Scanning probe microscopy (SPM), a key invention in nanoscience, has by now been extended to a wide spectrum of basic and applied fields. Its application to basic science led to a paradigm shift in the understanding and perception of matter at its nanoscopic and even atomic levels. SPM uses a sharp tip to physically raster-scan samples and locally collect information from the surface. Various signals can be directly detected by SPM in real space with atomic or nanoscale resolution, which provides insights into the structural, electronic, vibrational, optical, magnetic, (bio)chemical and mechanical properties. This Primer introduces the key aspects and general features of SPM and SPM set-up and variations, with particular focus on scanning tunnelling microscopy and atomic force microscopy. We outline how to conduct SPM experiments, as well as data analysis of SPM imaging, spectroscopy and manipulation. Recent applications of SPM to physics, chemistry, materials science and biology are then highlighted, with representative examples. We outline issues with reproducibility, and standards on open data are discussed. This Primer also raises awareness of the ongoing challenges and possible ways to overcome these difficulties, followed by an outlook of future possible directions.
Visualizing atoms on a solid surface has been a longstanding dream for researchers, and was finally fulfilled by the invention of scanning tunnelling microscopy (STM) in 1981 by Rohrer, Binnig and Gerber at IBM Zürich1. STM uses an atomically sharp biased metal tip to collect tiny currents from the metal surface, based on the quantum mechanical effect termed tunnelling (Fig. 1a). Owing to the highly localized nature of the tunnelling current, atomically resolved images could be obtained by raster-scanning the tip over the surface while using a feedback loop to keep the tunnelling current constant. Soon after the invention of STM, Binnig et al. were able to map the tip–sample interaction by atomic forces instead of the tunnelling current, which led to the birth of atomic force microscopy (AFM)2 (Fig. 1b). AFM is able to image almost any type of surface, unlike STM that requires conducting or semiconducting samples. AFM and STM take advantage of different feedback signals to maintain the tip–sample interaction, but the basic principle of operation is similar in both techniques and reminiscent of a record player, where a tip senses the surface topography of the sample via physical raster-scanning.
A large family of scanning probe microscopy (SPM) methods have emerged as variations of STM and AFM, by integrating nanosensors on the tip or coupling various electromagnetic waves with the tip–sample junction. The measurable physical quantities range from the electric current, force and capacitance to photons, magnetic/electric field, strain and temperature. The emergence of SPM in the then-fledgling field of nanotechnology changed researchers’ perception and understanding of matter at atomic or molecular levels. It doubtlessly opened up new possibilities and avenues in physics, chemistry, materials science, biology and medicine, and stimulates increasing numbers of students and researchers around the world.
SPM would not be possible without the piezoelectric effect, that is, the deformation of materials as the result of applying an electric field. The effect enables scanning with picometre precision by simply applying voltages to piezo elements. The core of the SPM is the scanner, which allows stably approaching the tip to the surface from a macroscopic distance to the nanometre scale. An atomically sharp tip is another key component of SPM ultimately determining the lateral resolution. In addition, vibrational isolation and high-gain, low-noise signal amplifiers are also critical for achieving a sufficiently high signal to noise ratio to ensure atomically resolved images by SPM.
This Primer starts by introducing the technical aspects of SPM (Experimentation) and the general features of SPM data (Results). The applications of SPM to physics, chemistry, materials science and biology are then highlighted with some representative examples (Applications). Afterwards, we discuss issues with reproducibility and field standards on open data (Reproducibility and data deposition). We also point out the limitations of SPM and possible ways to overcome those difficulties (Limitations and optimizations). Finally, some possible future directions of SPM are envisaged (Outlook).
In this section, we introduce the basics of STM and AFM experimental set-ups, including the key components to achieve high spatial resolution, the working principle and a guide to conduct SPM experiments. We also introduce some representative SPM variations based on STM and AFM, which can map out various physical quantities besides current and force. The sensing mechanism, advantages and applications of those SPM variations are briefly discussed.
Scanning tunnelling microscopy
STM has at its heart a very simple idea: a metal needle that is sharpened to a single atom is approached very close to a surface while a biased voltage between the tip and the surface is applied. When the tip–sample distance reaches the atomic-scale range, some electrons will jump between the tip and the sample, known as the tunnelling current. The tunnelling current is sensitive to the tip–sample distance; it has exponential dependence on the tip–sample distance. For example, in a clean vacuum tunnel junction, the tunnelling current decreases by a factor of ten when the tip–sample distance increases by 0.1 nm (the typical tip–sample distance is in the range 0.3–1 nm). This effect gives STM its atomic-scale lateral spatial resolution as the majority of the tunnelling current stems from only the last atom of the tip apex3 (Fig. 1a).
