Advertisement

Scanning Probe Microscopy in Materials Science

  • Bryan D. HueyEmail author
  • Justin Luria
  • Dawn A. Bonnell
Chapter
Part of the Springer Handbooks book series (SHB)

Abstract

The advent of scanning probe microscopy ( ) revolutionized surface science in the 1980s and facilitated the nanotechnology revolution in the ensuing decades. First scanning tunneling microscopy, then atomic force microscopy ( ) and near-field optical methods, were developed and employed for fundamental and applied research in many disciplines including physics, biology, chemistry, and a wide range of engineering fields. But SPM, especially AFM, has in particular contributed to materials science due to the fact that atomic to nanoscale resolution of materials properties can be achieved. Routine and specialized SPM approaches now provide measurements and maps not just of the topography, but also of local mechanical, electronic, magnetic, optical, thermal, chemical, and coupled properties. Important recent developments include increases in imaging speed, in situ and in operando studies, advanced probes, and even tomographic AFM. This chapter describes the concepts and implementation of these various SPM methods focused on new discoveries in materials science.

Scanning tunneling microscopy Atomic force microscopy Tip–surface interactions Kelvin probe force microscopy Scanning spreading resistance microscopy Scanning capacitance microscopy Near-field scanning optical microscopy Scanning impedance microscopy Nano-impedance microscopy and spectroscopy Piezoelectric force microscopy Dielectrics Piezoelectrics 

The quest toward understanding the behavior of condensed matter has relied on measuring structure, bonding, and properties at increasingly local levels. This has driven advances in techniques that probe both soft and hard materials directly as well as indirectly. Many of these advances are described in other chapters of this volume. While structure- and bonding-based probes had accessed molecular and atomic scales for decades, local determination of properties had been elusive. The emergence of scanning probes filled this gap.

There are three major classes of scanning probe techniques that access electronic, magnetic, optical, thermal, and mechanical properties. Scanning tunneling microscopy ( ), the first, is based on electrons tunneling between a metal tip and a sample, as described in Chap.  28. The distance sensitivity of tunneling imparts intrinsically high spatial resolution and the voltage dependence yields the local density of states. It is, however, generally applicable only to conducting materials. Another class of techniques is based on local optical responses induced and/or detected with a very fine probe or optical fiber. These techniques, e. g., near-field optical microscopy or scanning near-field optical microscopy, find extensive application in organic, biological, and plasmonic systems as in Chap.  21.

The focus of this chapter will be those probes that exploit mechanical interactions between a nanoscale tip and a surface, usually detected via the properties of a cantilever to which the tip is attached. The original cantilever probe method, atomic force microscopy ( ), is based on van der Waals interactions at the tip/surface junction. A cantilever is mechanically oscillated near its resonant frequency (usually \(10{-}500\,{\mathrm{kHz}}\)) and, at relatively small sample–tip separations (usually \(0.5{-}100\,{\mathrm{nm}}\)), the van der Waals interaction causes a force gradient that alters the oscillation. The cantilever motion is detected with laser reflection onto a photodiode. If this measurement is made continuously while the tip is scanned across a surface, the surface topography can be mapped by constantly adjusting the mean lever position in order to maintain a fixed tip–sample interaction. It was almost immediately understood that many other interactions could be detected with this scheme as well, and that these interactions might be distinguished by their distance dependence. For example, at a \({\mathrm{10}}\,{\mathrm{nm}}\) sample/tip separation the van der Waals interactions can be used to determine the topographic structure, while at \({\mathrm{200}}\,{\mathrm{nm}}\) an electrostatic ( ) or magnetic force ( ) would dominate the measurement.

The utility of local probes is illustrated by the fact that thousands of papers are published per year that use AFM. They have become ubiquitous at universities, national laboratories, and increasingly in industry, even including manufacturing environments. Many monographs have summarized the state of this field at various times, and several books are available that provide an introduction to the field and general overviews [25.1, 25.2, 25.3, 25.4]. While scanning probe microscopy ( ) systems are primarily used according to their original function—nanoscale topographic mapping—for over three decades since its invention researchers interested in materials properties have examined fundamental tip–surface interactions and extended SPM to probe local electronic transport, mechanics, and dielectric, ferroelectric, magnetic, thermal, and other properties. Since systematic descriptions of conventional SPM methods already abound, this chapter will therefore focus on recent advances in nanometer probes of complex properties, highlighting the potential insight they provide, as well as remaining challenges. First, factors leading to atomic resolution imaging based on forces will be described along with some example applications. This is followed by summaries of approaches to probe spatially localized electrical and dielectric properties as well as surface dynamics. A review of mechanical, chemical, and thermal properties follows, along with in situ/in operando SPM advances. Finally, we discuss exciting future prospects for SPM including next-generation probes, high speed scanning, multimodal measurements, and even tomographic AFM.

25.1 Imaging at Atomic Resolution with Force Interactions

There are a number of so-called imaging modes in AFM, based on various combinations of force detection, contrast mechanisms, and feedback routines. Confusion can arise since there is no universal naming convention amongst microscope suppliers. From a fundamental perspective the force regimes categorize three imaging modes: contact AFM (the tip applies a continuous force \(\approx 1{-}1000\,{\mathrm{nN}}\) normal to the surface of the sample, with concomitant shear loading); intermittent contact AFM (an oscillating cantilever tip is brought close to the sample so that it gently taps, or more aggressively strikes, the sample at the bottom of each excursion, ideally with sub-nN peak loads purely oriented normal to the surface); and true noncontact AFM (a tip oscillates with a much smaller magnitude and never contacts the surface, typically interacting via van der Waals forces instead). These common instrument configurations are illustrated in Fig. 25.1. For contact mode AFM, the cantilever deflection is simply detected and used as the primary feedback channel to track the surface height. With intermittent contact ( ) and noncontact (NC) AFM (more generally known as AC , alternating contact, or tapping™ modes), the cantilever oscillation amplitude, frequency, and/or phase are monitored and/or continually updated via a feedback loop . Generally, the system complexity and necessary user expertise increases as the tip–sample interaction weakens, albeit with the possible benefit of improved spatial resolution and minimized tip or specimen damage. Atomic resolution imaging is therefore typically achieved in noncontact mode, while most commercial AFM instruments are predominantly used in contact or IC/tapping modes.

Fig. 25.1

Schematic for surface imaging with AFM. The deflection and/or oscillation amplitude, frequency, or phase are monitored and either fixed or continually updated to achieve the various imaging modes described in the chapter

25.1.1 Operational Principles of Noncontact Atomic Force Microscopy

Noncontact atomic force microscopy ( ) refers to the group of techniques in which the tip of the cantilever oscillates in close proximity to the surface but never makes contact with it. Several review articles present details of imaging mechanisms [25.5, 25.6, 25.7], which we summarize below. It should be noted that only specific types of NC-AFM achieve atomic resolution for the simple reason that some interactions between the sample and tip, i. e., long-range van der Waals and electrostatic forces, are power law functions of order 2. This is not sufficient sensitivity to track distances of fractions of angstroms. If, however, the geometry is configured such that the tip experiences short-range van der Waals and/or bonding interactions during a substantial part of the cantilever oscillation, sensitivity is enhanced. In this situation, the local force between the sample and tip is the sum of the electrostatic, \(F_{\mathrm{elec}}\), van der Waals, \(F_{\mathrm{vdW}}\), and bonding \(F_{\mathrm{bonding}}\) forces
$$F_{\mathrm{tot}}=F_{\text{elec}}+F_{\mathrm{vdW}}+F_{\text{bonding}}\> .$$
Figure 25.2 illustrates the range over which these forces operate. Two types of short-range forces can play a significant role for separations less than \({\mathrm{10}}\,{\mathrm{nm}}\): dipole–dipole and covalent bonding. For any tip–surface distances, \(F_{\mathrm{electrost}}\), \(F_{\mathrm{capacitance}}\) and \(F_{\mathrm{vdW}}\) (large-range forces) are attractive. At the same time, short-range van der Waals forces and covalent forces are attractive at large distances and repulsive at small distances. The repulsive part of the interactions is shaded with pink for van der Waals forces and with blue for Morse forces. Figure 25.2 also illustrates that in order for short-range interactions to be the same order of magnitude as long-range interactions, which is a requirement for high resolution, tip oscillations should be within tens of nanometers of the surface.
Fig. 25.2

Distance dependence of short- and long-range forces between a tip and sample during noncontact AFM

Giessibl and Reichling [25.8] demonstrated the influence of the force regimes in imaging \(\mathrm{CaF_{2}}\)(111) at atomic resolution in both attractive and repulsive modes (Fig. 25.3a,b). The level of spatial resolution was facilitated by the use of a quartz tuning fork to oscillate the tip. The normalized frequency shifts for the attractive and repulsive interactions suggested that van der Waals forces are responsible for image formation. Note the difference in atomic-scale image contrast between the images acquired in the attractive and repulsive regimes. Interpretation of image contrast in terms of atomic and electronic structure requires an understanding of experimental parameters and a theoretical underpinning for sample–tip interactions.

Fig. 25.3a,b

High-resolution constant height images of \(\mathrm{CaF_{2}}\)(111) in (a) the attractive and (b) the repulsive mode of FM-AFM(1) mode. Reprinted from [25.8]. © IOP Publishing. Reproduced with permission. All rights reserved

25.1.2 Noncontact AFM Techniques

Mechanical oscillations of the cantilever lie at the heart of NC-AFM. Forces and force gradients acting between the tip and surface change the oscillation parameters and these parameters are sensitive to atomic-scale resolution. During operation three sets of parameters play the most important roles: cantilever-related (spring constant of the cantilever, the eigenfrequency of the cantilever, the quality factor of the cantilever), oscillation-related (amplitude, frequency shift) and image-related (either constant separation or constant height operation mode) parameters. Cantilever-related parameters are predetermined by the tip and are not variable during scanning. Changes in the other parameters define different AFM techniques, as shown in Table 25.1. It should be noted that NC-AFM experiments are usually carried out in high vacuum or in liquid in order to avoid water condensation between the tip and surface.

Table 25.1

Operational modes in noncontact AFM noncontact atomic force microscopy (NC-AFM)!operational mode

 

Amplitude of tip oscillations

Frequency shift of tip oscillations

Tip–surface separation

AM-AFM

Monitored (varied)

Constant

Constant

FM-AFM(1)

Constant

Monitored (varied)

Constant

FM-AFM(2)

Constant

Constant

Monitored (varied)

As the name implies, in AM-AFM the amplitude of the tip oscillation is monitored while frequency shift and separation are kept constant by feedback. Usually, AM-AFM is done at the resonant frequency of the cantilever, since this is the maximum oscillation amplitude. This mode is analogous to constant current STM, despite the difference in the physics of image formation. Note that the sensitivity is low because the amplitude depends on the tip–surface force averaged over the oscillation cycle [25.9],
$$A\cong A_{0}\left[1-4\left(\frac{\left\langle F_{\text{ts}}\right\rangle}{F_{0}}\right)^{2}\right]^{\frac{1}{2}}\> ,$$
(25.1)
where \(\left\langle F_{\text{ts}}\right\rangle\) is the average force over the oscillation cycle and \(F_{0}\) is the driving force. According to (25.1), AM-AFM senses the change of average force over the oscillation cycle at constant separation. The typical driving force might be estimated as \(F_{0}\approx kA_{0}\approx{\mathrm{10}}\,{\mathrm{N/m}}\times{\mathrm{50}}\,{\mathrm{nm}}={\mathrm{5\times 10^{-7}}}\,{\mathrm{N}}\). The change in average force that produces atomic resolution is usually on the order of \(E-8{-}E-10\,{\mathrm{N}}\). Thus, the smaller the oscillation amplitude, the better the tip senses the surface because of the decrease in \(F_{0}\). In order to achieve atomic resolution (vertical \(\approx{\mathrm{0.01}}\,{\mathrm{nm}}\) and lateral \(\approx{\mathrm{0.1}}\,{\mathrm{nm}}\)) the oscillation amplitude must be approximately between \(1{-}10\,{\mathrm{nm}}\). Small oscillation amplitude is achieved by either decreasing the driving force or increasing the spring constant. But a decrease of driving force leads to a decrease in the oscillation stability, while a substantial increase of the spring constant is not straightforward due to probe manufacturing challenges.

With routine spatial resolution of approximately \(\approx{\mathrm{2}}\,{\mathrm{nm}}\), AM-AFM is nevertheless ideal for many biological applications. In addition, the relatively small force minimizes destructive imaging of soft samples [25.10]. Examples of biological application AM-AFM are found in a review [25.5], which also describes the detailed theory of AM-AFM. Similar resolution has been demonstrated on inorganic surfaces. Resolution close to atomic level was demonstrated on calcite with a modified AM-AFM technique. F.M. Ohnesorge [25.11] operated the microscope in the separation region close to that for snap-into-contact instability. In this region, feedback with an inverted sign provides reasonably stable images of high resolution.

There are two FM-AFM techniques in Table 25.1, FM-AFM(1) and FM-AFM(2). For these two methods the oscillation amplitude is constant and either the frequency shift of oscillation (in constant height mode) or the change in piezoelectric movement (in constant force gradient mode) is varied. Atomic resolution was obtained almost simultaneously by Kitamura and Iwatsuki and Giessibl in 1995 using FM-AFM. Both groups operated the microscope in constant force gradient mode. The difference in the approaches was in the cantilever excitation: Kitamura and Iwatsuki used constant excitation mode and Giessibl used an automatic gain control of the excitation signal in order to maintain constant oscillation amplitude.

The FM-AFM image is not only aesthetically pleasing, it is a quantitative description of tip–surface interactions, hence, mathematical modeling of these interactions is often required to interpret the image contrast. The basic equation for image formation in the limit of small amplitudes (less than the tip–sample separation) simplifies to \(\Updelta f\left(z_{\text{c}}\right)=\left[f_{\text{o}}/\left(2k\right)\right]k_{\text{ts}}\left(z_{\text{c}}\right)\), where \({\Updelta}f\) is the frequency shift as a function of the lift height \(z_{\text{c}}\), \(f_{0}\) is the base frequency, \(k\) is the cantilever spring constant, and \(k_{\text{ts}}\) is the tip–sample separation-dependent force gradient [25.12]. Therefore the frequency shift image in FM-AFM(1) mode is a map of force gradient (\(k_{\text{ts}}\)) over the surface at constant separation; and the image in FM-AFM(2) mode is a map of the heights of constant tip–surface force gradient.

The basis for atomic resolution in FM-AFM is that the first derivative of the tip–surface force is monitored, in contrast to AM-AFM in which the force itself is monitored. Experimental data obtained in FM-AFM(1) can be converted into FM-AFM(2) data only when the distance dependence of the tip–surface potential is known. However, the requisite experimental parameters such as cantilever resonant frequency, spring constant and oscillation amplitude vary from one experiment to another. In order to compare experimental results obtained under different conditions the concept of a normalized frequency shift was developed by Giessibl [25.12]. The normalized frequency shift, \({\gamma}=(k{\Updelta}fA^{3/2})/f_{0}\) depends on the tip–surface potential and not on oscillation amplitude or oscillation frequency. Analytical solutions for basic tip–surface interactions (power law dependence and exponential decay) have also been developed [25.13]. This relates the magnitude of the tip–surface force to the image formation mechanism. This concept of a normalized frequency shift will be used in subsequent discussions of various applications.

25.1.3 Image Interpretation

Classical physics fails to quantitatively describe interactions between the tip and surface. One approach is to consider the interaction of a nanotip, a cluster at the end of the tip, which obeys quantum mechanical laws. In this case, chemical interactions between the nanotip and surface can be calculated based on the pair potentials between tip and surface atoms. Obviously, the nanotip does not represent the entire tip–surface interaction. Among the models developed to incorporate long-range forces the most popular is the representation of the tip as a cone with a hemispherical end. A complete description of the tip then includes a cone with a hemispherical cap (analytical description) with a nanotip at the end of the hemisphere (numerical modeling). Some information regarding the tip shape, conductivity, and charging is embedded in the experimental dependence of the cantilever frequency change versus tip–surface separation, which should be measured before and just after imaging [25.14, 25.15, 25.16, 25.17].

A common concept for Si and other semiconductor surfaces has been that the main component of the tip–surface interaction is the interaction of a dangling Si bond at the end of the tip with the surface atoms. This dangling bond can be well described using relatively small four- or ten-atom Si clusters saturated by H atoms [25.18]. Another approach is to assume from the outset that the tip is ionic (MgO) [25.19, 25.20]. To achieve atomic resolution, calculations showed that such nanotips must extend significantly beyond the main part of the tip to sufficiently localize the dominant tip–surface interaction.

Silicon tips under practical experimental conditions are likely to be contaminated by residual oxide, adsorbed hydrogen, water [25.21], or even materials transferred from the specimen. To compare the properties of clean and contaminated silicon tips, the electronic structures of Si\({}_{10}\) clusters with adsorbed contaminant species were calculated using density functional theory by Sushko et al [25.14]. The results showed that adsorbed hydrogen has no effect on the potential gradient from the uncontaminated silicon cluster; however, adsorbed oxygen and hydroxyl groups cause a significant change in the potential gradient. Both potentials decayed over a much longer distance than did that of the uncontaminated cluster, and the stronger gradients suggested a much stronger interaction with the surface. Interestingly, the potential gradient from a MgO cube corner with an O atom at the end was very similar to that of the oxygen-contaminated silicon cluster, a strong negative potential. Such a MgO cluster is a good model of a hard oxide tip, and has the important advantage that reliable interatomic potentials exists for MgO, alkali halides and other oxides.

Accordingly, Bennewitz and coworkers atomically resolved a copper(111) substrate, as well as a unit cell thick NaCl grown on that surface [25.17]. However, a MgO nanotip of only a few atoms does not sufficiently resolve the features actually observed in the experimental images. Different nanotip models for scanning force microscopy were compared to determine which most closely matched experimental results [25.17]. It was found that a 64-atom MgO nanotip with an oxygen atom at the apex, embedded in a macroscopic tip, gave quantitative agreement with the experimental image contrast. The MgO cube can also be orientated with a Mg ion at the apex, providing a strong positive instead of negative potential. For many SFM experiments on insulators, these variations of an ionic MgO tip model provide excellent quantitative agreements with the acquired images.

These observations demonstrate that interpretation of atomic-scale features from SPM imaging requires careful consideration of the electronic structure of the sample and tip. Some general principles emerge but should be reevaluated with respect to each sample.

25.1.4 Applications of NC-AFM

Over the last two decades NC-AFM has been exploited in the study of a vast range of compounds. Examples presented here illustrate various ways in which the role of atomic interactions manifest in image contrast.

The fact that AFM can be applied to insulating materials opened the door to understanding atomic interactions of oxide compounds. \(\mathrm{SrTiO_{3}}\) [25.22], NiO [25.24], \(\mathrm{CeO_{2}}\) [25.25], mica [25.26], and \(\mathrm{MoO_{3}}\) [25.27] have been imaged using FM-AFM. The (100) surface of strontium titanate attracted much attention not least because it is the best substrate for the deposition of epitaxial films of superconductive oxides. Unit cell resolution was obtained by T. Kubo and H. Nozoye [25.22] on a \(\mathrm{SrTiO_{3}}\)(100) single crystal in 2001. They observed the \(\sqrt{5}\times\sqrt{5}\) reconstruction using FM-AFM(2) mode. \(\mathrm{W_{2}C}\)-coated conductive tips were used to eliminate electrostatic charge on the tip and chemical interaction between the tip and surface, and to nullify capacitance forces. Figure 25.4a-da,b compares STM and NC-AFM images of the surface. The STM resolves only the Sr adatoms, while the NC-AFM resolves both the adatom and the underlying lattice. STM contrast on oxides contains both a geometric and electronic structure contribution, the relative magnitude of which cannot be determined a priori. In this case the geometric height of the Sr adatom appears to preclude resolution of the Ti lattice in unfilled state images. The AFM contrast, in principle, contains integrated charge density of all atoms so the oxygen sublattice can be imaged simultaneously.

