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LEEM, SPLEEM and SPELEEM

  • Ernst BauerEmail author
Chapter
Part of the Springer Handbooks book series (SHB)

Abstract

This chapter discusses some of the most important imaging methods with low-energy electrons, including: low-energy electron microscopy ( ), its extension to spin-polarized low-energy electron microscopy ( ), and its combination with spectroscopic photoemission and low-energy electron microscopy ( ). Other imaging methods mentioned only briefly in the chapter include ultraviolet photoemission electron microscopy ( ), mirror electron microscopy () , low-electron energy loss microscopy ( ), and Auger electron emission microscopy ( ). The instruments used in these imaging methods allow imaging not only in real space but also in reciprocal space, such as low-energy electron diffraction ( ) and angle-resolved photoelectron spectroscopy (ARPES in SPELEEM). The combination of these methods with complementary high-lateral-resolution methods renders imaging with low-energy electrons a comprehensive surface analysis tool.

Low-energy electron microscopy (LEEM) is an imaging method that makes use of elastically backscattered electrons with energies below about \({\mathrm{100}}\,{\mathrm{eV}}\), frequently \(<{\mathrm{10}}\,{\mathrm{eV}}\). In contrast to transmission electron microscopy ( ), which generally works with electrons in the \({\mathrm{100}}\,{\mathrm{keV}}\) range where backscattering is negligible, the backscattering cross sections for low-energy electrons are large enough to be useful for surface imaging. This was already evident in the classical diffraction experiments of Davisson and Germer [9.1], but it would be 35 years before the use of slow diffracted electrons for surface imaging was suggested [9.2], and another 23 years before convincing images could be published [9.3]. Thus, although diffraction of slow electrons and imaging with slow emitted electrons with resolution in the micrometer range were demonstrated [9.4] before TEM reached submicron resolution [9.5], LEEM became a viable imaging method only much later.

The reason for this late appearance of LEEM in electron microscopy is twofold: (1) For LEEM, well-defined surfaces are necessary, which in general requires ultrahigh vacuum ( ) and efficient surface cleaning procedures. Although these have been available for some time in glass systems, such as in Farnsworth's low-energy electron diffraction ( ) systems [9.6, 9.7, 9.8], glass systems are not very user-friendly, and metal UHV technology did not come into widespread use until the beginning of the 1960s. In fact, the first display-type LEED system that heralded the revival of LEED was a glass system [9.10, 9.9], as was the first unsuccessful model of a LEEM system [9.2]. (2) There was a widespread belief within the electron microscopy community, based on the fundamental theoretical work of Recknagel on emission electron microscopy [9.11], that the chromatic aberration of the objective lens would limit the resolution to such an extent as to make LEEM unattractive. This, of course, was a misunderstanding, as already pointed out in the early phase of the development of LEEM [9.12, 9.13]. In the decades since then, LEEM has slowly developed into a powerful surface imaging technique, as recounted elsewhere [9.14].

Over the past 10 years, developments have been focused on the combination of LEEM with x-ray-induced photoemission electron microscopy ( ), which resulted in the spectroscopic photoemission and low-energy electron microscope (SPELEEM) [9.15, 9.16], and on the correction of the aberrations of the objective lens [9.17]. Despite these efforts, however, LEEM still lags behind TEM in the technological state of the art.

This chapter reviews the basics of LEEM and its applications through the period up to about 2005. More recent developments are discussed in reviews listed at the end of this chapter and in Chap.  11. A related imaging method, spin-polarized LEEM (SPLEEM), which provides magnetic information, will also be discussed. Other methods, including mirror electron microscopy (MEM), which provides information mainly on the local surface potential; Auger electron emission microscopy (AEEM), which provides chemical information; electron energy loss microscopy ( ), which provides some electronic information; and secondary electron emission microscopy ( ), will be mentioned only briefly, as they have been used much less frequently, although they are also useful. Photoelectron emission microscopy ( ), in particular XPEEM, is included only in connection with the discussion of SPELEEM, because it is the subject of another chapter. The sections on SPLEEM and SPELEEM describe the present state of the art.

9.1 Electron Beam–Specimen Interactions

To understand the possibilities and limitations of LEEM and the associated techniques, a fundamental understanding of the interactions of slow electrons with condensed matter is necessary. The following interactions must be taken into account: elastic scattering, inelastic scattering, and quasielastic scattering (phonon and, in magnetic materials, magnon scattering). The interactions of slow electrons with matter are vastly different from those of fast electrons. In ferromagnetic materials, they also depend upon the relative orientation of the spin of the incident electrons and the electrons in the matter.

Consider first elastic scattering. Because of its low velocity \(v=\sqrt{2E/m}\), the interaction time of a slow electron is much longer than that of the fast electrons used in TEM, and an \(n\)-electron atom may no longer be considered undisturbed, but becomes an \(n+1\)-electron system during the interaction. Therefore, the incident electron experiences the temporary excitations of the \(n\)-electron atom. This can be taken into account by adding a correlation potential to the potential of the ground-state \(n\)-electron atom. Similarly, the repulsive interactions between electrons with the same spin due to the Pauli principle cause a spin-dependent potential that also has to be added. As a consequence, the scattering of slow electrons by the atoms that constitute the condensed matter can no longer be described by the first Born approximation, which assumes a static atom in the ground state and which is a good approximation at high energies. Instead, a partial wave analysis is necessary, taking into account the exchange and correlation potentials [9.18, 9.19]. No calculations of this type are available for condensed atoms, whose potentials are truncated by overlap with the neighbor atoms. Fortunately, the magnitudes of the correlation and exchange potential decrease rapidly with energy, so they may be neglected in the energy range of conventional LEED studies (usually above \({\mathrm{30}}\,{\mathrm{eV}}\)). In LEEM, however, they should be taken into account. This is a formidable task, and one that has not yet been mastered. Therefore, only some results of partial wave analysis calculations for truncated ground-state potentials will be given here.

In partial wave analysis  [9.20], the incident plane wave and the outgoing scattered wave are expanded into spherical harmonics centered at the atom, and the phase differences \(\eta_{l}\) between the incident and outgoing partial waves are calculated. In the nonrelativistic case, the scattering amplitude is given by
$$f(\theta,k)=\frac{1}{2\mathrm{i}k}\sum(2l+1)[\text{exp}(2\mathrm{i}\eta_{l}-1)]P_{l}(\cos\theta)\;,$$
(9.1)
with the sum over \(l\) extending from zero to infinity. \(k\) is the wave number, and the \(P_{l}\)'s are Legendre polynomials. The intensity distribution of the scattered electrons as a function of scattering angle \(\theta\) and energy \(E\sim\sqrt{k}\) is then simply \(\sim|f(\theta,k)|^{2}\). Figure 9.1 shows the angular distribution of the scattered intensity of \({\mathrm{50}}\,{\mathrm{eV}}\) electrons, calculated in this manner for realistic solid-state Ag, Al, and Cu atomic potentials [9.18].
Fig. 9.1

Angular distribution of \({\mathrm{50}}\,{\mathrm{eV}}\) electrons elastically scattered from Ag, Al, and Cu atoms in the solid state. After [9.18]

Here we see that not only is the total scattering cross section of Cu (\(Z=29\)) smaller than that of Al (\(Z=13\)), but its backscattering cross section is as well, and Al scatters nearly as strongly as the much heavier Ag atom (\(Z=47\)). The scattering is, however, strongly energy-dependent. This is illustrated for the scattering into a \(30^{\circ}\) cone around the backward direction in Fig. 9.2 [9.19], which shows that at very low energies, Cu scatters nearly as strongly as W (\(Z=74\)), while Al and Ag scatter much more weakly in the backward direction. It should be noted that the zero of the energy is the inner potential resulting from the overlap of the free atom potentials, so that the maxima of the W and Cu backscattering cross sections are just around the vacuum level.

Fig. 9.2

Energy dependence of the backscattering into a \(30^{\circ}\) cone around the backward direction for Ag, Al, Cu, and W atoms in the solid state. After [9.19]

In condensed matter, the electrons are, of course, scattered not only within one atom but also by the atoms surrounding it, causing strong multiple scattering. This is taken into account in LEED in the dynamic theory of electron diffraction [9.22, 9.23]. Another way to look at the problem of scattering in a periodic system is in terms of the band structure theory, if we assume that the \(n+1\)-electron system (\(n\) crystal electrons \(+\) incident electron) does not differ significantly from the \(n\)-electron system (Koopmans' theorem  [9.24]). Then the \(180^{\circ}\) backscattering from a single crystal surface is determined by the band structure \(E(\boldsymbol{k})\) perpendicular to the surface. This is illustrated in Fig. 9.3a,b for the W(110) surface [9.21]. The band structure in the [110] (\(\Upgamma\mathrm{N}\)) direction has a wide band gap between about 1 and \({\mathrm{6}}\,{\mathrm{eV}}\) above the vacuum level. An electron incident in this direction, therefore, does not find allowed states in the crystal and forms an evanescent wave. The extinction length of this electron wave in the crystal is quite short in the center of the gap, only about two monolayers [9.25], so that the electron is reflected before it is significantly attenuated by inelastic scattering. This, together with the strong backscattering cross section, causes the high reflectivity at about \(2{-}3\,{\mathrm{eV}}\). The second reflectivity peak is due to the low density of states in the crystal, as indicated by the steep bands. The band structure influence is strongly orientation-dependent. For example, on the W(100) surface, the band gap is located between 3 and \({\mathrm{5}}\,{\mathrm{eV}}\) above the vacuum level [9.21, 9.26], which causes a pronounced reflectivity peak at about \({\mathrm{4}}\,{\mathrm{eV}}\). This is preceded by a deep reflectivity minimum, which is caused by the strong inelastic scattering of the electron that could otherwise penetrate deeply into the crystal. A second reflectivity peak occurs around \({\mathrm{8}}\,{\mathrm{eV}}\), where the density of states in the crystal is small. This simple picture neglects the influence of surface effects. For quantitative agreement between experiment and theory, the surface barrier [9.27], surface resonances [9.21], and reconstruction have to be taken into account. For LEEM, these details are not important, at least at the present state of the art, because they mainly determine the reflected intensity and have little influence on the contrast.

Fig. 9.3a,b

Normal incidence specular reflectivity \(R\) of a W(110) surface (a) and band structure along the surface normal (b). After [9.21]

In general, the main factor determining the high surface sensitivity of LEEM is not the influence of the band structure and elastic scattering, but the strong attenuation of slow electrons by inelastic scattering. Inelastic scattering is due to single-electron excitations (electron–hole pair creation) and collective-electron excitations (plasmon creation). In the energy range of LEEM, single-electron excitations mainly involve valence band and weakly bound outer-shell core electrons. The universal inelastic mean free path ( ) curves typically found in the literature are of rather limited value at the low energies used, because they do not take into account the differences in the electronic structure of the various materials. Therefore, only some general features will be discussed and some specific examples will be given. In materials that may be described approximately by a free electron gas embedded in a homogeneous background of equal charge (jellium model) , the IMFP is a function of \(k/k_{\mathrm{F}}\) (\(k_{\mathrm{F}}\) Fermi wave number), with the electron density as parameter [9.18, 9.19, 9.28]. As an example, the attenuation length \(\mu=\text{IMFP}^{-1}\) of Al, for which the free electron approximation is good, is shown in Fig. 9.4 together with the attenuation coefficient \(\nu\) due to elastic backscattering, assuming a random distribution of Al atoms with bulk density (randium model) [9.29, 9.30]. The initial rise in \(\mu\) until the volume plasmon creation threshold at \(E_{\mathrm{T}}={\mathrm{17.5}}\,{\mathrm{eV}}\) (above vacuum level) is due to single-electron excitations. The maximum of \(\mu\) and the corresponding minimum of about \({\mathrm{0.3}}\,{\mathrm{nm}}\) of the IMPF at about \({\mathrm{37}}\,{\mathrm{eV}}\) is mainly due to plasmon losses. Figure 9.4 also shows that attenuation by elastic backscattering is much weaker above \(E_{\mathrm{T}}\) than that by inelastic scattering.

Fig. 9.4

Energy dependence of the attenuation coefficients \(\mu,\nu\) of slow electrons in Al by inelastic scattering and elastic backscattering, respectively. After [9.29]

For most metals, the jellium approximation is not useful, particularly for transition and noble metals. For example, in contrast to jellium, transition metals have a high density of unoccupied states just above the Fermi level into which excitations can occur. The deviation from jellium can be partially taken into account by replacing the \(\omega\) dependence in the Lindhard dielectric function \(\varepsilon_{\mathrm{L}}(\omega,q)\), which is used in the jellium calculations, with that obtained in the experiment for zero momentum \(q\) transfer, that is, by optical data for which \(q=0\). Results of such calculations [9.31] typically give minimum IMFPs in metals of \(0.3{-}0.5\,{\mathrm{nm}}\) at energies between 30 and \({\mathrm{120}}\,{\mathrm{eV}}\) for Mg and Au, respectively, with a rapid increase at low energies to values as high as \({\mathrm{2.4}}\,{\mathrm{nm}}\) in Si and \({\mathrm{3.5}}\,{\mathrm{nm}}\) in W at \({\mathrm{10}}\,{\mathrm{eV}}\), for example. Figure 9.5 illustrates the agreement between theory and experiment that can be obtained in this approximation [9.32]. The deviations below \(E-E_{\mathrm{F}}={\mathrm{5}}\,{\mathrm{eV}}\) are irrelevant for LEEM because the work function of Au is about \({\mathrm{5}}\,{\mathrm{eV}}\); those above \({\mathrm{50}}\,{\mathrm{eV}}\) are probably due to inaccurate 5p and 4f ionization cross sections. The agreement is surprisingly good considering that the \(q\) dependence of \(\varepsilon\) has been approximated by simple expressions and that correlation and exchange have not been taken into account. At energies below several tens of electronvolts, these are of comparable importance for inelastic and elastic scattering, in particular the influence of the detailed band structure and nondirect (\(q\neq 0\)) transitions [9.33]. For example, inclusion of exchange in the dielectric model of the IMFP gives IMFP values that are larger by a factor of 1.3 or more than without exchange [9.34].

Fig. 9.5

Energy dependence of the inelastic mean free path of electrons in Au. The points and dots are experimental data and the dashed and solid lines are theoretical data using different approximations. After [9.32]

The IMFPs calculated in this approximation for insulators are even larger, such as \({\mathrm{6}}\,{\mathrm{nm}}\) at \({\mathrm{10}}\,{\mathrm{eV}}\) for KCl [9.31]. For several groups of insulators with large band gaps (condensed noble gases, \(\mathrm{N_{2}}\), and organic dielectrics such as benzene or methane), no electronic excitations are possible at low energies. Here the (quasi)elastic mean free path ( ) determines the sampling depth. EMFP measurements in the energy range of \(2{-}15\,{\mathrm{eV}}\) give EMFPs up to \({\mathrm{10}}\,{\mathrm{nm}}\) [9.35]. An example is shown for solid Xe in Fig. 9.6 [9.36]. Thus the mean free path ( may be very long at low energies (\(\leq{\mathrm{10}}\,{\mathrm{eV}}\)), while at energies between about \(\mathrm{30}\) and \({\mathrm{100}}\,{\mathrm{eV}}\), depending upon the material, it may be only a few tenths of a nanometer. The large MFPs at very low energies are, however, not found frequently.