The STM tip is usually attached to piezoelectric control elements that allow the tip to be moved with atomic-scale precision (Fig. 2a,b). In almost all STM systems, the tip and the sample should be replaced with new ones in a convenient manner without violently changing the STM configuration. Generally, STMs are very sensitive to noise, which includes electronic noise and vibrational noise from the laboratory environment. Here, we focus on controlling some of these noise sources, from large to atomic scale. The scanner head of the microscope, or the STM body, has macroscopic dimensions typically in the range of a few centimetres. By contrast, the tip–sample distance is often smaller than 1 nm. Ideally, the tip–sample distance is kept stable at approximately 1 pm. As the tunnelling current is sensitive to the tip–sample distance (and, hence, to fluctuations in this distance), mechanical shaking causes noise in the tunnelling current. Vibrational noise, such as shaking of the laboratory floor and/or the vacuum chambers, must be reduced. The STM system must be built with a rigid scanner head that minimizes changes to the tip–sample distance, as some external shaking of the scanner head is unavoidable. Therefore, the equipment should be kept on a very quiet laboratory floor, usually the basement of the building. The lowest vibration levels are achieved in custom facilities built using heavy (100 ton) concrete blocks floating on special air springs, for example, at the Precision Laboratory of the Max Planck Institute for Solid State Research4. A custom building with a heavy concrete floor that is isolated from other buildings can also provide low vibration levels. However, even a well-built general laboratory building can have low levels of vibration below 10 Hz (the IBM Almaden laboratory), despite the increased floor-level vibrations above 10 Hz (Fig. 2c).
Quiet laboratory space must be complemented with a rigid STM scanner design with high mechanical resonance frequencies (Fig. 2b), which makes the microscope resistant against low-frequency shaking. In practice, the lowest frequencies of the STM scan head are found at 1–5 kHz; such a scan head is good at rejecting low-frequency vibrational noise from the building but it is important to limit higher-frequency mechanical noise sources, which can be effectively reduced by soft springs combined with eddy current damping (Fig. 2a). In practice, a properly built scanner head in a low-noise laboratory can reduce tip–sample shaking well below 1 pm, which limits the fluctuation of the detected tunnel current within several per cent.
It is seemingly an impossible task to move the STM tip by atomic-scale dimensions without adding noise, but this has been made possible with the use of piezoelectric materials such as lead zirconate or lead titanate ceramics1. A typical piezoelectric material used in STM will change its size by about 1 nm when a voltage of 1 V is applied across its sides1. Hence, stable high-voltage sources can hold the tip stable to better than 1 pm while allowing a maximum scan range around 1 μm. However, as for STM systems under ultra-high vacuum (UHV) conditions, it is necessary to change samples without opening the vacuum chamber. The tip must be moved at least 1 mm away from the sample before the sample can be extracted. Although piezoelectric materials are good at atomic-scale length changes, they cannot provide such large displacements; instead, this task is achieved by the coarse approach mechanism with a type of piezo motor, which is the kernel component of the STM scanner head (Fig. 2b). The action of such a motor can be easily visualized: the tip is held on a body — often made from a ceramic — which is mounted on piezoelectric materials. When the piezo materials move slowly, the ceramic body will follow. However, when the piezo materials move rapidly (>100 nm in 10 µs), the body will hold still owing to its inertia. Each step gives a motion in the range of 100 nm. This process can then be repeated many thousands of times to arrive at a macroscopic motion. Such a stick–slip motion5,6 is reliable in providing coarse motion in the range of a few millimetres, but is among the most difficult parts of STM design as it is challenging to provide a rigid enough movable motor with mechanical resonance frequency larger than several kilohertz. The well-known types of motor for the coarse approach include the louse type7, beetle type5, Pan type6 and various single-tube types.
