Resolving oxide surfaces – From point and line defects to complex network structures

Authors


  • This article will be published in edited form in Volume 3 “Properties of Composite Surfaces: Alloys, Compounds, Semiconductors” of the book series “Surface and Interface Science,” edited by K. Wandelt (Wiley-VCH, Weinheim, 2013), ISBN 978-3-527-41157-3.

Abstract

In the following, we demonstrate the atomic-scale analysis of oxide surfaces. Essential physical properties were extracted using noncontact atomic force microscopy (nc-AFM) and scanning tunneling microscopy (STM). The main focus has been put on the determination of surface structures. A review of the recent achievements towards atomic-scale resolution from highly crystalline to amorphous materials is provided. An overview of local probe microscopy and spectroscopy to get beyond the averaging character of diffraction methods is thereby summarized. In particular, surface defects of various dimensionality were investigated. Furthermore, acquisition of information on electronic properties is detailed. The presented material covers zero-dimensional (0D) point defects, one-dimensional (1D) line defects, and two-dimensional (2D) random networks, i.e., amorphous structures. First, we present spectroscopy data taken on thin MgO films grown on Ag(001). Distance- and bias-dependent nc-AFM and STM measurements were recorded on these films. The local work-function shift and electronic structure of color centers in the MgO surface were studied. In the next section, the structure determination of ultrathin alumina/NiAl(110) is shown. Atomically resolved nc-AFM reveals a detailed picture of various line defects in the film. Finally, we discuss the atomic structure of a recently discovered ultrathin vitreous silica film on Ru(0001). The atomic arrangement in the 2D random network, resembling the classical picture of Zachariasen, is analyzed in terms of the pair correlation function and ring-size distribution.

1 Introduction

Surface morphology, structure, physical, and chemical properties of bulk and epitaxial samples 1, 2 have been extensively studied by the use of scanning tunneling microscopy (STM) and atomic force microscopy (AFM) 3, 4. Special experimental implementations have been developed for low 5–8, ultralow 9, 10, and variable temperatures 11, 12. In addition, studies at high pressures 13, in liquids 14, at high speeds 15, 16, with high time resolution 17, and in magnetic fields 18 have been conducted. In the last few years, it has been demonstrated that noncontact atomic force microscopy (nc-AFM) can provide atomically resolved images comparable to STM 19–21, thereby, bridging to nanoscale science on insulating surfaces in general and oxide surfaces in particular 22. This article focuses on examples of the latter. Here, we use a setup where both methods, namely nc-AFM and STM, have been combined into one sensoring device, connecting the imaging and spectroscopy capabilities of these techniques.

Clearly, diffraction methods are still counted in the most powerful tools in the field of surface science. These technologies have led to the discovery of the majority of today's known surface structures. Their characterization had even been done before the STM and AFM were born. The era of atomistic structural analysis was ushered in by Max von Laue's invention of X-ray diffraction (XRD). Rapidly, scientists started to analyze crystalline and amorphous materials, i.e., glasses. The integrating nature of these techniques is leading to representative and coherent data, however, with an insensitivity to local effects and environments. This can be complemented by the use of modern local probe technologies, like STM and nc-AFM, providing locally resolved data in real space. The first steps for the analysis of amorphous materials by AFM and STM have been done in the groups of Wandelt and coworkers 23, Frischat and coworkers 24, and Güntherodt and coworkers 25.

Besides the great impact on many surface structures, diffraction patterns from large surface unit cells can be demanding to interpret. In the case of thin oxide films inconsistent structural models have been presented. A prominent example is the thin alumina film on NiAl(110), whose structure remained unclear for a long time. A comprehensive study by density functional theory (DFT) in combination with STM has finally proposed a suitable model 26.

For amorphous materials the structural analysis is hindered by the absence of sharp peaks in the diffraction pattern. The current understanding as well as the limits of XRD and neutron diffraction (ND) in the study of amorphous materials are reviewed by Wright 27. The basic picture for the atomic arrangement in silica and glasses in general goes back to the postulate from Zachariasen 28. This postulate has always been used as a starting point for the interpretation of XRD and ND measurements of glasses. Nevertheless, such 2D network structures have never been observed in real space before. Here, we show how modern surface science tools can clarify and complete the knowledge from diffraction methods.

Our work is focused on atomic-resolution imaging of oxide surfaces, giving access to their structural details including atomic positions, point and line defects as well as to their morphology within certain limits. Even the structure of amorphous materials is accessible with the presented instrumentation. The subject of our studies are ordered structures, defects and complex network structures in ultrathin oxide films on metal single crystals. The presented cases are magnesia/Ag(001), alumina/NiAl(110), and silica/Ru(0001) (see Fig. 1).

Figure 1.

Schematic of the analyzed sample systems: (a) magnesia/Ag(001), (b) alumina/NiAl(110) and (c) silica/Ru(0001). Different types of defects are present in these model systems ranging from 0D point defects to 2D random network structures, respectively.

2 Experiment

The employed instrumentation is optimized for high-resolution imaging in the nc-AFM and STM mode. The microscope setup (see Fig. 2) operates in ultrahigh vacuum (UHV) at cryogenic temperature (5 K). The most important advantage of operating at low temperatures is that it reduces damping of the force sensor and enhances the tip stability. But, also the reduction of thermal drift, piezocreep, piezohysteresis, and an overall significantly improved signal-to-noise ratio are important steps towards the achievement of high performance in microscopy measurements. Atomic-resolution imaging and stable spectroscopy of conducting and insulating surfaces are the main goals of this setup. The simultaneous recording of the tunneling current and frequency shift with the same microscopic tip allows for the local characterization of unique and complementary surface properties. Detailed investigation of surface structures and individual spectroscopy of specific surface sites, individual adatoms, and molecules can be performed only because of this high stability at cryogenic temperatures. The evaporation of various metals onto cold samples is implemented 29. Typical facilities for metal single crystal and oxide film preparation are part of this setup. In this study we make use of the knowledge from thin oxide film growth on metal single crystals used in the context of model catalysis. The application of thin films in comparison to bulk oxides has several advantages. The film systems can be grown in a reproducible manner under defined UHV conditions. Experimentalists can adjust the thickness and composition of these systems to their needs. But the most important one is the application of additional electron-sensitive surface science tools, thereby allowing for the simultaneous application of nc-AFM and STM. The experimental setup also houses a four-grid reverse view low electron energy diffraction (LEED) optics for the characterization of the surface structures as well as Auger electron spectroscopy (AES) of the sample systems. All measurements in this work were performed in UHV at 5 K. Further details on the experimental equipment can be found in Refs. 30–33.

Figure 2.

Schematic of the experimental setup. (a) The central design feature for providing mechanical vibration insulation for the microscope is the pendulum. It is evacuated, has a length of about 1 m and is suspended with steel bellows from the main UHV chamber. At its end the nc-AFM/STM head is mounted in an UHV environment. The pendulum is placed inside of an exchange gas canister filled with helium gas, which is surrounded by a liquid helium bath. The helium gas chamber prevents acoustic noise from perturbing the microscope, while permitting thermal coupling to the liquid cryogen (helium or sometimes nitrogen). The low-temperature ac amplifier is situated near the nc-AFM/STM head, while the room-temperature ac amplifier is mounted outside of the dewar. (b) Schematic of the microscope on its support stage: (A) Walker unit, (B) x-, y-piezo and (C) z-piezo of the tripod scanner unit, (D) dither piezo, (E) sensor carrier, (F) tuning fork assembly, (G) sample (not fully drawn), (H) sample holder (not fully drawn), (I) sample stage, (J) microscope stage, (K) Walker support, and (L) shear stack piezos. The support stage has a diameter of 100 mm.

The sensor in use is a quartz tuning fork, as presented in Ref. 32 with a cut Pt0.9Ir0.1 wire as a nc-AFM/STM tip (see Fig. 3). Tip preparation can be performed by field emission and/or dipping the tip into and pulling necks from the sample surface. This removes residual oxide contaminants, produces good tip configurations and has proven to be particularly useful with respect to the time-consuming handling of UHV and low temperatures. The tuning fork assembly and electronics are capable of simultaneous recording of the tunneling current IT and the frequency shift Δf while controlling the z-position of the tip via either of them 33. The tip-wire has a diameter of 250 µm and is electrically connected to the signal electronics through a thin Pt0.9Rh0.1 wire with a diameter of 50 µm. Both, tip and contact wire are electrically insulated from the tuning fork and its electrodes. The force signal is directly recorded via the tuning fork electrodes while the tunneling current is taken independently from the contact wire of the tip (Fig. 3). Excitation of the tuning fork along the tip axis is done with a separate slice of piezo (dither piezo) on top of the z-piezo actuator. The force-sensor parameters spring constant k = 22,000 N m−1, resonance frequency f0 = 17–22 kHz, quality factor Q = 8000–25,000 depend on the individual tuning forks. The oscillation amplitude Aosc has been set to values within the range 1–20 Å. The spring constant of the tuning fork sensor is significantly higher than typical spring constants of tip–sample interactions. This prevents a sudden “jump-to-contact” of the cantilever even at very small tip–sample distances and oscillation amplitudes. Also, the often observed instability and breakdown of oscillation amplitude after contact formation in the repulsive regime is reduced.

Figure 3.

Quartz tuning fork-based sensor device. (a) Photo and (b) a schematic of the sensor setup for nc-AFM and STM operation in UHV at low temperatures: dither piezo with connections P1, P2 for mechanical excitation in z-direction along the tip-axis. Quartz tuning fork on a ceramic carrier plate with a diameter of 15 mm. Electronically separated signal wires for force (T1, T2 contacts of the tuning fork) and current (µm wire) detection. The same tip senses both signals.

The great advantage of this setup is the simultaneous acquisition from frequency modulation (FM) force detection in combination with the tunneling current. This enables, for example, imaging of conducting, semiconducting as well as insulating sample systems via the nc-AFM signal and comparison to the IT signal. In general, it is interesting to measure the two signals as they may complement each other and the use of the same tip enables direct comparison. Pairs of curves from both channels recorded in a sweep in the z-direction and another one in bias voltage are possible (see Ref. 34). The sensor is operated by the sensor controller/FM-detector easyPLLplus from Nanosurf 35 in the self-exciting oscillation mode 36 at constant oscillation amplitude. The detected oscillation amplitude signal is fed into an automatic gain control circuit and is used to self-excite the quartz tuning fork mechanically by the dither piezoactuator. A phase shifter ensures that the spring system is excited at its resonance frequency. This operation mode of constant oscillation amplitude allows probing the regime of strong repulsive force in contrast to an operation mode at a constant excitation amplitude, where the oscillation amplitude decays as the vibrating tip penetrates the repulsive interaction regime 37. It furthermore readily facilitates theoretical analysis of the technique and results obtained with it. An additional custom-built analog FM detector has been used for the frequency-shift recording based on Ref. 38. The signal electronics has been described in Ref. 33. A unit by SPECS Zurich GmbH 39 has been used for the scan control and data acquisition.

