provide excellent results, complementing LEEM and PEEM imaging with valuable electronic structure information. Typical energy resolution in these experiments is in the range \(100{-}150\,{\mathrm{meV}}\).

Recently, cathode lens instruments developed specifically for high-resolution momentum microscopy have reached unprecedented energy resolution of \(\approx{\mathrm{10}}\,{\mathrm{meV}}\), and also provide high efficiency spin filtering [11.22, 11.23]. This novel class of high resolution ARPES instruments is undergoing rapid development, and we will not review them here. However, we expect such instruments to transform ARPES, with very high energy and momentum resolution, nanosecond time resolution, and high efficiency spin analysis.

11.3.2 ARRES

ARPES gives information on occupied electron band solids. What about unoccupied electron bands? The photoemission process is usually considered to consist of two steps: excitation from an electron from an occupied state to an unoccupied state, followed by coupling of the unoccupied state to a free electron state in the vacuum. It is clear that the unoccupied state plays an important role, but we do not have immediate access to that state. One approach is \(k\)-resolved inverse photoelectron emission spectroscopy ( ), in which the sample is illuminated with electrons of a given energy and parallel momentum [11.87, 11.88]. This electron is absorbed in an unoccupied band, followed by a transition to an occupied band under emission of a photon, which is subsequently detected. KRIPES has been used successfully to study the electronic structure up to a few eV above the Fermi level. However, it has distinct disadvantages. The cross-section for the inverse photoemission process is very small, resulting in high electron beam currents, weak signals, long data acquisition times, and the potential for electron-induced sample modifications.

It has long been known [11.89] that low-energy electron diffraction, particularly at low energies, is highly sensitive to the band structure of the solid. If the incoming electron encounters the crystalline sample at an energy and momentum that coincides with a bandgap in the unoccupied electronic structure, the electron has a very low probability of entering the solid, i. e., a high reflection probability. On the other hand, if the electron encounters a band with a high density of states, it is much easier for it to enter the solid, and reflection probability will be low. Over the years there have been several experiments to take advantage of this, usually by measuring total sample current as the incident angle and energy of an electron beam was varied, and, indeed, such measurements show band structure-like information [11.90, 11.91]. However, there are a few problems. By measuring the total current, no provisions are made to exclude the effects of secondary electrons. Secondly, momentum discrimination is made for the incident electron beam, but not for electrons leaving the sample. LEEM offers an opportunity to address both problems at the same time. The backfocal plane of the objective lens contains a momentum map of both the incident and the reflected electrons. By shifting the illuminating beam in the backfocal plane, a particular incident in-plane momentum can be selected. This corresponds to tilted illumination in a classical LEED experiment. In LEEM, as electron energy is changed, a fixed location in the backfocal plane corresponds to fixed in-plane momentum. Thus, as the electron energy is changed, the in-plane momentum stays constant, and the illumination angle automatically adjusts, increasing with decreasing energy. This incident electron beam encounters the crystalline sample and is specularly diffracted. The (\(0,0\)) LEED beam conserves the in-plane momentum of the incident electron beam, and inverts the out-of-plane momentum (i. e., energy is conserved for elastically diffracted electrons). Thus, if we accept only the electrons in the (\(0,0\)) LEED beam (using a contrast aperture) we achieve strict momentum and energy conservation. All electrons outside the contrast aperture (diffusely scattered elastic electrons, electrons diffracted in higher-order beams, and all inelastic electrons) are rejected by the contrast aperture. One restriction is that both the incident and the reflected beams are above the vacuum level, and, therefore, the energy region between the Fermi level and the vacuum level is not accessible. However, angle-resolved reflection electron spectroscopy ( ) gives access to the unoccupied bands in a manner that was not previously available [11.32, 11.33].

Figure 11.18a-c shows ARPES and ARRES data obtained in the Leiden ESCHER instrument for bulk graphite (a) and hBN (b) samples [11.33]. The ARPES data were obtained with a focused HeI source integrated in the LEEM/PEEM instrument. Theoretical bandstructure calculations are also shown. In the ARPES data, the \({\sigma}\) and \({\pi}\) bands are clearly resolved in the data. The ARRES data show reflectivity as a function of energy and momentum, with high reflectivity shown as red, and low reflectivity as blue. Thus, bandgaps correspond to red regions. For both graphite and hBN broad bandgap regions are seen near the centers of the figures. These bandgap regions correspond closely with the theoretical calculations (solid lines). The reflectivity can also be calculated explicitly for the ARRES experiment, based on a calculation of the band structure coupled with a LEED scattering calculation (ignoring inelastic effects). Figure 11.18a-cc shows such an explicit calculation for hBN. There is detailed agreement between the theory (Fig. 11.18a-cc) and the data (Fig. 11.18a-cb), demonstrating the power of this new technique.

Fig. 11.18a-c

ARPES (lower panels) and ARRES (upper panels) spectra on bulk graphite (a) and hBN (b). (c) Theoretical ARRES spectrum for bulk hBN calculated from first principles. Red regions (high reflectivity) correspond with bandgaps in the unoccupied valence band. After [11.33]

While Fig. 11.18a-c shows data for bulk samples, Fig. 11.19a-d shows ARRES data for two, three, and four layers of hBN (a), as well as two, three, and four layers of graphene (c). In the region below the bulk bandgap, we can see narrow states that correspond to the interlayer states that we encountered previously in the section on layer counting, at \(k=0\). Here, we now also see the dispersion of these states with in-plane momentum. As more layers are added, the number of interlayer states increases, and finally they merge into the bulk bands seen in Fig. 11.18a-c.

Fig. 11.19a-d

ARRES spectra for two, three, and four layers of hBN (a) and graphene (c). (b) Theoretical (top) and experimental (bottom) dispersion of interlayer states of hBN. (d) The same for graphene. After [11.33]

Again, the dispersions of these bands can be calculated explicitly. The comparison between experimental and theoretical dispersions is shown in Fig. 11.19a-db for hBN and in Fig. 11.19a-dd for graphene. The agreement is excellent.