Fig. 25.4a-d

SPM on (100) \(\mathrm{SrTiO_{3}}\). (a) STM image; (b) NC-AFM image (note that STM reveals Sr adatoms on the surfaced while NC-AFM resolves unit cells underneath). Reprinted with permission from [25.22]. Copyright 2001 by the American Physical Society. Low-temperature (c) STM and (d) NC-AFM for graphite, with a representative hexagon of the graphite structure superimposed on each. One atom per unit cell is resolved with STM and two per unit cell with NC-AFM. Reprinted from [25.23]. Copyright (2003) National Academy of Sciences, USA

Numerous layered compounds have been studied by NC-AFM, including mica [25.28], \(\mathrm{MoO_{3}}\) [25.27], etc. Highly oriented pyrolytic graphite is perhaps the most general, and is used as a calibration standard for SPM or as an atomically flat substrate for numerous studies of molecular adhesion, self-assembly, or film growth. As with most layered compounds, the graphite is easily prepared by cleavage to provide a clean, atomically flat surface. Despite the proverbial ease of imaging graphite by STM with atomic resolution, every second atom in the hexagonal surface unit cell is usually unresolved. Giessibl and coworkers [25.29] demonstrated that a low-temperature FM-AFM(1) with pico-Newton force sensitivity reveals the hidden surface atom (Fig. 25.4a-dc,d). This is another clear example that, despite similarity in implementation, and that combined AFM/STM microscopes are manufactured, differences between the image formation mechanisms of STM and NC-AFM are very important. One atom per unit cell is evident in the case of STM and two per cell in the case of NC-AFM. In STM the tip images the density of states at the tip bias, while in NC-AFM the tip images an equiforce surface. With an oscillation amplitude of \({\mathrm{300}}\,{\mathrm{pm}}\), cantilever spring constant of \({\mathrm{1800}}\,{\mathrm{N/m}}\), eigenfrequency of \({\mathrm{18076.5}}\,{\mathrm{Hz}}\), and peak frequency shift of \(\approx{\mathrm{5}}\,{\mathrm{Hz}}\), the normalized frequency shift (\({\gamma}\)) according to Sect. 25.1.2 is \({\mathrm{2.7}}\,{\mathrm{fN{\,}m^{0.5}}}\). The magnitude of the normalized frequency shift indicates that the contrast in FM-AFM(1) is due either to short-range van der Waals or to Morse forces.

The Si(111) (\(7\times 7\)) reconstruction has also long been a standard in surface science. The structure, based on minimization of the number of dangling bonds, took 20 years to solve. The ‘‘Dimer–Adatom–Stacking–fault'' model proposed by Takayanagi et al [25.30] is the currently accepted structure for the silicon(111) \(7\times 7\) surface. Immediately after the invention of the STM, Binnig and coworkers imaged the \(7\times 7\) reconstruction on Si(111) in real space by STM [25.31]. It took more than ten years before the first NC-AFM images of this \(7\times 7\) reconstruction were obtained, simultaneously by Kitamura and Iwatsuki [25.32] and Giessibl [25.33]. A number of semiconductor surfaces have also been imaged, including Si(111), (100), (110); GaAs(100); and InAs(110) [25.34]. The most technologically relevant, Si(100), undergoes a \(2{\times}1\) reconstruction. Figure 25.5a,b shows an atomic resolution FM-AFM(1) image by Yokoyama and coworkers [25.35]. The normalized frequency shift calculated for these images is \(\approx 0.435{\mathrm{fN{\,}m^{0.5}}}\), a magnitude which again suggests either short-range van der Waals or Morse forces, hence atomic resolution. Although the surface is known to adopt the \(2\times 1\) reconstruction, the distance between the dimer-like features in Fig. 25.5a,b is larger (\({\mathrm{0.35}}\,{\mathrm{nm}}\)) than of the expected structure (\(0.23{-}0.20\,{\mathrm{nm}}\)). The authors compare this result with a NC-AFM image of the hydrogen passivated surface on which the lateral dimensions agree with the expected positions of hydrogen atoms. This dilemma is resolved if the image mechanism is that of a Si dangling bond of the tip interacting with the surface. In the case of the clean (\(2\times 1\)) surface the contrast then relates to surface dangling bonds rather than dimer bonds and in the case of the passivated surface the contrast relates to the dangling bond–hydrogen interaction. These results further emphasize the role of chemical/bonding forces in the image mechanism.

Fig. 25.5a,b

NC-AFM (a) image of Si(100) \(2\times 1\) reconstructed surface, including one \(2\times 1\) unit cell outlined by a box, along with (b) line profile of the NC-AFM image where indicated by the dotted line. Reprinted from [25.35]. Copyright 2000 The Japan Society of Applied Physics

The surface of GaAs affords an excellent opportunity to examine differences in tip–surface interactions on the same surface [25.36]. Uehara et al compare the corrugations of As atoms and Ga atoms on a GaAs(110) surface at different tip–surface distances. Again FM-AFM(2) was used in order to obtain atomic resolution. In this case, though, the apparent distance between As atoms did not change with tip–sample distance, while the distance between Ga atoms did. This is explained by considering that the force on the surface atom increases with decreasing tip–sample distance. Therefore, the As feature is associated with valence charge distribution and is not sensitive to this range of forces, while the Ga feature is associated with a dangling bond, which can be displaced by the interaction with the tip. This is another case of using atomic bonding interactions for chemical specificity in AFM image contrast.

25.2 Imaging Properties: Advanced SPM Techniques

In addition to mapping topographic and atomic structure, variants of SPM are often used to probe local properties. The most common of these are electrostatic force microscopy ( ) and magnetic force microscopy ( ). In these straightforward measurements, the tip is lifted above the surface to a distance at which only long-range forces are detected. By expanding the mechanisms of force detection and utilizing all possible image modes, the list of properties that can be assessed is extensive. The cantilever can be driven mechanically, electrically, or with other signals. This can be done in contact or noncontact regimes. Amplitude and phase of first-, second-, and higher-order harmonics or modes can be detected. The relation between these operational regimes is sketched in Fig. 25.6. For example, the most widely used version of AFM is an intermittent contact, mechanically driven oscillation with amplitude- or phase-based detection. Piezoelectric force microscopy ( ) is most commonly in contact mode, electrically driven, and with phase-based detection. Static or periodic electric or magnetic fields can further be applied to the sample, independent of the tip signal. An underlying theme of the newest developments is the use of multiple signal modulations or high-order harmonics of modulated signals, widely employed for transport and dielectric properties. Investigations of friction, composition, thermal properties, and electrochemistry are reviewed as well. Finally, tip–based deposition, mechanical mapping, subsurface imaging, and even tomography with an AFM are discussed.

Fig. 25.6

Variations of SPM separated into six operational regimes, distinguished by condition of contact and type of driving signals

25.2.1 Transport Properties

Perhaps the most common of the so-called advanced SPM techniques is scanning surface potential microscopy ( ), also referred to as Kelvin probe force microscopy ( ), which maps the work function of surfaces [25.37, 25.38]. In SSPM, the cantilever oscillation is driven electrically. This is a noncontact (generally \(50{-}200\,{\mathrm{nm}}\) separation) probe, with feedback on the first harmonic. An AC voltage is applied to the tip. The force acting between the tip and surface is derived from the directional derivative of the energy stored in a capacitor,
$$F\left(z\right)=\frac{1}{2}\frac{\partial C(z)}{\partial z}\left(V_{\text{tip}}-V_{\text{surf}}\right)^{2}.$$
The tip potential is expressed as \(V_{\text{tip}}=V_{\text{dc}}+V_{\text{ac}}\sin{\omega}t\), so that the first harmonic of the force is
$$F_{1\omega}\left(z\right)=\frac{\partial C(z)}{\partial z}\left(V_{\text{dc}}-V_{\text{surf}}\right)V_{\text{ac}}.$$

\(V_{\mathrm{dc}}\) is varied until it matches the surface potential, \(V_{\text{surf}}\), at which point the first harmonic of the force \(F\) (with frequency \({\omega}\)) evidently becomes nullified. Thus, the applied \(V_{\mathrm{dc}}\) provides an effective map of the surface potential beneath the probe.

However, the apparent ease with which potential variations can be mapped belies the challenges in interpreting images on electrically [25.39, 25.40] and topographically inhomogeneous surfaces. In the cases of semiconductor and dielectric surfaces the electrostatic properties are not characterized solely by intrinsic potential and topography. SSPM images must be interpreted in terms of the effective surface potential, which includes capacitive interactions, surface and volume bound charges, double layers, and remnant polarization [25.41, 25.42, 25.43, 25.44], all of which can be further complicated by nonlocal heterogeneities for real surfaces and tip/cantilever geometries. For semiconductor surfaces, tip–induced band bending [25.45] can additionally offset local surface potentials [25.46]. Despite these challenges the obvious need to examine variations in local potential in electronic nanodevices spurred efforts to overcome some of the obstacles with careful analytical treatments that determined limits in quantification. The late 1990s saw SSPM applied to semiconductor [25.47, 25.48], organic [25.49], and ferroelectric [25.50, 25.51] surfaces, as well as to defects [25.52, 25.53] and photoinduced [25.54, 25.55] and thermal phenomena [25.56]. Practically, variations in potential can be determined with energy resolution of \(2{-}4\,{\mathrm{meV}}\) and spatial resolution on the order of \(50{-}100\,{\mathrm{nm}}\) or less. Therefore, although absolute values of potential are difficult to quantify, SSPM or Kelvin measurements are extremely sensitive to a wide range of electronic heterogeneities. This demonstrates a common but important theme for many AFM-based measurements: they provide extraordinary spatial resolution, information content, and opportunity for investigations of inhomogeneities, but calibrated local property measurements can be difficult to achieve.

Figure 25.7 shows a typical potential map of two self-assembled monolayers (SAM s) patterned by microcontact printing. In this case one SAM is an alkanethiol, while the other is a conjugated conductive molecule. The difference in surface potential is obvious but the basis of the difference is not entirely clear. There are, in principle, four contributions to the potential of a SAM: the substrate work function, the dipole in the surface bond (usually S–M or \(\mathrm{SiO_{\mathit{x}}}\)–Si), the dipole in the molecule, and the terminating end group. Eng et al showed that the potential of alkanethiols on Au increases with the increase of chain length [25.57]. Sugimura et al calculated dipole moments in a sequence of siloxane coupled molecules and the trends agreed with experiment [25.58]. These results provide evidence for the contribution of the molecular dipole to the measured surface potential. Alvarez et al [25.59] showed that for the SAM of alkanes on metal, the S–M bond dipole also affects the measured surface potential. While the quantification of the relative contribution of SAMs to surface potential is challenging, SSPM easily quantifies potential variations with meV energy resolution and is used routinely to characterize complex films.

Fig. 25.7

SSPM image of SAM of alkanethiol and conjugated molecules self-assembled on Au, patterned with microcontact printing. Courtesy of Rodolfo Alvarez

On samples with morphological variations, such as grains, SSPM in the presence of a lateral field can elucidate the behavior of individual microstructural features. This is illustrated in Fig. 25.8a-d, which shows the behavior of a polycrystalline ZnO surface under different applied lateral biases. The topography includes features caused by polishing scratches, polishing particles, orientation-dependent polishing rates, second phases, and pores. At zero bias, the surface potential is sensitive to the second phases and even distinct grain orientations (Fig. 25.8a-db). On application of \(-{\mathrm{1}}\,{\mathrm{V}}\) external bias laterally from left to right, clear potential steps at grain boundaries are evident (Fig. 25.8a-dc). This contrast inverts when the applied bias is reversed (Fig. 25.8a-dd), although not perfectly at second phases. Such results therefore provide the local voltage-dependent transport properties of a wide variety of microstructural features. Taking directional derivatives even allows the current flow to be determined at all imaged points.

Fig. 25.8a-d

Topography (a) and surface potential (bd) for three distinct lateral in situ biasing conditions of a ZnO varistor revealing individual grains, second phases, and highly voltage-sensitive grain boundaries. Unpublished, B.D. Huey, D.A. Bonnell

Although not explicitly stated, much SSPM is done in ambient conditions. Indeed the ease of measurement is a strong advantage for its use as a qualitative characterization tool. As with all ambient measurements, the possible interaction of the environment with the surface must be considered; indeed, there are situations in which these effects dominate. Some of the early studies involved imaging ferroelectric domains in air [25.60] and it was eventually understood that the strong field due to domain polarization at a surface is almost completely screened, presumably by adsorption. Domains are easily imaged but quantifying the magnitude of surface potential is challenging. In fact, the sign of the measured potential is sometimes opposite that of the domain potential. Ferroelectric domains represent an extreme case of local electric fields, but even for grain boundaries intersecting a surface the effect is observed. Figure 25.9 compares the potential of an atomically abrupt boundary in \(\mathrm{SrTiO_{3}}\) measured in air and in ultra-high vacuum ( ) [25.61]. The boundary contains an intrinsic charge, which results in a potential variation at the intersection with the surface. In ambient conditions the charge attracts compensating adsorbates and the measured difference in surface potential is under \({\mathrm{20}}\,{\mathrm{mV}}\). In UHV, the uncompensated difference in potential is on the order of \({\mathrm{90}}\,{\mathrm{mV}}\) and opposite in sign.

Fig. 25.9

KFM of a \(\Upsigma 5\) grain boundary in \(\mathrm{SrTiO_{3}(100)}\). Courtesy of Rui Shao

Two contact techniques, scanning spreading resistance microscopy ( ) [25.62, 25.63, 25.64] and scanning capacitance microscopy ( ) [25.65, 25.66, 25.67], have been developed to characterize semiconductors. In SCM, a high frequency capacitance sensor detects the tip–sample capacitance as the tip is scanned across the sample. In SSRM, a conducting tip is biased with respect to the sample and the direct current through the tip–surface contact is detected under force feedback control. The amount of current is determined by the local spreading resistance of the surface, which is related to the local conductivity. However, the native oxide layer on Si hinders tip–surface contact, such that carrier profiling in Si-based devices usually requires a tip coated with a hard but conducting material and a high spring constant cantilever to provide strong indentation forces (\(\approx{\mathrm{20}}\,{\mathrm{{\upmu}N}}\)) [25.68]. Doped diamond-coated tips are thus commonly used in spreading resistance measurements. With SCM, on the other hand, a smaller indentation force is necessary and thus metal-coated probes are typically suitable [25.69]. A sinusoidal voltage applied to the tip induces the depletion and accumulation of carriers, resulting in a change in capacitance, \({\Updelta}C\). In a semiconductor, this depletion/accumulation width is inversely related to the carrier concentration, so mapping \({\Updelta}C/{\Updelta}V\) yields a carrier concentration profile. Difficulties in quantification arise if the dopant concentration is nonuniform and when spatial resolution degrades due to low dopant concentrations. Analysis of SCM results are mathematically challenging, usually requiring or numerical approaches [25.70, 25.71, 25.72, 25.73]. However, SCM notably distinguishes the difference between n- and p-dopants in the sample, whereas SSRM does not. On the other hand, metallic and insulating samples give no contrast in a SCM image, while SSRM images defects in insulating and in metallic films [25.69].

Another transport-related technique for electronic property characterization on the nanoscale is scanning gate microscopy ( ). SGM is a two-scan technique. During the first scan topography of the sample is monitored in intermittent contact mode. During the second scan a sinusoidal voltage is applied across the sample, a biased tip is brought within proximity of the sample, and the magnitude of the current across the sample is measured as a function of tip position. The first implementation of SGM was demonstrated on a single-wall carbon nanotube in 2000 [25.74]. The tip acted as a gate electrode in this nanotube circuit. It was found that the Fermi surface of the nanotube was not uniform along its length. Researchers from Stanford [25.75], UC Berkeley [25.76], and the University of Pennsylvania [25.77] used SGM to good effect in nanotube-based electronic circuits illustrating the ability to quantify local properties in individual nanotubes and to demonstrate three-terminal device behavior. Researchers from UC Irvine [25.78] measured the gating effect of a biased AFM tip on ZnO nanowires and found it to be 200 times smaller than that of single-wall carbon nanotubes [25.75].

Research in the group of R.M. Westervelt extended the concept of using a SPM tip as a perturbing probe to visualize the flow of electron waves in a two-dimensional electron gas. They produced a planar electron gas \({\mathrm{57}}\,{\mathrm{nm}}\) below the surface in a GaAs/AlGaAs heterostructure, with a quantum point contact formed by a pair of gates on the surface. A biased tip near the surface will capacitively couple to the underlying electron gas. As the tip is scanned across the surface, it decreases the conductance through the contacts when it is over a region of high electron flow and has no effect over a region with low electron flow. Similar to SGM, the image is the current or conductance across the gap as a function of tip position on the surface. Figure 25.10 illustrates the geometry of the quantum point contact and the pattern of electron flow that results from a system with a density of \({\mathrm{4.5\times 10^{11}}}\,{\mathrm{cm^{-2}}}\), mobility of \({\mathrm{1\times 10^{6}}}\,{\mathrm{cm^{2}/Vs}}\), a mean free path of \({\mathrm{11}}\,{\mathrm{{\upmu}m}}\), and a Fermi wavelength of \({\lambda}_{\mathrm{F}}={\mathrm{37}}\,{\mathrm{nm}}\) [25.79]. These images were recorded with the sample and the SPM at \(T={\mathrm{1.7}}\,{\mathrm{K}}\). Electron transport in graphene and \(\mathrm{MoS_{2}}\) has similarly been imaged by Rathi et al [25.80].

Fig. 25.10

Experimental images (outside) and theoretical simulations (inside) of the flow of electron waves through a quantum point contact. Fringes spaced by half the Fermi wavelength demonstrate coherence in the flow. Reprinted from [25.79], with permission from Elsevier

Techniques such as SSPM/KFM and SCM/SGM can be combined into a single measurement where a sinusoidal voltage is applied to a cantilever driven on resonance, as with EFM [25.81, 25.82, 25.83]. The resonant frequency response is modulated through changing the applied voltage according to signals at multiple harmonics. In this way, both the surface potential and the spatial derivative of tip–sample capacitance can be derived. With further theoretical work and specific device geometries, it is possible to extract intrinsic electrical transport properties such as mobility [25.84, 25.85], diffusion length [25.55], and recombination rates. The temporal photoresponse of potential and capacitance can also be detected, providing insight into charge generation [25.86], trapping [25.87], and lifetime [25.88] effects. Further experimental control is possible through varying the intensity [25.88, 25.89] or wavelength [25.84, 25.90] of the illumination source.

To truly surpass the far-field resolution limit, near-field scanning optical microscopy ( ) approaches have been developed. Thoroughly reviewed elsewhere in this book, they enable optical investigations of nanostructures by using a tip–probe as an illumination source. Due to the local excitation and/or detection of photons, this scanning probe technique can be combined with many other optical methods to achieve enhanced resolution. Combined with photoluminescence spectra, for instance, it is possible to resolve single monomers [25.91]. Additionally, local carrier lifetime and charge trapping dynamics can be investigated through PL measurements [25.92, 25.93].

Even with a standard AFM, however, optically induced transport characteristics can be resolved by collecting photoinduced charges through a cantilever tip. Photoconductive AFM ( ) can measure both photogenerated free charges, as well as enhanced photoconductivities, which have also been reported with SSPM and EFM. When the work function of the tip is well matched with the density-of-states for the induced carrier of interest, current will flow through the tip to give a local measurement of charge transport. With respect to photovoltaics, when the applied potential on the tip matches the surface potential, any collected current can specifically be related to a local measurement of the effective short-circuit current. For example, Fig. 25.11 displays the measured \(I_{\mathrm{SC}}\) superimposed on topography for a \(\mathrm{MAPbI_{3}}\) thin film, revealing inter- and intragranular contrast [25.94]. The applied voltage to the tip when the current ceases to flow can equivalently be related to a local measurement of the open-circuit voltage. In polycrystalline materials, these current-voltage characteristics are crucial to measuring local conductivity [25.82, 25.95, 25.96], transport [25.97, 25.98], and charge generation [25.98]. Further local electrical characterization can be achieved through high-frequency oscillations of the tip voltage as well. Scanning microwave impedance microscopy ( ) uses a microwave source to observe variations in permittivity, conductivity, capacitance, and resistance [25.100, 25.99].

Fig. 25.11

Effective short-circuit current superimposed on topography for a polycrystalline \(\mathrm{MAPbI_{\mathbf{3}}}\) molecular perovskite solar cell. Reprinted with permission from [25.94]. Copyright 2016 American Chemical Society

The advantages of these various SPM measurements obviously depend on the materials under observation. For example, inorganic crystalline thin-film solar cells typically have minority carrier lifetimes on the order \(\approx\) 100 nanoseconds, which are evidently difficult to access experimentally. Organic bulk heterojunction solar cells, on the other hand, may exhibit surface potentials from free minority carriers on the order of milliseconds, allowing for time-dependent observations [25.101, 25.102, 25.81]. Organic materials are typically more susceptible to damage by heat and oxidation though, making them less suitable for pcAFM measurements and more appropriate for non- or intermittent-contact modes.