Fig. 9.6

Energy dependence of the elastic mean free path of slow electrons in solid Xe at \(T={\mathrm{45}}\,{\mathrm{K}}\). After [9.36]

They depend strongly on the density of unoccupied states into which bound electrons can be excited, as is clearly evident in an insulator with wide band gaps [9.35]. These are extreme cases inasmuch as their band gaps are so large that the density of unoccupied states becomes significant only at several electronvolts above the vacuum level. At the other extreme are transition metals with their unfilled \(\mathrm{d}\) bands with high density of states just above the Fermi level. Here the IMFPs are very short, as seen in Fig. 9.7 [9.37], in which the reciprocal values of the IMFPs are plotted as a function of the number of \(\mathrm{d}\) holes. The values shown are for electrons with energies between \(\mathrm{5}\) and \({\mathrm{10}}\,{\mathrm{eV}}\) above the Fermi energy. For Fe, the IMFP is only about \({\mathrm{0.5}}\,{\mathrm{nm}}\), and for Gd only \({\mathrm{0.25}}\,{\mathrm{nm}}\). In ferromagnetic materials, the density of unoccupied states differs between majority and minority spin states, which causes corresponding differences in the excitation probabilities. Calculations that take this into account show a significant difference between the IMFPs of incident electrons with majority and minority spin, as seen in Fig. 9.8 [9.38]. The zero of the energy is the Fermi energy; the work function of Fe is \({\mathrm{4.5}}\,{\mathrm{eV}}\), so that \({\mathrm{1}}\,{\mathrm{eV}}\) above the vacuum level, the IMFPs are only \(\mathrm{0.6}\) and \({\mathrm{0.2}}\,{\mathrm{nm}}\) for majority and minority spin electrons, respectively. At \({\mathrm{10}}\,{\mathrm{eV}}\) above the vacuum level, the corresponding values are \(\mathrm{0.45}\) and \({\mathrm{0.3}}\,{\mathrm{nm}}\), which are much lower than the \({\mathrm{1.6}}\,{\mathrm{nm}}\) obtained from the dielectric theory discussed above. For more information see [9.39].

Fig. 9.7

Reciprocal inelastic mean free path in \(\mathrm{nm^{-1}}\) of electrons with energies between 5 and \({\mathrm{10}}\,{\mathrm{eV}}\) above the Fermi level as a function of the number of holes in the 3d and 4d shells. After [9.37]

Fig. 9.8

Energy dependence of the inelastic mean free path of majority and minority spin electrons in Fe. After [9.38]

While the knowledge of reliable absolute numbers for elastic and inelastic mean free paths at low energy is still limited, the influence of phonon and magnon excitation on the effective sampling depth is much less well understood. Both processes involve only small energy losses up to several hundred million electronvolts, but can occur with large momentum transfer. In LEEM, only the electrons in a diffraction spot and its immediate environment contribute to the image formation. Therefore, energy losses with momentum transfer larger than that determined by the radius of the contrast aperture cause an attenuation of the intensity contributing to the image formation. At relatively low temperatures, this can be taken into account by the Debye–Waller factor . At higher temperatures, multi-phonon and -magnon excitations occur, causing increased attenuation, which may be described by an anharmonic Debye–Waller factor [9.40]. In this conventional description of the influence of phonons on the scattering from surfaces, there is no thickness dependence. However, in thin films, the number of electrons scattered outside the contrast aperture increases with increasing thickness, so an effective attenuation coefficient could be defined. This has not been done to date for several reasons:
  1. 1.

    There are no numbers for the cross sections for phonon and magnon scattering that could be compared with those for inelastic scattering.

     
  2. 2.

    With increasing temperature, there is frequently atomic disordering that causes diffuse scattering.

     
  3. 3.

    At high temperatures, thin films usually break up into three-dimensional () crystals before attenuation by these processes becomes significant.

     
A rough idea of the influence of thermal vibrations on the attenuation length may be obtained from the analysis of LEED patterns from Cu single-crystal surfaces. At \({\mathrm{50}}\,{\mathrm{eV}}\), the total attenuation length, which includes elastic backscattering, inelastic scattering, and phonon scattering, from the (111) surface is \({\mathrm{0.33}}\,{\mathrm{nm}}\) at \({\mathrm{300}}\,{\mathrm{K}}\) versus \({\mathrm{0.34}}\,{\mathrm{nm}}\) at \({\mathrm{0}}\,{\mathrm{K}}\) [9.41]. The difference is well within the limits of error of the values, so at least at this energy phonon scattering does not limit the sampling depth.

According to the present state of understanding, the sampling depth of LEEM and SPLEEM is determined primarily by inelastic and elastic backscattering. Depending upon the energy and electronic structure of the material, the sampling depth may be as small as a few tenths of a nanometer, for example, around the plasmon excitation maximum, in transition metals with a high density of unoccupied states above the Fermi level, or in band gaps along the \(\boldsymbol{k}\) direction normal to the surface. On the other hand, sampling depths as large as several nanometers can occur at very low energies, for example, in insulators and free-electron-like metals. In many cases this enables tuning of the sampling depth by proper choice of the energy, which makes LEEM and SPLEEM ideal for imaging of surfaces and thin films.

9.2 Instrumentation

The electron optics of a LEEM/SPLEEM instrument in the imaging section is essentially the same as that in emission electron microscopes, which date back to the 1930s. In these microscopes, the specimen is the cathode of a so-called cathode lens in which the slow emitted electrons are accelerated in a high field to the first of several image-forming electrodes of an electrostatic lens or to the entrance of a magnetic lens. This lens is the objective lens of the microscope, which produces a primary image with fast electrons. The subsequent electron optics is basically the same as in TEM. In fact, the first objective lens used in LEEM was a modified version of an electrostatic triode lens developed for PEEM [9.42].

To perform LEEM with such a system, fast electrons have to be injected from the high-energy side of the objective lens along its optical axis. In the cathode lens, they are decelerated to the desired low energy at the specimen. To be able to produce an image, this incident beam must be separated from the reflected beam by a beam divider. As a consequence, a LEEM or SPLEEM system has a bent optical axis. A schematic of the first instrument is shown in Fig. 9.9 [9.3]. The beam separator deflects the incident beam from a field emission gun that is focused by two quadrupoles, the deflection field, and optionally by a collimator lens into the back focal plane of the objective lens. They reach the specimen on parallel trajectories with an energy that is determined by the adjustable potential difference between field emitter and specimen. The specimen is imaged by the elastically reflected electrons into the center of the beam separator, and its diffraction pattern into the back focal plane of the objective lens where the angle-limiting contrast aperture is located. The astigmatism of the objective lens is corrected with a magnetic stigmator. The primary image in the center of the beam separator is imaged with a magnetic intermediate lens and a projective lens onto the final screen, and the diffraction pattern by adjusting the focal length of the intermediate lens. The electrostatic filter lens was originally intended to filter out secondary and inelastically scattered electrons, but was later removed because the dispersive properties of the magnetic beam separator were found to be sufficient to eliminate them from the image. A pair of multichannel plates enhances the image intensity on the fluorescent screen, allowing observation and image recording with a video camera at very low beam currents. Both illumination and imaging columns are equipped with deflectors and stigmators, some of which are indicated. Emission microscopy is possible with thermionic emission by heating the specimen, with photoelectrons generated by a \({\mathrm{100}}\,{\mathrm{W}}\) high-pressure Hg arc lamp, and secondary electrons using an auxiliary electron gun.

Fig. 9.9

Schematic of the first LEEM instrument . After [9.3]

While Fig. 9.9 shows the principle of the LEEM system, more recent instruments differ considerably in detail. For example, a transfer lens, which transfers the diffraction pattern from the back focal plane of the objective lens toward the front of the intermediate lens, is now inserted just behind the beam separator, so that the illuminating beam does not have to pass through the contrast aperture as in the original design. The electrostatic triode lens is now replaced by lenses with better resolution, such as the electrostatic tetrode lens, the magnetic diode lens, or the magnetic triode lens, which will be briefly discussed below. The beam separator has been improved in a variety of ways, including the use of close-packed or separated multiple magnetic prisms, concentric square or round pole pieces, or a Wien filter, resulting in deflection angles ranging from \(\mathrm{16}\) to \(90^{\circ}\), compared to the original \(60^{\circ}\). In addition, energy filters have been added to instruments so that they can also be used for AEEM, low electron energy loss microscopy ( ), energy-filtered SEEM, and spectroscopic PEEM.

Before discussing these components of a LEEM instrument, a short account of the various designs is appropriate. The first major development after the original instrument and a similar one [9.43] also used a beam separator with \(60^{\circ}\) deflection but with close-packed multiple magnetic prisms and only magnetic lenses, including the objective lens, a \(\mathrm{LaB_{6}}\) cathode, and a transfer lens so that the contrast aperture could be placed behind the beam separator [9.44]. The magnetic prism on the illumination side of the instrument can be excited differently from that on the exit side so that a higher beam energy is possible than on the imaging side, which allows AEEM when an energy filter is added to the instrument. The dense packing of the magnetic lenses together with the shielding of the beam separator and the specimen region makes the magnetic shielding used in the more open earlier instruments unnecessary. The addition of an energy filter allows not only AEEM but in combination with synchrotron radiation also spectroscopic x-ray PEEM [9.14, 9.45, 9.46]. This instrument, shown in Fig. 9.10, was built by the Arbeitsgruppe Bauer at the Technical University (TU) Clausthal in the early 1990s [9.47]. It is a precursor of the commercial instrument. The version with energy filter, the SPELEEM, which is presently the most versatile instrument, has been described repeatedly [9.48] in connection with PEEM. The cross section of another LEEM instrument (Fig. 9.11) [9.49] is shown here. Similar to the previous instrument (Fig. 9.10), it has densely packed magnetic lenses both in the illumination (top) and in the imaging (bottom) section. However, it uses a beam separator with \(90^{\circ}\) deflection that is incorporated in the vacuum system (center). The objective lens (right side) is a magnetic diode and consists of two sections with opposing image rotation. A commercial cold field emission electron gun (top) with an energy spread of about \({\mathrm{0.25}}\,{\mathrm{eV}}\) enables a theoretical resolution of \({\mathrm{0.4}}\,{\mathrm{nm}}\) at \({\mathrm{10}}\,{\mathrm{eV}}\). The right side is the specimen chamber and a preparation chamber plus airlock. This instrument presently holds the resolution record (\({\mathrm{0.5}}\,{\mathrm{nm}}\)) among the instruments without aberration correction.

Fig. 9.10

The final noncommercial LEEM instrument built by the Arbeitsgruppe Bauer at the TU Clausthal, Germany, for Arizona State University. Left and right front: illumination and imaging column, respectively. Center: beam separator. Center back: specimen chamber. Right back: preparation chamber and specimen exchange. From [9.47] ©IOP Publishing. Reproduced with permission. All rights reserved

Fig. 9.11

Cross section of a LEEM instrument with a \(90^{\circ}\) separator. The illumination column with the field emission gun is on top and the imaging column is at the bottom. The right side shows the specimen chamber, airlock, and part of the pumping system. After [9.49]

Fig. 9.12

Schematic of the mechanical configuration of a flange-on LEEM system. After [9.50]

The instruments described above are freestanding. There has long been a desire to add a LEEM instrument to existing UHV systems. To be practical, such LEEM systems must be much smaller and have small deflection angles. Two solutions were chosen: one uses a simple beam separator with a small deflection angle (\(10^{\circ}\)) [9.50], and the other uses three deflections by \(45^{\circ}\) [9.51]. In both cases, the instrument is mounted on an \(8^{\prime\prime}\) diameter UHV flange and can be attached to a UHV system via a \(6^{\prime\prime}\) diameter UHV flange. All lenses are electrostatic, including the electrostatic tetrode lens. In contrast to magnetic lenses, electrostatic lenses can be easily floated at high voltage. Therefore, the complete electron optics can be at high voltage so that the specimen can be near ground potential, whereas in the magnetic lens systems the specimen is at high voltage. Because of the compact design, high-voltage insulation requirements allow final energies of only \({\mathrm{5}}\,{\mathrm{keV}}\), in contrast to the \(15{-}20\,{\mathrm{keV}}\) used in the larger systems. Only the extraction electrode of the tetrode lens can be increased to \({\mathrm{15}}\,{\mathrm{kV}}\). External fields are screened by internal \(\mu\)-metal screening. Figure 9.12 shows the mechanical configuration of one of these flange-on LEEM instruments [9.50]. Its overall length is \({\mathrm{60}}\,{\mathrm{cm}}\) and its weight is about \({\mathrm{20}}\,{\mathrm{kg}}\).

Several other LEEM instrument designs have been proposed and in part realized. One design [9.52] included some interesting features such as a combined magnetic-electrostatic beam separator that allows different energies to be used in the illumination and imaging beams, an electrostatic tetrode combined with a Schwarzschild-type optical mirror objective, which focuses UV radiation onto the specimen for PEEM, and a \(70^{\circ}\) spherical condenser for electron energy filtering. Unfortunately, it never came into operation. In another design that is used in a commercial instrument [9.53], the beam separation is achieved by a Wien filter, into which the illumination beam enters at an angle of \(36^{\circ}\), while the imaging beam runs along its optical axis. A second Wien filter is used as an energy filter. This instrument has been used mainly for PEEM, MEM, and metastable impact electron emission microscopy ( ). Apparently, the difficulty in aligning the incident beam normal to the surface and keeping the imaging beam on-axis makes systematic LEEM studies with acceptable resolution difficult. A similar problem must be overcome in an instrument in which the beam separator is replaced by a W single crystal [9.54]. This crystal is tilted \(45^{\circ}\) against the optical axis and reflects a low-energy electron beam from a side-mounted gun along the optical axis. Exact normal incidence on the sample requires that the reflector is on the optical axis, which would obstruct the imaging beam. This instrument, called a double reflection electron emission microscope ( ), is also commercially available. Other LEEM instruments have been built as well, but their design has not been published.

All instruments discussed thus far suffer from the large chromatic and spherical aberrations of the objective lens. That these aberrations can be corrected with an electron mirror has been known for some time, but only during the past decade have efforts been made to develop aberration-corrected instruments. Simultaneously, however, the aberrations of the beam separator must be corrected. This has led to the design of a complex system [9.55, 9.56] which has already been realized in the so-called spectromicroscope for all relevant techniques ( ) [9.17, 9.57, 9.58], schematically shown in Fig. 9.13. Similar to the SPELEEM system, this instrument is designed for a wide range of operation modes [9.59], one of which is LEEM. The centerpiece is the beam separator, to which the illumination system, a field emission gun, the objective lens, and the mirror corrector are attached via field lenses (L). Beyond the beam separator, five electrostatic lenses transfer either the diffraction pattern in the plane of the contrast aperture between L3 and L4 or the primary image at various magnifications into the entrance of the \(\Upomega\)-type energy filter, where the field-limiting aperture is located. With the energy selection slit inserted, the resulting projective lens system produces an energy-filtered image or diffraction pattern on the channel plate-fluorescent screen unit, which is coupled to the CCD (charge coupled device ) camera using a fiber-optic coupler. Numerous deflectors (\(\mathrm{D}i\)) enable precise alignment, and several \(n\)-pole elements (\(n=2,6,12\)) are used for the correction of residual aberrations. The instrument operates at \({\mathrm{15}}\,{\mathrm{kV}}\) and is expected to have a resolution in LEEM of \({\mathrm{1}}\,{\mathrm{nm}}\) at \({\mathrm{10}}\,{\mathrm{eV}}\).