Fig. 11.20

Normal incidence LEEM reflectivity spectra for bulk hBN, and for bulk hBN with one to four monolayers of graphene on top. The presence of the characteristic interlayer state reflectivity oscillations for two, three, and four layers of graphene indicate weak coupling with the underlying hBN. After [11.33]

Finally, we show IV curves at \(k=0\) for thin graphene layers on a bulk hBN sample [11.33]. Since the interlayer states in Fig. 11.19a-d appear quite similar for graphene and hBN, one might expect significant coupling between these states in the two materials. In this case, the interlayer states for graphene on hBN would be quite different from graphene on–say–SiC(0001). In Fig. 11.20 we find that this is not the case. Rather than mixing with the hBN bands, the graphene interlayer states are undisturbed by the underlying hBN, indicating that coupling between hBN and graphene is very weak. In fact, the experimental spectra are well approximated by a linear combination of hBN and graphene spectra, with the hBN spectra showing diminishing intensity with increasing graphene thickness, as expected due the damping of the hBN intensity in the graphene overlayers. The \(1/e\) extinction distance of the hBN signal is about 1 graphene layer [11.33].

With both ARPES and ARRES seamlessly integrated in the LEEM/PEEM instrument, the analytical capability has now expanded tremendously. While imaging and simple LEEM-IV and LEED-IV analysis is mostly structure oriented, ARPES and ARRES offer access to the electronic structure of the sample in the same setup. ARPES data can be obtained on sample areas of \(\approx{\mathrm{1}}\,{\mathrm{{\upmu}m}}\). If a specific feature in the ARPES data is selected for image formation (using a contrast aperture placed in the energy spectrum), real space images can be obtained for that specific feature with spatial resolution far below \({\mathrm{100}}\,{\mathrm{nm}}\) [11.17, 11.92]. In ARRES, spatial resolution is even better, as the intrinsic signal is much higher. The data shown in Figs. 11.18a-c11.20 were obtained from a single pixel in the image, an area of about \(10\times{\mathrm{10}}\,{\mathrm{nm^{2}}}\).

A word about aberration correction : when the angle of the incident beam is scanned, and the image is formed with the specular (0,0) beam, the real-space image will undergo a lateral shift proportional to \(C_{3}{\alpha}^{3}\), where \(C_{3}\) is the spherical aberration coefficient, and \({\alpha}\) is the angle of the specular beam relative to the optical axis. Such image shifts can be quite large and make it more difficult to perform the experiment. With correction of \(C_{3}\), this image shift disappears, or is at least much reduced. Here, the principal goal is not to optimize spatial resolution but to reduce the image shift as a function of the beam tilt. It is an added benefit of aberration correction that is nice to have. One challenge for the future is to replicate the momentum and energy resolution that are available in ARPES [11.22, 11.23] also for ARRES. ARPES data show many fine features as a function of energy and momentum, and we may expect a similar level of detail in the unoccupied bands. It will require improvements in electron source energy resolution and in data acquisition routines to bring ARRES up to the ARPES level. However, there is no doubt that it will be extremely rewarding to do so.

11.4 Potentiometry

The LEED-IV curve contains an enormous amount of quantitative spectroscopic information that we can take advantage of in our studies of materials' properties. All the properties discussed so far are ground state or at least static properties: structure, atom concentrations, overlayer structure, layer thickness, and electronic band structure. However, the LEED-IV curve can also be used to study charge transport, by obtaining maps of the potential distribution on the surface of a sample, as current is passed by applying a potential difference across that sample.

2-D potentiometry is an old art that has been practiced for a long time. On large samples we can measure local potential by probing with a fine voltage probe. In the development of electron optics such potentiometry played an important role in the form of the electrolytic trough . In such a trough, electrodes with the shape of the lens electrodes are placed in an electrolytic bath. The equipotentials in the space between the electrodes are measured [11.93] in the electrolyte by a fine voltage probe. When the potential distribution is known, the electron trajectories can be calculated and the properties of the lens thereby obtained. With the advent of the digital computer such equipotential surfaces are now obtained much more readily and with much higher accuracy by numerical means. Scanning tunneling microscopy has also been used extensively to obtain potential distributions. Scanning tunneling potentiometry was first introduced [11.94] by Muralt and Pohl in 1986, only 4 years after the invention of the STM. For 2-D systems, the method was much refined [11.95] by Bannini et al in a study of the surface conductance of the Si(111)-(\(\sqrt{3}{\times}\sqrt{3}\))-Ag surface. In this method, two tips are placed on and in contact with the surface, and a potential is applied between them. A third STM tip is brought into tunneling range in an area between the two contacting tips, and the local potential is then determined at each location as the tip is scanned along the surface, resulting in a spatial map of the 2-D potential. In their work, Bannini et al found that the conductance on a given atomic terrace is high, and that most of the potential drop between the two contacting electrodes is localized at atomic steps. This method was later used by Ji et al to measure [11.96] atomic-scale transport in epitaxial graphene films on SiC(0001). In this system, too, it was found that most of the potential drop occurs at atomic steps, although the terraces between steps also show significant electrical resistance. This terrace resistance is higher, as the graphene layer is thinner.

Scanning probe methods have excellent spatial and voltage resolution, but they are also slow and experimentally very demanding. Potentiometry can also be done with a LEEM instrument, using the spatial shifts of LEED-IV curves with changing surface potential.

11.4.1 Work Function Mapping

The simplest form of such potentiometry is to measure the spatial distribution of the sample work function. At sufficiently high (negative) sample bias the incident electron beam will be reflected in front of the surface. In this so-called mirror mode, the electrons do not touch the surface. As the sample bias is gradually reduced, the electrons will at some point be able to reach the surface, and the imaging mode transitions from mirror mode to LEEM. At this Mirror-To-LEEM (MTL) transition there is a sharp drop in signal intensity, as all electrons are reflected in mirror mode, but a much smaller fraction is reflected in LEEM mode. The exact sample bias at which this occurs depends on the work function of the sample. If the work function is spatially non-uniform due to the presence of a mixture of surface structures, then the MTL transition as a function of the sample bias will also be spatially non-uniform, as can be easily determined by acquiring images as a function of the sample bias across the MTL transition. From this data set we can then determine the exact bias voltage of the MTL transition for each pixel in the image and obtain a 2-D map of the work function.

An example is given in Fig. 11.21, obtained [11.97] on a \({\mathrm{50}}\,{\mathrm{nm}}\) layer of \(\mathrm{MoO_{3.16}}\) grown on highly doped n-type Si wafers using DC-reactive sputtering and annealed at \({\mathrm{500}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\). The layer is super-oxidized relative to the normal \(\mathrm{MoO_{3}}\) thin film composition, giving rise to lateral variations in the Mo valency and work function.