There is no way to sharpen the tip to a single atom, and so in situ protocols have been developed for this task. Most often, we start with either a cut platinum/iridium wire or with an etched tungsten wire8. A cut wire has the advantage of fewer oxide films on its surface, whereas an etched tip has a much better macroscopic shape. The platinum/iridium tip can be produced by mechanical cutting or electrochemical etching, whereas the tungsten tip can only be made by etching owing to tungsten’s brittleness. For most STM measurements, the overall shape of the tip does not matter as the tunnelling only occurs from the atom or cluster of atoms at the very end of the tip. However, for some applications — most notably optical experiments — the macroscopic shape can have a pronounced effect on the plasmonic enhancement of Raman scattering and fluorescence9.
Lower temperatures are desirable for STM because of improved stability compared with room temperature, as well as higher energy resolution owing to the smaller thermal broadening of the electrons in both the tip and the sample. Eigler introduced a machine with a stable design operating at about 5 K reaching a tip–sample distance noise below 1 pm, which was used to build quantum corrals10 and move individual atoms11,12. Eventually, lower operating temperatures — down to 10 mK (ref.13) — were achieved; such ultra-low-temperature STM is also functional under high magnetic fields up to 30 T (ref.14). On the other extreme, STM has been used to image the growth of materials in situ at temperatures up to several hundred degrees Celsius15. STM has also been used to study catalytic processes under near-ambient pressures16. Whereas operation of STM in air is often complicated owing to the presence of water films on the surfaces of samples, STM can work in a more stable manner at a solid–liquid interface, where both the potential stability and the chemical composition inside the aqueous environments are well controlled17.
Atomic force microscopy
As STM can only probe conductive surfaces relying on the tunnelling current, AFM was conceived to extend atomic resolution to non-conducting surfaces2. The advantage of AFM is that it can be employed in a vacuum, an ambient atmosphere and a liquid, and from high to ultra-low temperatures. AFM shares many basic features and key components with STM, such as the vibrational isolation, scanning process, coarse-approaching mechanism and tip treatments. However, as AFM detects local force instead of the tunnelling current, there are some differences in the signal acquisition and the feedback loop (Fig. 1b). In AFM, a tip is mounted at the end of a flexible cantilever, which deflects linearly with the force applied. Contact mode AFM measures tiny deflections of the scanning cantilever and uses a force-feedback circuit to move the sample or tip held by a piezoelectric element in the z direction (maintaining a constant tip–sample distance) to keep the deflection, and thus the applied force, constant. Plotting the z-direction position (height) of the scanned surface pixel by pixel provides the sample topography. An important development for AFM was the optical lever system18, which reflects a laser beam on the backside of the cantilever to efficiently magnify the tiny cantilever deflections resulting from the interactions of the tip and the sample (Fig. 3a), thus largely enhancing the signal to noise ratio during data acquisition. An important development towards enabling biological AFM was the invention of a liquid cell in which the cantilever and the sample are immersed in physiological solution19.
Dynamical AFM uses oscillating cantilevers20. Concomitant amplitude modulation modes (for example, ‘intermittent contact’, ‘tapping’ or ‘oscillating’ mode) use feedback controls to oscillate the cantilever at resonant frequency and constant amplitude21 (Fig. 3b). Other oscillating modes apply frequency (frequency modulation) or phase (phase modulation) for feedback control (Fig. 3b). Such dynamic modes control the tip–sample interaction more gently compared with static AFM modes so that interaction forces are minimized.
Frequency modulation AFM (FM-AFM) is used for UHV and low-temperature physics22, as well as for biological applications23. FM-AFM is usually more precise than amplitude modulation AFM, as the time and frequency can be measured with higher accuracy than amplitude changes. However, force detection by amplitude modulation AFM is simpler and faster, and the amplitude changes with the tip–sample distance in a nearly monotonic manner. Time-lapse AFM imaging can monitor cellular machines at work at the nanoscale level24. When using a small cantilever with a high resonant frequency, time-lapse AFM can work at much faster speeds, which allows observation of machinery at a temporal resolution of ~100 ms (ref.25); this set-up is known as high-speed AFM.
It is more challenging to obtain high-resolution images in AFM systems, as forces have multiple long-range and short-range components and the force–distance relation between tip and sample can be more complicated than the current–distance relation in STM26,27. Presently, subatomic details such as orbitals or chemical bonds can be observed by probing short-range forces with chemically functionalized tips in high vacuum. Meanwhile, researchers developed a plethora of new AFM-based approaches to probe chemical, magnetic and friction forces, and to introduce different spectroscopies such as force spectroscopy with sub-piconewton sensitivity28,29 or single-molecule and single-cell force spectroscopy in biology30,31,32. Now, we approach the time at which AFM imaging simultaneously quantifies and structurally maps the various physical, chemical and biological properties of non-living and living objects24,33,34 (Fig. 3c).