Finally, for a wide range of oxide electronics in particular, ionic transport provides critical functionality rather than electronic transport. Examples include fuel cells, water splitting, and some catalytic reactions. In principle, such ionic transport can be detected by probing the local electrical potential or Faradic current, in which cases the techniques described above can be useful. For instance, impedance spectra have been acquired through the AFM probe with ZnO, metal/nitride test structures, and Nafion™ membranes [25.103].

On the other hand, electrochemical strain microscopy ( ) is a scanning probe technique that probes ionic motion directly. In ESM a biased SPM tip produces a local electric field that induces an electrochemical process under the tip. In functional oxide compounds this results in diffusive and electromigrative ionic currents. The local aggregation or dispersion of oxygen vacancies is necessarily associated with these processes and results in strain and surface displacements that can be detected by the SPM tip. The strain is approximately \(\approx{\mathrm{5}}\,{\mathrm{pm}}\). This is a contact method in which the conservative and dissipative contributions to the signal matter, and crosstalk can occur, therefore a differential detection method is required. In such differential detection schemes, the cantilever response is probed at more than one frequency at each spatial position. Several approaches have been implemented including dual frequency measurements [25.104], fast lock-in sweeps [25.105], intermodulation microscopy [25.106], and band excitation detection [25.107]. Using this detection strategy and plotting the response as a function of tip–applied voltage, a hysteresis loop can be produced that is characteristic of the electrochemical reaction at that specific location.

For example, Fig. 25.12a schematically illustrates a catalytic reaction pathway at a metal particle on an oxide electrolyte [25.108]. A predominant issue in this field is related to the reactivity at the triple points where metal, oxide and gas reactants meet. The oxidation and reduction reactions result in oxygen vacancy production and motion and consequently strain. Figure 25.12b displays hysteresis loops for Pt particles distributed on the surface, the underlying yttrium-stabilized zirconia substrate, and two representative triple point boundaries. Figure 25.12c superimposes the relative activity according to these ESM results on the topographic structure. These results clearly identify increased activity at the triple points compared to the substrate or particle surfaces, providing insights into the mechanism of this catalytic reaction as well as ideal microstructures for optimizing catalysis applications.

Fig. 25.12

(a) ESM schematic demonstrating the influence of a tip bias on the electrochemical potential of nearby mobile oxygen species, (b) ESM loops obtained at triple phase boundaries (TPB) as compared to pure Pt or YSZ, (c) measured electrochemical activity superimposed on Pt nanoparticles deposited on a YSZ substrate. Reprinted by permission from Springer Nature: Nature Chemistry [25.108]

25.2.2 Dielectrics and Piezoelectrics

Techniques to probe three classes of dielectric properties are presented here: dielectric constant and dielectric function; piezoelectricity; and ferroelectricity. Utilizing higher-order harmonic signals and clever detector design allows many variations of these properties to be detected, and a number of probes have been developed to quantify linear and nonlinear dielectric properties locally.

Of course impedance is a complex function that is frequency dependent and provides access to a wide range of properties including time dependence and dielectric function in addition to the dielectric constant. Dielectric function leads to polarization, electron state relaxation times, and ionic diffusion. The impedance, \(Z\left(\omega\right)=V\left(\omega\right)/I\left(\omega\right)=\left|Z\right|\mathrm{e}^{\mathrm{i}\phi}\), where i represents the imaginary unit. This depends on the capacitance as \(Z_{\text{C}}=1/\mathrm{i}\omega C=-\mathrm{i}/\omega C\), along with the loss tangent \(\tan\phi=1/\omega RC\). Therefore, impedance can include real and imaginary components with information about polarization and time constants. Depending on the property of interest, impedance is represented as a Cole–Cole/Nyquist plot , a Bode plot , or the frequency dependence of the loss tangent. Extracting materials properties from impedance measurements requires a model circuit that is equivalent to the constituents of the material or device. For example, \(R\) could relate to the linear resistance in a grain, \(C\) to the charge at an interface, \({\omega}\) to charge recombination rates, etc. In simple configurations, property analysis can be straightforward; in complex configurations, there can be ambiguities. This is a well-developed field for macroscopic characterization and Mason et al [25.109] nicely summarize potential artifacts along with strategies to eliminate them.

There are two configurations in which these properties can be probed locally. The first introduction of frequency dependence in scanning probes is referred to as scanning impedance microscopy ( ) [25.110]. This is a noncontact, first harmonic detection in which the oscillating electrical signal is applied to the sample instead of the tip. The tip can act either as a nonperturbing probe or as a local gate, in a configuration that allows both the amplitude, which is related to potential, and the phase, which is related to loss, to be quantified. The frequency dependence can be used to isolate relaxations associated with electron traps at interfaces and defects. Generally, the lower-frequency impedance response is dominated by resistive contributions while higher-frequency responses are dominated by capacitive contributions.

Shao et al implemented this technique on \(\mathrm{SrTiO_{3}}\) grain boundaries, determining the effect of atomic structure (Fig. 25.13a, from \(Z\)-contrast TEM) on local anomalies in the boundary resistance and capacitance character induced by interface dipole ordering [25.61]. Figure 25.13b shows the frequency dependence of the grain boundary phase shift \({\varphi}_{\text{gb}}\) in a bicrystal. The solid line fits of the resistive regime, relaxation frequency, and capacitive regime are superimposed. For comparison, surface potential images of such interfaces clearly display a potential barrier at the grain boundary (Fig. 25.13c). The temperature dependence of \(R_{\text{gb}}\) at two different tilt boundaries (Fig. 25.13d) reveals a complicated behavior for such barriers, with a negative temperature coefficient of resistance such as that expected in ferroelectric compounds but not in \(\mathrm{SrTiO_{3}}\).

Fig. 25.13

(a\(Z\)-contrast transmission electron microscopy of an Nb-doped \(\mathrm{SrTiO_{3}}\) tilt boundary. (b) Frequency dependence of grain boundary phase shift in \(\mathrm{SrTiO_{3}}\) bicrystal with various circuit terminations—solid lines are fits for grain boundary resistance and capacitance. (c) SSPM identifying a grain boundary intersecting the surface. (d) The temperature dependence of grain boundary resistance for two boundaries with distinct interface structures, as well as the single-crystal resistance, which is orders of magnitude lower and hence negligibly influences the boundary measurements. Courtesy of Rui Shao

The second approach to accessing frequency-dependent transport expands the frequency range to eight orders of magnitude and provides higher spatial resolution. Nanoimpedance microscopy and spectroscopy ( ) [25.111, 25.112] is a contact probe with force feedback, in which the oscillating bias signal is applied to the tip; current phase and amplitude are detected at the sample.

The first demonstration of NIM involved mapping of grain boundary limited transport within polycrystalline ZnO varistors using a one-terminal configuration [25.111]. Figure 25.14a-g shows the topography (Fig. 25.14a-ga,d), impedance modulus \(\log|Z|\) (Fig. 25.14a-gb,e), and phase \({\phi}\) (Fig. 25.14a-gc,f) images collected over an area of three ZnO grains at \(f={\mathrm{10}}\,{\mathrm{kHz}}\) with a probe bias of \(V_{\text{ac}}={\mathrm{50}}\,{\mathrm{mV}}\) and tip–sample DC biases of 35 and \({\mathrm{40}}\,{\mathrm{V}}\), respectively. The phase images show distinct differences in the transport mechanisms of the grains. The phase angle measured at grain 1 is \(-90^{\circ}\), indicative of purely capacitive transport. But the measured impedances of grains 2 and 3 decrease along with tip bias, characteristic of varistor-like transport. The Cole–Cole plot collected by spectroscopic NIM of a single ZnO grain boundary using a two-terminal configuration confirms this behavior (Fig. 25.14a-gg), manifested as two distinct relaxation processes associated with both grain boundary transport and the tip–sample Schottky contact.

Fig. 25.14a-g

NIM images for a polycrystalline ZnO varistor, evidencing correlations between (a,d) topography, (b,e) impedance modulus, and (c,f) phase. (g) Representative Cole–Cole plots for a single ZnO grain boundary. Reprinted from [25.111], with the permission of AIP Publishing

Of course scanning probe microscopy is based on interactions between the tip and surface, and is effective only because the interactions at the tip apex are stronger than similar interactions in the surrounding region. For example, the force between the tip and surface is much stronger than that between the cantilever and surface, so the signal is predominately that under the tip. In SIM and NIM the presence of these regional interactions limits the sensitivity. Figure 25.15 schematically illustrates the various stray capacitances that can contribute to the absolute value of the signal. In some cases, this stray capacitance contributes a constant background that can be ignored, but it does limit the ultimate sensitivity. Contributions to the stray capacitance originating from the tip–sample vicinity include tip–sample, cantilever-sample, and holder-sample capacitances. Pingree and Hersam addressed this issue with the introduction of a variable resistor-capacitor (RC ) bridge circuit that mediated the impact of these fringe capacitances and enhanced sensitivity by five orders of magnitude [25.113]. The bridge circuit effectively nulls the stray capacitance resulting in a NIM signal composed of only the local impedance.

Fig. 25.15

Schematic of geometry-defined stray capacitance effects, which may influence SPM-based electronic and transport measurements

Kathan-Galipeau et al developed torsional resonance nanoscale impedance microscopy ( ) [25.114]. This exploits the amplitude of torsional resonances of the cantilever to serve as the force feedback parameter, enabling near-field contact with loads on the order of \({\mathrm{10}}\,{\mathrm{nN}}\). They combined this level of near-surface force control with a stray capacitance compensation similar to that of Pingree and Hersam to achieve attofarad sensitivity. Consequently, they were able to quantify real and imaginary properties of monolayers of optically active peptides. Fumagalli et al took a different approach to improving capacitance sensitivity, leveraging current sensing microscopy (CAFM), except with AC detection. Coupled with the thickness acquired from simultaneous conventional AFM, this provided nanoscale maps of the local dielectric constant for bilayer membranes as depicted in Fig. 25.16 [25.115].

A complementary strategy to accessing linear and nonlinear dielectric properties is referred to as scanning nonlinear dielectric microscopy ( ) [25.116, 25.117] or near-field microwave microscopy ( ) [25.118, 25.119]. These approaches utilize a coaxial probe in which a sharp, center conductor tip protrudes from a grounded shield. The probe is actually the end of a transmission line resonator, which is coupled to a microwave source. The concentration of the microwave fields at the tip changes the boundary condition of the resonator, and hence its resonant frequency and quality factor. The magnitude of the perturbation depends on the dielectric properties of the sample, specifically, the change in resonant frequency, \(({\Updelta f_{0}})/{f_{0}}=g\Updelta\varepsilon^{\prime}\), where \(g\) is a constant, \(\Updelta\varepsilon^{\prime}\) is the real part of the dielectric constant, and \(\Updelta{1}/{Q}=q\Updelta\varepsilon^{\prime\prime}\), where \(q\) is a constant, and \(\Updelta\varepsilon^{\prime\prime}\) is the imaginary part of the complex dielectric constant. The spatial resolution of the microscope in this mode of operation is about \({\mathrm{1}}\,{\mathrm{{\upmu}m}}\). NFMM with coaxial resonators has been used successfully to quantitatively image sheet resistance, dielectric constant, dielectric polarization, topography, magnetic permeability, and the Hall effect. Lu et al have used NFMM on a ferroelectric (001) \(\mathrm{LiNbO_{3}}\) single crystal to distinguish variations in dielectric constant and ferroelectric domains. The growth process of this crystal results in periodic composition changes, which should alter the local dielectric constant. Different ferroelectric domains in this crystal have the same dielectric constant. But these two periodic variations, in composition and ferroelectric domain orientation, are not coincident. Since \(({\Updelta f_{0}})/{f_{0}}\) relates to dielectric constant and \({\Updelta}Q\) relates to loss associated with ferroelectric domain boundaries, images of each should and did demonstrate distinct periodicities [25.120]. Anlage et al separately demonstrated that high-order harmonic powers acquired by NFMM can further be used to spatially resolve local nonlinearities. For instance, in Anlage's work, the grain boundary area of a superconducting YBCO thin film deposited on a \(\mathrm{SrTiO_{3}}\) bicrystal was identified from the ratio of the powers in the second and third harmonics [25.121].

Fig. 25.16

Schematic for AC-based dielectric microscopy with subattofarad resolution applied to a bilayer biomembrane, providing the local membrane capacitance, complementary thickness, and calculated local dielectric constant. Reprinted with permission from [25.115]. Copyright 2009 American Chemical Society

In principle, utilizing higher-order harmonic signals and clever detector design allows dielectric constant, electrostriction, and piezoelectric properties to be detected. In practice, a number of probes have been developed to quantify linear and nonlinear dielectric properties locally. These have focused on electromechanical coupling coefficients, hysteretic ferroelectric domain switching, etc.

Piezoelectric force microscopy ( ) is a related scanning probe method that is used increasingly to determine electromechanical coupling coefficients at local scales. Like NIM, an oscillatory electric field is applied to a tip or sample while in contact (Fig. 25.17). If the material is piezoelectric, the field locally deforms the surface and oscillates the tip, generally known as the piezoresponse ( ) [25.122, 25.123] but technically according to the converse piezoelectric effect. In a ferroelectric material, domains with an upward polarization vector contract with a positive voltage applied to the probe, producing a phase shift of \({\delta}=180^{\circ}\). For downward oriented domains, the situation is reversed, and \({\delta}=0^{\circ}\) because the deformation is in phase with the field. The phase therefore indicates the out-of-plane (OP ) orientation of polarization. The piezoresponse amplitude, \(A=A_{1\omega}/V_{\text{ac}}\), defines the magnitude of this interaction. For the ideal case of a (100) surface of a tetragonal compound, \(A={\upalpha}d_{33}\), where \({\upalpha}\) is a proportionality coefficient close to unity [25.124], the piezoelectric constant, \(d_{33}\), is related to the polarization, \(P\), as \(d_{33}={\varepsilon}{\varepsilon}_{0}Q_{33}P\), where \(Q\) is the second-order electromechanical coefficient. For the general case, there are also in-plane components of polarization that can be accessed by measuring the lateral response of the tip to a field variation [25.125, 25.126]. Furthermore, the piezoelectric response is a tensorial function, the complexity of which depends on the symmetry of the compound and the orientation of the grain or crystal. Harnagea et al have shown that even for \(\mathrm{BaTiO_{3}}\) with relatively high symmetry [25.127], either the grain orientation or the in-plane component must also be known to determine domain orientation.

Fig. 25.17

Working principle of PFM. Applying an AC bias to a probe in contact with a sample generates a local electric field. If the material is piezoelectric the surface will distort according to the converse piezoelectric effect, with sensitivity to distinctly oriented domains

This is illustrated nicely by Gruverman and coworkers [25.128] who undertook the three-dimensional high-resolution reconstruction of the polarization vectors in a (111)-oriented \(\mathrm{Pb(Zr{,}Ti)O_{3}}\) ferroelectric capacitor by detecting the in-plane and out-of-plane polarization components using PFM. Figure 25.18a-e shows the amplitude and phase for the vertical Fig. 25.18a-ea,d and lateral Fig. 25.18a-eb,e contributions to the piezoresponse of a region that is nominally poled in the vertical direction. Despite exhibiting uniform vertical contrast, the lateral component exhibits significant variation. Knowing that this material is oriented in the (111) direction, the individual domain orientations can be determined, as sketched Fig. 25.18a-ec.

Fig. 25.18a-e

Vertical (a,d) and lateral (b,e) PFM for a PZT capacitor, including amplitude (top) and phase (bottom) images as well as a schematic (c). Equivalent PFM signals from a third perpendicular vector (only two are presented) allows complete determination of the three-dimensional polarization vectors. Reprinted from [25.128], with the permission of AIP Publishing

This vector PFM concept has been used to investigate ferroelectric phases embedded in nonferroelectric media such as glass [25.129], and to determine the relative ratio of certain domain orientations as a function of film morphology [25.130]. Such work enables domain wall orientations and charging to be identified, further revealing that domain wall density is often a strong function of the switching mechanism and progress [25.131]. This has been leveraged to develop a thermal switch [25.132] as well as electronic devices based on control [25.133] of conductive domain wall positions [25.134] or density [25.135] that are uniquely revealed or even written by PFM.

In PFM voltage spectroscopy [25.136], the piezoresponse (\(A_{1{\omega}}\)) and phase (\({\varphi}\)) are measured as a function of DC potential offset (\(V_{\mathrm{dc}}\)) on the tip [25.126, 25.127]. PFM spectroscopy yields local electromechanical hysteresis loops, quantifying remnant response and coercive bias, on the \(20{-}50\,{\mathrm{nm}}\) level. This is illustrated in Fig. 25.19a,b with \(\mathrm{PbTiO_{3}}\) [25.136]. The hysteresis curves are acquired on a \(\mathrm{PbTiO_{3}}\) film with \(\approx{\mathrm{100}}\,{\mathrm{nm}}\) grain size, before and after illumination by UV to demonstrate the effect of photoinduced charges on domain switching. The phase signal is related to polarization and therefore has the shape of a conventional \(P\)\(E\) hysteresis loop. The amplitude signal shows that strain also traces the conventional butterfly shape of ferroelectric hysteresis. These curves illustrate that a critical tip bias (field) is required to achieve polarization switching. A number of attempts to relate local hysteresis with crystallographic orientation and piezoresponse amplitude have correspondingly been reported [25.137].

Fig. 25.19a,b

Vertical phase (a) and amplitude (b) hysteresis loops of \(\mathrm{PbTiO_{3}}\) thin films as grown (open symbols) and after UV treatment (full symbols). Reprinted from [25.136], with the permission of AIP Publishing

One critical issue with regard to quantification and spatial resolution limits is the question of what volume is accessed by PFM. The answer is found by determining the decay of the electric field below the probe tip, which in turn depends on the dielectric constant and conductivity of the material. For oxide ferroelectric compounds the volume is on the order of \(20{-}200\,{\mathrm{nm}}\) [25.138, 25.139]. Consequently, for films thinner than this, or inclined domain structures, quantification requires accounting for this volume.

The question arises as to whether PFM influences the properties it is measuring. Recently, it was shown that the mechanical strain produced by the tip can suppress local polarization [25.140] or induce local ferroelectroelastic polarization switching [25.141, 25.142]. A quantitative analysis of the tip–induced potential and stress distribution is required to characterize local ferroelectric properties by SPM [25.143, 25.144, 25.145, 25.146, 25.147]. A rigorous treatment of the image contrast includes simultaneous electrostatic and electromechanical interactions. One complication in PFM is that both long-range electrostatic forces and the electroelastic response of the surface contribute to the PFM signal [25.148, 25.44]. Even under optimal conditions, the basis of the electroelastic contribution, \(A_{\text{piezo}}\), is not straightforward because of the complex geometry of the tip–surface junction. Some progress in the quantitative understanding of PFM has been achieved [25.149, 25.150, 25.151, 25.152]. Depending on the tip radius of curvature and the indentation force, PFM may correspond to the electroelastic response of the surface induced by the contact area (strong indentation limit) or be dominated by the electroelastic response of the surface due to the field produced by the spherical part of the tip (weak indentation limit). In these cases, the magnitude of surface and tip displacements is determined by the electromechanical coupling in the material. Alternatively, the signal can be dominated by the electrostatic tip–surface interactions (electrostatic limit) and have little relation to the properties of the material. Taking an approach familiar to materials scientists, the analytical solutions of these interactions can be presented as contrast mechanism maps that relate experimental conditions to properties of the material and delineate the conditions under which quantitative measurements can be obtained (Fig. 25.20) [25.149].

Fig. 25.20

Sketch of dominant PFM contrast mechanisms for typical ranges of tip radii and applied forces (assuming \(V_{\text{tip}}=V_{\text{surface}}\), and a \({\mathrm{0.1}}\,{\mathrm{nm}}\) dielectric gap between tip and sample). The dotted line delineates the region where stress-induced switching is possible. After [25.149]

25.2.3 Dynamic Processes

The goal of imaging surface dynamics with nanoscale resolution is an obvious extension of the many successful variations and applications of SPM. One of the most convenient and widely studied materials systems is ferroelectric polarization switching, given the typically oxide-based specimens that are mechanically robust, their often smooth surfaces diminishing tip–sample geometric convolution, and the discrete domain polarization directions, which are easily distinguished via their normal or lateral vector components. Many studies consider domains before and after poling, or more insightfully following a range of poling conditions such as poling duration. Simultaneous scanning and domain imaging, especially at high speeds on the order of frames per second [25.153], is also powerful. The distinct images in Fig. 25.21, for example, are extracted from a movie of 256 consecutive frames. These efficiently provided maps and statistics on nucleation and growth dynamics, including the spatial and energetic density of defect states [25.154]. Extensions of this concept with the multiferroic \(\mathrm{BiFeO_{3}}\) revealed a previously unrecognized two-step domain switching mechanism, which was then leveraged to develop a new magnetoelectric device [25.156].