A few general remarks concerning drift corrections in scanning probe microscopy (SPM) images should be made. LEED data or alternatively surface X-ray diffraction (SXRD) data are valuable references for SPM images. Sometimes, those images might be subject to linear drift or imperfect orthogonality of the x-, y-, and z-scan directions. Only if the analyzed images are corrected for or free of lateral drift and distortion, the nc-AFM or STM allow the determination of fractional coordinates of surface structures. If drift and distortion are very strong or detectably nonlinear, the acquired images may not be suitable for structural analysis at all. Prior to confirmation that drift, scanner distortion and tilt are removed from the individual images the unit cells have to be identified either directly by visual inspection or by self-correlation or Fourier analysis of the image. The latter methods imply periodicity and are of limited applicability for local and extended defects or disordered structures. Knowledge of the unit cells allows correction of distortion by comparison to LEED or SXRD data followed by application of appropriate matrix operations that stretch or skew the image in-plane without destroying the natural lateral relation between the points within the surface. Removal of noise by spectral spot selection in the 2D Fourier transformed image can be helpful but has to be treated with care in order not to lose information. This is of particular importance if not all atomic sites in larger unit cells are resolved. If every site is visible, Fourier analysis is not necessary.

3 Point defects in magnesia

Oxygen vacancies, also known as color centers, are electron-trapping point defects and are supposed to be involved in electron-transfer processes on the surface. Color centers are in the literature also referenced as F centers, originating from the German word “Farbe.” Depending on their charge state they are marked as F0, F+, or F2+, having two, one, or no electrons trapped. Such electrons in the color centers can be transferred to adsorbates such as Au atoms. The defect-free MgO surface is quite inert, while a defect-rich surface shows a high and complex chemical reactivity 40. In order to understand possible reaction pathways, a detailed characterization of color centers is highly desired. Information about their local position and thus coordination, electronic structure, local contact potential and possible adsorbate interaction are of fundamental interest (Fig. 4a). In the following, color centers on the MgO surface will be investigated in detail and they will be classified by their charge state.

Figure 4.

Magnesia thin films on Ag(111). (a) Schematic representation of the color centers in the MgO lattice at different terrace, step edges, kinks and corner sites. (b) Atomically resolved nc-AFM image of MgO on Ag(001) superimposed by a schematic illustration of the growth model: Mg atoms occupy hollow sites, i.e., they continue the Ag face-centered cubic lattice (a = 0.409 nm), O atoms occupy top sites. The MgO surface unit cell is indicated 32.

From calculations it has been proposed that color centers are directly involved in chemical reactions 41, 42, e.g., as adsorption sites due to more attractive defect–adsorbate interactions compared with the pristine MgO surface.

3.1 Pristine magnesia films

An nc-AFM image of the atomic arrangement of a perfect section of the MgO surface is shown in Fig. 4b. The film is two atomic layers thick, however, films with a thickness of two to eight layers show very similar images. It is interesting to note that one type of ion is imaged as a protrusion, while the other type of ion is imaged as a depression. This is a typical finding for ionic surfaces imaged by nc-AFM 43, 44. Since the density of electrons on the MgO surface is the highest above the oxygen atoms 45, the maxima in the nc-AFM image are thought to correspond to the positions of the oxygen atoms. Furthermore, electron paramagnetic resonance (EPR) spectra have shown that the preferred adsorption sites for Au atoms are on top of the oxygen ions on the terrace of the MgO surface 44. Assuming that the forces acting on such metal adatoms are comparable to those on the tip apex, one may conclude that there occurs a more attractive interaction between the oxygen sites and the tip. This results in a contrast where the oxygen ions are imaged as protrusions in a constant Δf nc-AFM image 32.

The preparation conditions of the MgO film on Ag(001) follow a route described in Ref. 46, where a stoichiometric composition was observed. This procedure has proven its applicability in many successful preparations. The Ag(001) was sputtered with Ar+ ions at a current density of 10 µA cm−2 and an acceleration voltage of 800 V for 15 min. Afterwards, the Ag(001) was annealed to 690 K for 30 min. The sputtering and annealing cycle was repeated several times. Mg was evaporated from a Knudsen cell in an oxygen atmosphere of 1 × 10−4 Pa at a substrate temperature of 560 K and a deposition rate of about 1 ml of MgO min−1. A certain amount of MgO can be grown onto the Ag(001) by linear extrapolation of a submonolayer coverage to the desired number of monolayers, assuming a constant sticking coefficient. This preparation method is only possible since the reaction kinetics of Ag with oxygen is very slow 47 compared with the reaction between Mg and O. Since the intrinsic defect density of the film is very small, color centers, such as F0, F+, and F2+, have been generated by operating the microscope in the STM mode at high currents IT = 6 nA and high voltages VS = 7 V or higher. Clean and well-grown MgO areas have been selected to ensure defined conditions. The defects are preferentially located at kinks and corners of step edges (for illustration see Fig. 4a). This means defect sites with a lower coordination number are preferred.

3.2 Color centers in magnesia

The high local resolution in the nc-AFM image shown in Fig. 4 is a prerequisite for structural studies. In the literature it has been debated how color centers are imaged by nc-AFM 43, 48 since a color center is a hole in the MgO lattice 40. The observed attraction of F0 centers originates from the charge density of the two trapped electrons, which are located in the center of the defect site. Due to the Coulomb repulsion, the trapped electrons repel each other and spill out of the defect site into vacuum 49, 50. Therefore, a considerably large charge density is situated above the surface. This charge density is supposed to interact with the tip, resulting in a strong attraction, as presented in Fig. 5. Since the doubly occupied F0 state is close to the Fermi level of the MgO/Ag(001) system 51, the charge density is also responsible for the strong peak in the tunneling current signal.

Figure 5.

Signal dependence on tip–defect distance. (a) Constant height line scans across an F0 defect situated at a step edge. The scan direction is along the step edge. The three presented channels have been measured simultaneously. The colors indicate different tip–sample distances. Note that the displacement of 4.5 Å has been chosen arbitrarily, since absolute values are generally unknown in scanning probe microscopy. (b) The oscillation amplitude is constant during the scan process. This excludes artifacts in frequency shift. (c) The tunneling current and (d) the frequency shift. Data were obtained at a sample voltage of VS = −50 mV 50.

Further insights into the interaction of tip and color center are gained by periodic supercell DFT calculations at the level of the generalized gradient approximation as implemented in the Vienna ab initio simulation package (VASP) code, which have been performed in the group of Pacchioni 52–54. The Pt0.9Ir0.1 tip has been modeled by a tetrahedral Pt4 cluster, whose geometry has been relaxed separately. The F0 color center has been created by removing an O atom from the top layer of a three layer MgO slab. The structure of the slab with the color center has been relaxed. The tip–surface interaction energy has been computed as a function of tip–sample distance of the apical Pt4 tip with respect to the top layer of the MgO slab. During these calculations the separately optimized tip structure was not allowed to relax. However, the relaxation of the MgO surface has been found to be very small for the calculated distances, where no direct contact is established. The outward relaxation of the O anion at 3.5 Å separation is about 0.12 Å.

The results of the experimental distance-dependent measurements and the corresponding theoretical results are also discussed in Ref. 50. At the defect site, the tip–sample interaction increases significantly with decreasing distance, mapping the defect as a protrusion (see also Fig. 6). From a structural point of view the positions of the defects are “holes,” i.e., missing oxygen atoms in the lattice. Defects as depressions as well as change of results with tip apex structure have been reported for NiO, CeO2, and TiO2 55–57.

Figure 6.

Spectroscopy on point defects. (a) nc-AFM image of 21 nm × 9 nm measured at a frequency shift of Δf = −1.6 Hz, an oscillation amplitude of Aosc = 0.34 nm and VS = −50 mV. Defects are indicated by circles. The position of the spectroscopy in (b) and (c) is indicated by red and blue. (b) STS on MgO. There are no states in the MgO-film (red), whereas electronic defect states (blue) at approximately 1 and −1 V exist. (c) Frequency shift versus sample voltage spectroscopy shows a quadratic dependence at the MgO film (red) and at the defects (blue). The maxima are at different sample voltages 58.

3.3 Assignment of color centers

In the first place, it is unknown which type of color center, F0, F+, or F2+, is imaged on the MgO surface. To gain further insight into the nature of the color centers we performed high-resolution Kelvin probe force microscopy (KPFM) measurements with single point-defect resolution (see Fig. 6). To acquire Δf versus VS curves on top of a defect, the Δf feedback was switched off. Subsequently, the frequency shift versus applied sample voltage was plotted and compared to equivalent reference measurements at the same height next to the defect. The parabolic behavior of the frequency-shift curves has been analyzed. The electrostatic force is always attractive, which is caused by the effect of mirror charges. This results in the parabolic dependence of the forces. The maximum of the parabola depends on the local effective contact potential ΔΦeff. It has been found that the MgO thin film shifts the Ag(001) work function and therewith the contact potential by about 1.1 eV. This MgO level is set as the reference for the defect levels and relative shifts refer to it. From measurements of numerous defects four different types were distinguished by their contact potential, which corresponds to the maximum position of the frequency shift versus sample voltage parabola. The results are collocated in Fig. 7. In the left-hand panel of Fig. 7a the four types are indicated by numbers and the MgO reference level is given (red bar). The graph b in the left-hand panel represents the measured contact potential with respect to the reference MgO level (bottom abscissa) and with respect to the Ag(001) level (top abscissa).

Figure 7.

MgO color center identification. (a) The left labeling assigns numbers to the defects. (b) The left graph shows the relative shift of the local (effective) contact potential with respect to the MgO surface (bottom abscissa) and with respect to the Ag(001) level (top abscissa). The covered range in the shifts results from measurements with different local resolutions due to different tip structures. The energy-level scheme presents the different energy levels of the defect types and their local contact potential shifts. (c) The central graph shows STS spectra of the respective defects. The maxima of the STS data have been highlighted. The covered abscissa range accounts for the statistics of the peak positions. (d) The assignment (AS) of defect types to color centers and negatively charged divacancies (DV) according to theory as well as their relative occurrence are given on the right-hand side 54.

For type I defects shifts of −50 to −25 meV below the MgO level were observed. These significant shifts can be explained by the presence of positively charged defects with respect to the surrounding area, resulting in a decrease of the local contact potentials. The charge-density distribution is significantly reduced at the positions of the defects compared with the surrounding MgO lattice. The presence of charges localized at defect sites induces a contact potential shift of the MgO/Ag(001) in analogy to the Helmholtz equation equation image 59. µ is the dipole moment induced by the localized charge at the site of the defect and the screening charge in the Ag(001) substrate and σ is the surface concentration. However, the full complexity is not covered by the Helmholtz equation and detailed calculations are still desired.