Fig. 11.21

(a) 2-D work function map of a \({\mathrm{50}}\,{\mathrm{nm}}\) \(\mathrm{MoO_{3.16}}\) layer grown on n-type Si, annealed under ultra-high vacuum ( ) conditions at \({\mathrm{500}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\). Field of view \({\mathrm{12}}\,{\mathrm{{\upmu}m}}\). (be) Single pixel IV curves obtained from the areas indicated in (a). Due to excess oxygen, the surface has formed various micrometer sized nano-aggregates with varying surface composition. Adapted from [11.97], with permission from Elsevier

Figure 11.21a shows the spatial variation of the work function (field of view \({\mathrm{12}}\,{\mathrm{{\upmu}m}}\)). The sample has formed highly convoluted, micrometer-sized nano-aggregates of various compositions, each with its own distinct work function. Figures 11.21b–e show image intensity versus bias voltage for the areas indicated in Fig. 11.21a; \(E_{0}\) is the nominal landing energy of the electrons (i. e., ignoring work function differences between electron emitter in the gun and sample), with sample bias decreasing from left to right. For low values of \(E_{0}\), all areas are in mirror mode, therefore all electrons are reflected, and the normalized image intensity is equal to 1. With decreasing sample bias (increasing \(E_{0}\)), different sample regions experience the MTL transition at different times. The map in Fig. 11.21a is derived from the intensity versus bias curves shown in Fig. 11.21b–e. Potential problems with this method are dicussed in [11.98].

11.4.2 Resistance Mapping

Work function maps show the spatial distribution of the surface potential due to structural variations across the surface. However, in many cases, we would like to measure potential variations resulting from an externally applied bias across the surface. If the surface is a perfectly uniform and homogeneous conductor, all we would see is a linear gradient in surface potential due to Ohm's law. However, if surface conductance shows local variations, due to a distribution of various structures, and/or the presence of defects such as atomic steps, dislocations, etc., such local variations in conductance give rise to local variations in the potential gradient.

Fig. 11.22a-c

The wavelength of the electron depends on the local surface potential. (a) At 0 applied bias potential the wavelength does not depend on location. (b) At positive applied bias potential the electrons are accelerated towards the substrate and wavelength is reduced but still does not depend on locations. (c) With a bias applied between the two electrodes, there is now a potential gradient across the sample and wavelength depends on location. After [11.38]

Let us have a sample with a 2-D conducting layer and with two electrical contacts on the surface, as is schematically shown in Fig. 11.22a-c. In Fig. 11.22a-ca,b, no potential is applied to the surface electrodes. In Fig. 11.22a-ca, the sample bias, \(V_{\mathrm{E}}\), is close to zero (relative to the potential of the electron source), so that the landing energy of the electrons is low, and the electron wavelength long. In Fig. 11.22a-cb, the sample biased is raised (more positive relative to the electron source), so that the landing energy of the electrons is increased, and their wavelength reduced; landing energy and electron wavelength depend on the surface potential of the sample. In Fig. 11.22a-cc, a potential difference is now also applied between the surface electrodes, with a positive potential (higher landing energy) on the left electrode, and a negative potential (lower landing energy) on the right electrode. Now, landing energy and electron wavelength depend on where we are between the two electrodes.

Figure 11.23b shows [11.38] a color-coded image of graphene films on SiC. The red, blue, and green regions are coded with respect to graphene layer thickness, with the corresponding LEED-IV curves shown in Fig. 11.23a. Regions 1 (blue) are monolayer graphene (on top of the non-conducting underlying buffer layer), regions 2 (green) are bilayer graphene, and regions 3 (red) are triple layer graphene. As we saw before, LEEM-IV data are used to determine graphene layer thickness, pixel by pixel. To the left and the right of the image are electrodes with which a potential difference can be applied in the plane of the surface, as in Fig. 11.22a-cc. Figure 11.23c shows LEED-IV curves obtained in locations a, b, and c in Fig. 11.23b, after applying a potential difference to the two electrodes. Also shown is a reference LEED-IV curve obtained when no voltage is applied. The LEED-IV curves in locations a, b, and c are shifted relative to this reference curve, as the potentials in locations a, b, and c are now no longer the same. The voltage shifts \({\Updelta}V_{\text{a}}\), \({\Updelta}V_{\text{b}}\), and \({\Updelta}V_{\text{c}}\) can be obtained by determining the shifts of the IV curves relative to the reference IV curves. Here this is demonstrated for bi-layer regions, but of course the same analysis can be performed, pixel by pixel, for single and triple layer regions, and a 2-D potential map can be extracted from the data, as shown in Fig. 11.23d. The 2-D potential distribution is highly non-uniform. In the center region with triple layer graphene, the potential gradient is small, as this region is highly conductive. In contrast, the potential gradients in the single layer regions to the left and the right is much higher. Most notably, abrupt potential drops are seen at the boundaries between single and triple layer graphene. At these boundaries the 2-D band structure of the material changes abruptly, giving rise to strong carrier scattering. Similar effects were seen in the STP study [11.96] by Ji et al

Fig. 11.23

(a) LEEM IV curves on locations 1, 2, and 3 in (b). (b) Color coded LEEM image taken inside the red circle marked in the inset in (a), on a graphene film on SiC between two Cr/Au electrical contacts. In (a) no bias voltage is applied between the contacts. (cIV curves in locations a, b, and c in (b), with a \({\mathrm{3}}\,{\mathrm{V}}\) bias difference applied to the electrodes. The minima in the IV curves are seen to shift with location. The reference curve show similar data without applied bias. From the shift between the data and the reference curves, a 2-D potential map is constructed, as shown in (d). From [11.38]

2-D potential images such as Fig. 11.23d were obtained as a function of the sign and the magnitude of the applied in-plane potential, and it was found that the results varied linearly with this potential, i. e., conductance on the terraces and the resistance of the atomic steps are purely ohmic in character. Figure 11.23 shows how the LEEM-IV technique can also be used as a spectroscopic method for studying non-equilibrium transport properties, in conjunction with pixel-by-pixel structural analysis, in this case linking resistance with graphene layer thickness variations and atomic steps.