Progress in instrumentation has been key to recent AFM developments. After the quartz tuning fork was first used as the force sensors for non-contact AFM35, one example of prominent progress is the development of the qPlus sensor, with one prong fixed to enhance the quality factor up to ~100,000 at small amplitude (<50 pm)28,36. The qPlus sensor’s self-sensing mechanism is enabled by the piezoelectricity of quartz, which converts mechanical deformations into electric signals. Besides the two electrodes used for collecting the induced charges resulting from the deformation, an extra metal line is deposited on the side of the quartz prongs and used for feeding through the tunnelling current, thus allowing simultaneous measurements under STM and AFM modes, where the spatial resolution of AFM has exceeded that of STM.
Imaging, spectroscopy and manipulation
A powerful feature of STM and AFM is the unique capability that imaging, local spectroscopy and manipulation are achieved with atomic-scale spatial resolution, all in the same research tool.
During SPM imaging, the tip height can be controlled by a feedback loop. If the feedback loop is activated, the corresponding image will be measured at constant current in STM or constant force in AFM. On the other hand, when the feedback is not used, the tip height is kept constant, resulting in the constant-height imaging mode. Under the constant-current/force mode, the tip–sample distance is determined by the preset current/force and typically higher resolution is obtained at smaller tip–sample distance, simultaneously with higher risk of tip damage. By contrast, constant-height imaging only works for flat surfaces, and the results are more straightforward to interpret owing to the absence of the feedback loop, but it suffers from thermal drift between the tip and the specific local structures such as atomic size defects or adsorbed molecules.
Spectroscopic measurements based on SPM can be achieved by fixing the tip at a specific position on the surface and recording the current/force as a function of bias voltage, tip height or time. For scanning tunnelling spectroscopy (STS) of STM, the differential conductance (dI/dV) curve reflects the electronic structure of samples based on the electrons tunnelling to the unoccupied electronic states above the Fermi level or, vice versa, tunnelling from the occupied electronic states below the Fermi level37. In some cases, the electrons can tunnel inelastically through the junctions owing to their coupling with vibration, photon–phonon interaction and spin38,39. The contribution of those inelastic electrons is usually small compared with the elastic ones and could be more prominent in second-derivative I(V) spectra (d2I/dV2), such as inelastic electron tunnelling spectroscopy (IETS) (Fig. 4A). To obtain dI/dV and d2I/dV2 spectra, a small voltage modulation is added to the bias, and the first-order and second-order components of I–V curves are extracted by lock-in amplifiers (Fig. 2a). In AFM-based force spectroscopy, the tip is approached and withdrawn from a sample surface while recording a force–distance curve (Fig. 4B). The force–distance curves allow analysis of repulsive and adhesive interactions between the tip and the sample, as well as sample deformation and elasticity40 (Box 1). AFM can combine imaging with force spectroscopy to simultaneously map mechanical, chemical and biological properties. Therefore, the AFM record for each pixel of the resulting AFM topography represents a force–distance curve, from which multiple parameters such as Young’s modulus and energy dissipation, pressures and tension can be extracted (Fig. 3c).
The SPM tip is not only a perfect probe for surface characterization but also acts as a nanoscale hand for manipulating single atoms or molecules11,41,42. Precise manipulation is usually achieved through voltage pulses or forces when the tip is positioned directly above the target sites. During such a process, the injected electrons can excite the vibrational modes of atoms or molecules and lead to diffusion, desorption and selective bond breaking or formation42,43,44. For vertical manipulation, an adsorbed molecule is picked up by an STM tip by injecting electrons into the surface, transferred above a target site and then released from the tip by applying a reversed bias voltage, leading to the formation of a new complex42 (Fig. 4C). For the lateral manipulation, the tip is brought close to the atom or molecule on the surface, such that the tip–sample interaction force is large enough to pull or push the atom or molecule moving over the diffusion barrier41,45 (Fig. 4D).