Defect type II shows a contact potential shift of ∼9 meV. This shift can be assigned to an F+. For an F+ the overall charge is positive, but on a very local scale the single electron has a probability above the surface, as derived by density functional theory calculations 49. The charge density spills out of the defect's site and has therefore a probability above the surface. The spill out of the negative charge changes the local dipole moment such that the local contact potential increases compared to the MgO/Ag(001) reference level. The electron charge is symmetrically distributed along the surface normal with its charge maximum located at the center of the defect.

Defect type III results in a shift of about 15–20 meV above the MgO level. The shift results from two charges present in a defect site and is thus attributed to an F0 color center. An F0 is neutral compared to the surrounding MgO lattice, but the two electrons have a large probability density above the surface due to Coulomb repulsion. The charges are as for type II symmetrically distributed and located in the center of the defect. Therefore, the charge does not belong to any Mg2+ site surrounding the defect. Thus, the oxidation state of the surrounding lattice is not affected by the trapped charges. The spill out of the charges results in a stronger dipole moment compared to defect type II and the measured shift is about twice as large as that for defect type II.

The strongest positive shift on the relative scale is that of type IV. The strong shift indicates that negative charges are involved. Therefore, this shift might result from divacancies (DVs) or OH groups trapped at low-coordinated Mg2+ sites. It is known that OH groups can trap electrons 60. However, OH groups and other adsorbates can be excluded since all defects occur only after high-voltage and high-current scanning and are not present on regular terraces and steps. With the above-mentioned scan parameters, adsorbates would be removed from the scan area. Furthermore, the defects occur only within the high current scan frame and not outside. Favored candidates are, therefore, DVs formed at step and corner sites since the formation energy at these sites is the lowest. The stability of DVs and their electron affinity have been confirmed by DFT calculations 61.

A DV is neutral compared with the surrounding MgO, since a complete Mg–O unit is missing. Due to the electron affinity of 0.6–1.0 eV, electrons can be trapped by the DV from the tunneling junction and the DV becomes negatively charged. The trapped electron of the DV is strongly localized at the Mg2+ site due to the attractive Coulomb interaction. Since the DV is negatively charged with respect to the surrounding MgO area, the additional dipole moment will increase the work function, resulting in the largest positive shift on the relative scale.

The covered ranges in the maximum positions originate from different tip structures, however, the reproducibility for two subsequent measurements with the same microscopic tip is within ±2 meV. All defect types analyzed show a characteristic “fingerprint” due to different charge states.

The measurements based on nc-AFM are supported by complementary STS. For all defects the local density of states (LDOS) has been detected. The tunneling spectra have been performed directly after the local contact potential measurements without moving the tip laterally, i.e., STS and KPFM have been performed with the same microscopic tip configuration at the same surface site. To prevent tip changes when doing STS at high voltages, the feedback on the tunneling current was switched on and dz/dVS was detected. The dz/dVS versus VS spectrum at constant tunneling current IT is closely related to the dIT/dVS versus VS spectrum at constant height z, see Ref. 62.

The tunneling spectra measured on the defects are compared with MgO spectra on the terrace next to the defect. The MgO reference spectra show no peaks within the voltage regime due to the band gap (compare red lines in Fig. 7). The spectra taken on the F2+ only show peaks in the unoccupied states at voltages of ∼1 V above the Fermi level (see Fig. 7). The F+ centers have both occupied and unoccupied electronic states within the bandgap. The electronic states are located within the bandgap of MgO. The occupied states are quite broadly distributed from −3.5 to −2.0 V below the Fermi level, depending on the defect location on the film 51. The empty states are at ∼1 V above the Fermi level. Considering the F0 color center, the doubly occupied state is higher in energy, approximately −1 V below the Fermi level, while the position of the unoccupied state is similar to F+ centers.

The negatively charged DVs only show a clear feature in the empty states at about 1 V. The corresponding occupied shallow state is expected to be very close to the Fermi level, i.e., in a region where the experiment cannot clearly detect states. However, F0 and DV are equally frequent and represent ∼85% of the total defects. F+ color centers are much less frequent and represent ∼10% and F2+ centers about 5%. These findings are in good agreement with the high formation energies of F2+ centers. By comparing the STS peak positions in Fig. 7, it becomes obvious that F2+ and DV defects are hardly distinguishable by their electronic structure but show a significant difference in the local contact potential due to the effect of a locally trapped charge on the surface dipole.

This demonstrates the great benefit of nc-AFM and KPFM in combination with STM and STS.

4 Line defects in alumina

Besides the aforementioned and thermodynamically inevitable point defects, materials comprise more involved deviations from the perfect crystalline arrangement. Various kinds of one-dimensional (1D) defects can occur in straight or curved lines throughout the material. Due to their particular character these defects are typically not allowed to end in the material unless they form closed loops or junctions with other defects. Therefore they are likely to affect surfaces. The simplest line defect at a surface is a step edge between adjacent terraces. Others are edge or screw dislocations or combinations of them. Emerging from the bulk or parallel to the surface plane they may intersect or perturb the surface to varying degrees. Dislocations are characterized by a line vector l lying tangential to the dislocation line and further by their Burgers vector b that measures a structural frustration in comparison to an unperturbed structure. The mutual angle of these two indicates edge (perpendicular) and screw (parallel) character of the defect. Dislocations create characteristic 0D defect structures upon intersection of the surface plane that has to be the starting point of a step edge if the dislocation is of screw type.

Defect identification and characterization proceeds from morphological information obtainable already at lower resolution to a full determination of structural parameters at atomic resolution. This includes the Burgers vector b. However, it is subject to the limitation that only the surface features are detectable of all 1D defects opening out into the surface, while the linear core structure is concealed from scanned probe methods 63–65.

It is conceivable that line defects of any kind can have pronounced effects on surface structure and morphology. This holds in particular for epitaxial layers like metal supported ultrathin oxides with their buried interfaces. Such boundaries may result in diverse translation, orientation and symmetry-related lattice-matching issues that lead to defect formation in many cases. In fact, the phase boundary can give rise to a special type of defect, called a misfit dislocation, which helps to accommodate lattice mismatches between film and substrate. Additionally, such epitaxy will in the general case produce domains due to different translation and/or point symmetry of the adjacent lattices. Domain boundaries separate these domains as planar defects and intersect the surface to the vacuum where probe microscopy shows them as line defects. Thus, while being technically planar defects, they result in a linear interruption of the perfect surface periodicity. Their treatment as line defects is further facilitated in the case of ultrathin films by their reduced extension normal to the surface. Here, the thickness of the film is of the order of a typical dislocation core diameter, i.e., few atomic distances. A system that exhibits several of the mentioned features is the ultrathin alumina film on NiAl(110).

4.1 Alumina film on NiAl(110)

The ultrathin aluminium oxide film on NiAl(110) – alumina/NiAl(110) – originated from studies in heterogeneous catalysis where it has been used as a model support for metal nanoparticles. Because NiAl is a highly ordered intermetallic, it offers ordered stoichiometric (110) surfaces for reliable film preparation. This, the thermodynamically preferred formation of aluminium oxide instead of nickel oxide, and a self-limiting growth allow a perfectly reproducible preparation of a highly ordered alumina film under UHV conditions. The film has been found to resemble γ-Al2O3 to some extent. But the STM- and DFT-based structural model as well as STM and nc-AFM data show a quasihexagonal structure with OS/AlS/Oi/Ali/NiAl(110) stacking, Al10O13 stoichiometry and only 5 Å thickness 26, 66, 67. As STM and nc-AFM played an important role in the determination of the film structure the system is a suitable and illustrative example for surface characterization by nc-AFM/STM.

In this well-studied case the domain boundaries in turn form junction lines with each other that leave 0D features in the surface plane as will be detailed below. For the associated misfit dislocations at the film–substrate interface this means formation of dislocation nodes as 0D features that mark the other end of the domain-boundary junction line. Only a selection of the defect types found in various (film) systems can be discussed on alumina/NiAl(110). Nevertheless, this example gives a good impression of the capabilities of force and current-related probe microscopy in the study of such defects.

The surface morphology of this film system is shown in Fig. 8. A step edge between two terraces in the alumina/NiAl(110) film is imaged subsequently by STM and nc-AFM. Evaluation of terrace size and step-height distributions, observation of step bunching, step orientation, and growth modes are the most obvious surface measurements available with these techniques. Step edges ending at screw dislocations are directly observable and step-height analysis may already give insight into surface and defect structure. For alumina/NiAl(110) the observed step heights are identical with integer multiples of the substrate step height (2 Å) and, furthermore, incompatible with the film thickness (5 Å). Here, the linear defect is obviously introduced by the substrate. However, when performing such measurements three main things – if z-calibration, e.g., via monoatomic steps of known height, is taken as a given – have to be assured for accurate height measurements: (i) correct leveling, (ii) absence of parabolic distortions along the line profile, and (iii) equal Δf(z) and IT(z) curves at equivalent points on either side of the step (bunch) chosen for height measurements. The latter prevents artifacts due to apparent height effects resulting from different electronic structures and interactions (e.g., LDOS, work function, interaction decay length) 68. Ideally, only terraces of identical surface termination should be compared for exact step-height determination. If this is taken into account the mentioned morphological measurements do typically require no detailed understanding of tip–sample interactions and contrast-formation mechanisms. Nevertheless, step edges between terraces with dissimilar surface termination can still provide information about the epitaxy. Steps from substrate to epilayer can directly reveal the lattice relation if unit-cell (atomic) resolution is obtained on both terraces 71. Furthermore, and on closed films or bulk samples, relative size, position, and orientation of the surface lattices reveal reconstructions, stacking sequences and degenerate surface structures with equivalent structures but different orientation. Studies on SrTiO3 (100) and alumina/Ni3Al(111) illustrate this 69, 70.

Figure 8.

Step edge within the ultrathin alumina on NiAl(110). (a) STM image: IT = 300 pA, VS = −1 V, scan range = 40 nm × 40 nm. (b) Subsequently recorded nc-AFM image of the same step edge (Δf = −50 Hz, Aosc = 1 Å, VS = −1 V, scan range = 40 nm × 40 nm). Its height of 2 Å matches the substrate step height and is incompatible with the film thickness of 5 Å 30. Line profiles were taken along the dashed trace in the respective image.

Other valuable information obtainable at this stage are coverage and thickness quantified by the number of monolayers. At coverage below one monolayer (ML) these microscopies are very useful tools for coverage calibration upon deposition from various physical and chemical deposition sources. If the problematic random sample character of local probes is compensated by numerous laterally distributed measurements nc-AFM/STM provide valuable coverage data on an area or even lattice or adsorption site basis (depending on the obtainable resolution) without knowledge of sticking coefficients, sensitivity factors or similar quantities. Above 1 ML the thickness may be determined as the number of monolayers covering the substrate as long as spots of bare substrate are accessible to the tip. MgO/Ag(001) provides a good example 71. Upon closing of the first layer(s), thickness measurements may be hampered by coverage changes across a terrace due to concealed substrate steps that can be considered subsurface line defects with respect to surface properties like, e.g., work function. Determination of the work function across terraces and step edges by Kelvin probe techniques may reveal varying film thicknesses for the first few monolayers coverage. While not applicable to alumina/NiAl(110) with its solely substrate-induced steps, the approach may provide insight for, e.g., the NaCl/Cu(111) and the MgO/Ag(001) systems 21, 54. Prerequisite for all measurements considered here are obviously surface structures that change much slower with time, e.g., by diffusion, adsorption, or desorption, than the imaging proceeds.