11.5 SPA-LEED

The intensity of the LEED beam varies with electron energy/wavelength, as we have seen in the preceding sections, and we can use these intensity variations to study local variations in structure, composition, electronic structure, potential, work function, etc. Thus, the LEED-IV curve adds a powerful spectroscopic tool to the LEEM instrument. However, the LEED spot also has an intensity profile in the momentum plane, at fixed electron energy, and this intensity profile contains additional information on surface structure that is not captured in the LEED-IV curve. Spot-profile analysis LEED ( ) was developed in the 1980s by, amongst others, Martin Henzler and coworkers [11.34] and Max Lagally and coworkers [11.35]. When a surface is perfectly ordered, step free, and without defects, the width of the diffracted beam is limited only by the coherence length of the electron beam. However, when the surface domains are smaller than the coherence length, or have a high step density or contain numerous disordered defects, the LEED spot broadens. This broadening, and its energy (i. e., wavelength) dependence contains information on the type of disorder on the surface and on its distribution. The LEEM instrument gives us access not only to the real-space image, but also to the reciprocal-space LEED pattern. A typical LEED pattern, obtained on the famous Si(111)-(7\({\times}\)7) surface, is shown in Fig. 11.24. Here, with wide terrace spacings and an exceptional degree of long-range order, the diffracted beams are very sharp.

Fig. 11.24

Si(111)-7\({\times}\)7 LEED pattern. The highly uniform and step-free sample morphology gives rise to very sharp diffraction spots. The high intensity at the lower left is due to secondary electrons dispersed away from the optical axis. From [11.86] © IOP Publishing. Reproduced with permission. All rights reserved

However, this is not always the case. For example, when a crystal is overgrown with a thin epitaxial film, the growth process often does not proceed uniformly. When growth is first started, small 2-D islands may nucleate on the flat substrate terraces, creating new atomic steps. These 2-D islands will expand, creating a landscape with small terraces occupying both the substrate level and the 2-D island level. Electrons reflected from the substrate and from the islands accumulate a path length difference equal to twice the island height. This path length difference will, in general, not be equal to \({\lambda}\) (where \({\lambda}\) is the electron wavelength), and the electrons reflected from the substrate and from the islands will, therefore, in general not be in phase. If the islands sizes are smaller than the electron coherence length, the reflected waves, which are not in phase, will add up coherently and give rise to a broadening of the LEED beam in reciprocal space [11.99]. The degree of broadening is directly related to the size distribution of the islands. We can measure the island height by varying the electron wavelength. When the wavelength exactly equals twice the island height, then all reflected electrons are in phase, and there is no broadening of the LEED spots. Thus, the LEED spots broaden periodically with electron wavelength, with the in-phase condition given by \(2h=n{\lambda}\), where \(h\) is the island height, and \(n{\geq}1\).

11.5.1 Epitaxial Growth

Dedicated SPA-LEED systems have been commercially available since the early 1980s. However, such systems average over a rather large beam spot and do not incorporate any optics for obtaining a real-space image. In LEEM, we can do both. Recently, the ESCHER instrument at Leiden University was equipped [11.36] with a pulsed laser deposition ( ) system for the growth of thin epitaxial oxide film in oxide substrates. Figure 11.25a shows LEEM images obtained during the homo-epitaxial growth of strontium titanate (STO ) at \({\mathrm{700}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\).

Before growth starts (0 unit cells, UC), we observe clear atomic steps on the surface (vertical dark lines). At 0.5 UC these steps are no longer visible due to surface roughness, but they re-appear at 1 UC coverage. This process repeats with each additional UC growth on the sample, although the step contrast at each completed UC slowly degrades. Figure 11.25 also shows the intensity (Fig. 11.25b) and width (Fig. 11.25c) of the (0,0) LEED beam as a function of the number of PLD pulses (i. e., total coverage) and as a function of the electron energy (Fig. 11.25b) or electron phase. In Fig. 11.25b, we find clear periodic intensity oscillations. The intensity starts out high at the maxima of the LEED-IV curve, but at 0.5, 1.5, 2.5, etc. unit cells added, the LEED intensity decreases due to out-of-phase interference between electrons reflected from different heights on the sample. At the same time, we find a phase-periodic broadening of the (\(0,0\)) beam at 0.5, 1.5, 2.5, etc. unit cell coverage (Fig. 11.25c). The width of the diffracted beams can become quite high, up to \({\mathrm{20}}\%\) of the Brillouin zone, implying that the 2-D islands are only a few unit cells wide, with very dense nucleation on the atomic terraces. Such small islands are not resolved in the LEEM image, and the step contrast, therefore, disappears at \(n+0.5\) unit cell coverages in Fig. 11.25a. From the un-resolved image in Fig. 11.25a (0.5 UC) we cannot tell the average lateral island size. However, from the width of the diffracted beam in Fig. 11.25c, we can. Thus, the SPA-LEED data complement the real-space image data.

Fig. 11.25

(a) LEEM images obtained during PLD growth of STO on STO. At 0 unit cells (i. e., the starting surface, 0 UC) atomic steps are clearly visible. Atomic steps disappear at \(n+0.5\) u.c. coverages (\(n=0{-}5\)), and re-appear at \(n=1{-}5\) coverages, although the contrast decreases with each additional until coverage due to increasing surface roughness. (b) (\(0,0\)) LEED beam intensity and (c) width oscillations as a function of the number of PLD pulses. The scattering phase is defined as \(S=(k_{\perp}d)/2\uppi\), with \(d\) the height of a unit cell \(\mathrm{SrTiO_{3}}\) and \(k_{\perp}\) the out-of-plane wave vector. % Bz stands for the percentage of the Brillouin zone. From [11.36]

11.5.2 Strain

In addition to spot broadening, we may also observe spot shifting in the LEED pattern, for instance, when a thin overlayer is strained relative to the underlying substrate. Man and Altman studied [11.37] small angle lattice rotations of monolayer graphene grown on a Ru(0001) substrate. Figure 11.26 shows a LEED pattern obtained on a \({\mathrm{3}}\,{\mathrm{{\upmu}m}}\) diameter area of such a sample, with graphene grown during ethylene exposure at \({\mathrm{1270}}\,{\mathrm{K}}\). The diffraction pattern shows a large number of spots, as the unit cells of the Ru surface and the graphene mesh have very different dimensions, giving rise to numerous spots due to double diffraction. While the (0,0) beam is sharp, the additional spots are azimuthally broadened, indicating an azimuthal spread of the graphene lattice relative to the Ru substrate (compared with the LEED pattern on Si(111)-7\({\times}\)7; (Fig. 11.24).