Fig. 9.13

Schematic of the electron-optical configuration of the SMART system. After [9.57]

9.3 Electron Optics

Unless there are resolution-limiting aberrations of the beam separator, the energy filter, other optical components or vibrations, electromagnetic fields, charging, or other disturbances, the chromatic and spherical aberrations of the objective lens determine the resolution. The aberrations of the accelerating field of the cathode lens cause resolution limit values that are much higher than those in transmission microscopy. These values can be calculated analytically by assuming that the lens may be separated into a homogeneous field in front of the specimen, which produces a virtual image behind the specimen, and an einzel lens, which produces a real image of the virtual image. Realistic calculations must consider the cathode lens as a unit, and such calculations have been made by many authors. A comparison of the resolution obtainable with an electrostatic triode, electrostatic tetrode, and magnetic triode lens (Fig. 9.14a-c) shows that the electrostatic tetrode and the magnetic triode lenses are much better than the original triode lens, because in the latter the field strength at the sample is low under focusing conditions (\(1.18{-}0.52\) versus \({\mathrm{10}}\,{\mathrm{kV/mm}}\) in the other two lens types) (Fig. 9.15) [9.60]. The data are for the optimal aperture, which is determined by minimizing the contributions of the aberration disks due to diffraction at the angle-limiting aperture, and chromatic and spherical aberrations. These contributions can be seen in Fig. 9.16a-c, together with the radius of the optimal aperture. From these figures it is clear that the magnetic triode is superior to the electrostatic tetrode in both resolution and transmission. Transmission does not play an important role in LEEM but is important in XPEEM with photoelectrons and secondary electrons, which have a wide angular distribution. Today, the magnetic diode, which differs from the triode only in that both pole shoes are at the same potential, is the standard in the best LEEM instruments without aberration correction, while the electrostatic tetrode is the domain of the smaller, purely electrostatic LEEM instruments. In the multimethod instruments [9.15, 9.16, 9.17, 9.44, 9.57, 9.58], combined electrostatic–magnetic cathode lenses, such as the magnetic triode, are useful because they allow the field strength at the specimen to be varied. Such a lens, with a design somewhat different from that shown in Fig. 9.14a-c, is used in the SMART instrument. Because the chromatic and spherical aberrations of the objective lens are corrected in this instrument by the mirror corrector, the largest aberrations are now those of the energy filter. The resolution improvement obtained by correction is shown in Fig. 9.17 as a function of angular acceptance for an initial energy of \({\mathrm{10}}\,{\mathrm{eV}}\), an energy width of \({\mathrm{2}}\,{\mathrm{eV}}\), and a final energy of \({\mathrm{15}}\,{\mathrm{keV}}\) [9.58]. The dashed lines show the contributions of the aberrations of the uncorrected lens, and the thin solid lines those of the energy filter. For LEEM instruments with \(\mathrm{LaB_{6}}\) or field emission guns that have lower energy widths, the resolution is still improved by about a factor of 5. The main advantage of aberration correction, the large increase in transmission, however, comes to bear only in emission microscopy, in particular in AEEM and XPEEM.

Fig. 9.14a-c

Schematic configurations of LEEM cathode lenses: (a) electrostatic triode, (b) electrostatic tetrode, and (c) magnetic triode. One-half of the electrodes/pole pieces, the electron energy \(E(z)\), and the electron ray path \(r(z)\) are shown. After [9.60]

Fig. 9.15

Comparison of the resolution \(\delta\) of the lenses shown in Fig. 9.14a-c for a final energy of \({\mathrm{20}}\,{\mathrm{keV}}\), an energy spread of \({\mathrm{0.5}}\,{\mathrm{eV}}\), and optimized aperture. After [9.60]

Fig. 9.16a-c

Energy dependence of the contributions of the spherical, chromatic, and diffraction aberrations (dashed, dotted, and dash–dotted lines) to the resolution \(\delta\) (solid line) at the optimal aperture with radius \(r\) for the lenses shown in Fig. 9.14a-c: (a) electrostatic triode, (b) electrostatic tetrode, and (c) magnetic triode. In (a), the field strength has to be changed for forming a real image (\({\mathrm{1.18}}\rightarrow{\mathrm{0.58}}\,{\mathrm{kV/mm}}\) for focus at infinity); in the other two lenses, \({\mathrm{10}}\,{\mathrm{kV/mm}}\) has been chosen. Energy spread \({\mathrm{0.5}}\,{\mathrm{eV}}\). After [9.58, 9.60]

Fig. 9.17

Resolution limit \(d\) as a function of the acceptance angle \(\alpha\) without and with correction of the spherical and chromatic aberrations. Data for the system shown in Fig. 9.13 for \({\mathrm{10}}\,{\mathrm{eV}}\) initial energy and \({\mathrm{2}}\,{\mathrm{eV}}\) energy spread. In the uncorrected system, \(d\) is limited by the chromatic and spherical aberrations (dashed lines), and in the corrected system by higher-order aberrations (solid lines). After [9.58]

The next critical component of a LEEM instrument is the beam separator. Early beam separators [9.3, 9.43] aimed only at the reduction of the unidirectional beam dispersion in the deflection plane. This was achieved with a D-shaped cutout in the round pole pieces [9.61]. The focusing action of the fringing field of the magnet was compensated by magnetic quadrupoles. In contrast to these first separators, which tried to eliminate its focusing action, later separators made use of it in order to obtain optimal image and diffraction pattern transfer in close-packed magnetic prism arrays. They consist of an array of inner pole pieces surrounded by a single outer pole piece with different relative excitations. Such arrays act almost like round lenses. They transfer image and diffraction planes stigmatically and distortion-free to corresponding planes behind the separator but at different settings [9.62, 9.63]. A \(90^{\circ}\) deflector with four inner prisms was suggested for the addition of a mirror corrector [9.63], and a \(60^{\circ}\) deflector with three inner prisms was realized in the first fully magnetic LEEM instrument [9.44]. If illumination and imaging beam have the same energy as in LEEM—in contrast to the more versatile instruments—then a single inner pole surrounded by an outer pole ring are sufficient. Both square [9.49, 9.55, 9.64, 9.65] and round \(90^{\circ}\) [9.66] separators have been proposed and built. With proper geometry and excitation ratio, astigmatic and distortion-free imaging can be achieved for image and diffraction planes with the same settings. For an aberration-corrected microscope, the aberrations of these separators would limit the resolution, and have to be corrected. This is achieved in the highly symmetric beam separator seen in Fig. 9.13 [9.67, 9.68, 9.69]. In small flange-on LEEM instruments, the design of the beam separator is determined less by minimizing aberrations than by geometry and space considerations [9.50, 9.51]. For example, to achieve parallel illumination and imaging beams within a minimum of space, the beams were translated achromatically [9.70] by magnets with field boundaries perpendicular to the beam and electrostatic cylinder lenses in order to achieve stigmatic focusing [9.51]. Finally, a Wien filter may also be used as a beam separator [9.71], though with some alignment difficulties.

Although the use of electron mirrors for the correction of lens aberrations was proposed many years ago [9.72, 9.73] and was suggested for the correction of the cathode lens aberrations in LEEM and PEEM instruments in the early 1990s [9.55, 9.62, 9.74], serious efforts have been made only in the past 20 years [9.75, 9.76, 9.77]. In addition to the first instrument, the SMART, there are now two commercial instruments equipped with a mirror corrector available.

An energy filter is not needed in simple LEEM instruments with sufficiently large separator deflection angles, because at low energies, at which the energy of the secondary electrons differs little from that of the elastically reflected electrons used for the LEEM image, the secondary electron intensity is small compared to the diffracted beam intensity. With increasing energy, when the elastically backscattered intensity decreases and the secondary electron intensity increases, the dispersive action of the sector field deflects a sufficient number of secondary electrons such that only a small fraction pass through the contrast aperture. Likewise, inelastic scattering in the high LEEM energy range occurs mainly in the forward direction, and so it can be seen in the backward direction only through diffraction, via energy loss either before or after diffraction. Therefore it is a second-order effect. Furthermore, the dispersion of the beam separator and the momentum transfer in the energy loss ensure that most inelastically scattered electrons do not pass through the contrast aperture. In the low LEEM energy range, inelastic scattering is lower in the forward direction but in general is weak, and thus does not contribute noticeably to image formation. The main advantage in having an energy filter in a LEEM instrument is that it eliminates the secondary and inelastically scattered electrons in the LEED pattern. In many cases this is not important, but in materials with high secondary electron yield, it improves the LEED pattern dramatically. An energy filter is also useful for quantitative analysis of the background in LEED patterns.

Fig. 9.18

The three fundamental modes of operation of a SPELEEM system. The various sections of the instrument are shown folded into one plane. In imaging and diffraction, the energy selection slit is inserted in the dispersive plane (DP), and the image/diffraction pattern behind the DP is imaged with the projector. The intermediate lens (IL) is used to switch between imaging and diffraction, simultaneously with the exchange of the contrast aperture in FPI and the field-limiting aperture in IIP. For fast spectroscopy, both apertures are inserted, the energy selection slit is removed, and the dispersive plane is imaged by the projector. After [9.15]

The main motivation for adding an energy filter to a LEEM instrument is its importance in multimethod techniques such as SPELEEM or SMART. It allows LEEM to be combined with low electron energy loss spectroscopy and microscopy. Furthermore, when higher beam energy can be used in the illumination beam than in the imaging beam, Auger electron emission spectroscopy ( ) and AEEM are possible as well. These various modes of operation of such an instrument are schematically shown in Fig. 9.18 [9.15, 9.48]. In SEEM, whether excited by electrons, x-ray photons, or energetic ion/neutrals, it allows selection of a narrow energy window from the wide secondary electron energy distribution. This leads to a noticeable improvement in resolution, also in the aberration-corrected systems, in which the correction rapidly deteriorates at low energies with decreasing energy [9.58]. A number of different energy filters are used in these multimethod instruments: one-hemispherical analyzer, two-hemispherical analyzers, a Wien filter, or an omega filter. As they are not essential for LEEM, they will not be discussed here.

9.4 Contrast

For imaging with LEEM , several contrast mechanisms are available, depending upon the specimen to be imaged. The fundamental contrast is diffraction contrast in crystalline samples or backscattering contrast in amorphous or fine-grained crystalline materials. The origin of the backscattering contrast is evident in Fig. 9.1. An example of its consequences is shown in Fig. 9.19. Because of the higher backscattering cross section of Co at the selected energy, the fine-grained polycrystalline Co squares appear bright compared to the Si surrounding, which is covered with native oxide. A slight preferred orientation of the Co layer enhances the contrast [9.78]. Typically, however, larger crystals or single crystalline layers with a well-defined orientation are studied. In this case, in addition to the specular beam ((00) beam), other diffracted beams may be used for imaging. An atomically flat single-crystal surface without steps and other defects produces contrast only when regions with different crystal structures are present. A standard example is the Si(111) surface when the unreconstructed (\(1\times 1\)) and reconstructed (\(7\times 7\)) structures coexist. Here, both normal and lateral periodicity differ and produce strong contrast (Fig. 9.20a,ba) [9.79]. Si(100) surface reconstruction occurs with the formation of dimer rows whose orientation rotates from terrace to terrace by \(90^{\circ}\), with constant normal periodicity. Here, the two resulting (\(2\times 1\)) domains are equivalent at normal incidence and well-centered aperture. Contrast is obtained by either tilting the incident beam or shifting the aperture somewhat in the direction of one of the rows. Using the \(1/2\) order spot of one of the domains gives maximum contrast (Fig. 9.20a,bb) [9.80]. Similar domain contrast can be obtained on all reconstructed surfaces on which reconstruction domains with different azimuthal orientations exist. All surfaces have steps or step bunches that will produce another contrast to be described below.

Fig. 9.19

Backscattering contrast from \({\mathrm{20}}\,{\mathrm{nm}}\)-thick Co squares on a Si substrate. The electron energy is \({\mathrm{5.1}}\,{\mathrm{eV}}\) and the diameter of the field of view is \({\mathrm{10}}\,{\mathrm{\upmu{}m}}\). Reproduced from [9.78], with the permission of AIP Publishing

Fig. 9.20a,b

Diffraction contrast from Si surfaces. (a) Si(111). (Normal incidence) contrast due to different normal periodicity of coexisting (\(1\times 1\)) (dark) and (\(7\times 7\)) (bright) structure. Electron energy \({\mathrm{10}}\,{\mathrm{eV}}\). Inset: LEED pattern. Reprinted from [9.79], with permission from Elsevier. (b) Si(100). (Oblique incidence) contrast due to different azimuthal orientation of coexisting (\(2\times 1\)) and (\(1\times 2\)) domains. Electron energy \({\mathrm{6}}\,{\mathrm{eV}}\). From [9.80]

In general, surfaces are heterogeneous not only in crystallography but also in composition and topography. Compositional differences are usually associated with crystallographic differences and produce, together with backscattering differences, diffraction contrast in the (00) beam. Here also, imaging with nonspecular beams is useful for identifying different coexisting phases, as illustrated in Fig. 9.21a-d [9.81], which is from a Si(111) surface covered with a submonolayer of Au. The three LEEM images are taken with the (00) beam and with nonspecular beams (\(1/5\)-order beams) of (\(5\times 2\)) superstructure domains. This enables the identification of the dark regions between the bright \((\sqrt{3}\times\sqrt{3})\)-R\(30^{\circ}\) structure regions in the specular image with different (\(5\times 2\)) domains.