4.2 Atomic sites in the surface unit cell

While plenty of morphological and structural information can be obtained with nc-AFM/STM already at low resolution and with uncalibrated measurements, one prime goal is the determination of atomic-scale surface structures, especially in low-temperature studies. Prerequisites for any structure study are a system with no or correctable, i.e., linear drift, a scanner producing sufficient resolution and calibration of its x, y, z scan axes.

Most lateral structures required to be resolved, range between 1 and 5 Å while atomic corrugations may range from several to several tens of picometers, but subtle superimposed features as small as 2 pm might also contain valuable information. This is the case on various alumina surfaces and in the spin contrast on NiO 73–76. In the following we exemplify a surface structural analysis with the case of alumina/NiAl(110) and compare the result to an established STM/DFT structural model. The analysis is based on topographical, i.e., constant Δf(z) or IT(z), images and therefore applicable to nc-AFM as well as STM. Similarly, the analysis can be done for constant-height measurements in both techniques. Figure 9a shows the geometric orientation of the alumina and NiAl(110) lattice meshes against each other as obtained from LEED 66, 77. A slightly parallelogram-shaped oxide lattice (10.55 × 17.88 Å, α = 88.7°) resides on the lattice of 16 times smaller (4.08 × 2.89 Å) rectangular NiAl(110) unit cells. Due to the reduced symmetry with respect to the substrate the oxide lattice can assume two mirror orientations A and B. In each orientation, the b2 lattice vector of the oxide is rotated away from NiAl[equation image] by plus (or minus) 24°, respectively, leading to two rotationally misaligned mirror domains.

Figure 9.

Atomic-site lateral positions from nc-AFM (STM) image data. (a) Geometric relation between oxide and substrate unit cells (oxide: 10.55 × 17.88 Å, α = 88.7°; NiAl(110): 4.08 × 2.89 Å). (b) Multiple overlays of protrusions with crosses within a single frame. (c) Average positions of crosses. (d) Stack of sets of average positions from several different images. (e) Averaged positions for each site in (d). (f) Comparison of positions in (e) with corresponding data from the mirror domain 75.

After confirming that unit cells in the considered high-resolution images match the shape and dimension of the corresponding ones known from diffraction a determination of x, y fractional coordinates proceeds as follows. The first scheme is based on the visual inspection of the images as shown in Fig. 9. First of all the reading error is quantified. Each protrusion in the unit cell is marked and this is done several times independently for one image (Fig. 9b and c). Scatter between the marked positions for each protrusion gives the uncertainty. As tip artifacts and changing contrasts may alter the apparent surface structure it is of utmost importance to clearly identify individual protrusions. This can be facilitated by grouping images according to certain image contrasts and repeating the scatter analysis for unit cells in different images within or across contrast groups. Comparison of different images (Fig. 9d and e) is absolutely necessary and does not just mean rescanning of one frame, but data obtained with another microscopic tip and possibly on a different surface preparation. This helps to avoid tip artifacts in the final structure and enforces reproducibility. Positions marked for one particular protrusion in various images must not scatter far enough to overlap with those taken for another protrusion (Fig. 9e). Only this enables identification of protrusions. Further, one can double check against the equivalent result from a mirror or rotational domain (Fig. 9f) and also against images recorded with different orientations of fast and slow scan directions. That all helps to exclude tip and feedback loop control artifacts. To take full advantage of the acquired data the drift correction may be followed by a mesh-averaging step, that is an averaging over equivalent pixels from all unit cells (unit meshes) within an image. This will reduce random noise. Note that so far protrusions not atomic sites have been discussed. How far the identified protrusions are identical with atomic or ionic sites in the basis of the unit cell has to be clarified. A part of this problem has been shown in the previous section for the Mg and O sublattices in MgO/Ag(001). Distinction may be possible by repetition of the above analysis for different image contrasts (possibly showing different species due to altered tip configurations and tip–sample interactions), consultation of external information such as from adsorption experiments or possibly straightforwardly from coordination in images obtained with different contrast or imaging parameters 26, 78. Interestingly, this should be easier in more complex structures like alumina/NiAl(110) than for the two MgO rocksalt sublattices of identical symmetry. Comparison of protrusion sites to a high-quality theoretical model may directly answer this question of chemical identity. In nc-AFM Δf(z) curves (z-spectroscopy) can provide chemical information if sites are compared that are visible and equivalent otherwise 79. For alumina/NiAl(110) an analysis of STM images combined with DFT calculations produced the currently accepted structural model of the unit cell 26. The model's surface structure in turn has been confirmed in detail by subsequent nc-AFM studies 75, 80. The second structure analysis scheme takes advantage of correlation averaging and is basically an automatized version of the first. A series of images, selected along the line of considerations described above, is stacked with aligned unit cells and subsequently averaged pixel by pixel. This method may also include mesh averaging and is typically used to remove random noise from images, but can also serve the purpose of structural analysis. These methods are applicable to images of lower resolution or higher noise level, respectively, as well as to high-resolution data if, e.g., strained surface areas are to be detected.

Analysis of in-plane strain components of a surface structure is possible if images are per se free of drift and distortion, or if a known structure is contained within the image for x, y-calibration. The latter could be a substrate of known lattice dimensions or an unstrained surface area. As in LEED studies 84 comparison is drawn to a reference/equilibrium structure of this material like a bulk crystal plane or epitaxial layers on different substrates either based on unit-cell dimensions or on atomic spacings.

A more specialized structure determination method for STM and nc-AFM shall be mentioned at this point: the assembly of molecular adsorbate layer structures from scratch, molecule by molecule, as has been shown for CO on Cu(211) 72. This helped to resolve ambiguities in the assignment of protrusions in images to either atomic sites or hollow sites between them. The latter issue has to be considered in coverage and structure analysis of dense and ordered adsorbate structures such as chains, compact islands, and fully covered terraces.

Once lateral positions of protrusions have been determined one can proceed to characterize the topography of the structure. Here, low noise is essential and only the best images should be considered. Results of such an analysis are shown in Fig. 10 for important structural elements in the alumina unit cell. In agreement with the theoretical model the two rectangular blocks of eight OS sites differ not just in their orientation within the unit cell, but also in their respective corrugation, relative height and even slightly in length. It should be mentioned here that topographic nc-AFM data give rather relative changes in z between sites (zEXP) than absolute distance to the substrate, as given in the DFT model (zDFT). The two structural elements of the unit cell align in the lattice to form rows along the oxides b1 directions that alternate along b2 to produce a wave-like topography. Each wave crest contains one type of orientation of the block of 8 OS sites, one oriented nearly parallel to NiAl[001] and the other at a larger angle to it 67, 75, 81. It is important to note that topographical analysis of SPM images at the atomic scale is a problematic task. Tip convolution 82 and electronic-structure effects, well known to hamper separation of geometric from electronic structure in STM images, play a similar role in nc-AFM images where different sites can be expected to interact differently due to different chemical nature 79 or due to structural (topography) effects, i.e., by different coordination of the tip by sample atoms. Depressions may lead to or contain protrusions at the position of their center. Simultaneous interaction with all sites along the circumference results in an increased interaction as compared to sites within the circumference or the surrounding flat surface. In addition, changing microscopic tip structures can produce a puzzling number of substantially different image contrasts 83. Convolution, i.e., “double/multiple-tip” effects at the atomic scale can effectively prevent resolution of all individual sites of the surface structure. In many cases, especially on ionic surfaces, but also for other materials, image contrasts also have been found to selectively show only one or a group of similar species (oxygen anions, metal cations) 26, 75, 78. The conclusion that certain nc-AFM images of alumina/NiAl(110) provide information about the surface topography is based on a resemblance of the contrast to a hard-sphere imaging mechanism and the good agreement with the DFT model.

Figure 10.

Comparison of experimental lateral and topographic data of alumina/NiAl(110) with the DFT structural model 26, 75, 80. (a) DFT model versus nc-AFM-derived lateral positions for both mirror domains. (b) Atomic-resolution nc-AFM image of a B domain of alumina/NiAl(110) (Δf = −2.75 Hz, Aosc = 3.8 Å, VS = −220 mV, scan range = 4.2 nm × 4.2 nm). The image is superimposed with Al and O positions from the DFT model for direct comparison 26. Green rectangles indicate the prominent structural building blocks of eight oxygen sites with their characteristic topography. (c) Line profiles across each row of four within the two inequivalent blocks of eight oxygen sites. The crosses give DFT height and position along a row of four 26 and are aligned with the respective first maximum on the left. Profiles and positions in the left diagram correspond to the block almost aligned with NiAl[001]. The diagram on the right hand side refers to the block of eight at a larger angle to NiAl[001]. The substrate axis is indicated by an arrow in the top right corner of (b).

4.3 Atomic arrangement in defect networks

Knowledge of the film structure and its epitaxy allows characterization of defects within this structure. In the case of alumina/NiAl(110) already early studies tried to gain structural information on the defect network. Most notable are the spot profile analysis-low energy electron diffraction (SPA-LEED) and STM results 67, 68, 77, 85. The film is commensurate only along [equation image] (row matching) and incommensurate along [001] as determined by (SPA-)LEED and SXRD 77, 86. This partially pseudomorphic epitaxy and the dimensions and symmetry of the unit cells make domain boundaries almost inevitable in alumina/NiAl(110). In fact, they are characteristic features of this film system (compare with Fig. 11) and affect its surface properties, e.g., nucleation of metal particles, significantly 87. Growth of the alumina film on vicinals to the (110) surface can suppress one of the mirror domains and therefore the associated reflection domain boundaries 88, 89. Likewise, strain-related boundaries can be suppressed by growth on other transition-metal aluminide substrates, while other types, like, e.g., rotation domain boundaries, may be introduced 90–92.

Figure 11.

Overview of the domain-boundary network within ultrathin alumina/NiAl(110). Roman numbers denote APDB types, while A,B indicate the respective mirror domain. Steps or step-cascades are lateral displacements in the path of type I APDBs. RDB denotes reflection domain boundaries. (a) STM image: IT = 400 pA, VS = 3.5 V, scan range = 100 nm × 100 nm. (b) nc-AFM image of a B domain of the alumina film containing two APDBs (Δf = −3.0 Hz, Aosc = 3.8 Å, VS = 1 mV, scan range = 15 nm × 11 nm). One “zigzagged” APDB II exhibiting structural units with different path orientation as well as an APDB I comprising straight and stepped segments. Red circles and green rectangles in dark (light) color mark OS sites and structural elements within the unit cell (at the APDBs).