Fig. 11.26

LEED pattern for a graphene monolayer grown on Ru(0001). While the center spot (over-exposed) is sharp, the surrounding LEED spots are azimuthally broadened due to in-plane lattice strain in the graphene layer. Reprinted with permission from [11.37]. Copyright 2011 the American Physical Society

Fig. 11.27

(a) LEED pattern as in Fig. 11.26, with some fractional order beams marked. (bd) Shadow dark-field images with (\(2/23,-2/23\)) LEED spots and (eg) with (\(-2/23,0\)) LEED spots. Aperture positions are indicated schematically. In-plane lattice strain and partial blocking of the diffracted beam by the contrast aperture give rise to the contrast on the bright terraces seen in (c,d) and (f,g). Reprinted with permission from [11.37]. Copyright 2011 the American Physical Society

Figures 11.27b,e show dark field images obtained with the (\(2/23,-2/23\)) and (\(-2/23,0\)) diffraction spots, respectively (Fig. 11.27a). The difference in the dark field intensities from terrace to terrace is caused by the chirality of the gr/Ru(0001) system [11.37]. In these two images, the contrast aperture is positioned over the center of the diffraction spots, so that, in spite of their width, they are fully transmitted by the contrast aperture. In Figs. 11.27c,d and 11.27f,g, the contrast aperture is shifted off-center, as shown in the insets, blocking parts of the diffracted beam. The images show the spatial distribution of these blocked parts of the diffracted beam, which show up in a darker contrast on the bright terraces. These shadow dark field images give an immediate sense of the 2-D distribution of the graphene rotations on the surface. These rotations are highly non-uniform, even on a sub-micrometer scale. This can be further quantified by obtaining micro-LEED data, where the diameter of the illuminating beam is restricted by an aperture in the illumination system to \(\approx{\mathrm{250}}\,{\mathrm{nm}}\). This micro-beam is then scanned across the surface, and a LEED pattern is obtained for each position in the 2-D scan. From each of these diffraction patterns the local rotation can be obtained quantitatively. Figures 11.28a,b show the results of such an experiment and analysis. Figure 11.28a shows a shadow dark field image as in Fig. 11.27d, which shows a qualitative 2-D strain map. Figure. 11.28b, obtained from a 2-D micro-LEED scan, shows quantitative results for the area indicated by the white square in Fig. 11.28a, with Moiré-rotations between \(-4\) and \(+6\) degrees. The observed rotations are not obviously correlated with the presence of atomic steps at the boundaries between black and white terraces in Fig. 11.28a.

Fig. 11.28

(a) Shadow dark-field image as seen in Fig. 11.29d. (b) LEED spot rotations obtained using micro-beam diffraction inside the white square marked in (a). Unlike image (a), image (b) provides quantitative strain information on the graphene monolayer. Reprinted with permission from [11.37]. Copyright 2011 the American Physical Society

11.6 LEEM-EELS

So far we have mostly restricted our discussion of LEEM to elastically scattered electrons. However, electrons also undergo inelastic scattering events, for instance, due the excitation of phonons, plasmons, excitons, etc. Electron energy loss spectroscopy of low-energy electrons has been developed, over several decades of research, into a highly sophisticated method with high momentum resolution and sub-meV energy resolution [11.100]. Obviously, the LEEM instrument will not be able to match this high level of technical sophistication. However, LEEM has the unique capability of combining EELS with imaging, much like PEEM-based ARPES combines electronic band structure studies with high spatial resolution. Integration of energy filtering in LEEM instruments is still not commonplace. However, a simple and effective in-line energy filter is incorporated in all IBM-developed SPECS LEEM/PEEM instruments [11.86], taking advantage of the chromatic dispersion of the prism array at the heart of the instrument. As discussed in the section on ARPES, this in-line energy filter obtains a (\(k_{x},E\)) slice from the (\(k_{x},k_{y},E\)) parabola at a given value of \(k_{y}\). Such a slice shows the full electron energy loss spectrum as a function of \(k_{x}\), for a fixed \(k_{y}\).

Figure 11.29 shows energy loss data obtained [11.40] on an Ag(111) island grown on a Si(111) substrate. Figure 11.29a displays the raw data (obtained with \({\mathrm{19}}\,{\mathrm{eV}}\) incident electrons), a gray-scale plot of electron intensity as a function of energy and \(k_{x}\) (\(Q_{\parallel}\)). Near the bottom of the figure, we find a bright line at zero energy loss, and an over-exposed (\(0,0\)) diffracted beam near the center. The zero-loss peak has a full width at half-maximum of \({\mathrm{0.3}}\,{\mathrm{eV}}\), composed of the incident electron energy spread of \({\mathrm{0.25}}\,{\mathrm{eV}}\), and a spectrometer resolution of \({\mathrm{0.16}}\,{\mathrm{eV}}\). At the top of the figure, the secondary electron intensity terminates at an upside down parabolic boundary. At \(3.5{-}4\,{\mathrm{eV}}\) energy loss, a pronounced surface plasmon loss feature is seen, with significant dispersion. Figure 11.29b shows the \(E\)-\(k_{x}\) dispersion of the plasmon loss peak, while the solid and dashed lines represent theoretical curves for bulk and thin film Ag. Thin film confinement effects (here for a 13-monolayer thick film) shift the loss peak to higher energies for thinner films. For the \({\mathrm{50}}\,{\mathrm{nm}}\) thick film studied here, the loss peak is close to the bulk value (solid line).

Fig. 11.29

(a\(k_{x}\)-\(E\) momentum versus energy loss spectrum on a \({\mathrm{50}}\,{\mathrm{nm}}\) thin Ag(111) island grown on Si(111). A clear plasmon loss feature is seen around \(Q_{\parallel}=0\) at \(3.5{-}4\,{\mathrm{eV}}\). The upper bound of the energy spectrum is seen at the top of the figure. (b) Dispersion data obtained from (a) compared with theory for bulk Ag (solid) and 13-monolayer thick Ag (dashed line). The inset shows the experimental geometry, using the prism array as an in-line energy filter. Reprinted with permission from [11.40]. Copyright 2008 the American Physical Society

The \(k_{x}\) dependence of the plasmon loss intensity is shown in Fig. 11.30 for incident electron energies of 19 and \({\mathrm{53}}\,{\mathrm{eV}}\). These intensities depend on the details of the scattering geometry, as well as the Ag dielectric function, and can be calculated theoretically. The brown lines show the results of such a theoretical analysis and are found to be in good agreement with the experiments.