Fig. 9.21a-d

Phase identification by dark-field imaging. The LEED pattern (a) of the Au submonolayer on Si(111) shows a hexagonal pattern from the \((\sqrt{3}\times\sqrt{3})\)-R\(30^{\circ}\) phase and two linear patterns from the (\(5\times 2\)) phase. The bright-field image (b) shows dark regions that are identified as (\(5\times 2\)) regions by imaging with (\(1/5\), 0), spots (c,d). Electron energy in (a) \({\mathrm{30}}\,{\mathrm{eV}}\) and in (bd) \({\mathrm{6}}\,{\mathrm{eV}}\). Reprinted from [9.81], with permission from Elsevier

Topography distorts the electric field distribution on the surface. This causes the usual topographic contrast, which is most evident near zero electron energy. Topography also produces diffraction contrast. This happens when surface elements are inclined against the average surface, for example, in small crystals on an otherwise flat surface. In a LEEM instrument, the positions of the LEED spots from a flat surface do not change with energy as they do in an ordinary LEED system. This is because the observed LEED pattern is a magnified image of the LEED pattern in the back focal plane of the objective lens, where the electrons have a constant high energy \(E=(h^{2}/2m)k^{2}\) independent of their initial energy. Because the wave number \(k\) is proportional to the refractive index \(n\), we have
$$k\sin\theta=k_{0}\sin\theta_{0}\;,$$
(9.2)
where \(\theta\) and \(\theta_{0}\) are the angles of the electron trajectories with the optical axis in the back focal plane and at the surface, respectively. For two-dimensional () diffraction
$$k\sin\theta_{0}=2\uppi h\;,$$
(9.3)
where \(h\) is the distance of the LEED spot \(h=(h_{1},h_{2})\) from the (00) beam, which is on the optical axis at normal incidence. Combining the two equations leads to
$$k\sin\theta=2\uppi h\;.$$
(9.4)
Thus the angular distance \(\theta\) of the LEED spot \(h\) in the back focal plane is independent of the initial energy \(E_{0}=(h^{2}/2m)k_{0}^{2}\), and depends only on the final energy \(E=(h^{2}/2m)k^{2}\). This is no longer true when the surface normal is inclined against the optical axis. Then the specular beam is off-axis, and the diffracted beams \(h\) move toward the specular beam with increasing energy. The simple geometric relations at normal incidence, which lead to \(E_{0}\)-independent spot positions, are no longer valid, and thus the spots now move in the back focal plane. An example of these spot movements is shown in Fig. 9.22, [9.82]. A simple geometric analysis enables deduction of the inclination of the surface.
Fig. 9.22

Drawing of the movements of LEED spots from faceted Cu silicide crystallites on a Si(111) surface. The open circles are from the Si(111)-\(\delta(7\times 7)\) structure. The small solid and shaded circles are from the crystallites. Increasing shading shows the movement of the spots with energy increasing from 3 to \({\mathrm{10.5}}\,{\mathrm{eV}}\). After [9.82]

Faceted surfaces, that is, surfaces on which all surface elements are tilted so that no specular beam is on the optical axis, can be imaged either by selecting an energy at which one of the diffracted spots passes through the optical axis or by tilting the illuminating beam or shifting the contrast aperture off axis into one of the specular beams. For large tilt angles, only the first mode is practical.

Another important contrast mechanism is the interference contrast on flat surfaces with height differences such as atomic steps. The step contrast was already observed in the early studies (Fig. 9.23) [9.3] and attributed to destructive interference between the wave fields reflected from the adjoining terraces within the lateral coherence length (Fig. 9.24a,ba). Detailed model calculations based on Fresnel diffraction from two adjoining straight edges shifted relative to each other by the step height produce all salient features of the step contrast [9.83, 9.84]. Here, some results of the general theory of image formation by a typical magnetic cathode lens will be given [9.85]. In the absence of aberrations, the reflection of slow electrons from a point source would produce an interference pattern that extends far out from the step. This would make image interpretation in the presence of several steps difficult. The spherical aberration reduces the range of the interference pattern significantly, and the chromatic aberration reduces it to one intensity maximum next to the step at energy spreads as low as \({\mathrm{0.5}}\,{\mathrm{eV}}\). The intensity distribution around the step depends upon the phase difference between the waves reflected from each side of the step, that is, upon the step height and the wave length, and upon the defocus. This is illustrated in Fig. 9.25 [9.85] for two phase shifts \(\Updelta\phi=n\uppi\) (\(n=0.5,1\)) and several defocus values \(\Updelta z^{*}=\Updelta z(C_{\mathrm{s}}\lambda)^{-1/2}\), where \(\Updelta z\) is the geometric defocus, \(C_{\mathrm{s}}\) the spherical aberration constant, and \(\lambda\) the wavelength. \(\Updelta z^{*}=0,1\) corresponds to the Gaussian image and to the Scherzer focus, respectively. For integer \(n\), the step contrast is symmetric and optimal at \(\Updelta z^{*}=0\); for noninteger \(n\) it is asymmetric, with the bright edge changing from one side of the step to the other when the sign of the defocus changes. Optimal contrast is achieved for slight defocus.

Fig. 9.23

Monatomic steps on an Mo(110) surface. Electron energy \({\mathrm{14}}\,{\mathrm{eV}}\). Reprinted from [9.3], with permission from Elsevier

Fig. 9.24a,b

Conditions for phase contrast in LEEM . (a) Step contrast. (b) Quantum size contrast. The penetration of the electron wave upon reflection is indicted

Fig. 9.25

Step contrast for the phase differences \(\Updelta\phi=\uppi\) (a) and \(\Updelta\phi=0.5\uppi\) (b) between the waves reflected from the terraces next to the step for zero defocus and small positive and negative defocus. Modified from [9.85]

A third contrast mechanism, the quantum size contrast, is also based on wave interference, which does not necessarily require crystal periodicity. In a thin film bounded by two parallel surfaces, the wave reflected from the bottom surface can interfere constructively or destructively with that reflected from the top surface, similar to a Fabry–Pérot interferometer, depending upon the wavelength \(\lambda\), the thickness \(t\), and the phase shifts \(\phi\) upon reflection at the surfaces (Fig. 9.24a,bb). Constructive interference, and therefore enhanced reflectivity, occurs whenever \(n(\lambda/2)+\phi=t\), where \(n\) is an integer and \(\lambda\) is the wavelength in the film, which differs from the vacuum wavelength by the inner potential. As a consequence, regions with different thickness appear in the image with different brightness. This was first observed in Cu films on Mo(110) [9.86] and has been since studied in detail in several other systems with the goal of determining the band structure \(k(E)\) above the vacuum level [9.83, 9.87, 9.88, 9.89] or spin-dependent electron reflectivity effects [9.90], or to understand specific features in thin-film growth [9.91, 9.92, 9.93].

To determine the band structure, the constructive interference condition above is rewritten by replacing \(\lambda\) by \(k=2\uppi/\lambda\), which leads to \(k(E)t-k(E)\phi(E)=n\uppi\). The energy-dependent phase term can be eliminated by choosing film thickness pairs \(t_{1}\), \(t_{2}\) for which this condition is fulfilled (with different \(n\)), which gives a set of \(k(E)\) values. With proper growth conditions regions with different thickness can be obtained (Fig. 9.26) [9.87] and analyzed quasisimultaneously. After subtraction of the reflectivity of a thick film, which does not show quantum size effects, the oscillations of the reflectivity due to constructive and destructive interference can clearly be seen. This is illustrated in Fig. 9.27 [9.88] for a ferromagnetic film in which the band structures of the majority and minority spin electrons differ by the exchange splitting. The reflectivity curve for the minority spin electrons is shifted relative to that of the majority electrons due to this splitting and is also damped more strongly due to the shorter IMFP of the minority electrons mentioned in Sect. 9.1.

Fig. 9.26

Quantum size contrast between regions with different thickness of a Fe film on W(110), taken with different electron energies, that is wavelengths. The images in the top row show the intensity and those at the bottom the magnetic signal (exchange asymmetry). Blue and red correspond to opposite magnetization directions. Reprinted from [9.87], with permission from Elsevier

Fig. 9.27

Quantum size oscillations of the reflectivity \(R\) of spin-up (circles) and spin-down (crosses) electrons in a six-monolayer-thick Fe film on W(110) as a function of energy. After [9.88]

9.5 Applications

The high intensity available in LEEM studies of single-crystal surfaces, which enables rapid image acquisition, and the high surface sensitivity, which strongly accentuates the topmost layer in imaging, both discussed in Sect. 9.1, along with the various contrast mechanisms described in Sect. 9.4, have made LEEM one of the most powerful methods for surface studies, particularly with regard to the thermodynamics of surfaces and the kinetics of surface processes. While most of this information came from detailed studies of semiconductor surfaces, mainly from Si(111) and Si(100) surfaces, important insight into surface processes has also been obtained from various metal and oxide surfaces, such as the \(\mathrm{TiO_{2}}\)(110) surface. The information obtained from such studies ranges from the chemical potential of adatoms, diffusion across terraces and steps, anisotropic step free energy, step stiffness, step mobility, step–step interactions, surface free energy and surface stress, vacancy exchange between the bulk and the surface, to nucleation, growth, phase transitions, self-organization, faceting, segregation, oxidation, and other surface and thin-film phenomena. Only some examples can be mentioned in the following subsections. These are organized according to the material, but the references will provide access to most of the relevant work conducted to date. For illustrations, results of the early exploratory work will be used, because the later quantitative studies require much more discussion.

9.5.1 The Si(111) Surface

The Si(111) surface is probably the surface most often studied with LEEM, mainly because of its phase transition from the reconstructed (\(7\times 7\)) to the disordered (\(1\times 1\)) at 1100 or \({\mathrm{1135}}\,{\mathrm{K}}\), depending upon the author. In precise LEED diffractometer measurements  [9.94, 9.95], the superstructure spots disappeared at \({\mathrm{1120}}\,{\mathrm{K}}\), and an intensity fit assuming a continuous transition gave a critical temperature of \({\mathrm{1100}}\pm{\mathrm{1}}\,{\mathrm{K}}\). However, no critical scattering was observed, which put into question earlier conclusions that the phase transition was second-order. The first LEEM measurements [9.79, 9.80, 9.96] demonstrated without doubt that the transition was first-order, as seen in the nucleation and growth of the (\(7\times 7\)) structure (Fig. 9.28a,b). The growth rate of the (\(7\times 7\)) domains was found to increase linearly with undercooling \(\Updelta T\), and for \(\Updelta T> {\mathrm{12}}\,{\mathrm{K}}\), nucleation also occurred on the terraces.

Fig. 9.28a,b

Nucleation and growth of the (\(7\times 7\)) structure at surface steps with different orientations at low supersaturation. Electron energy: (a\({\mathrm{10.5}}\,{\mathrm{eV}}\) and (b\({\mathrm{1.5}}\,{\mathrm{eV}}\). From [9.96], with permission of Bunsengesellschaft, Germany

The transition was found to be strongly influenced by impurities [9.97]. In particular, the apparent discrepancy between LEEM and the preceding LEED studies was attributable to near-surface contamination during the long measurement time near the phase transition needed in the quantitative LEED studies. This is illustrated in Fig. 9.29a,b [9.80], which shows that long annealing near the transition temperature completely destroys the regular domain structure. The LEED patterns differ only by a slightly higher background in the annealed sample, but the transition range is now much wider, similar to that in the LEED studies. On clean surfaces that have been quenched rapidly and have completely converted into the (\(7\times 7\)) structure, many domains of various sizes form. Upon subsequent annealing, they coarsen without preference to certain boundary orientations or number of bounding domain walls [9.98].

Fig. 9.29a,b

Comparison of a surface that was annealed for a long period around the transition temperature (a) and one that was cooled rapidly from \({\mathrm{1450}}\,{\mathrm{K}}\) to this temperature (b). Electron energy \({\mathrm{10.5}}\,{\mathrm{eV}}\). From [9.80]

Recent, more detailed studies [9.100, 9.101, 9.102, 9.103, 9.104, 9.105, 9.106, 9.107, 9.108, 9.99] have shed considerable light on the forces and processes involved in the phase transition, including adatom diffusion [9.100, 9.104, 9.99], the influence of the surface stress difference between the (\(7\times 7\)) and (\(1\times 1\)) phases and of long-range interactions on phase coexistence [9.101], shape [9.105] and distribution of the (\(7\times 7\)) domains [9.106], and other aspects. There are excellent reviews on these subjects [9.109, 9.110] where details may be found. Another phenomenon that has been studied with LEEM and which is closely related to the (\(1\times 1\))-to-(\(7\times 7\)) phase transition upon cooling is the faceting of vicinal (stepped) Si(111) surfaces [9.111, 9.112, 9.113]. Other studies have been concerned with the conditions for step flow growth instead of two-dimensional nucleation from which the parameters that determine the growth kinetics can be derived [9.114, 9.115, 9.116]. In and Sb surfactants that form a \((\sqrt{3}\times\sqrt{3})\)-\(\mathrm{R}30^{\circ}\) structure were found to either enhance or suppress step flow, respectively [9.117]. An apparently similar boron-induced surface structure \(((\sqrt{3}\times\sqrt{3})\)-\(\mathrm{R}30^{\circ}\)-\(\mathrm{B})\) has a quite different effect: it causes twinning [9.114].

9.5.2 Si(100)

This surface is the basis of semiconductor technology and, as such, has attracted particular attention. It was studied qualitatively in the early years of LEEM [9.80] (Fig. 9.20a,bb) and convincingly showed the nonequivalence of the A and B type steps, the lower-energy \(S_{\mathrm{A}}\) steps being smooth, while the higher-energy \(S_{\mathrm{B}}\) steps were rough. Step migration during sublimation [9.118] and interaction with dislocations formed by plastic deformation during cooling [9.119] were studied, as well as the enhancement of one domain upon elastic deformation [9.119, 9.80]. Other processes included consecutive Lochkeim formation during sublimation of flat regions [9.120] and homoepitaxial growth [9.120, 9.121, 9.122, 9.80]. From the terrace shape during growth close to equilibrium (Fig. 9.30a-d), a lower limit of the ratio of the step free energies of \(S_{\mathrm{B}}\) and \(S_{\mathrm{A}}\) of \(\beta_{\mathrm{B}}/\beta_{\mathrm{A}}\geq{\mathrm{2.6}}\) at about \({\mathrm{800}}\,{\mathrm{K}}\) was obtained. In other qualitative work [9.123, 9.124], the step morphology was studied in more detail as a function of miscut angle, which led to a step phase diagram ranging from a hilly phase near zero miscut via single-height wavy steps, to straight steps, to double-height steps at a miscut of about \(0.1^{\circ}\).

Fig. 9.30a-d

Images from a video taken during the homoepitaxial growth of Si(100) at low supersaturation so that growth can occur only from a defect at the lower edge of the image. Electron energy \({\mathrm{5}}\,{\mathrm{eV}}\). Reprinted from [9.121], with permission from Elsevier

In subsequent quantitative studies [9.125, 9.126, 9.127, 9.128, 9.129, 9.130, 9.131, 9.132, 9.133, 9.134, 9.135, 9.136], comprehensive information was deduced from step and island shapes and distributions. Many of the results can also be found in the reviews mentioned above [9.109, 9.110]. These include the determination of the mobility and stiffness of the \(S_{\mathrm{A}}\) and \(S_{\mathrm{B}}\) steps [9.125, 9.129], their free energy [9.125], and the anisotropy of the surface stress [9.136], and the extraction of the chemical potential, formation energy, and diffusion coefficients of adatoms from number, area, and distribution of two-dimensional islands [9.126, 9.130, 9.133]. On the more qualitative side, the fabrication of large step-free regions [9.128, 9.135] and of periodic gratings [9.131, 9.132, 9.134] by e-beam lithography, reactive ion beam etching, and high-temperature annealing has also contributed considerably to the understanding of the surface properties. Other methods of surface modifications have been studied as well. Oxygen etches the surface at high temperature and produces vacancy islands [9.137, 9.138, 9.139]. Arsenic was found to displace Si even on large terraces, driven by surface stress, causing two-dimensional island formation [9.140]. Boron segregation leads to strong temperature-dependent surface roughening at the monolayer level, forming a striped [9.141, 9.142] (Fig. 9.31a-h) or triangular-tiled surface structure [9.143, 9.144, 9.145]. Originally believed to be driven mainly by surface stress relaxation, it was later shown that a strong reduction in the step free energy of the \(S_{\mathrm{A}}\) steps was the main driving force [9.143, 9.144].