Tip preparation and functionalization
Atomically sharp tips are the key to achieving high resolution in SPM. They are usually produced by mechanical cutting or milling, electrochemical etching or more complicated nanofabrication such as focused ion beam systems46. However, the tip apex obtained by those methods is not sharp enough for atomically resolved imaging. To obtain an ideal tip terminated with a single atom or a small cluster of atoms, the tip needs to be treated (which includes both sharpening and functionalization) during scanning by poking the tip into the surface and grasping a small cluster of atoms. In STM experiments, the application of high voltages up to 10 V can be used for tip treatment, at a tip–sample distance of ~1 nm to induce field emission47. The atoms at the very end of the tip determine the spatial resolution of SPM, not the overall radius of curvature at the apex. In order to obtain high chemical resolution besides topography, one can also evaporate noble metal films such as gold and silver onto the conventional silicon AFM tip; this type of tip has been extensively used for nanoscale chemical analysis under ambient conditions48,49.
For SPM experiments performed in UHV and low-temperature conditions, the most controllable and precise way to get a well-defined sharp tip is functionalizing the tip apex by picking up a single atom or molecule on the surface50,51. Under such conditions, SPM with a CO-functionalized tip can image molecular orbitals52, owing to the p-wave orbitals of the CO molecule. The CO tip also allows access to the short-range Pauli repulsions, reflecting the variations of electron density in individual chemical bonds53. As the CO tip has a quadrupole-like charge distribution, it is also sensitive to the high-order electrostatic force54. One drawback of the CO tip is the lateral relaxation of the CO molecule at the tip apex, which leads to distortion or even artefacts in the SPM images. Functionalizing the tip at the atomic level, for example replacing the C–O group with oxygen55 and chlorine56, yields a more rigid tip with smaller relaxation of the tip apex. However, the resolution of those tips is usually poorer than for the CO tip, as strong relaxation of the CO molecule is also crucial to obtain sharply resolved structural resolution when the tip–sample distance is within the region of Pauli repulsion57.
For biological AFM imaging applications, tips are typically made of silicon or silicon nitride, which upon exposure to air and immersion into physiological buffer will feature an oxide layer at their surface58. To achieve sharper tips with higher aspect ratio, electron beam deposition can be used, resulting in the growth of an amorphous carbon-based apex, which is subsequently rendered hydrophilic using plasma cleaning59. Carbon nanotubes have been grafted as a quasi one-dimensional (1D) object at the end of AFM tips to create a super-sharp, very high aspect ratio apex, but despite efforts these tips have so far had no significant impact in the AFM field, likely because of nanotube buckling60. Overall for biological imaging applications in liquid, the tip–sample interaction forces range from short range (≈1–10 nm) to long range (>10 nm) and can be composed of a repertoire of different physical, chemical and biological interactions40. One approach to study these interactions is to functionalize the AFM tip.
Variations of SPM
By integrating microsensors on the tip or coupling the electromagnetic waves with different wavelengths into the tip–sample junctions, a large family of SPM methods have been developed since the invention of STM and AFM. In this section, we introduce some representative variations of SPM, which can map out various physical quantities besides current and force, such as magnetic/electric field, photons, strain, temperature, and dielectric and physiological responses. The sensing mechanism, advantages and applications of those SPM variations are briefly discussed in the following sections.
Despite achieving high spatial resolution in real space, one of the most interesting questions about SPM is the speed at which such a device could capture a signal in real time. High-speed image acquisition could be achieved by video-rate STM15,61, which typically scans a frame within a millisecond timescale. Recently, with the pulsed voltages, fast spin dynamics such as spin relaxation was investigated by electrical pump-probe STM at the level of a single atom62. As the bandwidth of the preamplifier and other electronics of SPM is limited to megahertz, ultra-fast dynamics within picoseconds and femtoseconds should be captured by incorporating pump-probe techniques into STM, leading to femtosecond laser STM63,64 and terahertz STM65,66. Examples of various time-resolved STM techniques can be found in Table 1.
Magnetic field-sensitive SPM
Magnetic field or spin-sensitive SPM is very useful for characterizing local magnetic structures and spin states in real space (Table 2). The simplest method for detecting the local magnetic field is by replacing the conventional non-magnetic probe with a magnetic probe, which is extensively used in magnetic force microscopy67,68, magnetic exchange force microscopy69 and spin-polarized STM70,71. Another avenue is grafting a micro-magnetic sensor such as a superconducting quantum interference device (SQUID) or Hall probe on the tip, constructing scanning SQUID microscopy72,73 and scanning Hall probe microscopy74. In addition, by incorporating microwaves into SPM to excite magnetic resonance, the magnetic sensitivity of SPM can be enhanced up to single electron or nuclear spin, such as electron spin resonance (ESR) STM75,76,77, magnetic resonant force microscopy78 and nitrogen vacancy-based SPM79.