Fig. 11.30

Momentum dependence of plasmon loss intensity in Fig. 11.29a for incident electron energies of 19 and \({\mathrm{53}}\,{\mathrm{eV}}\). Brown lines are theoretical predictions. Reprinted with permission from [11.40]. Copyright 2008 the American Physical Society

Of course, we can also use the rather intense plasmon loss peak to form a real space image of the sample, by placing a contrast aperture such that the plasmon loss peak is transmitted, and all other electrons blocked. Figure 11.31a is a PEEM image (using a Hg discharge lamp) of an Ag nanostructures grown on Si(001), while Fig. 11.31b is a plasmon loss image of the area indicated by the white box in Fig. 11.31a.

Fig. 11.31

(a) Hg PEEM image of Ag nano-islands grown on Si(001). The Ag islands are bright. (b) Ag plasmon loss image of the area inside the white box in (a). A line scan through the small feature inside the white circle in (b) is shown in (c), with a full width at half maximum of \({\mathrm{35}}\,{\mathrm{nm}}\), close to the smallest features seen with AFM on this sample. Reprinted with permission from [11.40]. Copyright 2008 of the American Physical Society

There is a clear correspondence between the features seen in the PEEM and plasmon loss images. Figure 11.31c shows a line scan across one of the smallest features in the plasmon loss image, inside the white circle. The peak in the line scan has a FWHM of \(\approx{\mathrm{35}}\,{\mathrm{nm}}\), close to the typical size of such clusters as measured with AFM.

In the section on atomic structure determination using LEED-IV data (Sect. 11.2.2), we already discussed single and double-layer graphene films grown on Ni(111), and the dependence of the plasmon loss peak on graphene layer thickness [11.41, 11.77]. For the single graphene layer, the \({\pi}\)-plasmon loss peak is absent due to strong electronic interaction with the Ni-d electrons. The second graphene layer is shielded from the Ni substrate by the first layer, and the \({\pi}\)-plasmon re-appears (Fig. 11.12)

EELS data acquisition in LEEM provides easy and quick access to such plasmon loss features. Typical data acquisition times in both spectroscopy and imaging modes are on the order of \({\mathrm{1}}\,{\mathrm{s}}\).

11.7 Radiation Effects with LEEM

While it is often tacitly assumed that low-energy electrons do little damage to the surface under study, we must keep in mind that this assumption is not always justified. Particularly in the case of organic thin films, radiation damage can be quite severe. Figure 11.32b shows [11.101] a dark-field LEEM image of a partial monolayer of pentacene grown on an Si(001) surface terminated with a monolayer of cyclo-octadiene (COD). COD attaches to the Si(001) surface by a cycloaddition reaction, maintaining the \(2{\times}1\) periodicity of the underlying substrate (Fig. 11.32a). Thus, the dark field image in Fig. 11.32a shows the typical alternation between bright and dark terraces seen [11.102] for (\(1/2,0\)) LEED beam dark field images of the clean surface. In Fig. 11.32b, about half of the surface has been overgrown with the pentacene monolayer (solid bright areas), while the non-overgrown Si surface (alternating dark–bright terraces) is still seen in the center of the image. The pentacene areas are bright, indicating a periodic pentacene lattice diffracting into the contrast aperture at the Si (\(1/2,0\)) lattice spacing. That is, the pentacene lattice is aligned with and registered to the Si substrate, and is therefore epitaxial. Without the COD interlayer such epitaxy does not occur.

Fig. 11.32

(a\({\mathrm{3.5}}\,{\mathrm{eV}}\) dark field LEEM image of Si(001) covered with a monolayer of cyclo-octadiene. (b) Same as (a), after deposition of 0.5 monolayer of pentacene (extended white areas labeled pentacene). Reprinted with permission from [11.101]. Copyright 2007 the American Chemical Society

The images in Fig. 11.32 were obtained with an electron energy of \(\approx{\mathrm{3.5}}\,{\mathrm{eV}}\), resulting in stable imaging conditions and little, if any, discernable radiation damage. However, when the electron energy is raised to \({\mathrm{10}}\,{\mathrm{eV}}\), the situation is very different, and the image is stable for less than 1 video frame. Presumably, electron irradiation at higher energies gives rise [11.103] to H desorption, cross-linking between molecules, and loss of order and periodicity. Electron-stimulated desorption ( ) has long been studied as an important scientific topic in its own right, elucidating a wealth of physical and chemical processes occurring during electron irradiation [11.104].

Electron-induced dissociation and cross-linking is used in polymeric resist materials to imprint patterns used in nano and micro-scale semiconductor device manufacturing (for example). Extreme ultra-violet ( ) lithography, using \({\mathrm{13.5}}\,{\mathrm{nm}}\) (\({\mathrm{91.5}}\,{\mathrm{eV}}\)) photons, is predicted to overtake \({\mathrm{193}}\,{\mathrm{nm}}\) lithography in the next few years [11.105]. With its shorter wavelength EUV lithography is more suitable for printing device features below \({\mathrm{20}}\,{\mathrm{nm}}\), requiring fewer masks, albeit at the expense of much more complex source and imaging technology, and dramatically increased tool cost. When an EUV photon is absorbed in a thin polymeric or polymer-containing resist film, it generates a photo-electron with an energy in the \(80{-}85\,{\mathrm{eV}}\) range. This high-energy electron interacts with the resist, giving rise to a cascade of lower-energy secondary electrons. It is not the photon, but the electrons that expose the resist, i. e., induce chemical modifications in the resist that allow a pattern to be printed in the film. An EUV exposure sets off this entire cascade all at once, making it difficult to discern the role that electrons of different energies, between 0 and \({\mathrm{90}}\,{\mathrm{eV}}\), may play in the exposure process. A LEEM instrument is perfectly suited to address that question: it features an electron illumination system with an energy resolution of \({\mathrm{0.25}}\,{\mathrm{eV}}\), and a continuously variable landing energy from 0 to several \({\mathrm{100}}\,{\mathrm{eV}}\).

Figure 11.33 shows three series of electron exposures  [11.44] of a \({\mathrm{20}}\,{\mathrm{nm}}\) thick PMMA film on a Si substrate, varying electron energy (relative to the Si substrate), electron dose, and electron current.