Fig. 9.31a-h

Images from a video taken during the segregation and desegregation of B from B-doped Si(100) during cooling and heating. Electron energy \({\mathrm{4.2}}\,{\mathrm{eV}}\); diameter of field of view \({\mathrm{7}}\,{\mathrm{\upmu{}m}}\) (\({\mathrm{5}}\,{\mathrm{cm}}\)). From [9.142]

9.5.3 Other Elemental Semiconductor Surfaces

On the silicon-on-insulator (SOI ) (100) surface, LEEM was used to determine the dislocation-induced strain [9.146]. On the Si(311) surface, the LEEM image intensity fluctuations in small surface regions were measured during the continuous disordering transition of the (\(3\times 1\)) reconstruction around \({\mathrm{965}}\,{\mathrm{K}}\), in order to determine the critical parameters [9.147].

The first-order transition at about \({\mathrm{1005}}\,{\mathrm{K}}\) from the high-temperature (\(1\times 1\)) to the low-temperature (\(16\times 2\)) structure of the Si(110) surface and the stress-stabilized coexistence of the two phases was the subject of another study [9.148]. Similar to the work on Si(111) and Si(100), various surface thermodynamic data have also been obtained for the Si(110) surface from island decay measurements [9.149]. Finally, a LEEM study of the (\(2\times 1\))-to-(\(1\times 1\)) phase transition above \({\mathrm{925}}\,{\mathrm{K}}\) on Ge(100) led to the conclusion that the transition was due to dimer breakup and roughening [9.150].

9.5.4 Thin Films on Semiconductors

Because of its importance in the semiconductor industry, Ge—or more precisely SiGe on Si(100)—is the most widely studied system to date [9.151, 9.152, 9.153, 9.154, 9.155, 9.156, 9.157, 9.158, 9.159, 9.160, 9.161]. This system initially forms a several-monolayer-thick layer that is highly strained depending upon alloy composition. From this layer, three-dimensional islands develop with facets that are dependent upon size and composition, leading to a rich variety of phenomena well suited for LEEM studies. The transition from the initial layer to the three-dimensional islands is strain-driven and does not require three-dimensional nucleation [9.156, 9.157, 9.159]. Surface steps play a critical role in the alloying of Ge with the Si(100) surface [9.160]. The results up to 2000 are summarized in an excellent review [9.161]. The growth of Ge on other Si surfaces has been studied in much less detail. On the (111) surface, the influence of the surfactant Sb on growth was studied [9.162], and on the (311) surface the transition from the two-dimensional layer to three-dimensional islands [9.163]. These showed a much more complicated facet structure than on Si(100). Finally, the growth of Ge on GaAs(100) was also studied briefly [9.164].

The growth of metals on semiconductor surfaces can also be studied very well with LEEM. Most of the work has been done on Si(111) surfaces, with some on Si(100), using video recording of the growth, diffusion, ordering, and disordering processes. Au on Si(111) is a good example: after several two-dimensional superstructures have formed with increasing coverage, three-dimensional particles grow that show an interesting temperature dependence due to the formation of an Au-Si eutectic [9.165, 9.81]. On vicinal Si(100) surfaces with a miscut of \(4^{\circ}\), adsorption of a monolayer of Au causes pronounced faceting at elevated temperatures [9.166, 9.167, 9.168, 9.169]. The growth of Ag on Si(111) has also been studied extensively [9.161, 9.170, 9.171, 9.172, 9.173], in particular the growth shape [9.171, 9.173], and has been used to demonstrate that buried interfaces can be imaged via their strain fields [9.172]. In the various studies of Ag on Si(100) [9.174, 9.175, 9.176], a strain-induced shape transition of Ag crystals into quantum wires [9.174] and bamboo-like growth [9.177] have been observed. Substrate material incorporation into the two-dimensional superstructure [9.176] and the influence of steps on the domain ordering in it [9.175] have been found. On vicinal Si(100), self-assembled Ag quantum wires form at high temperatures [9.178]. The growth of Cu on Si(111) has been studied on both the clean and the hydrogen-passivated surface [9.179, 9.180, 9.181, 9.182, 9.82]. Hydrogen termination strongly influences the formation of the two-dimensional (\(5\times 5\)) superstructure and the three-dimensional nucleation of Cu silicide. At higher temperatures, at which hydrogen is desorbed, large \(\mathrm{Cu_{3}Si}\) crystals form, in a variety of shapes and facets.

In Al films on Si(111), the two-dimensional phase diagram and the phase transitions between the phases have been studied [9.183]. The growth of Pb on Si(111) has been used to obtain an understanding of how interfactants, that is, substrate surface layers that remain at the interface during growth, produce quasi-monolayer-by-monolayer growth, using Au and Ag as interfactants [9.184, 9.185, 9.186]. Figure 9.32a,b illustrates the influence of an Au interfactant layer on the growth of Pb. On the Si(100) surface, Pb grows in \(\langle 111\rangle\)-oriented crystals on the two-dimensional initial layer. The crystals frequently have an ashtray shape due to the large supply of Pb atoms by diffusion on the initial layer [9.187]. On vicinal and high-index surfaces of Si, which have been faceted by Au adsorption, Pb grows in mesoscopic wires [9.188, 9.189]. In was found not to wet the Si(111)-(\(7\times 7\)) surface but to grow at low temperature, monolayer by monolayer, on the Si(111)-\((\sqrt{3}\times\sqrt{3}\))-R\(30^{\circ}\) surface with a variety of superstructures. Three-dimensional crystals that grow at somewhat higher temperatures have predominantly (100) orientation, with a surface reconstruction similar to that of the underlying two-dimensional layer [9.190, 9.191]. The Si(100) surface is etched at high temperatures by In similar to the situation mentioned above for Ag; at lower temperatures a superstructure forms [9.192].

Fig. 9.32a,b

Images taken during the growth of Pb on Si(111) at \({\mathrm{290}}\,{\mathrm{K}}\) with (a) and without Au surfactant (b). Electron energy \({\mathrm{8}}\,{\mathrm{eV}}\). Reprinted with permission from [9.184]. Copyright 2000 by the American Physical Society

Transition metals are highly reactive with Si and form silicides that are frequently more stable at high temperatures than Si. An example is Co. When deposited or annealed at high temperatures, Co layers form more or less hexagonal \(\mathrm{CoSi_{2}}\) crystals that show misfit dislocation contrast when sufficiently thin. When heated to temperatures at which Si sublimes, \(\mathrm{CoSi_{2}}\)-topped hillocks form because of the lower vapor pressure of \(\mathrm{CoSi_{2}}\) (Fig. 9.33) [9.193, 9.97]. At lower temperatures, the crystals are triangular and act as Co scavengers, cleaning the surrounding surface from Co so that it develops the (\(7\times 7\)) structure of the clean surface. At very low Co coverages, an interesting ring cluster (RC ) phase forms, which has been studied in considerable detail [9.194, 9.195, 9.196]. Ni forms a similar RC phase [9.197]. Another transition metal, Ti, spontaneously forms Ti silicide nanowires when deposited at about \({\mathrm{1120}}\,{\mathrm{K}}\). Their formation process and stability have been studied in detail [9.198].

Fig. 9.33

Hillocks on a Si(111) surface caused by \(\mathrm{CoSi_{2}}\) crystals during the sublimation of Si. Reprinted with permission from [9.97]. Copyright 1999, American Vacuum Society

Only a few nonmetal films on Si have been studied with LEEM: \(\mathrm{CaF_{2}}\) and Si nitride. In \(\mathrm{CaF_{2}}\) films, studies have investigated both the complexities of the formation of the first two layers [9.199] and the formation mechanism of the interfacial dislocation network with increasing film thickness [9.200]. The Si nitride work was concerned mainly with the formation of the initial epitaxial layer by reaction with \(\mathrm{NH_{3}}\) at high temperatures, which occurs via nucleation and growth of nitride domains similar to the (\(7\times 7\)) domains on the clean surface [9.201].

9.5.5 Wide-Band Semiconductors

Very little work has been done on these materials with LEEM. There is a cursory study of the temperature dependence of the structure of the 6H-SiC(0001) surface used as a substrate in the growth of GaN layers [9.202]. The structure of the GaN(0001) surface was studied with dark-field imaging, which enabled determination of the surface termination [9.203], similar to that of the SiC(0001) surface [9.204]. Several papers have demonstrated the importance of the Ga\(/\)N ratio in homoepitaxial growth of GaN [9.202, 9.204, 9.205], in particular the necessity of a Ga double layer on top of the GaN surface for the growth of films with (0001) surfaces [9.202, 9.205, 9.206]. The double layer shows an interesting phase transition [9.202]. Without an adsorbed Ga layer, the GaN films grow rough, with {\(10\bar{1}1\)} and {\(101\bar{2}\)} facets. GaN growth on 6H-Si(0001) is similar [9.207], and not as reported (incorrectly) in another paper [9.208], except that three-dimensional crystals form initially instead of the spiral and step flow growth in homoepitaxial growth on GaN.

9.5.6 Metal Surfaces

Refractory metal surfaces have been the most popular subject in LEEM because of their high melting point and low vapor pressure, allowing experiments to be conducted over a wide temperature range. W and Mo can be easily cleaned by heating in oxygen. The chemisorbed oxygen is then flashed off at high temperatures, a procedure that is not successful in Nb and Ta, in which oxygen goes into solid solution and can be partially removed only by lengthy sputter and annealing cycles. The imaging of the step structure on the Mo(110) surface (Fig. 9.23) was one of the first demonstrations of the power of LEEM, and step contrast has been a major tool in the study of surface processes on clean surfaces. While W(110) and Mo(110) have been used frequently as substrates for thin films, and to a much lesser extent W(100) and W(111), little has been published about the clean surface, except for a brief study of the Mo(110) surface [9.209]. Extensive work has been carried out, however, on epitaxial Mo(110) [9.210, 9.211, 9.212, 9.213, 9.214, 9.215] and Nb(110) [9.213, 9.216, 9.217, 9.218] layers grown on sapphire (\(11\bar{2}0\)) surfaces at high temperatures, which after proper cleaning produces surfaces that are comparable in quality to single-crystal surfaces. One complication is the interfacial strain and the dislocations introduced upon cooling and thermal cycling by the different thermal expansion coefficients between film and substrate. Nevertheless, pure surface quantities such as step stiffness could be extracted from such films. In the case of the Nb(110) films, the situation is complicated by the residual oxygen. This causes reconstruction and faceting [9.213, 9.216, 9.217], which in themselves are interesting processes and are useful for the study of extended defects [9.218]. Some work has been done on Ta(110) films as well [9.213].

Noble metal surfaces have also been the subject of several LEEM studies. For Pt(111) single-crystal surfaces, step stiffness, step–step interactions, step free energy [9.213, 9.215, 9.219], and bulk–surface vacancy exchange [9.220, 9.221] have been determined. For Pd(111) surfaces, the step stiffness [9.215] was obtained and sputter erosion processes [9.222] were observed. Studies of the island decay on Rh(100) indicated a new surface diffusion process [9.223]. Step fluctuation spectroscopy of Au(111) yielded the surface mass diffusion coefficient and the orientation-dependent step stiffness [9.224]. Dark-field imaging of the reconstructed Au(100) surface was used to establish the connection between the reconstruction domains and the step orientations (Fig. 9.34a-d) [9.225, 9.226, 9.80]. On the Ag(111) surface, a critical island size was found for layer-by-layer growth [9.227]. The Ehrlich–Schwoebel barrier, the energy barrier for diffusion across a step, was deduced from an investigation of the homoepitaxial growth of Cu on Cu(100) [9.228]. Similar to other fcc(110) surfaces, reconstruction of Pb(110) surfaces can be observed. A LEEM study of the various reconstructions, some of them alkali-induced, revealed the topography of the various phases and the influence of surface defects on the transitions between them [9.229, 9.230]. Finally, studies of the surface morphology of the NiAl(110) surface demonstrated the importance of bulk diffusion for surface smoothing [9.231]. Most experiments on clean surfaces rely on the step contrast discussed in Sect. 9.4, which illustrates its usefulness.

Fig. 9.34a-d

Au(100) surface. Bright-field image (a) and dark-field images (c,d) taken with the (\(5\times 1\)) superstructure reflections indicated in the LEED pattern (b). Electron energy in the images \({\mathrm{16}}\,{\mathrm{eV}}\). From [9.225]

9.5.7 Metal Layers on Metals

Although the growth of many metals on W(110) and Mo(110) has been studied with other methods, LEEM has been used infrequently, often only in a very cursory manner. Cu is the most frequently investigated layer material, both on Mo [9.122, 9.165, 9.232, 9.233, 9.86] and W. The growth on the two substrates is similar and has been studied in detail on W(110) [9.234]. Layer spacings have been determined using the quantum size effect discussed in Sect. 9.4 [9.235]. The more qualitative work on Mo revealed an interesting striped phase upon annealing at high temperatures, as well as details in the structural phase transition in the double layer. Layer spacings have also been obtained from the quantum size effect for Ag on W(110) [9.92]. Au has been studied briefly on Mo(110) in the submonolayer range, where it forms needle-like crystals [9.122, 9.233]. The transition from two- to three-dimensional growth of Pd layers on W(110) was the subject of a combined LEEM-XPEEM study [9.236]. In other works, the growth of Ag and Cu on the Ru(0001) surface served as a demonstration of the influence of substrate steps on the growth of three-dimensional crystals [9.237]. In the metal-on-metal systems discussed thus far, the substrate surface is not modified or is modified only slightly by the growing film. This is not the case on less densely packed surfaces such as the W(111) surface, where faceting occurs upon deposition of certain metals at high temperatures. Pt growth on W(111) is a case study for this process [9.238, 9.239]. The growth of ferromagnetic layers will be discussed in Sect. 9.6 in connection with SPLEEM.

In many cases, the deposited metal forms a surface alloy with the substrate. Pd on Mo(100) is an example that was studied in detail up to several monolayers using LEEM [9.240]. Clear alloying was observed up to a monolayer, followed by two-dimensional Pd growth without faceting. Alloying of Sn with Cu(111) is strikingly different: at very low coverages, large two-dimensional islands form that travel across the surface, leaving alloy behind and thereby decreasing in size [9.241]. Pb forms on the Cu(100) surface initially in several two-dimensional structures, followed by the growth of three-dimensional crystals. LEEM clearly shows the correlation between the crystals and the initial layer [9.242], evidence for the surface alloying in the initial layer at low coverages, followed by dealloying [9.243, 9.244]. The nature of the disordering transitions of these phases was also determined [9.244]. One of the most impressive results produced by LEEM to date is the self-assembly of stress domain patterns in the two-dimensional Pb-Cu alloy on Cu(111), which consist of domains of a Pb-rich and Pb-poor phase. This process has been studied in great detail, which has produced a wealth of information on stress-induced ordering phenomena [9.245, 9.246, 9.247, 9.248, 9.249], and has been well reviewed [9.250]. Finally, the influence of the interface between Pb droplets and the Cu(111) surface on the shape and melting of the droplets was the subject of a LEEM study [9.251, 9.252].