The STM overview as well as the nc-AFM image of higher resolution in Fig. 11 show examples of the domain-boundary network in alumina/NiAl(110) and underline the 1D character the defects gain in nc-AFM/STM measurements. Basically, the images reproduce their traces in the surface. It is obvious that different kinds of defects exist and that their appearance varies between the techniques and with imaging parameters. While some boundary paths are rather irregular, curved, and broad, others are regular, straight, and narrow. Some orientations and junction arrangements predominate and it becomes clear that they are subject to the mirror relation between domains A and B. This led to the designation of various boundary types that belong to the following groups: reflection domain boundaries (RDBs) between two mirror domains (A,B), nucleation-related translation domain boundaries (TDBs) between domains of equal orientation A or B but positioned on equivalent substrate sites incompatible with the respective other oxide lattice, and last but not least antiphase domain boundaries (APDBs). These are introduced to the oxide structure only after crystallization to facilitate strain relief towards the substrate 95. As they separate the film into nearly equidistant (∼9 nm) stripes of high aspect ratio and dominate the defect network with their highly ordered and frequent appearance 77, 87 an analysis of the 1D defects produced at their surface traces is prioritized in the following.

Explaining APDBs structures and their junctions: According to their appearance in STM and their orientation within the respective oxide domain four types of APDBs have been described. They are labeled A I, B I, A II, B II, A III, B III, A IV, B IV. The Roman letters can be omitted, if the mirror operation is considered, as structures in both reflection domains are interchangeable. A study of such defects is most conveniently done if large-scale as well as atomic scale information can be obtained. The wave-like stripes visible in nc-AFM images and certain STM images along b1 already prior to unit-cell resolution allow assessment of the boundary paths 67, 81. APDB type I runs strictly parallel to the b1 oxide lattice axis and is only interrupted by stepwise lateral shifts of the boundary path. Shifts only occur by one or multiple unit-cell lengths and most often along the longer diagonal of the unit cell. Type II runs roughly along the longer unit-cell diagonal, while type III connects junctions between type I and II in short (several nm), straight segments at small angles (∼15°) off b2. Type IV in turn runs at a rather defined angle of 39° against b1 across entire oxide patches and even intersects type I APDBs. Images showing unit-cell or even structural-element resolution like the nc-AFM image in Fig. 11b allow assessment of Burgers vector lengths and orientations. Atomic-resolution images like the ones shown in Fig. 12 reveal that the boundaries only affect certain structural elements within the unit cell. This results in a small number of well-defined recurring structures for each boundary type and explains to a large extent the rather regular appearance of the defect network. For APDB I a linear splitting of the unit cell parallel to b1 at the 8 OS block nearly aligned with NiAl[001] is found, as well as structures for steps and step cascades that account for lateral displacements of the boundary path. The straight segment is the most prominent and the only defect a DFT model has been derived for from the unit cell 93. All other models shown in Fig. 12 have been generated manually by positioning structures with the DFT fractional coordinates on the adjacent pristine oxide areas followed by insertion of additional sites at the boundaries. For APDB types II and III several structural building blocks are known, each of which enables another inclination of the boundary path against b2 (Fig. 12). While this results in a rather organic boundary path for APDB II with slightly changing directions APDB type III mainly occurs in short straight segments. All three (I–III) produce displacements of the adjacent lattices by 3 Å, but in different directions (±24° and ±36° off NiAl[equation image] and nearly parallel to [001] in the case of type III). The shifts are equivalent to one inserted site in each atom row of the quasihexagonal OS sublattice.

Figure 12.

Structural units enabling the local structures and global boundary paths of APDBs labeled by their boundary type. Red (blue) circles and green rectangles mark OS (AlS) sites and structural elements according to Ref. 26, lighter colors indicate deviations and added sites at the boundary. Yellow arrows show the Burgers vectors of the respective APDBs. APDB B I: basic structure for straight boundary path along b1, lateral step displacement (short diagonal), step cascade (long diagonal). APDB B II: path along b2, along long unit-cell diagonal, along diagonal of two sideways connected unit cells. Topographic depressions resembling footprints. APDB A III: path along b2, along long diagonal. APDB B IV: Unit based on displaced blocks of 4 OS, based on parallel blocks of 8 OS sites. See Refs. 67, 80, 93, 94 for details.

The particular lengths and directions of bI, bII, and bIII gain importance at the triple junction between the associated APDBs. The junction lines are oriented normal to the film surface and the intersection of a junction with the film surface is shown in Fig. 13. According to Frank's node rule the resulting junction line at the equilateral triangle of OS sites (marked by yellow arrows) does not have dislocation character itself. At such a junction no strain is built up, explaining why the surface is left unperturbed and flat at their sites.

Figure 13.

Junction between three APDBs of types I, II and III in an A domain of alumina/NiAl(110) (Δf = −2.5 Hz, Aosc = 3.8 Å, VS = −100 mV, scan range = 4.7 nm × 4.7 nm) 94. (a) Indication of the junction composition. (b) Same image with superimposed structural model and Burgers vectors. (c) Enlarged view of the marked area in (b). The junction line is encircled by a closed Burgers vector loop.

Comparison of the APDB Burgers vectors with the commensurate NiAl[equation image] lattice direction leads to the conclusion that components of bI, bII along NiAl[equation image] provide strain relief against the substrate, while bIII along [001] does not. This explains why type III plays only a minor role in terms of total boundary length. Type IV, on the other hand, produces an extraordinarily large displacement along b2, possibly too large for a simple misfit dislocation at the film/substrate interface. It is therefore considered that this type could be a particularly favorable and ordered type of TDB between two separate oxide patches originating from the oxide precursor during crystallization of the film.

The alumina film exhibits a complex boundary topography. Film topography is left rather flat by all boundary types. They have been shown to be shallow depressions (∼10 pm) despite a rather contradictory picture in large-scale nc-AFM and STM images. Certain imaging parameters in STM, see, e.g., Figs. 11 and 14, produce substantial elevations at most of the defect network while other parameters let the network disappear altogether. Also nc-AFM studies have assigned different topographies to the defect network. The first high-resolution nc-AFM study on this film system saw both protruding and sunken domain boundaries 81. This could be due to the doped silicon tip material of the microcantilevers used therein. With Pt/Ir tips that produce the topographic contrast detailed earlier in this text all boundaries have only been observed as shallow depressions. However, subtle changes in topography have been observed along individual boundaries. Laterally identical structures show unexpected 180° rotations of their topographic features 80. Examples are the step within an APDB I where the topography of the 6 OS structural element at the boundary changes in accordance with the twofold symmetry of the alumina structure. Similarly, structural building blocks in APDB II exhibit footprint-like topopgraphies which may occur either in sequence or rotated by 180°, at identical lateral order, see the second image in the top row and the first in the third row of Fig. 12. Whether this is a response to local strain in the rumpling of the OS layer or related to the film/substrate interface is under discussion. In the latter case it might allow gauging of the local registry, valuable information when it comes to studies on single adsorbates on alumina/NiAl(110) 96, 97.

4.4 Complex domain boundary network

Figure 14 summarizes the APDB network. Figure 14a shows one frequent network motif – entire oxide patches or even terraces sectioned into stripes of high aspect ratio by APDB types I and II – while Fig. 14b provides views of the observable boundary path orientations for the four APDB types and their junctions. The second common network motif, the mesh pattern, composed of a selection of more or less regular meshes in the shape of parallelograms of various angles and aspect ratios with truncated corners at the long diagonal is shown in Fig. 14c. Figure 14d illustrates a model for its formation via interaction between sets of misfit dislocations underlying type I and II APDBs. Subsequent dissociation of the fourfold nodes into two threefold nodes produces segments of a third dislocation type that underlies type III APDBs. The associated APDBs I–III allow this dislocation phenomenon to appear at the surface.

Figure 14.

Compilation of the alumina boundary types and a conceptual model APDB network formation. (a) NiAl(110) terraces covered with oxide areas with different mirror orientation (A,B marked by red and blue color). Different boundary types are labeled (IT = 150 pA, VS = 3.5 V, scan range = 80 nm × 107 nm). (b) Schematic showing the predominant orientation of different boundary types with respect to the oxide mirror domain lattices. (c) The mesh pattern, a network of APDBs I–III within a B domain (IT = 100 pA, VS = 5 V, scan range = 53 nm × 66 nm). (d) Sketch of a possible dislocation reaction mechanism underlying the creation of an APDB mesh pattern 94.

Here, a discussion of nucleation and symmetry-related boundaries is started. Reflection domain boundaries (RDBs) between mirror domains A, B, and nucleation-induced translation domain boundaries (TDBs) occur naturally within the film. This is due to the reduced point and translation symmetry of the large and slightly parallelogram-shaped oxide cell as compared to the small rectangular NiAl(110) unit cell. Figure 15 shows a triple junction (J1) between three individuals of these two boundary types together with a junction (J2) of a RDB with an APDB I. While the displacement at the TDB is evaluated directly by determining the separation between equivalent points in the adjacent lattices, RDBs are more illusive. The mirror relation between the lattices and the ill-defined positions of lattice origins and the mirror line seem to prevent assignment of mutual displacements. However, an unexpected feature of the film epitaxy partly resolves the issue: the presence of a coincidence site lattice (CSL), i.e., a set of lattice points common to the lattices of both mirror domains upon superposition. This superposition (without their respective basis) is called a dichromatic pattern, as one can arbitrarily assign a color to each of the two superimposed lattices. The CSL points have translation symmetry and their fraction with respect to the oxide lattice is given by the area ratio Σ of the CSL and oxide unit cells. Here, the CSL unit cell is rectangular, measures 46 × 78 Å with Σ = 19. The problem of translation is reduced to displacements within the CSL unit cell. Unfortunately, the latter is not fixed in space, but shifts in relation to lateral displacements of one of the adjacent oxide domains. In addition, such displacements may equal or entirely differ from the initiating displacement in magnitude and direction and may change the entire dichromatic pattern. This property of mutual oxide lattice translations is captured by another lattice of points that represents displacements that are symmetry conserving (DSC lattice). For the case of alumina/NiAl(110) this is the fine-meshed gray lattice within the CSL unit cell in Fig. 16. It must not be confused with the NiAl(110) unit cells. While its units have the same length they are significantly narrower (see Fig. 16) than the NiAl(110) surface cell. Translations between RDB domains that represent a DSC lattice translation conserve not only the CSL, but also the entire dichromatic complex that denotes the superposition of oxide lattices already decorated with their respective basis. However, the CSL and dichromatic complex get shifted laterally by varying amounts depending on the DSC translation. All translations other than DSC lattice translations change the dichromatic complex. Crystal boundaries with low Σ, such as the Σ = 5 boundaries in cubic structures of MgO and semiconductors or the Σ = 3n boundaries in certain metals, are frequently discussed as “special boundaries” as their preferential lattice matching often coincides with favorable properties, like good transport properties, low boundary energy and others. However, low Σ CSLs are not sufficient to conclude special boundary properties as several authors have pointed out 99, 100. This is in line with the findings for alumina/NiAl(110): the existing CSL, despite being formally of low Σ, is very large especially when compared to the atomic spacings governing the oxide basis. RDBs along low-index lines through the CSL (special boundaries) are therefore possible, but not probable. Accordingly, no periodicity within RDB planes has been observed. Boundary features like step displacements of the boundary path, which typically indicate dislocations on the DSC lattice along a RDB have not been found so far and no displacements at APDBs represents a DSC translation. The implications of the CSL for the film structure seem to be limited, at least for the rather fine-grained domain-boundary structure studied here. Domain coarsening and straightening of boundary paths at elevated temperatures and over longer heating periods may change this picture.