Fig. 11.33

(a) PMMA exposures as a function of electron current, energy, and dose. At each current (0.05, 1.6, and \({\mathrm{2.0}}\,{\mathrm{nA}}\)) we observe an exposure threshold that does not depend on dose. PMAA thickness \(20{\pm}{\mathrm{4}}\,{\mathrm{nm}}\), spin-coated onto a Si substrate. (b) An electron beam with current density \(I_{0}\) impinges on a PMMA film of thickness \(d\). \(E_{0}\) is the electron energy relative to \(V_{\text{substrate}}\). The surface may charge to a potential \(V_{\text{surface}}\). The charging potential \(V\) is defined as \(V=V_{\text{substrate}}-V_{\text{surface}}\). Reprinted with permission from [11.44]. Copyright 2017 the American Physical Society

Each white dot in Fig. 11.33a corresponds to a single electron exposure, with an exposure diameter of about \({\mathrm{5}}\,{\mathrm{{\upmu}m}}\). The sample position was advanced between exposures, with the electron beam blanked. After completion of a full exposure series, the sample was removed from the LEEM instrument, developed, and then viewed under an optical microscope. Strikingly, Fig. 11.33a shows that the PMMA film is exposed only when a lower-energy threshold is exceeded. At a beam current of \({\mathrm{0.05}}\,{\mathrm{nA}}\) the electron energy must be \({\mathrm{15}}\,{\mathrm{eV}}\) or higher, at \({\mathrm{2}}\,{\mathrm{nA}}\) \({\mathrm{18}}\,{\mathrm{eV}}\) or higher. At first, an energy threshold would seem to suggest that the electron energy must overcome some activation energy to break bonds in the PMMA. However, such an activation energy would not depend on the electron current, so something else must be going on.

Fig. 11.34

(ac) Electron energy spectra during electron exposure for \(E_{0}=14\), 15, and \({\mathrm{20}}\,{\mathrm{eV}}\), \({\mathrm{0.25}}\,{\mathrm{nA}}\), \({\mathrm{5}}\,{\mathrm{{\upmu}m}}\) Ø. The energy axis is similar to an energy loss scale. Thus, the highest energy at which signal is observed (i. e., the low energy cut-off of the secondary electrons) is a direct measure of the energy with which the electrons land. In (a) and (c) this corresponds to 0, and \(\approx{\mathrm{30}}\,{\mathrm{eV}}\), initially. Red lines in (b,c) are fits to the data, with \(g_{0}\), \(\mathrm{d}g_{0}/\mathrm{d}t\), \(E_{1}\), and \(\mathrm{d}E_{1}/\mathrm{d}t\) given from top to bottom. Reprinted with permission from [11.44]. Copyright 2017 of the American Physical Society

Figure 11.34 shows EELS spectra at \(k_{x}=k_{y}=0\) obtained during electron exposure, for incident electron energies (relative to the Si substrate) of 14, 15, and \({\mathrm{20}}\,{\mathrm{eV}}\). For the \({\mathrm{14}}\,{\mathrm{eV}}\) exposure, we see only elastically reflected electrons, without any lower energy electrons. At \({\mathrm{15}}\,{\mathrm{eV}}\), initially we see the same: only elastically reflected electrons. However, after a few seconds of exposure, the spectrum broadens. The peak at \({\mathrm{0}}\,{\mathrm{eV}}\) loss stays, but a secondary electron signal slowly develops, shifting to the right with time. This indicates that a very different phenomenon is taking place. The absence of secondary electrons in Fig. 11.34a indicates [11.44] that the surface of the PMMA film charges up to the electron beam energy and reflects all incident electrons without exposing the film. At \({\mathrm{15}}\,{\mathrm{eV}}\), the PMMA initially charges almost to the beam energy so that the spectrum is still narrow, but some electrons, with nearly \({\mathrm{0}}\,{\mathrm{eV}}\) energy, reach and expose the PMMA film. The PMMA becomes more conductive due to electron exposure; surface charging is reduced, and electron landing energy increases continuously as exposure proceeds. In Fig. 11.34c, surprisingly, the initial spectrum width of \({\mathrm{30}}\,{\mathrm{eV}}\) exceeds the incident energy of \({\mathrm{20}}\,{\mathrm{eV}}\) by \({\mathrm{10}}\,{\mathrm{eV}}\). In Fig. 11.34b, we observe the slow appearance of secondary electrons with prolonged exposure. These secondary electrons reduce the net incident electron current on the sample. If the number of secondary electrons becomes larger than the number of incident electrons (secondary electron emission coefficient greater than 1), the net incident current changes sign, and surface charging changes sign. This explains why in Fig. 11.34c the initial width of the electron spectrum exceeds the nominal incident energy. Accumulation of positive surface charge accelerates the incident electrons. Again, during exposure the PMMA film becomes more conductive, leading to reduced charging (relative to an uncharged surface). However, a second phenomenon takes place at the same time. While in Fig. 11.34c the initial secondary electron emission coefficient is greater than 1, it reduces during exposure. When it drops below 1 the net incident current changes sign, and after about \({\mathrm{10}}\,{\mathrm{s}}\) we observe an abrupt drop in the width of the energy spectrum.

During exposure of the PMMA film, the net current conducted through the film to the substrate must balance the net incident current (incident electrons minus secondary electrons leaving the sample). It can be shown [11.44] that this balance can be expressed by the following simple equation
$$\pm g_{0}V^{2}=1-\left(\frac{E_{0}-V}{E_{1}}\right)^{\alpha}$$
(11.2)
where \(g_{0}\) is the normalized conductance of the PMMA film for space-charge limited Mott–Gurney transport [11.106], \(E_{0}\) is the nominal incident electron energy relative to the Si substrate, \(V\) is the surface charging potential of the PMMA, and \(E_{1}\) is the incident electron energy for which secondary electron emission [11.107] is equal to 1. The exponent \({\alpha}\) is between 0.5 and 1.5 but is not critical [11.44]. The \({\pm}\) sign accounts for either positive or negative charging of the PMMA. This simple equation gives rise to a surprisingly rich set of phenomena, fully explaining the experimental results. The red solid lines in Figs. 11.34b,c were obtained from this simple theory, with initial values of \(g_{0}\) and \(E_{1}\), and their time derivatives as specified in the figure.

In these experiments, radiation damage is a feature rather than a problem, and the LEEM instrument with its excellent control of electron energy and real-time EELS capability is extremely useful in building a basic understanding of what is happening during electron exposure.