9.5.8 Reactions on Metal Surfaces

Although LEEM is well suited for the study of reactions on surfaces with gases or impurities from the bulk, very little work has been done up to now. Segregation of impurities from the bulk and the formation of precipitation products on the surface are routinely observed before the crystal has been cleaned completely. Surface carbide formation on W and Mo surfaces is an example. Images of such carbides and of carbides formed by CO dissociation have been published [9.122, 9.211, 9.232], but the precipitation process was never studied in detail. As far as oxidation is concerned, only three systems have been studied: the initial oxidation of W(100) [9.254, 9.255], the low-oxygen-coverage region on Nb(100) [9.256], and the growth of oxide domains on NiAl(110) [9.257]. All three studies show interesting, unexpected phenomena.

More work has been done on surface reactions in which the reaction products are desorbed, that is, in heterogeneous catalysis. The first studies looked with very limited resolution at reactions of CO with \(\mathrm{O_{2}}\) [9.258, 9.259] and with NO [9.260], and at the reaction of NO and \(\mathrm{H_{2}}\) [9.261], mainly at the propagation of the reaction front and its pinning by defects. On Pt(110), pattern formation during CO oxidation has been studied [9.262, 9.263], and on Rh(110) the reaction of NO [9.253] and of \(\mathrm{O_{2}}\) with \(\mathrm{H_{2}}\) [9.264, 9.265]. Most of this work has been done with low resolution, but the possibilities for LEEM in this particular field are evident in some studies [9.253, 9.264, 9.265]. The contrast is due to the fact that surface regions with different reactant composition have different structures, which produce characteristic LEED patterns. These can be used for dark-field imaging of these regions [9.253]. Such dark-field images are shown in Fig. 9.35a-d for the \(\text{NO}+\mathrm{H_{2}}\) reaction on Rh(110). The propagation of a spiral wave reaction is imaged with the diffraction spots of pure N phases (Fig. 9.35a-da,b), a mixed \(\mathrm{N}+\mathrm{O}\) phase (Fig. 9.35a-dc), and a pure O phase (Fig. 9.35a-dd), which occur during the oscillatory reaction. Because of the high brightness, LEEM is preferable to PEEM because it allows one to follow the kinetics of the reaction wave propagation, and it is superior to MEM because of its better resolution.

Fig. 9.35a-d

Dark-field images taken during the reaction of NO with \(\mathrm{H_{2}}\) on Rh(110) with LEED spots characteristic of the various phases in the oscillatory reaction. Reprinted from [9.253], with permission from Elsevier

9.5.9 Oxides and Nitrides

The only LEEM work on oxides published up to now is that on the \(\mathrm{TiO_{2}}\)(110) surface [9.266, 9.267, 9.268, 9.269]. \(\mathrm{TiO_{2}}\) is a particularly good example of the influence of the exchange of defects between the bulk and the surface on its structure, as its stoichiometry can vary considerably. On the nonstoichiometric surface, a (\(1\times 1\))-to-(\(1\times 2\)) phase transition occurs as a function of temperature due to vacancy exchange between the bulk and the surface, which has been studied thoroughly [9.266, 9.267, 9.268]. When exposed to oxygen, the nonstoichiometric surface grows via step flow at high temperatures, but via two-dimensional nucleation at lower temperatures. With suitable growth conditions, the surface topography can be changed and the oxygen content of the bulk can be increased [9.269, 9.270]. The only nitride studied to date—silicon nitride and GaN, which were discussed in Sects. 9.5.5 and 9.5.6, respectively, excepted—is the (111) surface of TiN layers. These layers form mounds with spiral steps or stacks of two-dimensional islands. The mass transport at high temperatures can be studied well by following the step motion and the diffusion processes, and constants can be derived from it [9.270, 9.271].

The applications discussed in this subsection clearly show the many possibilities for LEEM in the study of surfaces and thin films of a wide variety of materials. Important information on the physical and chemical properties of surfaces and thin films has been extracted from these studies. These can be found in the references cited. Diffraction contrast, step contrast, and quantum size contrast, together with real-time capability, are the essential features that make LEEM so powerful in these studies. It should also be emphasized that LEEM is primarily an imaging method for in situ studies. Sample exchange is more time-consuming than in standard transmission and scanning electron microscopy because the sample has to be transferred into ultrahigh vacuum, usually after cleaning in a preparation chamber, and then aligned in the microscope. These steps are necessary because of the high surface sensitivity of the method and because the sample is part of the objective lens, so its surface must be exactly perpendicular to the optical axis.

An important aspect of LEEM is that it can be easily combined with other, in part complementary, surface imaging techniques. MEM is useful whenever no strong diffracted beam is available for imaging, for example, on fine-grained polycrystalline or amorphous samples. In this case, the sample potential is chosen such that the electrons cannot penetrate the sample. Contrast is then determined by surface topography, surface potential, and work function differences. MEM has been used, for example, in the study of chemical reactions [9.258, 9.259]. Ultraviolet light-excited photoemission electron microscopy ( ) is probably the most popular auxiliary imaging method in LEEM instruments. It is used when fields of view larger than those possible in LEEM have to be imaged or in samples in which it produces better contrast than LEEM. A good example is the study of the growth of pentacene films on oxidized Si [9.272, 9.273]. The application range of UVPEEM is the same as that of MEM, but the resolution is generally much better. Synchrotron radiation-excited XPEEM provides chemical information and chemically specific magnetic information. It can be easily combined with LEEM, in particular in instruments equipped with an energy filter. This is the SPELEEM mentioned in Sect. 9.2, whose application will be discussed in Sect. 9.7 of this chapter. XPEEM is a subject of another chapter in the book.

Other imaging methods possible in LEEM instruments include thermionic emission electron microscopy ( ). TEEM is generally useful only for samples with locally varying work functions and that can be heated high enough for thermionic emission. Metastable impact electron emission microscopy ( ) is another imaging method with limited application range. In this method [9.274, 9.275], de-excitation of metastable \(\mathrm{He^{*}}\) atoms at the surface causes electron emission up to energies of \(15{-}20\,{\mathrm{eV}}\). Because of the chromatic aberration, resolutions of \({\mathrm{100}}\,{\mathrm{nm}}\) or less can be achieved only with a band-pass energy filter [9.276]. The main application for MIEEM is in the study of adsorbates, which consist of regions with different de-excitation processes. In LEEM instruments that allow higher energies in the illumination system than in the imaging system, SEEM and in particular AEEM are possible. AEEM is useful for chemical analysis but inferior to XPEEM because of the larger characteristic peak width and the larger background. As in XPEEM, a band-pass energy filter is indispensable for selection of a narrow energy band at the Auger electron peaks. The energy filter is also useful for SEEM, whose application range is similar to that of UVPEEM and MEM.

9.6 Spin-Polarized LEEM (SPLEEM)

SPLEEM is a version of LEEM that requires a separate treatment because it does not give structural but magnetic information. It differs from LEEM only in that the illumination system produces a partially spin-polarized electron beam. The polarization is achieved by illuminating a GaAs(100) surface with circular polarized light, with the wavelength corresponding to the band gap of GaAs. The surface is activated by Cs and \(\mathrm{O_{2}}\) exposure to negative electron affinity so that electrons that have been excited to the bottom of the conduction band can escape the surface. Optical selection rules produce a spin selection in the excitation process such that the spin of the emitted electrons points normal to the surface, either inward or outward depending upon the helicity (right or left) of the exciting light. Ordinary GaAs cathodes usually have a polarization of only about \(20{-}30\%\). Details of this kind of cathode can be found in Pierce [9.277], a more recent analysis of its properties [9.278]. The theoretical degree of polarization of this cathode is limited to \({\mathrm{50}}\%\) by the spin degeneracy of the valence band of GaAs. The degeneracy can be eliminated by strain, resulting in a theoretical degree of polarization of \({\mathrm{100}}\%\). Polarization of \({\mathrm{92}}\%\) has been achieved with a strained GaAs/GaAsP superlattice on a GaAs substrate [9.279]. Replacing the GaAs substrate with GaP enables illumination of the cathode from the backside through a close-proximity lens, resulting in a very small emission area and brightness of more than \({\mathrm{1\times 10^{7}}}\,{\mathrm{A{\,}cm^{-2}{\,}sr^{-1}}}\) at an extraction voltage of \({\mathrm{20}}\,{\mathrm{kV}}\), higher than that of \(\mathrm{LaB_{6}}\) electron sources by more than a factor of 10 [9.280]. With a strain-compensated superlattice, the quantum efficiency can be further increased by nearly a factor of 10 [9.281].

In the first generation of spin-polarized electron guns, the electron beam is deflected \(90^{\circ}\) after extraction from the cathode by a combined electrostatic-magnetic sector field. In pure electrostatic deflection, the direction of the spin polarization \(\boldsymbol{P}\) is unchanged, and in pure magnetic deflection \(\boldsymbol{P}\) is deflected \(90^{\circ}\); if both fields are used for \(90^{\circ}\) deflection, \(\boldsymbol{P}\) can be rotated in any direction in the plane, indicated in Fig. 9.36 [9.282].

Fig. 9.36

Schematic of the spin manipulator . After [9.282]

In the early SPLEEM studies [9.283, 9.284, 9.285, 9.286, 9.287, 9.288], only electrostatic deflection was available. Later, the magnetic rotator lens indicated in the figure was added, which allows \(\boldsymbol{P}\) to rotate in any direction in space [9.282]. Usually, however, only three directions are selected, one normal to the surface of the crystal and the other two in preferred directions in the surface plane (easy and hard magnetic axes). The spin manipulator shown in Fig. 9.36 is incorporated in the original LEEM described in Sect. 9.2 (Fig. 9.9) and in a second instrument [9.289, 9.51]. The more recent SPLEEM instruments have a straight optical axis, and the rotation of the spin from along the optical axis to perpendicular to it was initially achieved by a simple Wien filter. The spin rotation around the optical axis was achieved with the magnetic lenses of the LEEM illumination optics [9.290]. Finally, with an eight-pole Wien filter, the spin can be rotated in any direction without using the illumination lenses [9.291].

The magnetic contrast is due to the fact that the \(180^{\circ}\) backscattering from magnetic materials depends upon the relative orientation of the spin of the incident electrons and of the electrons in the material, or in other words, upon the relative orientation of the polarization \(\boldsymbol{P}\) and the magnetization \(\boldsymbol{M}\). The intensity in the image is then given by \(I=I_{\text{str}}+c\boldsymbol{P}\cdot\boldsymbol{M}\), where \(I_{\text{str}}\) is determined by the structure and topography of the surface, \(c\) is a small proportionality constant, and the dot indicates the scalar product. Pure magnetic contrast is obtained by subtracting two images taken with opposite \(\boldsymbol{P}\) directions, pixel by pixel. Maximum contrast obviously occurs for \(\boldsymbol{P}\parallel\pm\boldsymbol{M}\). For \(\boldsymbol{P}\perp\boldsymbol{M}\), the contrast between magnetic domains with opposite magnetization vanishes, and only the domain walls produce contrast. Maximum contrast requires imaging at very low energies, typically a few electronvolts. At these energies the exchange splitting of the band structure and the difference between the inelastic mean free paths of the spin-up and spin-down electrons, which were mentioned in Sect. 9.1, cause the strongest difference between the backscattering for the two spin directions. Because the magnetic signal is only a small fraction of the total signal, the signal-to-noise ratio in the difference image is small and frequently limits the resolution [9.292]. The addition of two images with opposite \(\boldsymbol{P}\) directions produces only structural contrast, which makes SPLEEM ideal for the correlation between magnetism and structure. More information on magnetic contrast formation may be found in several SPLEEM reviews [9.142, 9.293, 9.294, 9.295, 9.296, 9.39].

In most SPLEEM studies, the ferromagnetic samples are prepared in situ while observing the magnetic structure together with the crystal structure and topography via several contrast mechanisms. However, ex situ-prepared samples can also be studied after proper surface cleaning, as illustrated in Fig. 9.37 for a Co(0001) surface that had been sputter-cleaned and annealed [9.284]. Ex situ-prepared samples can also be studied when passivated with a thin layer that is sufficiently transparent for slow electrons such as noble metals [9.297]. In this method, it must be taken into account that such overlayers can change the magnetization in the film below [9.298, 9.299]. The in situ studies cover single ferromagnetic layers, ferromagnetic layers covered with nonmagnetic overlayers, ferromagnetic–nonmagnetic–ferromagnetic sandwiches, and small ferromagnetic crystals.

Fig. 9.37

SPLEEM image of the closure domains on a Co(0001) surface. Electron energy \({\mathrm{2}}\,{\mathrm{eV}}\). From [9.284], reproduced with permission

Under certain conditions, large regions of a thin Fe film can be grown with constant thickness and atomically flat surfaces. These show pronounced quantum size effects (Fig. 9.26) [9.87]. The intensity reflected from regions with different thickness shows pronounced spin-dependent quantum size oscillations as a function of energy (Fig. 9.27) [9.88], from which the exchange-split band structure above the vacuum level [9.300, 9.88] and the spin dependence of the inelastic mean free path [9.301] can be derived.

The early SPLEEM work concentrated on Co films on W(110) without [9.283, 9.284, 9.285] and with [9.286] nonmagnetic overlayers, on Co on Au films on W(110) [9.287], and on initial studies of Co\(/\)Cu\(/\)Co sandwiches [9.288]. Some of the more interesting results were the large difference in the damping of the magnetic signal by Cu and Pd overlayers due to the different inelastic mean free paths in these materials, and the quantum size effect in the magnetic signal with increasing Cu overlayer thickness [9.286]. This phenomenon was later studied in considerable detail in Cu films on fcc Co(100) on Cu(100) [9.90] and in MgO films on Fe(100) on MgO(100) [9.302].

The introduction of the spin manipulator finally enabled measurement of all three \(\boldsymbol{M}\) components. First, it was found that Co films on W(110) have up to about 10 monolayers and interesting wrinkled magnetization, with \(\boldsymbol{M}\) tilting with increasing thickness in an apparent oscillatory manner toward in-plane [9.303]. In contrast, the out-of-plane to in-plane spin-reorientation transition ( ) in Co layers on Au(111) layers on W(110) was found to occur in a completely different manner within a small thickness range [9.304]. Subsequent work revealed that in addition to the effects of the film and substrate material (e. g., Co on Ru(0001) [9.305]), other parameters such as substrate step structure (e. g., Ni on Cu(100) [9.306, 9.307]), noble metal overlayers (e. g., on Co on Ru(0001) [9.308]), hydrogen adsorption (e. g., on Co on Ru(0001) [9.309]), underlayers (Fe on one [9.310] and two [9.311] Cu monolayers on W(110)), and growth conditions (deposition rate, residual gas pressure, e. g., in Fe on Cu(100) [9.312, 9.313]) exerted a strong influence on this transition with increasing thickness. For the latter system, the usefulness of SPLEEM for local hysteresis curve measurements was also demonstrated [9.314]. A good example of the power of SPLEEM is the study of the SRT of Fe-Co alloy layers on Au(111) layers on W(110) [9.315, 9.316]. As shown in Fig. 9.38a,b, the magnetic contrast is already quite strong at \(\mathrm{1.22}\) monolayers, increases only slightly with thickness, and then decreases when the film approaches the spin reorientation transition at about \(\mathrm{2.7}\) monolayers. During the approach of the transition, a pronounced striped phase develops and the magnetization tilts increasingly, but abruptly converts into large, predominantly in-plane magnetized domains. The surface has large step bunches pointing toward and away from the vapor source, which causes the transition to occur earlier or later. In lateral averaging studies, this would smear out the transition so that it would appear more continuous. Many other details can be extracted from the SPLEEM images, which indicate a rather complex transition.