Fig. 25.21

Ferroelectric switching mechanisms analyzed during in situ poling based on 256 consecutive high-speed PFM images in a single area. Reprinted from [25.154] with permission from John Wiley and Sons

Movies of topographic or constant electron density maps were employed even earlier to monitor surface dynamics. The Besenbacher group led many efforts in high-speed STM to directly monitor catalysis [25.158]. Rost et al developed video rate SPM tools for UHV investigations primarily of atomic and molecular surface motion [25.159]. Nanoscale imaging of dynamic biological processes in liquid have especially garnered attention. In pioneering work by the Ando group, Fig. 25.22, a Myosin V molecule is imaged walking along an actin filament, directly revealing for the first time this fundamental biomolecular transport mechanism [25.155].

Fig. 25.22

(a) Successive AFM images showing processive movement of M5-HMM in \({\mathrm{1}}\,{\mathrm{{\upmu}M}}\) ATP. The arrowhead identifies a streptavidin molecule, arrows signal the coiled-coil tail of M5-HMM tilted towards the minus end of actin, and scan area is \(130{\times}{\mathrm{65}}\,{\mathrm{nm}}^{2}\) with a scale bar of \({\mathrm{30}}\,{\mathrm{nm}}\). (b) Schematic of two-headed M5-HMM bound and (c) in motion. Reprinted by permission from Springer Nature: Nature [25.155]

25.2.4 Mechanical, Chemical, and Thermal Properties

Of course the very term atomic force microscopy highlights the important role SPM plays in local mechanical measurements. Classic examples include Pethica's observations of atomic-scale energy dissipation [25.160], the Schwarz group's work in 3-D reconstructions of chemical forces between atoms on a tip and sample [25.161], Jarvis' report imaging hydration layer for lipid bilayers [25.162], and intramolecular force mapping for bacterial surface layers by Müller et al [25.163]. On a slightly larger spatial scale, similar work has provided valuable insight into the nanoscale properties of biomolecules [25.164], protein adhesion for marine mussels [25.165], at the surfaces of cells [25.166], and for other soft materials [25.167].

Atomically modulated friction has been resolved as well with friction force microscopy ( ), revealing stick-slip mechanisms and under some conditions continuous sliding resulting in superlubricity [25.168]. FFM is also instrumental for studies of atomic and nanoscale wear [25.169]. Bhushan et al have widely investigated hydrophobicity, adhesion, and friction with AFM [25.170]. Landman et al correlated such measurements to atomistic modeling [25.171]. And for surfaces exhibiting distinct chemical functional groups or patterns, Frisbie et al even demonstrated chemomechanical sensitivity via chemical force microscopy ( ) [25.172]. Molecular recognition was similarly reported based on specific hydrogen bonding for complementary bases of DNA [25.173]. Compositional mapping based on indentations, friction, phase imaging, torsional resonances (TRAFM), and related concepts are even more widespread at the nanoscale and larger [25.174].

But stiffness or modulus mapping of nano- to microscale structures is far more common with AFM, typically based on one or many approach and retraction curves. Interpreting these force–distance curves according to Hertzian mechanics (\(F=E^{*}\sqrt{R^{*}z^{3}}\)) is both analytically straightforward and reasonably effective for a surprising range of tip–specimen variations (\(E^{*}\) is the reduced bulk modulus and \(R^{*}\) the reduced radius). More sophisticated mechanical models [25.175], and in the past decade real-time mechanical mapping [25.176], have also been increasingly employed. However, given typical probe stiffness values from 0.01 to \({\mathrm{100}}\,{\mathrm{N/m}}\), conventional indentation studies are usually limited to relatively low modulus materials such as polymers and biological samples [25.174]. Substantial effort has especially been made to investigate the mechanical properties of living cells, connecting the results to cell type, disease states, cell division, drug delivery, local function, etc..

For less compliant materials, phase imaging sometimes provides insight into local mechanical properties. However, the correspondingly low tip–sample forces can be highly susceptible to variations in adhesion, especially as a function of humidity [25.177]. For this reason, a family of SPM-based methods was developed essentially by combining the spatial resolution of AFM with the mechanical sensitivity to stiff materials of ultrasonics. Such work has enabled nanoscale investigations of phase transitions for metals and oxides [25.179], and even elastic inhomogeneities for hard TiN coatings [25.180]. Ultrasonic force microscopy ( ) [25.181], for example, provides contrast even for subtle changes in modulus as with nanoscale heterostructures of Si and SiGe. This is based on sample vibrations at sufficiently high frequencies that dynamic lever stiffening causes angstrom-scale indentations, coupled with low-frequency modulations to which the relatively soft lever can detectably respond [25.182]. For atomic force acoustic microscopy ( ) [25.183], on the other hand, higher amplitude oscillations are employed specifically at the contact resonance frequency, leading to contrast that is both highly sensitive to the reduced modulus of the tip–sample junction as well as highly quantifiable and relatable to more macroscopic studies. This includes realizing loss and storage moduli at the nanoscale, which agree with DMA studies [25.184], as well as maps of local elastic stiffness and damping (Fig. 25.23a,b), which follow predicted rules of mixtures for titanium alloys [25.157]. Such measurements are even feasible in liquids [25.187].

Fig. 25.23a,b

AFAM (a) maps and (b) spectra for a titanium alloy, with specific contact resonance frequencies \(\omega\) for distinct microstructural phases (\(\upbeta\), \(\upalpha^{*}\), \(\upalpha\)) due to their unique mechanical properties. Reprinted from [25.157], with permission from Elsevier

Such sensitivity to contact resonances has been leveraged in other clever ways as well. Instead of studying nanomechanics, characteristic infrared ( ) radiation vibrational spectra can be detected at the nanoscale. This is possible by sweeping the wavelength of a pulsed IR source, optimally at the contact resonance frequency. Recording the resulting magnitudes of thermally induced surface vibrations yields IR absorption spectra similar to those acquired at the macroscale, thereby providing local chemical content for features as small as \({\mathrm{20}}\,{\mathrm{nm}}\) across [25.188]. This is depicted schematically in Fig. 25.24a-d, including the topography and relative IR absorption at the \(\mathrm{CH_{2}}\)-wagging mode wavenumber of \({\mathrm{1340}}\,{\mathrm{cm^{-1}}}\) for islands of self-assembled monolayer PEG (polyethylene glycol) on gold [25.178]. This imaging mode is particularly sensitive to plasmonic effects, as demonstrated by the similar photothermal-induced resonance imaging method [25.189]. Superresolution photoactivated AFM equivalently employs the visible spectrum for absorption-contrast-based imaging [25.190].

Fig. 25.24a-d

Nano-IR investigation of PEG self-assembled monolayer patches on a gold substrate. The pulsed IR source, focused on the specimen at the tip apex, induces local thermal expansion due to optical absorbtion as sketched (d) where the frequency can even reveal local mechanical properties (b). Sweeping the IR wavenumber can thus yield local IR spectra, even for nanoscale islands according to the topography (a), enabling composition mapping (c) based on specific IR absorption bands. Adapted from [25.178] with permission of The Royal Society of Chemistry

More traditional combinations of AFM and optics are also increasingly common, for instance with standard or total internal reflection fluorescence microscopy, confocal microscopy, laser scanning systems, and even superresolution [25.191]. The substantial SPM subfield of scanning near-field optics merits an entire separate chapter, but briefly either detects the near-field signal with an optical fiber or leverages the enhanced optical field at a probe apex where the tip essentially acts as a nanoantenna [25.192]. This enables high spatial resolution Raman microscopy, which allows chemical identification of adsorbed species [25.193] and even direct DNA sequencing [25.194]. Crystalline phases and orientations can even be mapped via scattering near-field microscopy coupled with infrared vibrational spectroscopy [25.195]. Other near-field variations have given insight into the origins of circular dichroism [25.196], while combining a nanoantenna probe with IR-enabled direct molecular vibrations to be detected [25.197].

25.2.5 In Situ and In Operando SPM

Beyond simply investigating materials properties at the nanoscale, SPM is also operable in a wide range of environmental conditions to enable in situ, in vitro, and in operando imaging. This is a crucial capability since the function of many technologically important materials systems and devices depends on dynamic processes in complex environments.

PCAFM has already been discussed for studies of photovoltaics as a function of illumination intensity, wavelength, or pulse duration [25.198]. Many AFM measurements are made as a function of humidity [25.199] or temperature as well, most commonly to monitor phase changes and their concomitant influence on mechanical, optical, electronic, or magnetic properties. In scanning thermal microscopy ( ) [25.201] and its variations, an active probe [25.202] serves as a heat source or temperature sensor, enabling direct temperature or thermal property mapping [25.203], even in liquids [25.204].

There are also numerous examples of SPM recording various stages in island or film deposition to determine nucleation and growth mechanisms. Fibrin polymerization, a key contributor for blood clotting, was imaged very early on in SPM development [25.205]. Such two-dimensional crystallization [25.206] or aggregation [25.207] of proteins is now regularly monitored in situ. This is feasible in air, vacuum, or liquid as demonstrated by studies of DNA supercoiling [25.208].

Dynamic surfaces, topographically and mechanically, are also accessible. As an example, while nanoelectromechanical sensors have been developed to further improve SPM technologies [25.209], resonant modes in oscillating microcantilevers have been directly mapped [25.210]. Elegant nanostethoscopy of vibration spectra generated by living (or dying) cells and sensed by an SPM probe has been demonstrated as well [25.211]. Sokolov extended this concept to living insects, as depicted in Fig. 25.25 [25.185, 25.186]. Very recent updates to these concepts yielded measurements of mass fluctuations in single living mammalian cells [25.212]. Nanoscale measurements of the frequency, phase, and force of beating myocardial cells [25.213] and cell patches [25.214] are another excellent example of nanoscale imaging of active materials.

Fig. 25.25

(a) Schematic of an AFM experiment on the elytra surface of a living ladybird beetle (H. convergens). From [25.185], reproduced with permission. (b) Frequency-dependent mechanical oscillations of the beetle in response to a flashing monochromatic light (\({\mathrm{10}}\,{\mathrm{dB}}\) shift per spectrum superimposed for readability). Acoustic noise in the room also shown (bottom) for comparison. Reproduced with permission from [25.186], published under CC-BY 5.0 license

Of course there are many examples of leveraging the high spatial resolution of an SPM probe for nanoscale electrochemistry via scanning electrochemical microscopy ( ) [25.215] and its variants. With rechargeable lithium ion batteries, mechanical failure of solid electrolyte interphases on silicon electrodes is an important technological challenge due to electrode expansion and contraction during cycling. Accordingly, Kumar et al monitored nanoscale swelling of Si electrode islands during charging and discharging, as well as crack development as a function of cycling [25.216]. Breitung similarly monitored morphology during lithiation of nano-Si electrodes [25.217], Wang reported measurements for \(\mathrm{Fe_{3}O_{4}}\) anodes [25.218], and Balke mapped ion diffusion times for \(\mathrm{LiCoO_{2}}\) cathodes [25.219].

But aside from monitoring electrochemical processes, researchers have also realized the potential of the fine AFM probe apex for lithographic anodization, for example to prepare and then test nanomechanical Si [25.220] and Al [25.221] devices. Nanolithography was achieved with self-assembled monolayers [25.222] and polymer brushes [25.223] as well. This concept of local anodization allowed the formation of patterned \(\mathrm{H_{2}}\)-sensing \(\mathrm{TiO_{2}}\) nanowires [25.224] and bipolar switches from NiO nanodots [25.225]. In the field of photoelectrochemical water splitting, nanoscale current/potential spectroscopy has additionally been reported for cobalt oxyhydroxide phosphate photoanodes, revealing functionality as a hole collector and as a catalyst for oxygen evolution [25.226].

More customized SPM systems have been developed for extreme environmental conditions and parameter control. Examples include systems with high position accuracy [25.227], variable magnetic field imaging [25.228], imaging during controlled specimen strain [25.229], cryogenic SPM [25.230], and high-temperature scanning [25.231]. For instance, in order to directly access local properties at high temperatures Nonnenmann et al developed an environmental chamber that allows SPM to be used under fuel cell operating conditions (up to \({\mathrm{600}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\), air atmosphere). Figure 25.26a-ca,b illustrates the operation of a solid oxide fuel cell, the potential distribution across the cell, and the design for the in operando system [25.200]. SSPM (KFM) results then provided local potential variations on cross-sectioned fuel cells at \({\mathrm{600}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\) at the cathode/electrolyte interface (left), within the electrolyte (center), and at the electrolyte/anode interface (right). The surface potential images and profiles, especially at the interfaces, clearly indicate that the SOFC is functioning [25.232].

Fig. 25.26a-c

Schematic of the operational concepts for a solid oxide fuel cell (a) and an in situ SOFC investigation by SPM (b). Images are displayed for each component (c) in a biased symmetrical LSF-YSZ SOFC, collected at \({\mathrm{600}}\,{\mathrm{{}^{\circ}\mathrm{C}}}\), including the cathode, electrolyte, and anode, with interfaces identified by light dotted lines. The topography, surface potential from SSPM, and SSPM cross-sections from each reveal a general slope due to the in situ laterally applied biases as well as pronounced contrast steps at the electrode/electrolyte interfaces. Reprinted with permission from [25.200]. Copyright 2013 American Chemical Society

25.3 Future Trends

Since its invention more than 30 years ago, advances in SPM have primarily revolved around improved resolution, enhanced stability, and especially novel property measurements. Continued progress is certain because of the novel insight SPM can provide, but there are several noteworthy trends for future developments that deserve particular attention.

25.3.1 Atomic Resolution and Increasingly Sophisticated Probes

There is recent evidence that some of the property probes may achieve atomic resolution. Eguchi et al have obtained atomic-scale electrostatic potential maps with KFM, as exemplified by Fig. 25.27a-c which compares NC-AFM and SSPM of a Ge\(/\)Si(105) surface with a model of the atomic structure [25.233]. Rugar et al have demonstrated the measurement of a single spin of an electron [25.234]. Mechanical properties have been demonstrated with angstrom resolution even in fluids [25.235]. While further work is needed to confirm the absence of artifacts in these measurements, these observations are exciting in that they portend a future of atomic resolution property imaging. Advances in high-precision cantilevers and tips could unite NC-AFM imaging of structure with similar resolution imaging of potential, work function, dielectric function, etc. Concomitant advances in the physics of tip–surface interactions will be necessary when we need to interpret, for example, an atomic resolution dielectric constant.

Fig. 25.27a-c

Atomic resolution (a) NC-AFM and (b) KFM for Ge\(/\)Si(105), with molecular models sketched at right and (c) cross-sections from horizontal overlays as indicated (\(l\)\(l^{\prime}\)). Reprinted with permission from [25.233]. Copyright 2004 by the American Physical Society

In an ideal world it would be useful to combine multiple probes with a variety of options for sample stimulation for comprehensive analysis. This vision is schematically illustrated in Fig. 25.28. Scanning probes with multiple transport-related tips are commercially available, but combined electrical, optical and magnetic probes remain a significant challenge. Probe-based deposition has also long been demonstrated, for example with dip pen nanolithography ( ) [25.236]. Enhanced functionality in fluids is additionally important especially for studies of biological specimens. For instance, the SCUBA© probe cleverly combines liquid compatibility with the high \(Q\) benefits of AC-imaging modes in air [25.237]. This is achieved by oscillating the lever inside a waterproof shell, with a fine opening through which the tip apex protrudes into a liquid environment for scanning, but where fluid cannot exchange with the trapped air inside.

Fig. 25.28

Generalized approach to SPM, with control over tip modulation, sample stimulation, experimental environment, and detection mechanism to characterize a wide range of materials properties

25.3.2 High-Speed SPM

Despite this progress and promise, SPM remains a relatively slow technique compared to complementary equipment such as electron and ion microscopy. More than ten years ago several breakthroughs suggested much higher scan speeds would become commonplace, including massively parallel scanning with multiple probes [25.238] as well as video-rate SPM [25.239]. Incessantly improving computational capabilities, detection bandwidths, data acquisition rates, and even write times for data storage are also important to this movement towards high-speed imaging. However, practical image times remain on the order of \(\approx\) four minutes per frame for most of the \(\approx{\mathrm{40000}}\) systems presently installed worldwide, with \(10{\times}\) to \(100{\times}\) enhancements recently becoming more widespread following many development efforts to improve SPM scanners, detection systems, and feedback loops [25.240, 25.241].

Higher-speed scanning provides particular benefits in terms of improved throughput for incorporation in manufacturing settings, experimentally practical times for multiparametric investigations, and novel observations of dynamic processes as described in Sect. 25.2.3. Such work is made possible partially through perpetual progress in computational capabilities, detection bandwidths, data acquisition rates, and even write times for data storage. There is value in simply returning to the fundamental mechanisms for SPM contrast as well. For instance, the error (feedback) channels during conventional contact or intermittent mode AFM imaging (lever deflection or amplitude, respectively) are nearly always only used to qualitatively assess imaging parameters. But these signals actually contain valuable quantitative information as well. When properly calibrated, the error signal can be reincorporated with the simultaneously acquired AFM height data to better reconstruct the true topography of a surface. For instance, Fig. 25.29a-i displays raw height images for trace (left column) and retrace directions (center column) when scanning at normal (first image row) and high (second row) rates [25.242]. Subtracting the trace from the retrace image reveals a substantial difference between the two (right column), especially at higher speeds when the feedback is less effective. The error-corrected or true-topography image (third row) incorporates the scan-direction-dependent error signal, reintroducing features from the real surface structure that are otherwise lost by constraints in the raw height channel. This concept can even be extended for better property measurements as well [25.242]. Such simple reconsiderations of how SPM systems operate can therefore improve imaging in future as well as legacy systems, in this case partially to push the limits of scanning speeds but also to equivalently correct for too-low feedback gain settings that are a common mistake made by inexpert SPM users. Autoadjusting scan parameters, self aligned cantilevers, and other software and hardware adjustments designed to simplify ease of use remain crucial before there can be more widespread implementation of SPM.

Fig. 25.29a-i

Schematics of AFM height and deflection signals at feature edges, with height images in the (a,d,g) trace and (b,e,h) retrace scan directions. The difference (c,f,i) between trace and retrace images is indicative of scan-direction-related error in surface tracking, at normal imaging speeds (ac) and especially for high speeds (df), but can be almost completely corrected (gi) by recombining the height and deflection data. Reprinted from [25.242]. ©IOP Publishing. Reproduced with permission. All rights reserved

New scanner designs have been especially critical for advancing scanning rates, by pushing system resonances into higher frequencies. Smoothly accelerating or decelerating the probe when reversing the scan direction is simple but necessary to minimize exciting the existing system resonances. Along these lines, pure sinusoidal scanning for the fast-scan direction has allowed true video-rate imaging, especially when leveraging resonant scanners such as quartz tuning forks [25.239]. Another promising approach is fully circular scanning based on phase-locked sinusoidal \(x\) and \(y\) actuation, each \(90^{\circ}\) out of phase and with slowly increasing amplitudes to trace a surface with an Archimedean spiral pattern [25.243, 25.244]. Of course in such cases data acquisition is no longer strictly rectilinear. These methods therefore require additional onboard or postprocessing if conventional image analysis tools—which implement gridded arrays of data pixels—will continue to be used for interrogating and visualizing SPM data [25.245]. Directly working with vectorized data instead of grids of pixels represents another likely direction for future SPM hardware and software developments.