Figure 15.

Translation and mirror-symmetry-related boundaries 94. (a) Composite image of RDB segments within alumina/NiAl(110), a TDB, an APDB I as well as their junctions J1 and J2 separating the domains 1, 1′, 2 and 3 (Δf = −1.7 Hz, Aosc = 3.8 Å, VS = −250 mV, scan range = 15 nm × 8.7 nm). The arrow indicates the displacement between B domains 1 and 2. Dashed angles indicate inclinations of the RDB boundary path towards the b2 lattice axis of domain 1. (b) The figure shows the image superimposed with a structural model. The CSL cell from Fig. 16 is indicated. OS sites in red, black and purple distinguish oxide domains separated by RDBs and TDB.

Figure 16.

Translations across RDBs. (a) Overlay of lattices with basis for both alumina/NiAl(110) mirror domains (dichromatic complex). The coincidence site lattice cell as well as the related DSC lattice are indicated. Blue encircled positions mark a (near) coincidence of inequivalent sites from the red and black basis. (b) Alumina/NiAl(110) CSL and DSC and enlarged sections for direct comparison with the Burgers vectors of APDBs and a TDB 94.

In conclusion, the use of a CSL description in the case of alumina/NiAl(110) provides a reasonable starting point for a consistent treatment of both mirror domains (A,B) in relation to each other. Furthermore, it enables an analysis of the various oxide translation domain boundaries in terms of translation and symmetry properties of the dichromatic complex of the alumina mirror domains.

4.5 Spectroscopy across extended line defects

As for point defects in MgO on Ag(001) the line defects in the alumina on NiAl(110) surface have been characterized with respect to their electronic properties 98. STS measurements show defect states within the bandgap of the film 101. Together with DFT calculations they could be assigned to an oxygen-deficient defect center located at the scission within each unit cell along the straight segments of APDB I 93. The location can be identified in the nc-AFM topography images as a large oxygen quadrangle. From the STS/DFT results it has been concluded that charge is transferred to the NiAl(110) substrate, leading to a F2+-like center. The resulting band bending is observable in Kelvin probe measurements with nc-AFM 98. Figure 17 shows the resulting work function shifts detected at points along a line across two parallel straight segments of APDB I. The figure further illustrates the determination of ΔΦ from electrostatic force parabola, an implementation of the Kelvin probe method. A notable deviation between the measured 20 meV and the theoretically predicted 1 eV is rationalized by averaging over adjacent areas by the long-range interaction and the comparably bulky mesoscopic tip shape. With defect states at equal energies 101 and similar oxygen deficiency the description of the defects within other APDBs is supposed to proceed correspondingly.

Figure 17.

Spectroscopy at line defects. (a) STM image of two type I APDBs (IT = 100 pA, VS = 3 V, scan range = 18 nm × 11 nm). Contact potential measurements have been performed point-wise along the dotted line. Electrostatic force parabola recorded at the red and blue crosses are shown in (b). The shift in their maxima indicates the contact potential difference and amounts to 20 mV. (c) Contact potential differences between sites along the line in (a) and recorded with the Kelvin probe measurements shown in (b). The flat topography channel confirms the absence of crosstalk to the CPD measurement 98.

From the first LEED and SPA-LEED studies over STM and DFT proposals, a final verification for the alumina film structure on NiAl(110) by nc-AFM has been shown. In this article we have verified how nc-AFM can provide clear structural assignments for surface units cells and even domain-boundary networks. The analysis of these complex surface structures has already given hope for also understanding sample systems where periodicity and symmetry is completely missing and where only short-range order due to chemical bonds is present, e.g., amorphous materials.

5 Atomic structure of a thin vitreous silica film

This section focuses on the atomic arrangement in the vitreous silica bilayer on Ru(0001). As already introduced in the beginning, most of the surface structures and reconstructions were known before the rise of AFM and STM. The strength of these techniques lies in the high local resolution in real space, enabling the investigation of single adsorbates, molecules, and defects on the surface. But is it possible to resolve the local atomic structure of an amorphous system? The application of scanning probe techniques to cleaved glass surfaces 23, 24, 102–104 and to glassy metals 25 has been shown. However, a detailed and unambiguous atomistic assignment of the observed structures was not possible due to rough surfaces and large corrugations. Therefore, to investigate the atomic structure of amorphous materials by nc-AFM or STM, an atomically flat glass is required.

Silica is the prototype glass network former and the basis of many glasses. As it is one of the most abundant materials on earth, it is relevant in various branches of modern technologies, e.g., in semiconductor devices, optical fibers and as a support in industrial catalysis.

In a recent publication, we presented an atomically resolved STM image of a bilayer of vitreous silica that was prepared on a Ru(0001) support 105. The film exhibited a complex ring network with a log-normal ring-size distribution 106. Shortly after, a similar film was observed on graphene by scanning transmission electron microscopy (STEM) 107. These findings prove the existence of a new class of materials: two-dimensional (2D) glasses. Furthermore, random molecular ring networks have been reported 108, 109.

Herein, we present a detailed analysis of the atomic structure of the silica film exhibiting a vitreous phase. First, we discuss atomically resolved nc-AFM images and the procedure to determine the atomic model of the film. Afterwards, following Wright's classification of the structural order in amorphous network solids 27, 110, the order of range I–IV will be evaluated.

5.1 Assignment of atomic positions

Before we discuss the atomic structure of the vitreous silica bilayer, it is useful to look at the postulates made by Zachariasen 28. At that time, there was a large debate about whether glasses are built up from crystalline material 111. Zachariasen attempted to rule out the crystallite hypothesis. First, he assumed that the bonding forces between the atoms in a glass and in a crystal should be essentially identical, because both have comparable mechanical properties. According to Zachariasen, the main feature that distinguishes a glass from a crystal is the lack of periodicity and symmetry. Furthermore, to sketch an atomic picture of a glass, Zachariasen used the predictions made by Goldschmidt, who suggested that tetrahedral atomic configurations are required to form glasses 112. Because it was difficult to draw a three-dimensional (3D) picture, Zachariasen made use of a two-dimensional (2D) analogy. Figure 18d depicts Zachariasen's scheme of the atomic arrangement in a glass. The black dots represent the cations (A) and the white circles depict the O atoms. The glass structure lacks periodicity and long range order. This is due to the large variety of A–O–A angles that bridge two neighboring building units. The angular diversity leads to a structure consisting of differently sized rings. Figure 18d became the most widespread picture to illustrate the atomic structure of a glass. Furthermore, Zachariasen's postulates were very useful in explaining diffraction experiments on glasses 113. Zachariasen's scheme of the atomic arrangement in a glass was later termed a “continuous random network.”

Figure 18.

Assignment of atomic positions. (a) Atomically resolved constant height nc-AFM image (VS = 100 mV, Aosc = 2.7 Å, scan range = 5.0 nm × 5.0 nm). (b) Image from (a), partly overlayed with O model (red balls). (c) Image from (a), overlayed with the complete model of the topmost Si (green balls) and O atoms. (d) Zachariasen's picture of the atomic arrangement in a glass 28. (e) Schematic showing the geometrical construction of the circumscribed circle. (f) An oblique view on two connected rings in the vitreous bilayer.

Figure 18a shows an atomically resolved constant height nc-AFM image of the vitreous silica film (scan size = 5.0 nm × 5.0 nm). The image reveals the complex atomic arrangement of this 2D network being very similar to Zachariasen's scheme.

We observed protrusions at atomic separations arranged in triangles. Based on this triangular symmetry and by comparing to Zachariasen's model we assigned the protrusions to one face of a tetrahedral SiO4 building block. Consequently, the protrusions are triangles of three O atoms (red balls in Fig. 18b). Sensitivity to the Si positions would result in a different local structure. Based on the O coordinates, we determined the position of the Si atoms by calculating a circumscribed circle around every O triangle. The geometrical construction of the circumscribed circle is schematically explained in Fig. 18e. By this method, a point is found that has the same distance to the triangle's corners. By placing a green ball corresponding to a Si atom in the center of each resulting circle, we completed the 2D model of the topmost O and Si atoms.

In Fig. 18c, the nc-AFM image is completely covered by the structural model. The film shows rings of different size and did not exhibit any crystalline order. All atoms are arranged in SiO3 triangles. No under- or overcoordinated species were observed. In 3D, this structure corresponds to a network of corner-sharing SiO4 tetrahedra. While the film is vitreous in the xy-plane (substrate plane), it is highly ordered in the z-direction. This is visualized in Fig. 18f showing an oblique view on a silica bilayer cluster consisting of two differently sized rings (one 9-ring and one 5-ring). The SiO4 tetrahedra of the first layer are linked via bridging O atoms to the SiO4 units of the second layer with a Si–O–Si angle of 180°. The linking O atoms represent a mirror plane. This particular structural element leads to a flat and 2D film. In other words, the film structure consists of four-membered rings standing upright and connected randomly, forming the 2D ring network.

The vitreous structure of the thin silica film is consistent with a weak coupling to the metal support. As the underlying metal is crystalline, the film's registry to the substrate is lost. Thus, the film is structurally decoupled from the metal support.

The atomically resolved nc-AFM image and the derived model of the topmost layer are the starting point for further evaluation of the thin film's structure. Note that we only use the topmost O and Si positions derived from the nc-AFM image for the statistical evaluation presented here. To compensate for the lack of information in the third dimension, we took the height difference between the topmost Si and O atoms from the density functional theory (DFT) model for the crystalline silica bilayer (52 pm) 114. In Ref. 115 we have proven that this assumption is valid.

In the following part of this section, the atomic structure of the vitreous silica bilayer is discussed. Here, we follow the classification introduced by Wright who divided the order in network solids in four ranges: (I) structural unit, (II) interconnection of adjacent structural units, (III) network topology, and (IV) longer range density fluctuations 27, 110.

5.2 Range I: The structural unit

In this section, the internal structure of the tetrahedral unit is analyzed (for a schematic of a tetrahedron, see inset of Fig. 19e). A tetrahedron is primarily defined by the tetrahedral angle, which is the angle between the center and two corners, as well as the side length. Another characteristic parameter is the distance from the center to one corner. Therefore, we will evaluate the Si–O and the O–O distance, as well as the O–Si–O angle.