Fig. 9.38a,b

The spin-reorientation transition in a Fe-Co alloy layer on Au(111). (a) Shows the out-of-plane component of the magnetization and (b) the in-plane component. Electron energy \({\mathrm{2.5}}\,{\mathrm{eV}}\) and diameter of field of view \({\mathrm{10}}\,{\mathrm{\upmu{}m}}\). Reprinted with permission from [9.316]. John Wiley & Sons

Ordered substrate surface alloys have a significant influence on the evolution of magnetization with film thickness, as illustrated for Fe on noble metal surface alloys on W(100) [9.317]. The substrate orientation, however, has a much stronger influence on this evolution due to the strong dependence of the magnetic structure on the microstructure of the film, which is determined by the misfit and symmetry of the interface. This is evident from a comparison of Co [9.318, 9.319] and Fe [9.300, 9.320, 9.321, 9.88] films grown on W(110), W(100), and W(111). In contrast to the predominantly lateral growth on W(110) and W(111), Co grows on W(100) on top of a nonmagnetic double layer in three-dimensional needle-shaped crystals bounded by facets so that no electrons are reflected along the optical axis in the energy range in which the magnetic signal is strong [9.318]. Only when the film is continuous can a weak magnetic signal be seen. Fe grows on all three surfaces initially two-dimensionally, but the film experiences considerable structural changes thereafter, which cause major changes in the magnetic structure. For example, on W(111), magnetization disappears at room temperature in one-monolayer intervals at the end of the two-dimensional growth [9.320], and on W(100), a complex SRT sets in at this stage, breaking up the original large single domains [9.321].

SPLEEM is also very well suited for the study of exchange coupling. Coupling through nonferromagnetic metal layers is mediated by quantum size oscillations, which cause ferromagnetic, antiferromagnetic, or biquadratic coupling between the layers, depending upon interlayer thickness and interface roughness, as demonstrated for Co\(/\)Au\(/\)Co [9.322] and Co\(/\)Cu\(/\)Co trilayers [9.323]. The strong local coupling at an antiferromagnetic interlayer, however, imposes the domain structure of the interlayer on the ferromagnetic layer, as illustrated by the system Fe\(/\)NiO\(/\)Fe [9.324].

Perpendicular magnetization in ferromagnetic superlattices is of great interest for spin-current devices. To understand its evolution with increasing number \(n\) of periods, SPLEEM was used in a study of a prototype system, \(\mathrm{(Ni_{2}Co)_{\mathit{n}}}\) grown on W(110) [9.325, 9.326, 9.327]. The fast image acquisition—compared with other magnetic imaging methods—allowed quasicontinuous imaging of in-plane and out-of-plane magnetization during growth. Figure 9.39 shows selected images from such a growth sequence. The magnetization is initially in-plane, and turns with increasing \(n\), oscillating out-of-plane due to the increasing number of Ni\(/\)Co\(/\)Ni interfaces, staying nearly completely out-of-plane after \(n=4\), with some in-plane magnetization left only at step bunches. Perpendicular magnetization up to large film thickness has also been obtained by intercalating Co under graphene on Ir(111), thanks to high Co\(/\)graphene interface anisotropy [9.328, 9.329]. The magnetization is completely out-of-plane up to 13 monolayers, in contrast to six monolayers without graphene cover. The transition to in-plane magnetization occurs over a wide thickness range of between 13 and four monolayers, with a complex, wavy three-dimensional spin distribution. This system shows another interesting effect: a breakdown of the spin asymmetry above a film thickness-independent energy, causing the loss of magnetic contrast [9.330].

Fig. 9.39

The evolution of the perpendicular magnetization in a \(\mathrm{Ni_{2}Co}\) multilayer with increasing number of layers. The bottom row show the in-plane images, the center row the out-of-plane images, and the top row enlarged regions of the in-plane images, marked by the frames in the bottom row and contrast-enhanced to reveal the domain boundaries. A LEEM image of the surface covered with one \(\mathrm{Ni_{2}Co}\) pair shows the step (bunches) on the surface. From [9.325]

While most of the SPLEEM work been done on magnetic domains, domain walls were studied only briefly in the early years [9.331], until domain wall devices made domain walls an important subject. Systems with chiral domain walls enable fast wall motion with low-threshold currents. The Dzyaloshinskii–Moriya interaction, which occurs at interfaces with broken inversion symmetry, allows control of the chirality. In thin films, interfaces can be controlled easily and studied in situ with SPLEEM. Studies of several interface systems, Fe\(/\)Ni bilayers on Cu(100) [9.332], \(\mathrm{(Co/Ni)_{\mathit{n}}}\) multilayers on Pt(111) [9.333] and Ir [9.334], and a Fe/Ni bilayer on W(110) [9.335] have brought considerable insight into interface engineering of monochiral domain walls. An overview of this work, which has led to the design of a skyrmion phase [9.336], can be found in [9.337].

The systems discussed thus far were all laterally unconfined. In confined systems, an additional anisotropy, the shape anisotropy, plays an increasing role [9.338, 9.339, 9.340]. This is illustrated in Fig. 9.40a-g for Fe crystals on W(110). Confinement in one direction leads to either closure domain Fig. 9.40a-ga,b [9.338] or single domain Fig. 9.40a-gc,d [9.339] formation depending upon the width of the long crystals, and a similar behaviour is seen in small crystals depending upon lateral extension. An example of sub-\({\mathrm{100}}\,{\mathrm{nm}}\)-sized crystals is shown in the images of a Fe film on W(001) Fig. 9.40a-ge,g [9.321].

The crystals have formed clusters during the breakup of a highly strained Fe film, with a more or less random magnetization distribution within the clusters. In contrast, the magnetization \(\boldsymbol{M}\) is preferentially aligned along the \(\langle 110\rangle\) directions in the three-monolayer-thick regions shown in Fig. 9.40a-gf, while in the four-monolayer-thick regions, \(\boldsymbol{M}\) is precisely aligned along the \(\langle 100\rangle\) directions. In spatially well-separated Co on Ru(0001) nanocrystals, in addition to the single-domain states, vortex domains occur, varying with thickness and height, which was presented in a corresponding phase diagram [9.341].

Fig. 9.40a-g

Size dependence of the magnetic domain structure. (ad) One-dimensional Fe crystals on W(110) forming a closure domain structure above \({\mathrm{1}}\,{\mathrm{\upmu{}m}}\) width (a,b) (reprinted with permission from [9.338], John Wiley & Sons), and single, shape anisotropy-determined domains below \({\mathrm{1}}\,{\mathrm{\upmu{}m}}\) width (c,d) (reprinted from [9.339], with permission from Elsevier). The crystals are aligned along the W[001] direction, the polarization along (a,c) and perpendicular to the length of the crystals. (ef) Fe nanocrystals formed during growth on W(001) at \({\mathrm{600}}\,{\mathrm{K}}\). (e) LEEM image, showing three- and four-monolayer-thick regions in addition to nanocrystal clusters on top of the wetting layer; (f,g) show the angular magnetization distribution in the three-monolayer regions (preferentially along \(\langle 110\rangle\)) and in the nanocrystal clusters (nearly random) in the color wheel code. Because of the low energy (\({\mathrm{0.5}}\,{\mathrm{eV}}\)), the clusters are not resolved in LEEM. In SPLEEM, the magnetic contrast allows partial resolution. (eg) reprinted with permission from [9.321]. Copyright 2017 by the American Physical Society

The phase diagram of ultrathin ferromagnetic films has been studied extensively with lateral-averaging methods, which give mean values over regions varying in magnetic properties, in particular of the critical behavior. This problem can be overcome with SPLEEM, thanks to its high lateral resolution. An example is the study of a Fe monolayer on two monolayers of Au on W(110) with a locally strongly varying step density. Finite size effects caused the ferromagnetic-to-paramagnetic transition in regions with small terrace width at a significantly lower temperature than on wide terraces. Averaging over all terraces led to an incorrect Curie temperature and critical exponents, while selecting only the largest terrace gave the correct value expected for the 2-D Ising model [9.342].

SPLEEM is not limited to the study of ferromagnetic materials, but can be used equally successfully for ferrimagnetic materials. Magnetite is a particularly interesting ferrimagnetic compound because of its transition from the cubic high-temperature phase to a monoclinic low-temperature phase (Verwey transition). A study of the (100) surface with SPLEEM/LEEM found that the surface develops a roof-like distortion during the phase transition but maintains its surface reconstruction [9.343]. Contrary to the easy \(\langle 111\rangle\) magnetization directions in the bulk, the magnetization in the surface is in-plane along the \(\langle 011\rangle\) direction and has a complicated domain structure [9.344].

Concluding this section, the strengths of SPLEEM should be emphasized once more: correlation with the microstructure, fast image acquisition compared to other magnetic imaging methods, high surface sensitivity, and easy access to all three magnetization components.

9.7 SPELEEM

A LEEM instrument that is equipped with an energy filter enables real-space and reciprocal-space imaging with emitted electrons, in particular photoelectrons, and converts the instrument into a spectroscopic photoemission and low-energy electron microscope ( ), as mentioned already in Sects. 9.2 and 9.3 [9.15, 9.45, 9.46, 9.48]. The increasing availability of SPELEEM instruments at synchrotron radiation sources has led to numerous studies combining LEEM or LEED with x-ray photoemission spectroscopy ( ) and microscopy (XPEEM), and also in particular angle-resolved spectroscopy ( ), which is frequently called \(k\)-space imaging. This section discusses work in which real- and/or reciprocal-space imaging with reflected and energy-selected emitted electrons is combined. Pure photoemission microscopy and spectroscopy studies, along with their theoretical background, are discussed in Chap.  10.

Figure 9.41a-c [9.345] shows the three fundamental operation modes of a SPELEEM: imaging, diffraction, and spectroscopy—or real-space, reciprocal-space, and energy-space imaging. While energy filtering in LEEM is necessary only if at the same time strong emission occurs, such as thermionic emission at high temperatures, in LEED it is useful for eliminating inelastically scattered and secondary electrons from the background. Of course, in the emission modes of operation, energy filtering is always needed in order to select the electrons with the desired energy. Before concentrating on the commonly used photoemission modes, which require an external excitation source, Auger electron emission microscopy ( ) using the LEEM electron gun should be briefly discussed. This was the only method for spectroscopic imaging before bright synchrotron radiation light became available, and soon displaced it. The desire for chemical imaging to complement the structural imaging with LEEM in a laboratory environment may see a resurrection of this method. The possibilities and limitations are illustrated in an early experiment shown in Fig. 9.42.

Fig. 9.41a-c

Schematic of the SPELEEM operation modes. Several lenses, except the objective lens, and the field-limiting and angle-limiting apertures are switched between the different modes. After [9.345]

Fig. 9.42

Auger electron emission image of a thin Ag microcrystal on a contaminated Si(111) surface. Images were taken in \({\mathrm{2}}\,{\mathrm{eV}}\) steps with \({\mathrm{1}}\,{\mathrm{eV}}\) resolution around the \(M_{4,5}\) VV transitions, requiring \({\mathrm{15}}\,{\mathrm{s}}\)/image. The spectra were obtained by integration of \({\mathrm{1.5}}\,{\mathrm{\upmu{}m^{2}}}\) regions. From [9.45]

The short image acquisition time is due to the high electron impact ionization cross sections: at \(3{-}5\) times the energy of the inner shell involved in the Auger transition (here \(M_{4,5}\)), this cross section is comparable to that near the maximum of the x-ray photo ionization cross sections, making AEEM intensities comparable to XPEEM intensities. This is particularly true for shells with low inner-shell ionization energies. For example, for the Ag \(M_{4,5}\) levels, it is nearly \({\mathrm{100}}\%\). However, there are two drawbacks: (i) the characteristic peaks are usually much wider because two valence bands (V) are involved, and (ii) the background is much higher. Therefore, XPEEM is preferable whenever available. In the laboratory, in addition to spectroscopic imaging, AEEM enables the study of noncrystalline or rough surfaces, in which LEEM fails. All that is needed to convert a LEEM instrument into an AEEM instrument is an auxiliary high-voltage supply so that the illuminating beam can be put at a sufficiently higher energy than the imaging beam and a split beam separator with a higher deflection field on the illumination site.

In combination with photoemission methods, LEEM and LEED frequently serve only to determine the quality of the film surface, the film thickness, and the crystal structure. In other studies, photoemission methods play the supporting role, as will be illustrated by a number of studies in the following. Some reviews cover additional examples [9.142, 9.345, 9.346, 9.347]. In one combination of LEEM and photoemission methods, (x-ray absorption PEEM), the energy filter is not needed, only a monochromatic photon beam, because contrast stems from energy-dependent absorption of the photon beam. Its most important application is in x-ray magnetic circular dichroism PEEM ( ). The combination with LEEM has been very fruitful in enabling a better understanding of ferromagnetic systems such as MnAs films on GaAs(100) [9.348, 9.349], as such understanding, both of the LEEM images [9.350] and of the XMCDPEEM images [9.351, 9.352], has been challenging. Figure 9.43a,b shows (x-ray magnetic linear dichroism PEEM) Fig. 9.43a,ba and an XMCDPEEM image 9.43a,bb of a MnAs film.

Fig. 9.43a,b

XMLDPEEM and XMCDPEEM image of a \({\mathrm{300}}\,{\mathrm{nm}}\)-thick MnAs film on GaAs(100) at room temperature at which paramagnetic (gray in (b)) and ferromagnetic phases (black/white in (b)) coexist with a complicated domain structure. Reprinted with permission from [9.349]. Copyright 2007, American Vacuum Society

In antiferromagnetic samples, magnetic information can be obtained without SPLEEM or x-ray magnetic dichroism PEEM if they show antiferromagnetism-caused superstructure spots in the LEED pattern. Using these spots in LEEM, this was demonstrated convincingly for NiO by comparison with XMLDPEEM images (AFM-LEEM) [9.353]. In general, LEEM and LEED are used in magnetic studies mainly for the determination of the crystal structure and the particle size and shape. For example, for the correlation of the magnetization on the surface of three-dimensional Fe crystals on Mo(110) with that in the bulk, it was necessary to precisely determine the shape of the crystals [9.354]. In an XMCDPEEM study of the magnetization distribution in three-monolayer-thick triangular Co crystals on Ru(0001) as a function of crystal size, LEEM was essential for the preparation and structural characterization of the crystals [9.355]. In the XMCDPEEM study of the magnetization pattern and Curie temperature of nanometer-thick magnetite crystals, LEED also had to be used for the determination of the crystal structure [9.356].