11.8 Electron-Volt Transmission Electron Microscopyin the LEEM Instrument

In this final section, we will discuss one more cathode-lens-based experimental setup in which we use neither photo-electrons, nor reflected or secondary electrons, but transmitted electrons. Of course, for low-energy electrons to be transmitted through a sample, that sample has to be very thin. However, the universal curve for the inelastic electron mean free path [11.108] (Fig. 11.35) shows that this mean free path, while getting shorter and shorter as the electron energy decreases from high energies to lower energies, increases again as the electron energy drops below \(\approx{\mathrm{30}}\,{\mathrm{eV}}\).

Fig. 11.35

Universal inelastic mean-free path, attenuation length given in units of monolayers of electrons as a function of electron energy. A deep minimum is seen at \(20{-}50\,{\mathrm{eV}}\). The graph suggests a mean free path of \(1{-}10\,{\mathrm{nm}}\) at \({\mathrm{6}}\,{\mathrm{eV}}\) and as large as \({\mathrm{100}}\,{\mathrm{nm}}\) at \({\mathrm{1}}\,{\mathrm{eV}}\). Reprinted with permission from [11.108]. Copyright John Wiley and Sons

Indeed, the plot suggests that at \({\mathrm{1}}\,{\mathrm{eV}}\) the mean free path can be as long as \({\mathrm{100}}\,{\mathrm{nm}}\)! We saw above that pentacene can be imaged with impunity at \({\mathrm{3.5}}\,{\mathrm{eV}}\), without any electron-induced damage. At this low energy there are very few electron energy loss processes, and one might expect the mean free path to be long. Of course, if we want to use transmitted electrons through an electron-transparent sample, we must also have an electron source behind the sample. Figure 11.36 shows how a simple electron source can be incorporated inside the standard LEEM/PEEM sample holder [11.45, 11.46].

Fig. 11.36

eV-TEM geometry in a LEEM/PEEM microscope. A compact electron source behind the thin sample generates electrons with \(0{-}100\,{\mathrm{eV}}\) energy. The electrons are transmitted through the sample and then accelerated to the column energy of \({\mathrm{15}}\,{\mathrm{keV}}\) by applying a \({\mathrm{15}}\,{\mathrm{kV}}\) bias voltage to the thin sample (cathode objective lens at ground potential). After [11.46]

The electron source illuminates a thin sample mounted on a \({\mathrm{3}}\,{\mathrm{mm}}\) TEM grid from behind. The bias between the emitter and the sample (and, therefore, the electron energy) can be varied from \(0{-}100\,{\mathrm{V}}\). Transmitted electrons enter the strong electrostatic field between sample and cathode objective lens and are accelerated to the column energy of \({\mathrm{15}}\,{\mathrm{keV}}\). The imaging optics is exactly the same as in LEEM/PEEM (Fig. 11.7a,b). That such a simple scheme works is shown in Fig. 11.37, an eV-TEM image of multilayer graphene suspended on lacey carbon on a TEM grid. The lacey carbon network is easily recognized in this image. The graphene film shows up behind the lacey network as a patchwork of micrometer sized domains of varying image intensities. The different gray levels correspond to different graphene layer thicknesses. Naively, one might think that the image gets darker with each additional graphene layer, but this is not true. We have seen that the LEED-IV curves (i. e., for a reflected electron beam) for multilayer graphene contain minima and maxima depending on the number of layers in the film [11.79] (Sect. 11.2.3). The same is true in transmission. Where we observe a minimum in reflection, we find a maximum in transmission, and vice versa. Thus, we can count layers in transmission just like we can in reflection. In the eV-TEM experiment we retain access to the LEEM experiment and we can perform eV-TEM and LEEM experiments on the same areas. The setup also allows for eV-TEM/EELS.

Figure 11.37 also shows a small hole in the graphene film (bright intensity, lower right), which enables absolute quantification of the transmitted zero-loss intensity as function of electron energy and a direct comparison with zero-loss reflectivity, and, therefore, direct access to the integrated inelastic loss channels.

Fig. 11.37

eV-TEM image of multi-layer graphene on holey carbon. Graphene areas with different layer thicknesses (1–4 layers) show different contrast, depending on layer thickness and electron energy. A small hole (bright area) seen in the lower right provides an absolute electron brightness calibration

At present, eV-TEM is still in its infancy, but we expect that—over time—it will become another important member of the cathode lens microscopy family, as it offers yet another and powerful tool for the study of nanoscale materials, including biological molecules and biomembranes. At electron energies below \(\approx{\mathrm{5}}\,{\mathrm{eV}}\) we may expect reduced radiation damage, while still maintaining \(1{-}2\,{\mathrm{nm}}\) spatial resolution in an aberration-corrected instrument. We note that eV-TEM is complementary to low-energy electron point projection microscopy , a method championed by Fink et al [11.109] and by Spence et al [11.110] In this case, a shadow image is made from an object with coherent low-energy electrons emitted from a point-like electron source. The shadow image is a hologram, and the object must be reconstructed from the hologram. While the setup is very simple (there is essentially no electron optics involved), analytical capabilities are very limited. For instance, there are no provisions for energy filtering, and an inelastic background (which in itself can have coherence, as well as band structure effects [11.111]) is always present in the images.

11.9 Conclusion

It is impossible to discuss the full range of cathode-lens-based capabilities and experiments within the confines of a single chapter, or even a single book. The companion chapters by Ernst Bauer on LEEM, and by Jun Feng and Andreas Scholl on PEEM give a broader view than I can provide in this chapter by itself. Bauer's book [11.2] on surface microscopy with low-energy electrons provides yet more detail. However, we must accept that written texts are necessarily historic in nature. Cathode lens microscopy was there during the earliest days of electron microscopy, only to languish for many decades. Bauer brought it back from obscurity about 30 years ago, and it has finally blossomed into an exciting and impactful field of research. As I close my laptop computer, experiments are going on that I have never heard about, but that will change what I will do next month, next year. This chapter provides a partial and selective update over the last 10 years. Another update will be required in another 10 years, as the pace of development is still accelerating, both in terms of equipment and experimental capabilities, and in terms of application areas. That next chapter may be yours to write.

Notes

Acknowledgements

The author is grateful to Jim Hannon, Michael Altman, Sense Jan van der Molen, Jan Aarts, Alexander van der Torren, Johannes Jobst, Daniel Geelen, and Eugene Krasovskii for their generous support and assistance in putting this chapter together. Thanks are also due to Ernst Bauer for numerous discussions and inspiration.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.IBM T.J. Watson Research CenterYorktown Heights, NYUSA

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