25.3.3 Multimodal and Big Data

A rapidly emerging subfield within SPM is multimodal, multiparametric, and big-data approaches. These leverage increasingly sophisticated experimental automation and multichannel, high-speed data acquisition. For instance, gigabyte-scale datasets based on repeated pixel-by-pixel or frame-by-frame measurements are becoming commonplace for many advanced SPM investigations, continuously sweeping electric or magnetic fields, acoustic excitation frequencies or amplitudes, illumination wavelengths or intensities, temperature, humidity, etc. Simultaneous detection in multiple frequency ranges is also increasingly feasible and valuable, especially for studies where it is beneficial to monitor lever responses at multiple resonances and/or harmonics [25.246]. High-speed imaging alone is generating large datasets that provide insight into new materials, such as efficiently mapping the hydration layer on calcite [25.247]. Thorough analyses of such big data experiments must eventually leverage combinatorial, neural network, principal component, and related approaches [25.248]. This presents collaboration and piggyback opportunities with several scientific communities facing similar challenges, especially the ongoing Materials Genome Initiative that coincidentally is the natural successor to the National Nanotech Initiative , which initially fostered many of the SPM developments and applications reviewed herein.

25.3.4 Subsurface and Tomography

Literally taking SPM in another direction, the importance of subsurface materials properties has increasingly been recognized. The presence or properties of some underlying features can be nondestructively inferred by understanding and leveraging the fundamental contrast mechanisms for several SPM variations. With SThM, subsurface heterogeneities in thermal properties can be critical to the primary contrast mechanism, i. e., thermal dissipation, yielding hints of underlying feature depths, dimensions, and/or thermal diffusivity [25.249, 25.250]. Depth dependencies of electronic properties can also be detected, for instance resolving single-walled carbon nanotubes ( s) embedded in a polyimide matrix via their contribution to capacitance gradients detected at their surface by scanning Kelvin probe force microscopy [25.251]. Alternately, wavelength-dependent effective absorption depths for some materials can be utilized to excite photocarriers within controllable depths, again giving insight into subsurface materials and properties [25.252].

For highly deformable materials such as compliant polymer systems or biological cells, subsurface stiffness mapping is feasible based on continuous analysis of indentation curves as a function of depth [25.253, 25.254, 25.255]. Multifrequency approaches can similarly detect stiff features buried beneath a soft overlayer [25.256]. But for less compliant systems—e. g., higher modulus polymers, metal alloys, semiconductors, or even ceramics—subsurface mechanical properties can still be accessible at the nanoscale by marrying SPM with traditional nondestructive testing approaches such as ultrasonics. In fact this was recognized early during the development of UFM, AFAM, and related methods, for instance to identify subsurface film delamination via the associated change in transmitted longitudinal ultrasonic vibrations [25.257]. Heterodyne versions of ultrasonic microscopies employed related contrast mechanisms to visualize buried gold nanoparticles as well as voids or other curing inconsistencies for a polymeric low-K dielectric [25.258]. Figure 25.30a-d presents an excellent example of such research [25.259], in which (a) and (b) display topography and phase images from conventional AC-mode imaging for a graphite flake that is \(\approx{\mathrm{50}}\,{\mathrm{nm}}\) thick or more in the regions that are obviously folded. The flake is deposited on a patterned COC film, yielding supported as well as suspended regions that are not detectable with typical AFM imaging. During ultrasonic force microscopy, on the other hand, the simultaneously acquired topography remains unchanged while UFM contrast clearly reveals the underlying pattern. By combining theory and simulations that account for the influence of such buried structures on surface-resolved mechanical properties, effective depth information has more recently been achieved for amorphous SiOC:H patterned features [25.260], silicon nanowires beneath polymer films [25.261], and subsurface cavities similar to those above [25.262].

Fig. 25.30a-d

Conventional AC-AFM (a) topography and (b) phase images for a \({\mathrm{50}}\,{\mathrm{nm}}\) thick graphite flake folded on a substrate of pillars, above (c) contact AFM and subsurface pillars resolved by UFM (d). Reprinted from [25.259]. © IOP Publishing. Reproduced with permission. All rights reserved

More directly, investigations of specimen cross-sections have long been employed by the microscopy and surface science communities to image subsurface microstructural features. This includes SPM on fracture surfaces or mechanically polished sections. Shallow-angle sectioning, for instance via beam exit argon ion polishing, is especially promising. Parts of the initial surface remain intact for conventional SPM, while in the same field of view any underlying features can be directly observed even if they only extend to nanoscale depths due to simple geometric enhancement by the shallow polishing angle [25.263, 25.264].

Common to all of these approaches for subsurface information is a focus on explicitly minimizing any surface modifications. Increasingly, however, knowing materials properties throughout the whole 3-D structure with nanoscale resolution is crucial to understanding fundamental mechanisms and/or optimizing materials performance for real applications, for systems including semiconductors, photovoltaics, composites, biomedical devices, additive manufacturing, etc. Nondestructive technologies for volumetric imaging in related fields includes tomographic x-ray diffraction [25.265] as well as its medical twin (CAT scans) [25.266], magnetic resonance imaging [25.267], 3-D confocal microscopy [25.268], and transmission electron tomographic microscopy [25.269]. Serial sectioning is also increasingly employed, usually combining focused ion beam microscopy for material removal and electron or ion microscopy for imaging [25.270]. Each of these substantial fields have made profound contributions to fundamental and applied science since their development, even establishing entire commercial industries. But while they all share the capability of providing some kind of structure-based contrast throughout a material, body, cell, tissue, or even nanoscale specimen, none of them provide direct access to material properties such as electrical, magnetic, thermal, optical, mechanical, or coupled characteristics at the nanoscale.

Accordingly, several approaches have been demonstrated for serial repetition of SPM and specimen sectioning. The complex nano- and microstructure within a block-copolymer has been revealed by serial AFM and plasma treatment [25.271]. There are many examples of AFM of microtomed specimens as well [25.272], even those prepared in situ [25.273] or at cryogenic temperatures as is common for biomedical imaging [25.274]. More directly, lithography studies based on manipulating molecules, nanodissection [25.275], or sculpting few-nm-deep features [25.276, 25.277] have inspired SPM measurements where the probe apex is purposefully used to remove material and thereby expose underlying features. Prominent examples include using an AFM probe as a scalpel [25.278] to alternately measure and reveal conduction pathways in 3-D, including filamentary transport pathways in \(\mathrm{HfO_{2}}\) and even \({\mathrm{5}}\,{\mathrm{nm}}\) resistive memory devices [25.279, 25.280]. Figure 25.31 displays a similar example that identifies \(xz\), \(yz\), and \(xy\) cross-sections of photoconduction pathways in a polycrystalline CdTe solar cell during illumination [25.97]. In fact, the full dataset includes photocurrents throughout the entire thickness of the \(\approx{\mathrm{2}}\,{\mathrm{{\upmu}m}}\) thick film. This work uniquely revealed highly carrier-dependent planar defects, which often interconnect at interfaces, promoting the possibility that instead of degrading efficiencies as trap sites such features can in fact improve solar cell performance by enhancing separation of photocarriers. Such tomographic computed tomography AFM ( ) investigations are promising for future fundamental and applied research where 3-D properties are crucial to ultimate device function, optimization, or reliability.

Fig. 25.31

Schematic of CTAFM, acquired throughout a polycrystalline CdTe solar cell during illumination from beneath, displaying arbitrary cross-sections of photoconduction from tomographic nanoscale voxels (Unpublished, J. Luria and B.D. Huey)

25.4 Conclusion

The rapid pace of SPM advances over the past three decades shows no sign of slowing in the future. Atomic resolution imaging is becoming ever more common and the range of local properties that can be quantified is expanding. Dynamic studies are increasingly accessible, particularly as high-speed topographic and property mapping becomes more commercially available. In situ and in operando investigations are also increasingly valuable and experimentally practical. Chemical detection with SPM resolution remains a critical area for development. The advantages of big-data approaches are inevitable, especially with multimodal and multiparametric investigations. Finally, subsurface and tomographic studies will enable next-generation fundamental and applied advances in nanoscience and nanotechnology.

Notes

Acknowledgements

BDH and JL acknowledge support from the DoE Sunshot program. DAB acknowledges financial support from NSF and DoE. Dr. Sergei Kalinin and Dr. James Steffes are each gratefully acknowledged for helpful and informative discussions. The authors are also grateful to Nikhila Balasubramanya and Luis Ortiz for assistance with manuscript details, and to Maxim Nikiforov for his considerable input on a previous edition of this chapter.