The combination of LEEM and LEED with XPEEM and XPS is particularly important when structural changes cause chemical changes and vice versa. The changes may be caused by heating, electron or photon irradiation, or chemical reactions. While irradiation effects are generally disturbing, they can also be useful for surface modification, as was done, for example, in the case of the \(\mathrm{TiO_{2}}\)(110) surface. Here, MEM, LEED, and XPS were combined in a study of one-dimensional ( ) Au crystals on the irradiation-modified surface [9.357]. Another application of irradiation is Ag(111) surface patterning by irradiation-assisted oxidation [9.358]. Examples of studies of temperature-induced changes include the metal–insulator transition in epitaxial \(\mathrm{VO_{2}}\) films on \(\mathrm{TiO_{2}}\)(110) [9.359, 9.360], the phase transformations in thin iron oxide films on Pt(111) and Ag(111) surfaces [9.361], or the cleaning of ZnO powders, in which reactive growth was studied with LEEM, XPEEM, and XPS [9.362].

Reactive growth is a field in which SPELEEM is indispensable. A prime example is the growth of Fe on ZnS(100) [9.363, 9.364], in which several reaction products are formed. One of these, which in earlier transmission electron microscopy/diffraction studies had been interpreted as Fe, required LEEM, LEED, XPSPEEM, and XMCDPEEM for reliable identification as \(\mathrm{Fe_{3}S_{4}}\). This was achieved by taking many XPEEM images around the Fe 3p and S 2p photoelectron energies and measuring the intensities in windows set on the crystals of interest, which produced the spectra shown in Fig. 9.44a-d. XMCDPEEM was used to check the magnetic state and to determine a lower limit of the Curie temperature. Quantitative evaluation was limited mainly by the aberrations of the objective lens, which produced contributions from the surroundings of very small crystals to their signal, and by the fact that the \(\mathrm{Fe_{3}S_{4}}\) crystals were faceted and had an unknown angular distribution of the emission. Similar problems must be expected in the analysis of small or faceted crystals formed in other reactive growth systems, for example, in the study of the growth of Co germanide crystals on Ge(100), in which the chemical state of the crystals was determined by selected area XASPEEM [9.365]. For larger crystals with flat surfaces and well-known structure, these problems do not occur, for example, in the study of the oxidation pathways of iron oxides on Ru(0001) [9.366]. In another SPELEEM study, MEM and LEED were combined with near-edge x-ray absorption fine structure (NEXAFS) to determine the influence of crystal orientation and grain boundaries on the oxidation of polycrystalline Ni. Surprisingly, at higher temperature (\({\mathrm{673}}\,{\mathrm{K}}\)), no oxidation occurred around the grain boundaries and on the grains. NiO crystals in the \({\mathrm{1}}\,{\mathrm{\upmu{}m}}\) range formed on the otherwise clean surface [9.367].

Fig. 9.44a-d

LEEM image taken with \({\mathrm{3}}\,{\mathrm{eV}}\) electrons (a) and windows set in the XPSPEEM image (b) from which the XPS spectra (c,d) were obtained. A is a Fe crystal with a chemisorbed S layer, B is greigite. It requires two components for fitting (surface and bulk) in the S 2p spectrum (c) and a completely different majority-to-minority spin ratio for fitting the Fe 3p spectrum (d), indicating a completely different electronic structure. Reproduced from [9.363], with permission from the Royal Society of Chemistry

SPELEEM has been used in a variety of other studies of oxides. MEM and XPSPEEM were combined with AFM to investigate the contact potential difference between SrO and \(\mathrm{TiO_{2}}\) on the phase-separated \(\mathrm{SrTiO_{3}}\)(100) surface [9.368]. Another phenomenon, which could not have been demonstrated without SPELEEM, is the quantum size effect ( ) in the oxidation of thin-metal films. This was done with Mg [9.369] and Al [9.370] films on W(110) by using the QSE contrast in LEEM for local thickness determination and the O 2p contrast in XPSPEEM for measuring the local oxide coverage. The most extensively studied oxide, however, is \(\mathrm{CeO_{2}}\), which plays an important role in catalysis as catalyst support material. It is very radiation-sensitive, and so the emphasis is generally on LEEM and LEED, while XPEEM and XPS are used only briefly to determine the oxidation state. Examples include studies on the growth and structure of (111) [9.371] and (100) [9.372] oriented \(\mathrm{CeO_{2}}\) crystals on Ru(0001), the reduction process from \(\mathrm{CeO_{2}}\) to \(\mathrm{Co_{2}O_{3}}\) on Ru(0001) [9.373], and the growth and structure of another oxide, \(\mathrm{Pr_{2}O_{3}}\), on Ru(0001) [9.374].

In other work on ceria on metal substrates, both reflection and emission imaging and spectroscopy were used, with more emphasis on the latter. The first of these studies [9.375] explored the possibilities for imaging the oxidation state of ceria islands on a Re(0001) substrate by using resonant \(\mathrm{Ce^{3+}}\) (4f\({}^{1}\)) and \(\mathrm{Ce^{4+}}\)(4f\({}^{0}\)) valence band XPS as well as Re 4f and O 1s, the latter to determine the oxidation state of the substrate. Resonance XPS makes use of the chemical shift between the two oxidation states. When the photon energy is slightly above the lower binding energy, emission from only this state will occur, and if it is above the higher binding energy, electrons from both states are emitted. Proper spectrum subtraction provides high sensitivity in the distinction between different binding states, simultaneously minimizing radiation damage, as illustrated convincingly in this study. A second study made use of this method in an investigation of the growth, morphology, and oxidation state of thin ceria crystals on Rh(111) and of Au nanoparticles on these crystals as a model system for the water-gas reaction [9.376]. In the most detailed work, the reoxidation of thin \(\mathrm{CeO_{2}}\) nanoislands on Rh(111) after reduction by photon irradiation was investigated [9.377]. Figure 9.45 illustrates the experimental procedure. The images on top were recorded during the slow decrease of the oxygen pressure starting from nearly completely oxidized \(\mathrm{CeO_{2}}\) at the energies characteristic for \(\mathrm{Ce^{4+}}\)(red) and \(\mathrm{Ce^{3+}}\) (blue) at \(\mathrm{3.5}\) and \({\mathrm{1.5}}\,{\mathrm{eV}}\) binding energy in the valence band spectrum, shown at the bottom right. With decreasing loss of oxygen due to irradiation, conversion into \(\mathrm{Ce_{2}O_{3}}\) occurs, and at the lowest pressure, partial reduction to metallic \(\mathrm{Ce^{0}}\), as seen in the intensities plotted below the images. At the bottom, enlarged sections of the images shown on the top are shown at several states of the reduction process, together with a dark-field LEEM image. Reoxidation was found to occur via spillover from oxygen adsorbed on the Rh surface.

Fig. 9.45

Resonant Ce 4d–4f spectroscopy of the reduction of \(\mathrm{CeO_{2}}\)(111) islands on Rh(111) by photon irradiation. Reprinted with permission from [9.377]. Copyright 2016 American Chemical Society

SPELEEM has also been used successfully for elucidating surface processes that occur at metal surfaces during catalysis, albeit at low pressures. The water formation reaction \(\mathrm{H_{2}}+\mathrm{O_{2}}\) in the presence of submonolayer adsorbed metals on Rh(110) has been the subject of several studies. It was found that the reaction induces a lateral distribution of the metal into metal-rich and metal-poor regions with well-defined reaction fronts [9.265, 9.378]. With co-adsorbed Au and Pd, well-defined stripe phases were formed at coverages between \(\mathrm{0.3}\) and \(\mathrm{0.7}\) monolayers under certain reaction conditions (temperature, gas pressures) [9.379, 9.380]. Similar adsorbate redistribution processes were found with adsorbed \(\mathrm{VO_{2}}\) on Rh(111) [9.381]. In a study of chemical waves and rate oscillations in the same reaction on Rh(111) covered with a NiRh alloy, XPEEM and XPS were also used for local composition analysis [9.382]. Another interesting application is the monitoring of the local coverage of adsorbates during chemical wave propagation using the XPS signals of the adsorbates involved. This was done in the \(\text{NO}+\mathrm{H_{2}}\) reaction on Rh(110) with low potassium coverages. The lateral chemical resolution of XPEEM gave detailed insight into the propagation process, for example, showing that K accumulated in front of the N front [9.383]. A final example is the location of chemically active oxygen on Ag(111). The chemical shift of the O 1s peak between the oxygen-reconstructed terraces and step bunches enabled imaging of the location of an oxygen species with higher binding energy at step bunches, which were identified as the chemically active sites [9.384].

Probably the most extensive use of SPELEEM has been in the study of graphene on metals and SiC, particularly the intercalation of metals and gases between graphene and the substrate, driven by the many possible applications of graphene. Of the more than 50 studies using SPELEEM published up to 2016, only a few can be cited here as examples of the method. More information can be found in [9.142, Chap. 6.1]. Most of the work has been on SiC—the intercalation studies nearly inclusively—but some interesting studies also on metal surfaces. On SiC, graphene is generally formed by sublimation of Si in situ in UHV or, better, in inert gases at high pressure, which enables better control of the sublimation process. On metals, decomposition of a hydrocarbon gas or segregation of C from C-doped crystals is used. Depending on the goal of the studies, either all or a few selected SPELEEM methods are used. These include LEEM for determining the topography, selected-area LEED for local structure analysis, \(I_{00}(V)\) for the measurement of the number of graphite layers, XPS of the elements involved (substrate, graphene, adsorbate, intercalant) for the determination of their bonding states, XPEEM for imaging of the lateral distribution of these elements, XPEEM at the K and \(\Upgamma\) points in reciprocal space (where graphene has a high and zero density of states, respectively), and \(\boldsymbol{k}\)-space (\(k_{\mathrm{x}}\), \(k_{\mathrm{y}}\)) imaging at constant energy \(E\) and of \(E(\boldsymbol{k})\) in a plane through the \(\mathrm{K}\) point for the analysis of the Dirac cone characteristic for graphene.

Figure 9.46a-f [9.385] shows an example of some of these methods. The graphene flake, which had been grown by decomposition of ethylene at high temperature, developed upon cooling to room temperature the striations seen in the LEEM and XPEEM images. The XPEEM image at the K point shows no intensity in the stripes, suggesting no graphene. However, there is intensity in the \(\Upgamma\) point image, which is attributed to regions with contact to the substrate, resulting in contributions of the substrate density of states. Most of the flake, however, is decoupled from the substrate, as the intensity in the K point image and the \(\boldsymbol{k}\)-space data in the center shows. Thus the graphene layer is rippled and attached to the substrate only along periodic lines, as shown in the LEED pattern. The period is below the resolution of the images, which show only regions with more extended contact with the substrate. In other studies, particularly when more than one graphene monolayer are involved, \(I_{00}(V)\), XPS, and \(E(\boldsymbol{k})\) cuts play a major role in the determination of the thickness, bonding, and band structure as a function of thickness. This is illustrated, for example, in [9.386], which summarizes some of the work up to 2011. A study of the electronic band structure of a graphene trilayer on SiC uses LEEM to locate regions with the desired thickness, identified by \(I_{00}(V)\) curves, to image the Dirac cone \(E(\boldsymbol{k})\) via ARPES [9.387], as a function of thickness. SPELEEM was also very useful for more device-oriented studies. One example is the study of nanoribbons grown on sidewalls of trenches, which are of interest because of the high electron mobility in them [9.388]. Another is the fabrication of semiconducting graphene ribbons on nitrogen-doped SiC [9.389]. In both studies, nearly all methods mentioned above were used for characterization.

Fig. 9.46a-f

Graphene monolayer island on an Ir(100) surface. (a) LEEM image taken with the diffraction spots marked in the LEED pattern (b) XPEEM images taken at the (e) K and (f\(\Upgamma\) point near the Fermi energy \(E_{\mathrm{F}}\), respectively, (c\(\boldsymbol{k}\)-space cut near Fermi level, (d\(E(\boldsymbol{k})\) in-plane through K point. \(E_{\mathrm{D}}\) is the energy of the Dirac point (the tip of the Dirac cone shown in (d), which is a measure of the doping of the graphene. Reprinted with permission from [9.385]. Copyright 2013 American Chemical Society

A fascinating application of SPELEEM is the study of intercalation between substrate and graphene. As already mentioned in Sect. 9.6, many Co monolayers can be intercalated between graphene and an Ir substrate [9.328, 9.329]; however, in most cases only one is used. The first was \(\mathrm{H_{2}}\), which was used to break the strong bond between the first C layer on SiC, transforming it into a graphene monolayer. Many other atoms and compounds followed: Li, Na, Cs, Si, Ge, Al, Cu, Au, Pt, Bi, AlBr, NiC. Only a few recent studies, in which references to older work can be found, can be mentioned here. Na [9.390], Al [9.391], and Cu [9.392] were intercalated between graphene and SiC by deposition and annealing at metal-dependent temperatures. XPS combined with LEEM and LEED is essential in this method for the distinction between adsorbed and intercalated material. Intercalation of Na was enhanced by soft x-ray irradiation. Intercalated Al was found to be stable up to high temperatures and to form ordered Al, Si, and AlSi phases as identified by LEED and XPS. Intercalated Cu also produced a superlattice and resulted in a significant modification of the electronic structure of graphene, as seen in the formation of mini-Dirac cones. Another intercalation method is segregation from the substrate. This was demonstrated with graphene on C-doped Ni on which annealing produced a Ni carbide intercalation layer [9.393]. Segregation and dissolution in the substrate are reversible, which allows switching between different coupling strengths between graphene and the substrate. Still another method for intercalation is by ion implantation, which can be used if other methods fail, as demonstrated for Bi intercalation [9.394]. Ion bombardment does not produce a two-dimensional intercalation layer if the atoms have only weak interactions with the substrate, such as noble gas atoms. In this case, the intercalated atoms form nanobubbles which can be stable under GPa pressures. Ar 2p XPS shows that their size increases with increasing temperature, from small clusters at room temperature, and becoming visible in LEEM and XPEEM after annealing to very high temperatures (\(> {\mathrm{1000}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\)) [9.395]. This example illustrates that gases can be kept at high pressures under graphene, which makes graphene-covered surfaces ideal systems for gas reactions at high pressures. Experiments along this line have already been performed in separate LEEM-UVPEEM and XPS systems, but not yet in SPELEEM instruments.

A final example of the importance of combining LEEM and XPEEM is the study of the phase separation and coexistence in a two-dimensional FeNi alloy monolayer on a W(110) surface. LEEM shows a complex pattern on the \({\mathrm{100}}\,{\mathrm{nm}}\) scale. Without chemical analysis with high-resolution XPEEM, it would be impossible to understand this phase separation process [9.396].

Concluding this section, the examples discussed here clearly show the power of SPELEEM in many applications. By proper combination of the various methods available in SPELEEM instruments at synchrotron radiation sources, many problems can be much better solved than by studying them in separate instruments. With the continued development of high-brightness laboratory x-ray sources and the use of AEEM, SPELEEM studies should become feasible in the laboratory as well.

Notes

Acknowledgements

The author thanks Anastassia Pavlovska for preparing the figures, references, permissions and for the editorial work of this chapter.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dept. of PhysicsArizona State UniversityTempe, AZUSA

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