Figure 19.

Characterization of range I order in the vitreous silica film. (a) Image from Fig. 18a, overlayed with colored bars representing the Si–O nearest-neighbor (NN) distance (see scale bar). (b) A histogram of the Si–O NN distances. Average values from diffraction experiments on bulk vitreous silica are indicated by black arrows 116, 117. (c) Image from Fig. 18a, superimposed by colored bars representing the O–O NN distance (see scale bar). (d) A histogram of the O–O NN distances. Results from diffraction experiments on bulk vitreous silica are indicated by black arrows 116, 117. (e) Histogram of the O–Si–O angles. The black arrow indicates the angle inside a regular tetrahedron (109.47°).

Figure 19a shows the model from Fig. 18a with colored bars connecting all Si–O nearest neighbors (NNs). The color scale represents the Si–O bond length (see scale bar).

Figure 19b displays a histogram of the Si–O distances. A Gaussian was fitted to the data and yielded an Si–O mean distance of 0.16 nm with a standard deviation of 0.01 nm. This is in good agreement to X-ray diffraction (XRD) 116 and neutron diffraction (ND) 117 data that were obtained on bulk vitreous silica (black arrows in Fig. 19b).

The O–O NN distances are visualized in Fig. 19c. It becomes clear that O–O distances are equally distributed throughout the whole image. A histogram of the O–O NN distance is shown in Fig. 19d. By fitting the data with a Gaussian we obtained a mean O–O NN distance of 0.26 ± 0.03 nm. As the black arrows indicate, our experimental value agrees well with XRD and ND measurements on bulk vitreous silica 116, 117.

In addition, we computed all O–Si–O angles in the atomic model (see histogram in Fig. 19e). The intratetrahedral angle showed a symmetric distribution with an average of 107° and a standard deviation of 17°. This value agrees well with the 109.47° angle in a regular tetrahedron and the 109.8° angle deduced from XRD experiments on bulk vitreous silica 116.

Hence, the range I order in the thin vitreous silica film reproduces the structural parameters derived from diffraction measurements on bulk vitreous silica. However, range I order is not characteristic of the vitreous nature, as it consists of well-defined building blocks (SiO4 tetrahedra). Characteristic features of the vitreous structure can be found in the longer ranges.

5.3 Range II: Connection of structural units

Range II is characterized by the connection of neighboring tetrahedral building blocks (see Fig. 20c for a schematic). This connection can be evaluated by looking at the distance between the tetrahedral centers and the angle connecting them (see arrows in Fig. 20c). Therefore, in this section, the Si–Si NN distance and the Si–O–Si angle are analyzed.

Figure 20.

Characterization of range II order in the vitreous silica film. (a) Image from Fig. 18a, overlayed with colored bars representing the Si–Si NN distance (see scale bar). (b) Histogram of the Si–Si NN distances. Average values from diffraction experiments on bulk vitreous silica are indicated by black arrows 116, 117. (c) Two SiO4 tetrahedral units connected via the bridging O atom. Si–Si distance and the Si–O–Si angle are indicated by black arrows. (d) Histogram of the Si–O–Si angles. For a comparison, values from ab initio calculations 118, XRD 116 and molecular model from Bell and Dean 119 are indicated by black arrows.

Figure 20a shows the real-space distribution of Si–Si NN distances. Colored bars represent the distance between two neighboring Si atoms (see scale bar). The corresponding histogram is plotted in Fig. 20b. A Gaussian fit to the data yielded a mean Si–Si NN distance of 0.30 ± 0.02 nm. XRD and ND results on bulk vitreous silica are slightly larger than our measurements (see black arrows in Fig. 20b). This is connected with a larger variety of Si–O–Si angles in 3D discussed hereafter.

The histogram of the Si–O–Si angles is shown in Fig. 20d. We observed a characteristic asymmetric shape of the Si–O–Si angle distribution. By fitting the data with a Gaussian function, we obtained a mean Si–O–Si angle of 139° with a standard deviation of 3°.

The Si–O–Si angle has been largely debated in the literature 27, 120. As it connects two tetrahedral building blocks, it is a very important angle for vitreous networks. The original XRD measurements on bulk vitreous silica from Mozzi and Warren yielded a most probable Si–O–Si value of 144° 116. Some years later, the data were re-analyzed by Da Silva et al. 121. They found 152° to be the most probable value for the Si–O–Si angle. Furthermore, Bell and Dean obtained a similar value for their hand-built model of bulk vitreous silica 119. When these authors attempted to build a structure with a mean Si–O–Si value of 144°, they observed poor agreement with experiment. Ab initio simulations of bulk vitreous silica yielded mean Si–O–Si angles ranging from 143.4° to 152.2°, depending on the potential, basis set and the structural optimization scheme applied 118. A detailed analysis of the literature on measured and simulated Si–O–Si angles can be found in Ref. 120. These authors estimate the most probable Si–O–Si angle of bulk vitreous silica to be situated near 147° with a full width at half maximum of 23–30° (corresponding to a standard deviation of 10–13°). If we compare all these Si–O–Si values to the angles calculated from distances of the 2D silica network in this study, we find a difference of about 4–13°.

The smaller Si–O–Si angles are an intrinsic feature of 2D vitreous networks. Figure 21 illustrates the different interconnections of tetrahedral units in 2D and 3D vitreous silica. In 2D, the connection of the building blocks is constrained by the flat structure of the film (see Fig. 21a for a side view). There is a maximal Si–O–Si angle, which cannot be surpassed, because the Si atoms of a certain layer all lie in one plane. This effect is expressed in a characteristic sharp edge in the Si–O–Si distribution of a 2D vitreous network (see Fig. 20d). However, in 3D, the Si–O–Si angles can assume a larger range of values, as there are more degrees of freedom (see Fig. 21b). A sharp boundary in the distribution is absent 120.

Figure 21.

Comparison of Si–O–Si angles in 2D and 3D vitreous networks (Si green, O red) 122. (a) A side view on the building block of the 2D vitreous silica bilayer. Here, the Si–O–Si angle is constrained by the flat structure. (b) Four SiO4 tetrahedra connected in 3D space. The Si–O–Si angles can assume a wider spectrum of values due to more degrees of freedom.

5.4 Range III: Network topology

Range III order is the most discussed yet least understood topic in glass studies. It is in this range that striking differences of crystals and glasses are found (for a detailed comparison of crystalline and vitreous regions of the thin silica film see Ref. 115). To characterize range III order in the thin vitreous silica film, we evaluated longer-range distances, the ring statistics, and the Si–Si–Si angles.

A useful way to characterize the atomic order in a material is to compute the pair correlation function (PCF). The great advantage of this method is the direct comparison to PCFs derived from diffraction experiments using a Fourier transformation. We calculated longer-range distances for our model and compared it to literature values.

Figure 22a shows pair distance histograms (PDHs) for Si–O (blue), O–O (red), and Si–Si (green) derived from the nc-AFM model. A PDH is a histogram of distances between all atoms in the model, plotted versus the radial distance (r). Additionally, peaks are marked by vertical colored bars. The first peaks in all three distributions correspond to the respective NN distances (see Fig. 22b), which were already discussed in Sections and 5.3. Second peaks represent the next NN distances. Apparently, the second peaks are broader, more diffuse and exhibit a larger background than the first peaks. This is an intrinsic feature of the vitreous nature of the film: whereas the first peaks represent order of range I and II, the following peaks characterize range III order, and are therefore broader.

Figure 22.

Evaluation of pair distances in the experimental atomic model. (a) Pair distance histograms (PDHs) for Si–O (blue curve), O–O (red curve), and Si–Si (green curve). Peaks are indicated by vertical colored bars for first and second NN. (b) Small cutout of the vitreous silica model. Colored bars indicate the distances that were evaluated in (a).

Furthermore, we found good agreement between the PCF of the vitreous silica film and the PCFs obtained in diffraction studies of bulk vitreous silica. The total pair correlation function of the experimentally derived structural model, equation image, was obtained by summing up the different PDHs using X-ray and neutron scattering factors of Si and O according to the formula in Refs. 119, 123. equation image was additionally normalized by equation image to account for the 2D structure of the thin film. Figure 23a gives a comparison between equation image and the PCF obtained in an X-ray diffraction experiment on bulk vitreous silica, which was carried out up to a radial distance of 0.7 nm (black curve, retraced from Ref. 116). In Fig. 23b, we compare equation image to neutron scattering measurements (black curve, retraced from Ref. 117). The major peak positions, their relative magnitudes and peak shapes of equation image indicate reasonable agreement with the XRD and ND PCFs. The small deviations stem from the different dimensionality of the compared systems: whereas the silica bilayer on Ru(0001) is flat and 2D, the silica glass studied in diffraction experiments is 3D.

Figure 23.

Pair correlation functions (PCFs). (a) Comparison of the total PCF, equation image (orange curve), with the PCF obtained from X-ray diffraction measurements on bulk vitreous silica (black curve, retraced from Ref. 116). (b) Comparison of equation image (orange curve) to results from neutron scattering on vitreous silica (black curve, retraced from Ref. 117). Colored bars reproduce the respective PDH peak positions from Fig. 22a.

Another way to characterize the network topology of the thin vitreous silica film is by looking at the ring-size distribution. The ring-size distribution is not directly attainable from diffraction measurements and other averaging techniques. Therefore, the presented model system offers the unique possibility in studying this quantity in real space. We define the ring size s as the number of Si atoms per ring. As rings are quite large objects, a large statistical sample is required. Therefore, for the evaluation of rings, we use a large, atomically resolved STM image (Fig. 24a). In contrast to the nc-AFM image from Fig. 18, this particular STM image shows a sensitivity to the Si atoms. Note that the sensitivity of the scanning probe tip is mainly dominated by the microscopic tip termination (see Ref. 115 for an overview of different tip contrasts in STM). In Fig. 24b, the STM image is superimposed by the atomic model of the topmost Si and O atoms. As in Fig. 18c, a complex ring network is revealed. The real-space visualization of the ring-size distribution is presented in Fig. 24c. Colored circles represent the polygonal area spanned by the Si atoms of every ring. This quantity is directly correlated to the ring size (see scale bar in Fig. 24c). Strikingly, the environment of a ring depends on its size. Rings with more than six Si atoms tend to be surrounded by smaller rings. The ring arrangement is governed by the possible angles inside an SiO4 tetrahedron and angles connecting two tetrahedra (see range I and range II, as well as the discussion of Si–Si–Si angles hereafter). A histogram of the ring sizes from the STM image including ring fractions at the image boundaries is depicted in Fig. 24d. The smallest rings in the STM image consisted of four Si atoms and the biggest of nine Si atoms. The most common ring has six Si atoms. The distribution is asymmetric around the maximum. Being more precise, the ring-size distribution of the vitreous film follows a characteristic log-normal behavior. The log–normal ring-size distribution of a 2D random network was first pointed out by Shackelford and Brown 106 who analyzed an extended Zachariasen network. The origin lies in the connectivity requirements of 2D random networks 106. Fitting a log–normal distribution function to the silica/Ru(0001) ring-size distribution shows good agreement with the experimental distribution shape (dashed lines in Fig. 24d and e). The inherent log-normal law of the ring size distribution can also be verified by looking at a log–normal plot (Fig. 24e). In theory, a perfect log–normal distribution gives a straight line on log–normal probability paper. The black circles represent the experimental ring statistic and indeed lie on a straight line (see red dashed line in Fig. 24e serving as a guide to the eye).