References

  1. D. Bonnell: Scanning Probe Microscopy and Spectroscopy: Theory, Techniques, and Applications (Wiley, Weinheim 2001)Google Scholar
  2. G. Friedbacher, H. Fuchs: Classification of scanning probe microscopies, Pure Appl. Chem. 71, 1337–1357 (1999)CrossRefGoogle Scholar
  3. E. Meyer, H.J. Hug, R. Bennewitz: Scanning Probe Microscopy: The Lab on a Tip (Springer, Berlin 2013)Google Scholar
  4. S.V. Kalinin, A. Gruverman: Scanning Probe Microscopy: Electrical and Electromechanical Phenomena at the Nanoscale, Vol. 1 (Springer, New York 2007)CrossRefGoogle Scholar
  5. R. García, R. Perez: Dynamic atomic force microscopy methods, Surf. Sci. Rep. 47, 197–301 (2002)CrossRefGoogle Scholar
  6. F.J. Giessibl: Advances in atomic force microscopy, Rev. Mod. Phys. 75, 949 (2003)CrossRefGoogle Scholar
  7. W.A. Hofer, A.S. Foster, A.L. Shluger: Theories of scanning probe microscopes at the atomic scale, Rev. Mod. Phys. 75, 1287 (2003)CrossRefGoogle Scholar
  8. F.J. Giessibl, M. Reichling: Investigating atomic details of the CaF2(111) surface with a Qplus sensor, Nanotechnology 16, S118 (2005)CrossRefGoogle Scholar
  9. A. San Paulo, R. García: Tip-surface forces, amplitude, and energy dissipation in amplitude-modulation (tapping mode) force microscopy, Phys. Rev. B 64, 193411 (2001)CrossRefGoogle Scholar
  10. C. Möller, M. Allen, V. Elings, A. Engel, D.J. Müller: Tapping-mode atomic force microscopy produces faithful high-resolution images of protein surfaces, Biophys. J. 77, 1150–1158 (1999)CrossRefGoogle Scholar
  11. F. Ohnesorge: Towards atomic resolution non-contact dynamic force microscopy in a liquid, Surf. Interface Anal. 27, 379–385 (1999)CrossRefGoogle Scholar
  12. F.J. Giessibl: Forces and frequency shifts in atomic-resolution dynamic-force microscopy, Phys. Rev. B 56, 16010 (1997)CrossRefGoogle Scholar
  13. F.J. Giessibl, H. Bielefeldt: Physical interpretation of frequency-modulation atomic force microscopy, Phys. Rev. B 61, 9968 (2000)CrossRefGoogle Scholar
  14. P.V. Sushko, A.S. Foster, L.N. Kantorovich, A.L. Shluger: Investigating the effects of silicon tip contamination in noncontact scanning force microscopy (Sfm), Appl. Surf. Sci. 144, 608–612 (1999)CrossRefGoogle Scholar
  15. M. Guggisberg, M. Bammerlin, C. Loppacher, O. Pfeiffer, A. Abdurixit, V. Barwich, R. Bennewitz, A. Baratoff, E. Meyer, H.-J. Güntherodt: Separation of interactions by noncontact force microscopy, Phys. Rev. B 61, 11151 (2000)CrossRefGoogle Scholar
  16. S. Sounilhac, E. Barthel, F. Creuzet: The electrostatic contribution to the long-range interactions between tungsten and oxide surfaces under ultrahigh vacuum, Appl. Surf. Sci. 140, 411–414 (1999)CrossRefGoogle Scholar
  17. R. Bennewitz, A.S. Foster, L.N. Kantorovich, M. Bammerlin, C. Loppacher, S. Schär, M. Guggisberg, E. Meyer, A.L. Shluger: Atomically resolved edges and kinks of NaCl islands on Cu(111): Experiment and theory, Phys. Rev. B 62, 2074 (2000)CrossRefGoogle Scholar
  18. R. Pérez, I. Štich, M.C. Payne, K. Terakura: Surface-tip interactions in noncontact atomic-force microscopy on reactive surfaces: Si(111), Phys. Rev. B 58, 10835 (1998)CrossRefGoogle Scholar
  19. A. Shluger, A. Livshits, A. Foster, C. Catlow: Models of image contrast in scanning force microscopy on insulators, J. Phys. Condens. Matter 11, R295 (1999)CrossRefGoogle Scholar
  20. A.L. Shluger, A.L. Rohl: A model of the interaction of ionic tips with ionic surfaces for interpretation of scanning force microscope images, Top. Catal. 3, 221–247 (1996)CrossRefGoogle Scholar
  21. M. Zaibi, J. Lacharme, C. Sebenne: Water vapour adsorption on the Si(111)-(7×7) surface, Surf. Sci. 377, 639–643 (1997)CrossRefGoogle Scholar
  22. T. Kubo, H. Nozoye: Surface structure of SrTiO3(100)-($$\sqrt5 \times \sqrt5$$)-R26.6°, Phys. Rev. Lett. 86, 1801 (2001)CrossRefGoogle Scholar
  23. S. Hembacher, F.J. Giessibl, J. Mannhart, C.F. Quate: Revealing the hidden atom in graphite by low-temperature atomic force microscopy, Proc. Natl. Acad. Sci. 100(22), 12539–12542 (2003)CrossRefGoogle Scholar
  24. H. Hosoi, K. Sueoka, K. Hayakawa, K. Mukasa: Atomic resolved imaging of cleaved NiO(100) surfaces by NC-AFM, Appl. Surf. Sci. 157, 218–221 (2000)CrossRefGoogle Scholar
  25. K.-I. Fukui, Y. Namai, Y. Iwasawa: Imaging of surface oxygen atoms and their defect structures on CeO2(111) by noncontact atomic force microscopy, Appl. Surf. Sci. 188, 252–256 (2002)CrossRefGoogle Scholar
  26. R. Coleman, Q. Xue, Y. Gong, P. Price: Atomic force microscope study of etched tracks of low-energy heavy ions in mica, Surf. Sci. 297, 359–370 (1993)CrossRefGoogle Scholar
  27. S. Suzuki, Y. Ohminami, T. Tsutsumi, M. Shoaib, M. Ichikawa, K. Asakura: The first observation of an atomic scale noncontact AFM image of MoO3(010), Chem. Lett. 32, 1098–1099 (2003)CrossRefGoogle Scholar
  28. Y. Seo, H. Choe, W. Jhe: Atomic-resolution noncontact atomic force microscopy in air, Appl. Phys. Lett. 83, 1860–1862 (2003)CrossRefGoogle Scholar
  29. S. Hembacher, F.J. Giessibl, J. Mannhart: Force microscopy with light-atom probes, Science 305, 380–383 (2004)CrossRefGoogle Scholar
  30. K. Takayanagi, Y. Tanishiro, M. Takahashi, S. Takahashi: Structural analysis of Si(111)-7×7 by UHV-transmission electron diffraction and microscopy, J. Vac. Sci. Technol. A 3, 1502–1506 (1985)CrossRefGoogle Scholar
  31. G. Binnig, H. Rohrer, C. Gerber, E. Weibel: 7×7 reconstruction on Si(111) resolved in real space, Phys. Rev. Lett. 50, 120 (1983)CrossRefGoogle Scholar
  32. S.-I. Kitamura, M. Iwatsuki: Observation of 7×7 reconstructed structure on the silicon (111) surface using ultrahigh vacuum noncontact atomic force microscopy, Jpn. J. Appl. Phys. 34, L145 (1995)CrossRefGoogle Scholar
  33. F.J. Giessibl: Atomic resolution of the silicon (111)-(7×7) surface by atomic force microscopy, Science 267, 68–71 (1995)CrossRefGoogle Scholar
  34. A. Schwarz, W. Allers, U. Schwarz, R. Wiesendanger: Simultaneous imaging of the in and as sublattice on InAs(110)-(1×1) with dynamic scanning force microscopy, Appl. Surf. Sci. 140, 293–297 (1999)CrossRefGoogle Scholar
  35. K. Yokoyama, T. Ochi, A. Yoshimoto, Y. Sugawara, S. Morita: Atomic resolution imaging on Si(100)2×1 and Si(100)2×1:H surfaces with noncontact atomic force microscopy, Jpn. J. Appl. Phys. 39, L113 (2000)CrossRefGoogle Scholar
  36. N. Uehara, H. Hosoi, K. Sueoka, K. Mukasa: Non-contact atomic force microscopy observation on GaAs(110) surface with tip-induced relaxation, Jpn. J. Appl. Phys. 43, 4676 (2004)CrossRefGoogle Scholar
  37. J. Weaver, D.W. Abraham: High resolution atomic force microscopy potentiometry, J. Vac. Sci. Technol. B 9, 1559–1561 (1991)CrossRefGoogle Scholar
  38. M. Nonnenmacher, M. O'Boyle, H.K. Wickramasinghe: Kelvin probe force microscopy, Appl. Phys. Lett. 58, 2921–2923 (1991)CrossRefGoogle Scholar
  39. A. Henning, T. Hochwitz: Scanning probe microscopy for 2-D semiconductor dopant profiling and device failure analysis, Mater. Sci. Eng. B 42, 88–98 (1996)CrossRefGoogle Scholar
  40. H. Jacobs, P. Leuchtmann, O. Homan, A. Stemmer: Resolution and contrast in Kelvin probe force microscopy, J. Appl. Phys. 84, 1168–1173 (1998)CrossRefGoogle Scholar
  41. S.V. Kalinin, D.A. Bonnell: Local potential and polarization screening on ferroelectric surfaces, Phys. Rev. B 63, 125411 (2001)CrossRefGoogle Scholar
  42. S. Cunningham, I.A. Larkin, J.H. Davis: Noncontact scanning probe microscope potentiometry of surface charge patches: Origin and interpretation of time-dependent signals, Appl. Phys. Lett. 73, 123–125 (1998)CrossRefGoogle Scholar
  43. S.V. Kalinin, C. Johnson, D.A. Bonnell: Domain polarity and temperature induced potential inversion on the BaTiO3(100) surface, J. Appl. Phys. 91, 3816–3823 (2002)CrossRefGoogle Scholar
  44. K. Franke, H. Huelz, M. Weihnacht: How to extract spontaneous polarization information from experimental data in electric force microscopy, Surf. Sci. 415, 178–182 (1998)CrossRefGoogle Scholar
  45. C. Donolato: Electrostatic tip–sample interaction in immersion force microscopy of semiconductors, Phys. Rev. B 54, 1478 (1996)CrossRefGoogle Scholar
  46. Y. Leng, C.C. Williams, L. Su, G. Stringfellow: Atomic ordering of gainp studied by Kelvin probe force microscopy, Appl. Phys. Lett. 66, 1264–1266 (1995)CrossRefGoogle Scholar
  47. M. Tanimoto, O. Vatel: Kelvin probe force microscopy for characterization of semiconductor devices and processes, J. Vac. Sci. Technol. B 14, 1547–1551 (1996)CrossRefGoogle Scholar
  48. T. Hochwitz, A.K. Henning, C. Levey, C. Daghlian, J. Slinkman, J. Never, P. Kaszuba, R. Gluck, R. Wells, J. Pekarik: Imaging integrated circuit dopant profiles with the force-based scanning Kelvin probe microscope, J. Vac. Sci. Technol. B 14, 440–446 (1996)CrossRefGoogle Scholar
  49. M. Fujihira: Kelvin probe force microscopy of molecular surfaces, Annu. Rev. Mater. Sci. 29, 353–380 (1999)CrossRefGoogle Scholar
  50. X. Chen, H. Yamada, T. Horiuchi, K. Matsushige, S. Watanabe, M. Kawai, P. Weiss: Surface potential of ferroelectric thin films investigated by scanning probe microscopy, J. Vac. Sci. Technol. B 17, 1930–1934 (1999)CrossRefGoogle Scholar
  51. T. Tybell, C. Ahn, J.-M. Triscone: Ferroelectricity in thin perovskite films, Appl. Phys. Lett. 75, 856–858 (1999)CrossRefGoogle Scholar
  52. P. Bridger, Z. Bandić, E. Piquette, T. McGill: Measurement of induced surface charges, contact potentials, and surface states in GaN by electric force microscopy, Appl. Phys. Lett. 74, 3522–3524 (1999)CrossRefGoogle Scholar
  53. Q. Xu, J. Hsu: Electrostatic force microscopy studies of surface defects on GaAs/Ge Films, J. Appl. Phys. 85, 2465–2472 (1999)CrossRefGoogle Scholar
  54. A. Chavez-Pirson, O. Vatel, M. Tanimoto, H. Ando, H. Iwamura, H. Kanbe: Nanometer-scale imaging of potential profiles in optically excited n-i-p-i heterostructure using Kelvin probe force microscopy, Appl. Phys. Lett. 67, 3069–3071 (1995)CrossRefGoogle Scholar
  55. T. Meoded, R. Shikler, N. Fried, Y. Rosenwaks: Direct measurement of minority carriers diffusion length using Kelvin probe force microscopy, Appl. Phys. Lett. 75, 2435–2437 (1999)CrossRefGoogle Scholar
  56. S. Kalinin, D. Bonnell: Dynamic behavior of domain-related topography and surface potential on the BaTiO3(100) surface by variable temperature scanning surface potential microscopy, Z. Metallkd. 90, 983–989 (1999)Google Scholar
  57. J. Lü, E. Delamarche, L. Eng, R. Bennewitz, E. Meyer, H.-J. Güntherodt: Kelvin probe force microscopy on surfaces: Investigation of the surface potential of self-assembled monolayers on gold, Langmuir 15, 8184–8188 (1999)CrossRefGoogle Scholar
  58. H. Sugimura, K. Hayashi, N. Saito, N. Nakagiri, O. Takai: Surface potential microscopy for organized molecular systems, Appl. Surf. Sci. 188, 403–410 (2002)CrossRefGoogle Scholar
  59. D.A. Bonnell, R.A. Alvarez, S.V. Kalinin: Directed assembly of nanometer-scale molecular devices, US Patent 6982174 (2006)Google Scholar
  60. M. Abplanalp, L. Eng, P. Günter: Mapping the domain distribution at ferroelectric surfaces by scanning force microscopy, Appl. Phys. A 66, S231–S234 (1998)CrossRefGoogle Scholar
  61. R. Shao, M.F. Chisholm, G. Duscher, D.A. Bonnell: Low-temperature resistance anomaly at SrTiO3 grain boundaries: Evidence for an interface-induced phase transition, Phys. Rev. Lett. 95, 197601 (2005)CrossRefGoogle Scholar
  62. P. De Wolf, T. Clarysse, W. Vandervorst, L. Hellemans: Low weight spreading resistance profiling of ultrashallow dopant profiles, J. Vac. Sci. Technol. B 16, 401–405 (1998)CrossRefGoogle Scholar
  63. P. De Wolf, R. Stephenson, T. Trenkler, T. Clarysse, T. Hantschel, W. Vandervorst: Status and review of two-dimensional carrier and dopant profiling using scanning probe microscopy, J. Vac. Sci. Technol. B 18, 361–368 (2000)CrossRefGoogle Scholar
  64. P. De Wolf, J. Snauwaert, L. Hellemans, T. Clarysse, W. Vandervorst, M. D'Olieslaeger, D. Quaeyhaegens: Lateral and vertical dopant profiling in semiconductors by atomic force microscopy using conducting tips, J. Vac. Sci. Technol. A 13, 1699–1704 (1995)CrossRefGoogle Scholar
  65. J. Matey, J. Blanc: Scanning capacitance microscopy, J. Appl. Phys. 57, 1437–1444 (1985)CrossRefGoogle Scholar
  66. R. Barrett, C. Quate: Charge storage in a nitride-oxide-silicon medium by scanning capacitance microscopy, J. Appl. Phys. 70, 2725–2733 (1991)CrossRefGoogle Scholar
  67. Y. Huang, C.C. Williams, M. Wendman: Quantitative two-dimensional dopant profiling of abrupt dopant profiles by cross-sectional scanning capacitance microscopy, J. Vac. Sci. Technol. A 14, 1168–1171 (1996)CrossRefGoogle Scholar
  68. T. Hantschel, P. Niedermann, T. Trenkler, W. Vandervorst: Highly conductive diamond probes for scanning spreading resistance microscopy, Appl. Phys. Lett. 76, 1603–1605 (2000)CrossRefGoogle Scholar
  69. P. De Wolf, E. Brazel, A. Erickson: Electrical characterization of semiconductor materials and devices using scanning probe microscopy, Mater. Sci. Semicond. Process. 4, 71–76 (2001)CrossRefGoogle Scholar
  70. J. Marchiando, J. Kopanski: Regression procedure for determining the dopant profile in semiconductors from scanning capacitance microscopy data, J. Appl. Phys. 92, 5798–5809 (2002)CrossRefGoogle Scholar
  71. J. Yang, F.C.J. Kong: Simulation of interface states effect on the scanning capacitance microscopy measurement of p-n junctions, Appl. Phys. Lett. 81, 4973–4975 (2002)CrossRefGoogle Scholar
  72. Š. Lányi, J. Török, P. Řehůřek: Imaging conducting surfaces and dielectric films by a scanning capacitance microscope, J. Vac. Sci. Technol. B 14, 892–896 (1996)CrossRefGoogle Scholar
  73. S. Belaidi, P. Girard, G. Leveque: Electrostatic forces acting on the tip in atomic force microscopy: Modelization and comparison with analytic expressions, J. Appl. Phys. 81, 1023–1030 (1997)CrossRefGoogle Scholar
  74. S.J. Tans, C. Dekker: Molecular transistors: Potential modulations along carbon nanotubes, Nature 404, 834–835 (2000)CrossRefGoogle Scholar
  75. T.W. Tombler, C. Zhou, J. Kong, H. Dai: Gating individual nanotubes and crosses with scanning probes, Appl. Phys. Lett. 76, 2412–2414 (2000)CrossRefGoogle Scholar
  76. A. Bachtold, M. Fuhrer, S. Plyasunov, M. Forero, E.H. Anderson, A. Zettl, P.L. McEuen: Scanned probe microscopy of electronic transport in carbon nanotubes, Phys. Rev. Lett. 84, 6082 (2000)CrossRefGoogle Scholar
  77. S.V. Kalinin, D.A. Bonnell, M. Freitag, A. Johnson: Tip-gating effect in scanning impedance microscopy of nanoelectronic devices, Appl. Phys. Lett. 81, 5219–5221 (2002)CrossRefGoogle Scholar
  78. Z. Fan, J.G. Lu: Electrical properties of ZnO nanowire field effect transistors characterized with scanning probes, Appl. Phys. Lett. 86, 032111 (2005)CrossRefGoogle Scholar
  79. R.M. Westervelt, M.A. Topinka, B.J. LeRoy, A.C. Bleszynski, K. Aidala, S.E.J. Shaw, E.J. Heller, K.D. Maranowski, A.C. Gossard: Imaging electron waves, Physica E Low Dimens. Syst. Nanostruct. 24, 63–69 (2004)CrossRefGoogle Scholar
  80. S. Rathi, I. Lee, D. Lim, J. Wang, Y. Ochiai, N. Aoki, K. Watanabe, T. Taniguchi, G.-H. Lee, Y.-J. Yu, P. Kim, G.-H. Kim: Tunable electrical and optical characteristics in monolayer graphene and few-layer MoS2 heterostructure devices, Nano Lett. 15, 5017–5024 (2015)CrossRefGoogle Scholar
  81. R. Giridharagopal, G. Rayermann, D. Ginger: Electrical scanning probe microscopy on solar cell materials, Scanning Probe Microsc. Energy Res. 7, 28 (2013)Google Scholar
  82. X.-D. Dang, M. Guide, T.-Q. Nguyen: Organic solar cell materials and devices characterized by conductive and photoconductive atomic force microscopy, Scanning Probe Microsc. Energy Res. 7, 62 (2013)Google Scholar
  83. D.A. Bonnell, S.V. Kalinin: Scanning Probe Microscopy for Energy Research, Vol. 7 (World Scientific, Singapore 2013)CrossRefGoogle Scholar
  84. L. Bürgi, T. Richards, M. Chiesa, R.H. Friend, H. Sirringhaus: A microscopic view of charge transport in polymer transistors, Synth. Metals 146, 297–309 (2004)CrossRefGoogle Scholar
  85. L. Bürgi, H. Sirringhaus, R. Friend: Noncontact potentiometry of polymer field-effect transistors, Appl. Phys. Lett. 80, 2913–2915 (2002)CrossRefGoogle Scholar
  86. J.J. Choi, J. Luria, B.-R. Hyun, A.C. Bartnik, L. Sun, Y.-F. Lim, J.A. Marohn, F.W. Wise, T. Hanrath: Photogenerated exciton dissociation in highly coupled lead salt nanocrystal assemblies, Nano Lett. 10, 1805 (2010)CrossRefGoogle Scholar
  87. J.L. Luria, N. Hoepker, R. Bruce, A.R. Jacobs, C. Groves, J.A. Marohn: Spectroscopic imaging of photopotentials and photoinduced potential fluctuations in a bulk heterojunction solar cell film, ACS Nano 6, 9392–9401 (2012)CrossRefGoogle Scholar
  88. D.C. Coffey, D.S. Ginger: Time-resolved electrostatic force microscopy of polymer solar cells, Nat. Mater. 5, 735–740 (2006)CrossRefGoogle Scholar
  89. R. Sinton, A. Cuevas: A quasi-steady-state open-circuit voltage method for solar cell characterization. In: Proc. 16th Eur. Photovolt. Sol. Energy Conf. (2000) pp. 1152–1155Google Scholar
  90. J.L. Luria, K.A. Schwarz, M.J. Jaquith, R.G. Hennig, J.A. Marohn: Spectroscopic characterization of charged defects in polycrystalline pentacene by time- and wavelength-resolved electric force microscopy, Adv. Mater. 23, 624–628 (2011)CrossRefGoogle Scholar
  91. P.F. Barbara, A.J. Gesquiere, S.-J. Park, Y.J. Lee: Single-molecule spectroscopy of conjugated polymers, Acc. Chem. Res. 38, 602–610 (2005)CrossRefGoogle Scholar
  92. A. Arias, J. MacKenzie, R. Stevenson, J. Halls, M. Inbasekaran, E. Woo, D. Richards, R. Friend: Photovoltaic performance and morphology of polyfluorene blends: A combined microscopic and photovoltaic investigation, Macromolecules 34, 6005–6013 (2001)CrossRefGoogle Scholar
  93. A. Cadby, G. Khalil, A. Fox, D. Lidzey: Mapping exciton quenching in photovoltaic-applicable polymer blends using time-resolved scanning near-field optical microscopy, J. Appl. Phys. 103, 093715 (2008)CrossRefGoogle Scholar
  94. Y. Kutes, Y. Zhou, J.L. Bosse, J. Steffes, N.P. Padture, B.D. Huey: Mapping the photoresponse of CH3NH3PbI3 hybrid perovskite thin films at the nanoscale, Nano Lett. 16, 3434–3441 (2016)CrossRefGoogle Scholar
  95. Y. Kutes, B.A. Aguirre, J.L. Bosse, J.L. Cruz-Campa, D. Zubia, B.D. Huey: Mapping photovoltaic performance with nanoscale resolution, Prog. Photovolt. Res. Appl. 24, 315–325 (2016)CrossRefGoogle Scholar
  96. B.H. Hamadani, S. Jung, P.M. Haney, L.J. Richter, N.B. Zhitenev: Origin of nanoscale variations in photoresponse of an organic solar cell, Nano Lett. 10, 1611–1617 (2010)CrossRefGoogle Scholar
  97. J. Luria, Y. Kutes, A. Moore, L. Zhang, E.A. Stach, B.D. Huey: Charge transport in CdTe solar cells revealed by conductive tomographic atomic force microscopy, Nat. Energy 1, 16150 (2016)CrossRefGoogle Scholar
  98. D.C. Coffey, O.G. Reid, D.B. Rodovsky, G.P. Bartholomew, D.S. Ginger: Mapping local photocurrents in polymer/fullerene solar cells with photoconductive atomic force microscopy, Nano Lett. 7, 738–744 (2007)CrossRefGoogle Scholar
  99. M. Tuteja, P. Koirala, V. Palekis, S. MacLaren, C.S. Ferekides, R.W. Collins, A.A. Rockett: Direct observation of CdCl2 treatment induced grain boundary carrier depletion in CdTe solar cells using scanning probe microwave reflectivity based capacitance measurements, J. Phys. Chem. C 120, 7020–7024 (2016)CrossRefGoogle Scholar
  100. C. Gao, T. Wei, F. Duewer, Y. Lu, X.-D. Xiang: High spatial resolution quantitative microwave impedance microscopy by a scanning tip microwave near-field microscope, Appl. Phys. Lett. 71, 1872–1874 (1997)CrossRefGoogle Scholar
  101. J.R. O'Dea, L.M. Brown, N. Hoepker, J.A. Marohn, S. Sadewasser: Scanning probe microscopy of solar cells: From inorganic thin films to organic photovoltaics, MRS Bulletin 37, 642–650 (2012)CrossRefGoogle Scholar
  102. R. Giridharagopal, G. Shao, C. Groves, D.S. Ginger: New SPM techniques for analyzing OPV materials, Mater. Today 13, 50–56 (2010)CrossRefGoogle Scholar
  103. R. O'Hayre, M. Lee, F.B. Prinz: Ionic and electronic impedance imaging using atomic force microscopy, J. Appl. Phys. 95, 8382–8392 (2004)CrossRefGoogle Scholar
  104. B.J. Rodriguez, C. Callahan, S.V. Kalinin, R. Proksch: Dual-frequency resonance-tracking atomic force microscopy, Nanotechnology 18, 475504 (2007)CrossRefGoogle Scholar
  105. A. Kos, D. Hurley: Nanomechanical mapping with resonance tracking scanned probe microscope, Meas. Sci. Technol. 19, 015504 (2007)CrossRefGoogle Scholar
  106. D. Platz, E.A. Tholén, D. Pesen, D.B. Haviland: Intermodulation atomic force microscopy, Appl. Phys. Lett. 92, 153106 (2008)CrossRefGoogle Scholar
  107. S. Jesse, S.V. Kalinin, R. Proksch, A. Baddorf, B. Rodriguez: The band excitation method in scanning probe microscopy for rapid mapping of energy dissipation on the nanoscale, Nanotechnology 18, 435503 (2007)CrossRefGoogle Scholar
  108. A. Kumar, F. Ciucci, A.N. Morozovska, S.V. Kalinin, S. Jesse: Measuring oxygen reduction/evolution reactions on the nanoscale, Nat. Chem. 3, 707 (2011)CrossRefGoogle Scholar
  109. D. McLachlan, J.-H. Hwang, T. Mason: Evaluating dielectric impedance spectra using effective media theories, J. Electroceram. 5, 37–51 (2000)CrossRefGoogle Scholar
  110. S.V. Kalinin, D.A. Bonnell: Scanning impedance microscopy of electroactive interfaces, Appl. Phys. Lett. 78, 1306–1308 (2001)CrossRefGoogle Scholar
  111. R. Shao, S.V. Kalinin, D.A. Bonnell: Local impedance imaging and spectroscopy of polycrystalline ZnO using contact atomic force microscopy, Appl. Phys. Lett. 82, 1869–1871 (2003)CrossRefGoogle Scholar
  112. R. O'Hayre, G. Feng, W.D. Nix, F.B. Prinz: Quantitative impedance measurement using atomic force microscopy, J. Appl. Phys. 96, 3540–3549 (2004)CrossRefGoogle Scholar
  113. L. Pingree, M.C. Hersam: Bridge-enhanced nanoscale impedance microscopy, Appl. Phys. Lett. 87, 233117 (2005)CrossRefGoogle Scholar
  114. K. Kathan-Galipeau, X. Chen, B. Discher, D.A. Bonnell: Mapping dielectric properties with torsionally stabilized nano impedance microscopy: Hard materials to biomolecules, Microsc. Today 19, 16–20 (2011)CrossRefGoogle Scholar
  115. L. Fumagalli, G. Ferrari, M. Sampietro, G. Gomila: Quantitative nanoscale dielectric microscopy of single-layer supported biomembranes, Nano Lett. 9, 1604–1608 (2009)CrossRefGoogle Scholar
  116. C. Gao, X.-D. Xiang: Quantitative microwave near-field microscopy of dielectric properties, Rev. Sci. Instrum. 69, 3846–3851 (1998)CrossRefGoogle Scholar
  117. Y. Cho, A. Kirihara, T. Saeki: Scanning nonlinear dielectric microscope, Rev. Sci. Instrum. 67, 2297–2303 (1996)CrossRefGoogle Scholar
  118. D. Steinhauer, C. Vlahacos, S. Dutta, F. Wellstood, S.M. Anlage: Surface resistance imaging with a scanning near-field microwave microscope, Appl. Phys. Lett. 71, 1736–1738 (1997)CrossRefGoogle Scholar
  119. D. Steinhauer, C. Vlahacos, F. Wellstood, S.M. Anlage, C. Canedy, R. Ramesh, A. Stanishevsky, J. Melngailis: Imaging of microwave permittivity, tunability, and damage recovery in (Ba,Sr)TiO3 thin films, Appl. Phys. Lett. 75, 3180–3182 (1999)CrossRefGoogle Scholar
  120. Y. Lu, T. Wei, F. Duewer, Y. Lu, N.-B. Ming, P. Schultz, X.-D. Xiang: Nondestructive imaging of dielectric-constant profiles and ferroelectric domains with a scanning-tip microwave near-field microscope, Science 276, 2004–2006 (1997)CrossRefGoogle Scholar
  121. S.-C. Lee, S.M. Anlage: Spatially-resolved nonlinearity measurements of YBa2Cu3O7−δ bicrystal grain boundaries, Appl. Phys. Lett. 82, 1893–1895 (2003)CrossRefGoogle Scholar
  122. C. Durkan, M. Welland: Investigations into local ferroelectric properties by atomic force microscopy, Ultramicroscopy 82, 141–148 (2000)CrossRefGoogle Scholar
  123. A. Gruverman, O. Kolosov, J. Hatano, K. Takahashi, H. Tokumoto: Domain structure and polarization reversal in ferroelectrics studied by atomic force microscopy, J. Vac. Sci. Technol. B 13, 1095–1099 (1995)CrossRefGoogle Scholar
  124. S.V. Kalinin, E. Karapetian, M. Kachanov: Nanoelectromechanics of piezoresponse force microscopy, Phys. Rev. B 70, 184101 (2004)CrossRefGoogle Scholar
  125. L. Eng, H.-J. Güntherodt, G. Schneider, U. Köpke, J. Muñoz Saldaña: Nanoscale reconstruction of surface crystallography from three-dimensional polarization distribution in ferroelectric barium-titanate ceramics, Appl. Phys. Lett. 74, 233–235 (1999)CrossRefGoogle Scholar
  126. A. Roelofs, U. Böttger, R. Waser, F. Schlaphof, S. Trogisch, L. Eng: Differentiating 180° and 90° switching of ferroelectric domains with three-dimensional piezoresponse force microscopy, Appl. Phys. Lett. 77, 3444–3446 (2000)CrossRefGoogle Scholar
  127. M. Alexe, A. Gruverman, C. Harnagea, N. Zakharov, A. Pignolet, D. Hesse, J. Scott: Switching properties of self-assembled ferroelectric memory cells, Appl. Phys. Lett. 75, 1158–1160 (1999)CrossRefGoogle Scholar
  128. B.J. Rodriguez, A. Gruverman, A. Kingon, R. Nemanich, J. Cross: Three-dimensional high-resolution reconstruction of polarization in ferroelectric capacitors by piezoresponse force microscopy, J. Appl. Phys. 95, 1958–1962 (2004)CrossRefGoogle Scholar
  129. S.V. Kalinin, B.J. Rodriguez, S. Jesse, J. Shin, A.P. Baddorf, P. Gupta, H. Jain, D.B. Williams, A. Gruverman: Vector piezoresponse force microscopy, Microsc. Microanal. 12, 206–220 (2006)CrossRefGoogle Scholar
  130. J.F. Ihlefeld, B.M. Foley, D.A. Scrymgeour, J.R. Michael, B.B. McKenzie, D.L. Medlin, M. Wallace, S. Trolier-McKinstry, P.E. Hopkins: Room-temperature voltage tunable phonon thermal conductivity via reconfigurable interfaces in ferroelectric thin films, Nano Lett. 15, 1791–1795 (2015)CrossRefGoogle Scholar
  131. J. Desmarais, J.F. Ihlefeld, T. Heeg, J. Schubert, D.G. Schlom, B.D. Huey: Mapping and statistics of ferroelectric domain boundary angles and types, Appl. Phys. Lett. 99, 162902 (2011)CrossRefGoogle Scholar
  132. P.E. Hopkins, C. Adamo, L. Ye, B.D. Huey, S.R. Lee, D.G. Schlom, J.F. Ihlefeld: Effects of coherent ferroelastic domain walls on the thermal conductivity and kapitza conductance in bismuth ferrite, Appl. Phys. Lett. 102, 121903 (2013)CrossRefGoogle Scholar
  133. J.R. Whyte, R.G.P. McQuaid, P. Sharma, C. Canalias, J.F. Scott, A. Gruverman, J.M. Gregg: Ferroelectric domain wall injection, Adv. Mater. 26, 293–298 (2014)CrossRefGoogle Scholar
  134. P. Sharma, Q. Zhang, D. Sando, C.H. Lei, Y. Liu, J. Li, V. Nagarajan, J. Seidel: Nonvolatile ferroelectric domain wall memory, Sci. Adv. 3, e1700512 (2017)CrossRefGoogle Scholar
  135. G. Catalan, J. Seidel, R. Ramesh, J.F. Scott: Domain wall nanoelectronics, Rev. Mod. Phys. 84, 119–156 (2012)CrossRefGoogle Scholar
  136. A. Gruverman, B.J. Rodriguez, R. Nemanich, A. Kingon: Nanoscale observation of photoinduced domain pinning and investigation of imprint behavior in ferroelectric thin films, J. Appl. Phys. 92, 2734–2739 (2002)CrossRefGoogle Scholar
  137. S.V. Kalinin, A. Gruverman, D.A. Bonnell: Quantitative analysis of nanoscale switching in SrBi2Ta2O9 thin films by piezoresponse force microscopy, Appl. Phys. Lett. 85, 795–797 (2004)CrossRefGoogle Scholar
  138. L.M. Eng, M. Bammerlin, C. Loppacher, M. Guggisberg, R. Bennewitz, R. Lüthi, E. Meyer, T. Huser, H. Heinzelmann, H.-J. Güntherodt: Ferroelectric domain characterisation and manipulation: A challenge for scanning probe microscopy, Ferroelectrics 222, 153–162 (1999)CrossRefGoogle Scholar
  139. X. Lu, F. Schlaphof, S. Grafström, C. Loppacher, L. Eng, G. Suchaneck, G. Gerlach: Scanning force microscopy investigation of the Pb(Zr0.25Ti0.75)O3/Pt Interface, Appl. Phys. Lett. 81, 3215–3217 (2002)CrossRefGoogle Scholar
  140. A. Kholkin, V. Shvartsman, A.Y. Emelyanov, R. Poyato, M. Calzada, L. Pardo: Stress-induced suppression of piezoelectric properties in PbTiO3: La thin films via scanning force microscopy, Appl. Phys. Lett. 82, 2127–2129 (2003)CrossRefGoogle Scholar
  141. M. Abplanalp, J. Fousek, P. Günter: Higher order ferroic switching induced by scanning force microscopy, Phys. Rev. Lett. 86, 5799 (2001)CrossRefGoogle Scholar
  142. M. Labardi, C. Polop, V. Likodimos, L. Pardi, M. Allegrini, E. Vasco, C. Zaldo: Surface deformation and ferroelectric domain switching induced by a force microscope tip on a La-Modified PbTiO3 thin film, Appl. Phys. Lett. 83, 2028–2030 (2003)CrossRefGoogle Scholar
  143. A. Roytburd, S. Alpay, V. Nagarajan, C. Ganpule, S. Aggarwal, E. Williams, R. Ramesh: Measurement of internal stresses via the polarization in epitaxial ferroelectric films, Phys. Rev. Lett. 85, 190 (2000)CrossRefGoogle Scholar
  144. C. Ganpule, A. Stanishevsky, S. Aggarwal, J. Melngailis, E. Williams, R. Ramesh, V. Joshi, C. Paz de Araujo: Scaling of ferroelectric and piezoelectric properties in Pt/SrBi2Ta2O9/Pt thin films, Appl. Phys. Lett. 75, 3874–3876 (1999)CrossRefGoogle Scholar
  145. M. Alexe, C. Harnagea, D. Hesse, U. Gösele: Patterning and switching of nanosize ferroelectric memory cells, Appl. Phys. Lett. 75, 1793–1795 (1999)CrossRefGoogle Scholar
  146. J.J. Urban, J.E. Spanier, L. Ouyang, W.S. Yun, H. Park: Single-crystalline barium titanate nanowires, Adv. Mater. 15, 423–426 (2003)CrossRefGoogle Scholar
  147. W.S. Yun, J.J. Urban, Q. Gu, H. Park: Ferroelectric properties of individual barium titanate nanowires investigated by scanned probe microscopy, Nano Lett. 2, 447–450 (2002)CrossRefGoogle Scholar
  148. S. Hong, J. Woo, H. Shin, J.U. Jeon, Y.E. Pak, E.L. Colla, N. Setter, E. Kim, K. No: Principle of ferroelectric domain imaging using atomic force microscope, J. Appl. Phys. 89, 1377–1386 (2001)CrossRefGoogle Scholar
  149. S.V. Kalinin, D.A. Bonnell: Imaging mechanism of piezoresponse force microscopy of ferroelectric surfaces, Phys. Rev. B 65, 125408 (2002)CrossRefGoogle Scholar
  150. C.S. Ganpule: Nanoscale Phenomena in Ferroelectric Thin Films, Ph.D. Thesis (Univ. of Maryland, College Park 2001)Google Scholar
  151. C. Harnagea: Local Piezoelectric Response and Domain Structures in Ferroelectric Thin Films Investigated by Voltage-Modulated Force Microscopy, Ph.D. Thesis (Martin Luther Universität, Halle, Wittenberg 2001)Google Scholar
  152. R. Shao, D.A. Bonnell: Scanning probes of nonlinear properties in complex materials, Jpn. J. Appl. Phys. 43, 4471 (2004)CrossRefGoogle Scholar
  153. R. Nath, Y.-H. Chu, N.A. Polomoff, R. Ramesh, B.D. Huey: High speed piezoresponse force microscopy: <1 frame per second nanoscale imaging, Appl. Phys. Lett. 93, 072905 (2008)CrossRefGoogle Scholar
  154. B.D. Huey, R. Nath Premnath, S. Lee, N.A. Polomoff: High speed spm applied for direct nanoscale mapping of the influence of defects on ferroelectric switching dynamics, J. Am. Ceram. Soc. 95, 1147–1162 (2012)CrossRefGoogle Scholar
  155. N. Kodera, D. Yamamoto, R. Ishikawa, T. Ando: Video imaging of walking myosin V by high-speed atomic force microscopy, Nature 468, 72–76 (2010)CrossRefGoogle Scholar
  156. J.T. Heron, J.L. Bosse, Q. He, Y. Gao, M. Trassin, L. Ye, J.D. Clarkson, C. Wang, J. Liu, S. Salahuddin, D.C. Ralph, D.G. Schlom, J. Íñiguez, B.D. Huey, R. Ramesh: Deterministic switching of ferromagnetism at room temperature using an electric field, Nature 516, 370 (2014)CrossRefGoogle Scholar
  157. M. Kalyan Phani, A. Kumar, W. Arnold, K. Samwer: Elastic stiffness and damping measurements in titanium alloys using atomic force acoustic microscopy, J. Alloys Compd. 676, 397–406 (2016)CrossRefGoogle Scholar
  158. L.R. Merte, G. Peng, R. Bechstein, F. Rieboldt, C.A. Farberow, L.C. Grabow, W. Kudernatsch, S. Wendt, E. Laegsgaard, M. Mavrikakis, F. Besenbacher: Water-mediated proton hopping on an iron oxide surface, Science 336, 889–893 (2012)CrossRefGoogle Scholar
  159. M.J. Rost, L. Crama, P. Schakel, E.V. Tol, G.B.E.M. van Velzen-Williams, C.F. Overgauw, H. ter Horst, H. Dekker, B. Okhuijsen, M. Seynen, A. Vijftigschild, P. Han, A.J. Katan, K. Schoots, R. Schumm, W. van Loo, T.H. Oosterkamp, J.W.M. Frenken: Scanning probe microscopes go video rate and beyond, Rev. Sci. Instrum. 76, 053710 (2005)CrossRefGoogle Scholar
  160. P.M. Hoffmann, S. Jeffery, J.B. Pethica, H. Özgür Özer, A. Oral: Energy dissipation in atomic force microscopy and atomic loss processes, Phys. Rev. Lett. 87, 265502 (2001)CrossRefGoogle Scholar
  161. B.J. Albers, T.C. Schwendemann, M.Z. Baykara, N. Pilet, M. Liebmann, E.I. Altman, U.D. Schwarz: Three-dimensional imaging of short-range chemical forces with picometre resolution, Nat. Nanotechnol. 4, 307 (2009)CrossRefGoogle Scholar
  162. T. Fukuma, M.J. Higgins, S.P. Jarvis: Direct imaging of individual intrinsic hydration layers on lipid bilayers at ångstrom resolution, Biophys. J. 92, 3603–3609 (2007)CrossRefGoogle Scholar
  163. D.J. Müller, W. Baumeister, A. Engel: Controlled unzipping of a bacterial surface layer with atomic force microscopy, Proc. Natl. Acad. Sci. 96, 13170–13174 (1999)CrossRefGoogle Scholar
  164. H.G. Hansma, K.J. Kim, D.E. Laney, R.A. Garcia, M. Argaman, M.J. Allen, S.M. Parsons: Properties of biomolecules measured from atomic force microscope images: A review, J. Struct. Biol. 119, 99–108 (1997)CrossRefGoogle Scholar
  165. H. Lee, N.F. Scherer, P.B. Messersmith: Single-molecule mechanics of mussel adhesion, Proc. Natl. Acad. Sci. 103, 12999–13003 (2006)CrossRefGoogle Scholar
  166. D.J. Müller, Y.F. Dufrêne: Atomic force microscopy: A nanoscopic window on the cell surface, Trends Cell Biol. 21, 461–469 (2011)CrossRefGoogle Scholar
  167. M. Radmacher, R.W. Tillmann, M. Fritz, H.E. Gaub: From molecules to cells: Imaging soft samples with the atomic force microscope, Science 257, 1900–1905 (1992)CrossRefGoogle Scholar
  168. A. Socoliuc, R. Bennewitz, E. Gnecco, E. Meyer: Transition from stick-slip to continuous sliding in atomic friction: Entering a new regime of ultralow friction, Phys. Rev. Lett. 92, 134301–134301 (2004)CrossRefGoogle Scholar
  169. T.D.B. Jacobs, R.W. Carpick: Nanoscale wear as a stress-assisted chemical reaction, Nat. Nanotechnol. 8, 108 (2013)CrossRefGoogle Scholar
  170. Z. Burton, B. Bhushan: Hydrophobicity, adhesion, and friction properties of nanopatterned polymers and scale dependence for micro- and nanoelectromechanical systems, Nano Lett. 5, 1607–1613 (2005)CrossRefGoogle Scholar
  171. U. Landman, W.D. Luedtke, N.A. Burnham, R.J. Colton: Atomistic mechanisms and dynamics of adhesion, nanoindentation, and fracture, Science 248, 454–461 (1990)CrossRefGoogle Scholar
  172. C.D. Frisbie, L.F. Rozsnyai, A. Noy, M.S. Wrighton, C.M. Lieber: Functional group imaging by chemical force microscopy, Science 265, 2071–2074 (1994)CrossRefGoogle Scholar
  173. T. Boland, B.D. Ratner: Direct measurement of hydrogen bonding in DNA nucleotide bases by atomic force microscopy, Proc. Natl. Acad. Sci. USA 92, 5297–5301 (1995)CrossRefGoogle Scholar
  174. R. García, R. Magerle, R. Perez: Nanoscale compositional mapping with gentle forces, Nat. Mater. 6, 405 (2007)CrossRefGoogle Scholar
  175. N.A. Burnham, O.P. Behrend, F. Oulevey, G. Gremaud, P.J. Gallo, D. Gourdon, E. Dupas, A.J. Kulik, H.M. Pollock, G.A.D. Briggs: How does a tip tap?, Nanotechnology 8, 67 (1997)CrossRefGoogle Scholar
  176. K. Sweers, K. van der Werf, M. Bennink, V. Subramaniam: Nanomechanical properties of α-synuclein amyloid fibrils: A comparative study by nanoindentation, harmonic force microscopy, and peakforce QNM, Nanoscale Res. Lett. 6, 270 (2011)CrossRefGoogle Scholar
  177. R. Szoszkiewicz, B. Bhushan, B.D. Huey, A.J. Kulik, G. Gremaud: Correlations between adhesion hysteresis and friction at molecular scales, J. Chem. Phys. 122, 144708 (2005)CrossRefGoogle Scholar
  178. A. Dazzi, C.B. Prater: AFM-IR: Technology and applications in nanoscale infrared spectroscopy and chemical imaging, Chem. Rev. 117, 5146–5173 (2017)CrossRefGoogle Scholar
  179. R.K. Vasudevan, H. Khassaf, Y. Cao, S. Zhang, A. Tselev, B. Carmichael, M.B. Okatan, S. Jesse, L.-Q. Chen, S.P. Alpay, S.V. Kalinin, N. Bassiri-Gharb: Acoustic detection of phase transitions at the nanoscale, Adv. Funct. Mater. 26, 478–486 (2016)CrossRefGoogle Scholar
  180. J. Hidalgo, C. Montero-Ocampo, M. Cuberes: Nanoscale visualization of elastic inhomogeneities at TiN coatings using ultrasonic force microscopy, Nanoscale Res. Lett. 4, 1493 (2009)CrossRefGoogle Scholar
  181. K. Yamanaka, H. Ogiso, O. Kolosov: Ultrasonic force microscopy for nanometer resolution subsurface imaging, Appl. Phys. Lett. 64, 178–180 (1994)CrossRefGoogle Scholar
  182. B.D. Huey: AFM and acoustics: Fast, quantitative nanomechanical mapping, Annu. Rev. Mater. Res. 37, 351–385 (2007)CrossRefGoogle Scholar
  183. U. Rabe, W. Arnold: Acoustic microscopy by atomic force microscopy, Appl. Phys. Lett. 64, 1493–1495 (1994)CrossRefGoogle Scholar
  184. J.P. Killgore, D.G. Yablon, A.H. Tsou, A. Gannepalli, P.A. Yuya, J.A. Turner, R. Proksch, D.C. Hurley: Viscoelastic property mapping with contact resonance force microscopy, Langmuir 27, 13983–13987 (2011)CrossRefGoogle Scholar
  185. I. Sokolov: Toward the nanoscale study of insect physiology using an atomic force microscopy-based nanostethoscope, MRS Bulletin 37, 522–527 (2012)CrossRefGoogle Scholar
  186. N.V. Guz, M.E. Dokukin, I. Sokolov: Atomic force microscopy study of nano-physiological response of ladybird beetles to photostimuli, PLOS ONE 5, e12834 (2010)CrossRefGoogle Scholar
  187. M. Kocun, A. Labuda, A. Gannepalli, R. Proksch: Contact resonance atomic force microscopy imaging in air and water using photothermal excitation, Rev. Sci. Instrum. 86, (2015)Google Scholar
  188. W.I. Gruszecki, A.J. Kulik, E. Janik, J. Bednarska, R. Luchowski, W. Grudzinski, G. Dietler: Nanoscale resolution in infrared imaging of protein-containing lipid membranes, Nanoscale 7, 14659–14662 (2015)CrossRefGoogle Scholar
  189. B. Lahiri, G. Holland, V. Aksyuk, A. Centrone: Nanoscale imaging of plasmonic hot spots and dark modes with the photothermal-induced resonance technique, Nano Lett. 13, 3218–3224 (2013)CrossRefGoogle Scholar
  190. S. Lee, O. Kwon, M. Jeon, J. Song, S. Shin, H. Kim, M. Jo, T. Rim, J. Doh, S. Kim, J. Son, Y. Kim, C. Kim: Super-resolution visible photoactivated atomic force microscopy, Light Sci. Appl. 6, e17080 (2017)CrossRefGoogle Scholar
  191. L. Zhou, M. Cai, T. Tong, H. Wang: Progress in the correlative atomic force microscopy and optical microscopy, Sensors 17, 938 (2017)CrossRefGoogle Scholar
  192. F. Keilmann, R. Hillenbrand: Near-field microscopy by elastic light scattering from a tip, Philos. Trans. Royal Soc. A 362, 787–805 (2004)CrossRefGoogle Scholar
  193. B. Pettinger, B. Ren, G. Picardi, R. Schuster, G. Ertl: Nanoscale probing of adsorbed species by tip-enhanced Raman spectroscopy, Phys. Rev. Lett. 92, 096101 (2004)CrossRefGoogle Scholar