Figure 24.

The ring-size distribution in 2D vitreous silica 115. (a) Large atomically resolved STM image of the vitreous silica film revealing the Si positions (VS = 2 V, IT = 50 pA, scan range = 12.2 nm × 6.6 nm). (b) Image from (a) superimposed by the atomic model of the topmost Si and O atoms. (c) Real-space visualization of the ring-size distribution. The colored circles represent the polygonal area of the rings (see scale bar). (d) Histogram of the ring-size distribution, based on the STM image in (a). Colored polygons indicate the different rings. The red dashed curve is a log–normal fit to the data. (e) A log–normal plot of the ring-size distribution. The dashed straight line serves as a guide to the eye.

Figure 25 presents the result of the Si–Si–Si angle computation, based on the experimental model from Fig. 24b. The Si–Si–Si angle expresses the internal structure of the ring (see also inset of Fig. 25g). Figure 25a–f display histograms of the Si–Si–Si angle inside 4- to 9-membered rings, respectively. In addition, for every ring size, the edge angle of the corresponding regular polyhedron is marked by a black arrow. The Si–Si–Si angles scatter around the polyhedral angles showing that the rings in the vitreous silica film have a distorted shape. The sum of all ring contributions is plotted in Fig. 25g. The Si–Si–Si angle shows a broad distribution, having a maximum at 120° corresponding to the average edge angle inside the most frequent, i.e., sixfold, ring. The broadness of the distribution further shows how flexible this 2D network structure can be.

Figure 25.

Histograms of Si–Si–Si angles. (a–f) Histograms of Si–Si–Si angles inside 4- to 9-membered rings. Arrows and numbers at the top indicate edge angles in regular polyhedra. (g) Total Si–Si–Si angle distribution. Contributions from different ring sizes are colored correspondingly.

A Fourier analysis can also shed light on longer-range correlations within the vitreous silica film. Figure 26a depicts a cutout from the STM image in Fig. 24a. A fast Fourier transformation (FFT) of this image is displayed in Fig. 26b. The FFT reveals two diffuse circles in reciprocal space. Similar circles appeared in the LEED image of the purely vitreous film 124. Fourier back-transforms unveil the origin of the two circles.

Figure 26.

Fourier analysis of an STM image of vitreous silica. (a) Cutout from the STM image in Fig. 24a (VS = 2 V, IT = 50 pA, scan range = 7.0 nm × 7.0 nm). (b) 2D FFT of image (a) revealing two circles. (c) Fourier back-transform of the inner FFT circle showing the porous morphology of the silica film. (d) Fourier back-transform of the outer FFT circle resolving the atomic protrusions.

Figure 26c illustrates an inverse Fourier transform of the inner FFT circle only. Clearly, the porous structure of the bilayer is visible, however, it lacks the atomic protrusions. The inner FFT circle corresponds to a 1/k value of 5.3 Å, k being a vector in reciprocal space and equation image. This length is exactly equal to the average NN distance between two pores in the 2D silica film. From the coordinates in Fig. 24b, an average NN distance between the centers of two rings of 5.3 ± 0.7 Å was obtained. For a crystalline film, which consists of sixfold rings only, the calculated ring-to-ring distance is only slightly larger (5.4 Å 114). Thus, the inner FFT circle represents the network structure and can be explained in terms of a rotationally invariant ring-to-ring correlation. Therefore, the inner FFT and LEED circle are closely related to the first sharp diffraction peak of bulk vitreous silica, which was attributed to the periodicity of the holes in the network structure 125–127.

If we look at Fig. 26d, depicting the Fourier back-transformation of the outer FFT circle, the origin of this circle becomes obvious. The back-transform of the outer FFT circle only reproduces the atomic protrusions of the Si atoms from the STM image. Consequently, the outer circle's 1/k value of 3.0 Å perfectly matches the Si–Si NN distance (compare with Fig. 20b).

5.5 Range IV: Density fluctuations

To study the order of range IV, the 2D mass density of the silica film was evaluated (Fig. 27). The atomic model from Fig. 24b was used as a basis for the density determination (green wireframe in Fig. 27). Beneath the wireframe, small colored boxes depict the 2D mass density in mg m−2 (box size = 0.34 nm × 0.30 nm; see scale bar in Fig. 27). For every small box, the 2D mass density of a 2 nm × 2 nm slab around it was calculated (white dashed square in Fig. 27). The size of the slab was chosen large with respect to the typical ring size. The slab comprises the whole bilayer structure, i.e., not only the topmost SiO4 tetrahedra, but also the lower ones.

Figure 27.

Analysis of the silica film's 2D mass density. The green wireframe corresponds to the model from Fig. 24b. The colored boxes are a real-space representation of the 2D mass density (see scale bar). The white dashed box displays the bilayer slab used to calculate the 2D mass density.

We found that the 2D mass density varied from 1.46 to 1.83 mg m−2. The total 2D mass density amounted to 1.65 mg m−2, which is just twice the 2D mass density of graphene 128. The pure crystalline phase of the silica bilayer is with a 2D mass density of 1.68 mg m−2 just slightly denser. Evidently, the 2D mass density of the vitreous film locally fluctuates. This most probably originates from the local ring environment: an area with large rings has a lower density than an area consisting of smaller rings. This way, the 2D mass density is lower in the lower left corner of the model, and higher towards the center of the image, which is dominated by smaller rings, i.e., four- to sevenfold rings.

6 Concluding remarks and outlook

Deviations from perfect crystallinity in surfaces of thin oxide films were studied by means of low-temperature nc-AFM/STM in UHV. In addition to imaging the topography of the surface termination, KPFM was employed. The data was contrasted with STS results for a deeper insight into the nature of the defects. The spectroscopy was performed with a very high spatial resolution of the order of 1 nm.

In the first study, magnesia on Ag(001) was presented. Different point defects, which are the most frequently discussed ones in literature, were studied. For the first time, the point defects on an MgO surface could be unambiguously identified. This has been done using KPFM and STS measurements in comparison with DFT calculations. The point defects were distinguished as DV, F0, F+, and F2+ color centers. These color centers influence the surface chemistry by significantly increasing the reactivity of the almost inert surface of the defect-free MgO.

The nc-AFM investigation on alumina on NiAl(110) unveiled the surface structure of the domain and at the domain boundaries with atomic resolution. New boundary types and structures could be described in detail, leading to an understanding of their role and interrelation in the film's characteristic defect networks. Apart from the determined lateral structure and topography, charge transfer at F2+-like centers, which has been predicted by DFT calculations, was experimentally verified for the domain boundaries. These studies show that nc-AFM in combination with STM can be successfully used beyond imaging.

Finally, the structure of an atomically flat and extended vitreous thin silica film on Ru(0001) has been presented. nc-AFM/STM revealed the thin film's atomic arrangement consisting of corner-sharing SiO4 units. These silica building blocks form a complex network that lacks long-range order and registry to the substrate. This model system proves Zachariasen's predictions of a random network theory for glass structures valid. The unique opportunity to study vitreous structures with a local technique at the atomic level has thereby been shown for the first time. An atomic model of the topmost Si and O atoms has been directly derived from nc-AFM/STM images. We made a statistical analysis of the structure. The atomic structure has been discussed in the following ranges: the SiO4 tetrahedral unit, interconnection of adjacent structural units, network topology, and longer-range density fluctuations. Distances, angles, PCFs and histograms of ring sizes were given. A comparison between the PCF derived from our experimental model and the PCF obtained in diffraction experiments on bulk vitreous silica was drawn and showed satisfying agreement. A Fourier transformation was analyzed for further insights into range III. An evaluation of range IV suggested that the local 2D mass density is determined by the ring environment. This vitreous silica model system, which can be investigated by well-established surface-science tools, provides the unique possibility to study an amorphous two-dimensional model system with atomic resolution in real space. This work opens the way to further studies about the vitreous nature of this film. For example, it is of great interest to directly study the amorphization process. This can be achieved by high-resolution electron microscopy. Furthermore, studying the interaction of the film with single adsorbates or molecules could clarify the properties of oxide materials used in industrial catalysis, which are usually also amorphous.

In these studies we have shown how modern SPM techniques like nc-AFM and STM can complete and clarify the atomistic models, which we have gained so far from diffraction methods. The benefits of locally resolving complex surface structures are obvious. A direct assignment from the gained images is possible. The employed high-resolution imaging and spectroscopy significantly improves our understanding of the surface structure and chemistry of complex materials.

Acknowledgements

The authors thank Hans-Joachim Freund for his help and advice. Hans-Peter Rust and Gero Thielsch are gratefully acknowledged for major contributions to the development and maintenance of the experimental setup. Furthermore, we acknowledge Christin Büchner, Lars Heinke, Thomas König and Stefanie Stuckenholz for their help and fruitful discussions.

Biographical Information

Markus Heyde received his Ph.D. in physical chemistry in 2001 from the Humboldt-Universität in Berlin. He was awarded with a Feodor Lynen Fellowship of the Alexander von Humboldt Foundation and from 2001 until 2003, he worked in the Materials Sciences Division at the Lawrence Berkeley National Laboratory in the groups of Gabor A. Somorjai and Miquel Salmeron. In 2003, he joined as a research associate the group of Hans-Joachim Freund. Since 2007 he is heading the atomic force microscopy group in the Chemical Physics department of the Fritz-Haber-Institut der Max-Planck-Gesellschaft in Berlin.

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Biographical Information

Georg H. Simon, after undergraduate and master's studies at the Victoria University of Wellington in New Zealand and the University of Rostock in Germany, obtained his PhD in physics in 2010 from the TU Berlin. His thesis work was carried out in the atomic force microscopy group in the Chemical Physics department at the Fritz-Haber-Institut der Max-Planck-Gesellschaftin Berlin. Since 2011 he is member of the molecular surface science group of Karl-Heinz Ernst at EMPA, the Swiss Federal Laboratories for Materials Science and Technology.

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Biographical Information

Leonid Lichtenstein studied physics at the University of Hamburg in Germany and at Université Paris-Sud XI in France. He obtained his Ph.D. in physics in 2012 from the Free University in Berlin. His thesis work was carried out in the atomic force microscopy group in the Chemical Physics department at the Fritz-Haber-Institut der Max-Planck-Gesellschaft in Berlin. From 2010 to 2012 he was a member of the International Max Planck Research School “Complex Surfaces in Materials Science.”

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