  194. E. Bailo, V. Deckert: Tip-enhanced Raman spectroscopy of single RNA strands: Towards a novel direct-sequencing method, Angew. Chem. Int. Ed. 47, 1658–1661 (2008)CrossRefGoogle Scholar
  195. E.A. Muller, B. Pollard, H.A. Bechtel, P. van Blerkom, M.B. Raschke: Infrared vibrational nanocrystallography and nanoimaging, Sci. Adv. 2, e1601006 (2016)CrossRefGoogle Scholar
  196. A.B. Khanikaev, N. Arju, Z. Fan, D. Purtseladze, F. Lu, J. Lee, P. Sarriugarte, M. Schnell, R. Hillenbrand, M.A. Belkin, G. Shvets: Experimental demonstration of the microscopic origin of circular dichroism in two-dimensional metamaterials, Nat. Commun. 7, 12045 (2016)CrossRefGoogle Scholar
  197. F. Lu, M. Jin, M.A. Belkin: Tip-enhanced infrared nanospectroscopy via molecular expansion force detection, Nat. Photonics 8, 307–312 (2014)CrossRefGoogle Scholar
  198. R. Giridharagopal, P.A. Cox, D.S. Ginger: Functional scanning probe imaging of nanostructured solar energy materials, Acc. Chem. Res. 49, 1769–1776 (2016)CrossRefGoogle Scholar
  199. R. Price, P.M. Young: Visualization of the crystallization of lactose from the amorphous state, J. Pharm. Sci. 93, 155–164 (2004)CrossRefGoogle Scholar
  200. S.S. Nonnenmann, R. Kungas, J. Vohs, D.A. Bonnell: Direct in situ probe of electrochemical processes in operating fuel cells, ACS Nano 7, 6330–6336 (2013)CrossRefGoogle Scholar
  201. C.C. Williams, H.K. Wickramasinghe: Scanning thermal profiler, Appl. Phys. Lett. 49, 1587–1589 (1986)CrossRefGoogle Scholar
  202. J. Lee, T. Beechem, T.L. Wright, B.A. Nelson, S. Graham, W.P. King: Electrical, thermal, and mechanical characterization of silicon microcantilever heaters, J. Microelectromech. Syst. 15, 1644–1655 (2006)CrossRefGoogle Scholar
  203. H.M. Pollock, A. Hammiche: Micro-thermal analysis: Techniques and applications, J. Phys. D 34, R23 (2001)CrossRefGoogle Scholar
  204. P.D. Tovee, O.V. Kolosov: Mapping nanoscale thermal transfer in-liquid environment-immersion scanning thermal microscopy, Nanotechnology 24, 465706 (2013)CrossRefGoogle Scholar
  205. B. Drake, C. Prater, A. Weisenhorn, S. Gould, T. Albrecht, C. Quate, D. Cannell, H. Hansma, P. Hansma: Imaging crystals, polymers, and processes in water with the atomic force microscope, Science 243, 1586–1589 (1989)CrossRefGoogle Scholar
  206. I. Reviakine, W. Bergsma-Schutter, A. Brisson: Growth of protein 2-D crystals on supported planar lipid bilayers imagedin situby AFM, J. Struct. Biol. 121, 356–362 (1998)CrossRefGoogle Scholar
  207. W. Hoyer, D. Cherny, V. Subramaniam, T.M. Jovin: Rapid self-assembly of a-synuclein observed by in situ atomic force microscopy, J. Mol. Biol. 340, 127–139 (2004)CrossRefGoogle Scholar
  208. Y.L. Lyubchenko, L.S. Shlyakhtenko: Visualization of supercoiled DNA with atomic force microscopy in situ, Proc. Natl. Acad. Sci. 94, 496–501 (1997)CrossRefGoogle Scholar
  209. M. Li, H.X. Tang, M.L. Roukes: Ultra-sensitive nems-based cantilevers for sensing, scanned probe and very high-frequency applications, Nat. Nanotechnol. 2, 114–120 (2007)CrossRefGoogle Scholar
  210. M. Rivas, V. Vyas, A. Carter, J. Veronick, Y. Khan, O.V. Kolosov, R.G. Polcawich, B.D. Huey: Nanoscale mapping of in situ actuating microelectromechanical systems with AFM, J. Mater. Res. 30, 429–441 (2015)CrossRefGoogle Scholar
  211. S. Sharma, J.K. Gimzewski: Application of AFM to the nanomechanics of cancer, MRS Advances 1, 1817–1827 (2016)CrossRefGoogle Scholar
  212. D. Martínez-Martín, G. Fläschner, B. Gaub, S. Martin, R. Newton, C. Beerli, J. Mercer, C. Gerber, D.J. Müller: Inertial picobalance reveals fast mass fluctuations in mammalian cells, Nature 550, 500 (2017)CrossRefGoogle Scholar
  213. J. Liu, N. Sun, M.A. Bruce, J.C. Wu, M.J. Butte: Atomic force mechanobiology of pluripotent stem cell-derived cardiomyocytes, PLOS ONE 7, e37559 (2012)CrossRefGoogle Scholar
  214. N. Neerajha, V. Varun, D.H. Bryan, Z. Pinar: Modulation of the contractility of micropatterned myocardial cells with nanoscale forces using atomic force microscopy, Nanobiomedicine 3 (2016),  https://doi.org/10.1177/1849543516675348CrossRefGoogle Scholar
  215. S. Amemiya, A.J. Bard, F.-R.F. Fan, M.V. Mirkin, P.R. Unwin: Scanning electrochemical microscopy, Annu. Rev. Anal. Chem. 1, 95–131 (2008)CrossRefGoogle Scholar
  216. R. Kumar, A. Tokranov, B.W. Sheldon, X. Xiao, Z. Huang, C. Li, T. Mueller: In situ and operando investigations of failure mechanisms of the solid electrolyte interphase on silicon electrodes, ACS Energy Lett. 1, 689–697 (2016)CrossRefGoogle Scholar
  217. B. Breitung, P. Baumann, H. Sommer, J. Janek, T. Brezesinski: In situ and operando atomic force microscopy of high-capacity nano-silicon based electrodes for lithium-ion batteries, Nanoscale 8, 14048–14056 (2016)CrossRefGoogle Scholar
  218. S. Wang, W. Zhang, Y. Chen, Z. Dai, C. Zhao, D. Wang, C. Shen: Operando study of Fe3O4 anodes by electrochemical atomic force microscopy, Appl. Surf. Sci. 426, 217–223 (2017)CrossRefGoogle Scholar
  219. N. Balke, S. Jesse, A.N. Morozovska, E. Eliseev, D.W. Chung, Y. Kim, L. Adamczyk, R.E. García, N. Dudney, S.V. Kalinin: Nanoscale mapping of ion diffusion in a lithium-ion battery cathode, Nat. Nanotechnol. 5, 749 (2010)CrossRefGoogle Scholar
  220. S. Sundararajan, B. Bhushan, T. Namazu, Y. Isono: Mechanical property measurements of nanoscale structures using an atomic force microscope, Ultramicroscopy 91, 111–118 (2002)CrossRefGoogle Scholar
  221. Z.J. Davis, G. Abadal, O. Hansen, X. Borise, N. Barniol, F. Perez-Murano, A. Boisen: AFM lithography of aluminum for fabrication of nanomechanical systems, Ultramicroscopy 97, 467–472 (2003)CrossRefGoogle Scholar
  222. H. Sugimura, T. Hanji, K. Hayashi, O. Takai: Surface modification of an organosilane self-assembled monolayer on silicon substrates using atomic force microscopy: Scanning probe electrochemistry toward nanolithography, Ultramicroscopy 91, 221–226 (2002)CrossRefGoogle Scholar
  223. W.-K. Lee, K.C. Caster, J. Kim, S. Zauscher: Nanopatterned polymer brushes by combining AFM anodization lithography with ring-opening metathesis polymerization in the liquid and vapor phase, Small 2, 848–853 (2006)CrossRefGoogle Scholar
  224. Z. Li, M. Wu, T. Liu, C. Wu, Z. Jiao, B. Zhao: Preparation of TiO2 nanowire gas nanosensor by AFM anode oxidation, Ultramicroscopy 108, 1334–1337 (2008)CrossRefGoogle Scholar
  225. L. Nuri, J. William, L. Chunli, M. Christian: Size dependent bipolar resistance switching of NiO nanodots for low-power and multi-state operation, Nanotechnology 25, 415302 (2014)CrossRefGoogle Scholar
  226. M.R. Nellist, F.A.L. Laskowski, J. Qiu, H. Hajibabaei, K. Sivula, T.W. Hamann, S.W. Boettcher: Potential-sensing electrochemical atomic force microscopy for in operando analysis of water-splitting catalysts and interfaces, Nat. Energy 3, 46–52 (2017)CrossRefGoogle Scholar
  227. J. Lazar, P. Klapetek, M. Valtr, J. Hrabina, Z. Buchta, O. Cip, M. Cizek, J. Oulehla, M. Sery: Short-range six-axis interferometer controlled positioning for scanning probe microscopy, Sensors 14, 877–886 (2014)CrossRefGoogle Scholar
  228. J.-O. Jung, S. Choi, Y. Lee, J. Kim, D. Son, J. Lee: Versatile variable temperature and magnetic field scanning probe microscope for advanced material research, Rev. Sci. Instrum. 88, 103702 (2017)CrossRefGoogle Scholar
  229. Y. Nahas, F. Berneau, J. Bonneville, C. Coupeau, M. Drouet, B. Lamongie, M. Marteau, J. Michel, P. Tanguy, C. Tromas: An experimental UHV AFM-STM device for characterizing surface nanostructures under stress/strain at variable temperature, Rev. Sci. Instrum. 84, 105117 (2013)CrossRefGoogle Scholar
  230. J.A. Galvis, E. Herrera, I. Guillamon, J. Azpeitia, R.F. Luccas, C. Munuera, M. Cuenca, J.A. Higuera, N. Diaz, M. Pazos, M. Garcia-Hernandez, A. Buendia, S. Vieira, H. Suderow: Three axis vector magnet set-up for cryogenic scanning probe microscopy, Rev. Sci. Instrum. 86, 013706 (2015)CrossRefGoogle Scholar
  231. K.V. Hansen, Y. Wu, T. Jacobsen, M.B. Mogensen, L. Theil Kuhn: Improved controlled atmosphere high temperature scanning probe microscope, Rev. Sci. Instrum. 84, 073701 (2013)CrossRefGoogle Scholar
  232. W.G. Bessler, S. Gewies, M. Vogler: A new framework for physically based modeling of solid oxide fuel cells, Electrochim. Acta 53, 1782–1800 (2007)CrossRefGoogle Scholar
  233. T. Eguchi, Y. Fujikawa, K. Akiyama, T. An, M. Ono, T. Hashimoto, Y. Morikawa, K. Terakura, T. Sakurai, M. Lagally: Imaging of all dangling bonds and their potential on the Ge/Si(105) surface by noncontact atomic force microscopy, Phys. Rev. Lett. 93, 266102 (2004)CrossRefGoogle Scholar
  234. D. Rugar, R. Budakian, H. Mamin, B. Chui: Single spin detection by magnetic resonance force microscopy, Nature 430, 329–332 (2004)CrossRefGoogle Scholar
  235. C.A. Amo, A.P. Perrino, A.F. Payam, R. Garcia: Mapping elastic properties of heterogeneous materials in liquid with angstrom-scale resolution, ACS Nano 11, 8650–8659 (2017)CrossRefGoogle Scholar
  236. K. Salaita, Y. Wang, C.A. Mirkin: Applications of dip-pen nanolithography, Nat. Nanotechnol. 2, (2007)Google Scholar
  237. D. Ziegler, A. Klaassen, D. Bahri, D. Chmielewski, A. Nievergelt, F. Mugele, J.E. Sader, P.D. Ashby: Encased cantilevers for low-noise force and mass sensing in liquids. In: Proc. 2014 IEEE 27th Int. Conf. Micro Electro Mech. Syst. MEMS (2014) pp. 128–131,  https://doi.org/10.1109/MEMSYS.2014.6765590CrossRefGoogle Scholar
  238. S.C. Minne, G. Yaralioglu, S.R. Manalis, J.D. Adams, J. Zesch, A. Atalar, C.F. Quate: Automated parallel high-speed atomic force microscopy, Appl. Phys. Lett. 72, 2340–2342 (1998)CrossRefGoogle Scholar
  239. A.D.L. Humphris, M.J. Miles, J.K. Hobbs: A mechanical microscope: High-speed atomic force microscopy, Appl. Phys. Lett. 86, 034106 (2005)CrossRefGoogle Scholar
  240. G. Schitter, M.J. Rost: Scanning probe microscopy at video-rate, Mater. Today 11, 40–48 (2008)CrossRefGoogle Scholar
  241. M.B. Viani, T.E. Schäffer, G.T. Paloczi, L.I. Pietrasanta, B.L. Smith, J.B. Thompson, M. Richter, M. Rief, H.E. Gaub, K.W. Plaxco, A.N. Cleland, H.G. Hansma, P.K. Hansma: Fast imaging and fast force spectroscopy of single biopolymers with a new atomic force microscope designed for small cantilevers, Rev. Sci. Instrum. 70, 4300–4303 (1999)CrossRefGoogle Scholar
  242. J.L. Bosse, B.D. Huey: Error-corrected AFM: A simple and broadly applicable approach for substantially improving AFM image accuracy, Nanotechnology 25, 155704 (2014)CrossRefGoogle Scholar
  243. I.A. Mahmood, S.O. Reza Moheimani: Fast spiral-scan atomic force microscopy, Nanotechnology 20, 365503 (2009)CrossRefGoogle Scholar
  244. D. Ziegler, T.R. Meyer, A. Amrein, A.L. Bertozzi, P.D. Ashby: Ideal scan path for high-speed atomic force microscopy, IEEE ASME Trans. Mechatron. 22, 381–391 (2017)CrossRefGoogle Scholar
  245. Z. Dominik, R.M. Travis, F. Rodrigo, B. Christoph, L.B. Andrea, D.A. Paul: Improved accuracy and speed in scanning probe microscopy by image reconstruction from non-gridded position sensor data, Nanotechnology 24, 335703 (2013)CrossRefGoogle Scholar
  246. E.T. Herruzo, A.P. Perrino, R. Garcia: Fast nanomechanical spectroscopy of soft matter, Nat. Commun. 5, 3126 (2014)CrossRefGoogle Scholar
  247. C. Marutschke, D. Walters, D. Walters, I. Hermes, R. Bechstein, A. Kuhnle: Three-dimensional hydration layer mapping on the (10.4) surface of calcite using amplitude modulation atomic force microscopy, Nanotechnology 25, 335703 (2014)CrossRefGoogle Scholar
  248. S.V. Kalinin, E. Strelcov, A. Belianinov, S. Somnath, R.K. Vasudevan, E.J. Lingerfelt, R.K. Archibald, C. Chen, R. Proksch, N. Laanait, S. Jesse: Big, deep, and smart data in scanning probe microscopy, ACS Nano 10, 9068–9086 (2016)CrossRefGoogle Scholar
  249. A. Hammiche, H.M. Pollock, M. Song, D.J. Hourston: Sub-surface imaging by scanning thermal microscopy, Meas. Sci. Technol. 7, 142 (1996)CrossRefGoogle Scholar
  250. M.J. Pereira, J.S. Amaral, N.J.O. Silva, V.S. Amaral: Nano-localized thermal analysis and mapping of surface and sub-surface thermal properties using scanning thermal microscopy (SThM), Microsc. Microanal. 22, 1270–1280 (2016)CrossRefGoogle Scholar
  251. O.A. Castaneda-Uribe, R. Reifenberger, A. Raman, A. Avila: Depth-sensitive subsurface imaging of polymer nanocomposites using second harmonic Kelvin probe force microscopy, ACS Nano 9, 2938–2947 (2015)CrossRefGoogle Scholar
  252. E.M. Tennyson, J.A. Frantz, J.M. Howard, W.B. Gunnarsson, J.D. Myers, R.Y. Bekele, J.S. Sanghera, S.-M. Na, M.S. Leite: Photovoltage tomography in polycrystalline solar cells, ACS Energy Lett. 1, 899–905 (2016)CrossRefGoogle Scholar
  253. K. Radotic, C. Roduit, J. Simonovic, P. Hornitschek, C. Fankhauser, D. Mutavdzic, G. Steinbach, G. Dietler, S. Kasas: Atomic force microscopy stiffness tomography on living Arabidopsis thaliana cells reveals the mechanical properties of surface and deep cell-wall layers during growth, Biophys. J. 103, 386–394 (2012)CrossRefGoogle Scholar
  254. J.D. Beard, R.H. Guy, S.N. Gordeev: Mechanical tomography of human corneocytes with a nanoneedle, J. Investig. Dermatol. 133, 1565–1571 (2013)CrossRefGoogle Scholar
  255. C. Roduit, S. Sekatski, G. Dietler, S. Catsicas, F. Lafont, S. Kasas: Stiffness tomography by atomic force microscopy, Biophys. J. 97, 674–677 (2009)CrossRefGoogle Scholar
  256. D. Ebeling, B. Eslami, S.D.J. Solares: Visualizing the subsurface of soft matter: Simultaneous topographical imaging, depth modulation, and compositional mapping with triple frequency atomic force microscopy, ACS Nano 7, 10387–10396 (2013)CrossRefGoogle Scholar
  257. A.P. McGuigan, B.D. Huey, G.A.D. Briggs, O.V. Kolosov, Y. Tsukahara, M. Yanaka: Measurement of debonding in cracked nanocomposite films by ultrasonic force microscopy, Appl. Phys. Lett. 80, 1180–1182 (2002)CrossRefGoogle Scholar
  258. G.S. Shekhawat, V.P. Dravid: Nanoscale imaging of buried structures via scanning near-field ultrasound holography, Science 310, 89 (2005)CrossRefGoogle Scholar
  259. F. Dinelli, P. Pingue, N.D. Kay, O.V. Kolosov: Subsurface imaging of two-dimensional materials at the nanoscale, Nanotechnology 28, 085706 (2017)CrossRefGoogle Scholar
  260. G. Stan, E. Mays, H.J. Yoo, S.W. King: Nanoscale tomographic reconstruction of the subsurface mechanical properties of low-k high-aspect ratio patterns, Nanotechnology 27, 485706–485706 (2016)CrossRefGoogle Scholar
  261. A.P. Perrino, Y.K. Ryu, C.A. Amo, M.P. Morales, R. Garcia: Subsurface imaging of silicon nanowire circuits and iron oxide nanoparticles with sub-10 nm spatial resolution, Nanotechnology 27, 275703 (2016)CrossRefGoogle Scholar
  262. C. Ma, Y. Chen, W. Arnold, J. Chu: Detection of subsurface cavity structures using contact-resonance atomic force microscopy, J. Appl. Phys. 121, 154301 (2017)CrossRefGoogle Scholar
  263. O.V. Kolosov, I. Grishin, R. Jones: Material sensitive scanning probe microscopy of subsurface semiconductor nanostructures via beam exit Ar ion polishing, Nanotechnology 22, 185702 (2011)CrossRefGoogle Scholar
  264. J.L. Bosse, I. Grishin, B.D. Huey, O.V. Kolosov: Nanomechanical morphology of amorphous, transition, and crystalline domains in phase change memory thin films, Appl. Surf. Sci. 314, 151–157 (2014)CrossRefGoogle Scholar
  265. S.T. Ho, D.W. Hutmacher: A comparison of micro CT with other techniques used in the characterization of scaffolds, Biomaterials 27, 1362–1376 (2006)CrossRefGoogle Scholar
  266. D.J. Brenner, E.J. Hall: Computed tomography—An increasing source of radiation exposure, N. Engl. J. Med. 357, 2277–2284 (2007)CrossRefGoogle Scholar
  267. S.M. Smith, M. Jenkinson, M.W. Woolrich, C.F. Beckmann, T.E.J. Behrens, H. Johansen-Berg, P.R. Bannister, M. De Luca, I. Drobnjak, D.E. Flitney, R.K. Niazy, J. Saunders, J. Vickers, Y. Zhang, N. De Stefano, J.M. Brady, P.M. Matthews: Advances in functional and structural MR image analysis and implementation as FSL, NeuroImage 23(Suppl 1), S208–S219 (2004)CrossRefGoogle Scholar
  268. K. Carlsson, N. Aslund: Confocal imaging for 3-D digital microscopy, Appl. Opt. 26, 3232–3238 (1987)CrossRefGoogle Scholar
  269. K. Lange, R. Carson: EM reconstruction algorithms for emission and transmission tomography, J. Comput. Assist. Tomogr. 8, 306–316 (1984)Google Scholar
  270. X. Zhong, D.J. Rowenhorst, H. Beladi, G.S. Rohrer: The five-parameter grain boundary curvature distribution in an austenitic and ferritic steel, Acta Mater. 123, 136–145 (2017)CrossRefGoogle Scholar
  271. A. Sperschneider, M. Hund, H.G. Schoberth, F.H. Schacher, L. Tsarkova, A.H.E. Müller, A. Böker: Going beyond the surface: Revealing complex block copolymer morphologies with 3D scanning force microscopy, ACS Nano 4, 5609–5616 (2010)CrossRefGoogle Scholar
  272. Y. Chen, J. Cai, T. Zhao, C. Wang, S. Dong, S. Luo, Z.W. Chen: Atomic force microscopy imaging and 3-D reconstructions of serial thin sections of a single cell and its interior structures, Ultramicroscopy 103, 173–182 (2005)CrossRefGoogle Scholar
  273. A.E. Efimov, A.G. Tonevitsky, M. Dittrich, N.B. Matsko: Atomic force microscope (AFM) combined with the ultramicrotome: A novel device for the serial section tomography and AFM/TEM complementary structural analysis of biological and polymer samples, J. Microsc. 226, 207–217 (2007)CrossRefGoogle Scholar
  274. A.E. Efimov, H. Gnaegi, R. Schaller, W. Grogger, F. Hofer, N.B. Matsko: Analysis of native structures of soft materials by cryo scanning probe tomography, Soft Matter 8, 9756–9760 (2012)CrossRefGoogle Scholar
  275. S. Scheuring, J. Seguin, S. Marco, D. Lévy, B. Robert, J.-L. Rigaud: Nanodissection and high-resolution imaging of the rhodopseudomonas viridis photosynthetic core complex in native membranes by AFM, Proc. Natl. Acad. Sci. 100, 1690–1693 (2003)CrossRefGoogle Scholar
  276. D. Pires, J.L. Hedrick, A. De Silva, J. Frommer, B. Gotsmann, H. Wolf, M. Despont, U. Duerig, A.W. Knoll: Nanoscale three-dimensional patterning of molecular resists by scanning probes, Science 328, 732–735 (2010)CrossRefGoogle Scholar
  277. A.W. Knoll, D. Pires, O. Coulembier, P. Dubois, J.L. Hedrick, J. Frommer, U. Duerig: Probe-based 3-D nanolithography using self-amplified depolymerization polymers, Adv. Mater. 22, 3361–3365 (2010)CrossRefGoogle Scholar
  278. A. Schulze, T. Hantschel, A. Dathe, P. Eyben, X. Ke, W. Vandervorst: Electrical tomography using atomic force microscopy and its application towards carbon nanotube-based interconnects, Nanotechnology 23, 305707 (2012)CrossRefGoogle Scholar
  279. U. Celano, L. Goux, R. Degraeve, A. Fantini, O. Richard, H. Bender, M. Jurczak, W. Vandervorst: Imaging the three-dimensional conductive channel in filamentary-based oxide resistive switching memory, Nano Lett. 15, 7970–7975 (2015)CrossRefGoogle Scholar
  280. U. Celano, L. Goux, A. Belmonte, K. Opsomer, A. Franquet, A. Schulze, C. Detavernier, O. Richard, H. Bender, M. Jurczak, W. Vandervorst: Three-dimensional observation of the conductive filament in nanoscaled resistive memory devices, Nano Lett. 14, 2401–2406 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dept. of Materials Science & EngineeringUniversity of ConnecticutStorrs, CTUSA
  2. 2.Microelectronics Engineering and TechnologyRaytheonAndover, MAUSA
  3. 3.Dept. of Materials Science & EngineeringUniversity of PennsylvaniaPhiladelphia, PAUSA

Personalised recommendations