Electric field-sensitive SPM
To map out the surface potential or charge with high resolution, typically a conductive SPM tip biased with variable voltage is used (Table 3). One form of electric field-sensitive SPM is scanning capacitance microscopy80, where the local capacitive coupling between the tip and the sample is detected for deriving the local dielectric and electrical properties. Another option for sensing local potential is the integration of a microelectric sensor such as a single-electron transistor onto the tip81. For single charge detection, the tip should be brought as close as possible to the sample, which requires a sharp metal tip instead of a microelectric sensor, such as in Kelvin probe force microscopy82. Piezoresponse force microscopy (PFM) is another important electric-field sensitive SPM83,84, in which a modulated pressure is applied locally on the sample by the tip and its piezoelectric response is monitored during scanning.
Although surface characterization with atomic resolution is ever-present in UHV and low-temperature experiments, it remains challenging for use in aqueous environments. The self-assembly and reactivity of supramolecular systems inside non-ionic organic liquids has been investigated by liquid-phase STM85,86,87. Meanwhile, working at the solid–electrolyte interfaces, electrochemical STM (EC-STM) is developed with four electrodes including the tip, working electrode, counter electrode and reference electrode, which are controlled by a bipotentiostat17,88. As EC-STM only works on conductive surfaces, liquid-phase non-contact AFM was developed for imaging the local structures on insulator–liquid interfaces89,90. In order to characterize complex biological systems such as living cells in physiological buffers with high spatial resolution, scanning ion conductance microscopy should be chosen91. In this system, the ion current flow from the tip to the reference electrodes in the solution is monitored and used for feedback to control the tip–surface distance. Compared with EC-STM and liquid-phase AFM mentioned above, scanning ion conductance microscopy provides the unique possibility of locally probing the ion transport of biological systems by monitoring the ion current92. Similarly, AFM can scan a hollow microcantilever to perform scanning ion conductance microscopy measurements, which is also called fluid force microscopy, to patch clamp or to manipulate living cells93,94. Examples of liquid-phase SPM can be found in Table 4.
Electrical transport-compatible SPM
In order to make SPM suitable for investigating local electron transport properties both on the surface and the interface of samples such as 2D material-based novel electronic devices, various electrodes should be fabricated on the surface in addition to the bias electrode, acting as source, drain and electric gates. Immediately after the appearance of STM, scanning tunnelling potentiometry was invented for investigating the local distribution of potential and inhomogeneous conductivity of metals and semiconductors95. Without the need for detecting the tunnelling current, scanning gate microscopy uses a conductive tip as the movable electric gate and is capable of revealing the local gating effects on the transport currents from the source and drain96,97. As the electrodes for transport measurements are usually fixed by nanofabrication, much more precise and flexible positioning of such electrodes was realized by multi-probe STM98,99 (Table 5).
To optically probe the structural, dielectric and chemical properties with visible sub-wavelength resolution, scanning near-field optical microscopy (SNOM) was developed and has been widely used in the past decades100 (Table 6). SNOM makes use of the evanescent components of the light highly confined near the surface, thus overcoming the diffraction limit of far-field optics. Generally, a sharpened optical fibre with a metal shield and a nanoscale aperture is used as the light source or detector for scanning. However, the spatial resolution is limited by the aperture size of the optical fibre, with a typical value of 30–50 nm. By contrast, apertureless SNOM such as scattering-type SNOM101 uses a metallic AFM tip as the near-field scatterer and works in a dynamical mode for suppressing the background far-field signals, which improves the spatial resolution up to 1 nm (ref.102). Furthermore, making use of a sharp noble tip and highly confined surface plasmon101, the efficiency of Raman scattering in the tip–sample gap is enhanced several orders of magnitude as compared with conventional far-field Raman experiments, such as tip-enhanced Raman spectroscopy (TERS)9,48. Recently, TERS has demonstrated its ability in identifying and resolving chemical structures of single molecules with sub-nanometre resolution9. Benefiting from the local plasmon confined within the tunnelling junction, scanning tunnelling microscope-induced luminescence was also developed and applied for detecting the optical emission from the electronic and vibrational transition at the single-molecule level103. Apart from working within the range of visible light, it is also attractive for investigating the dielectric response of materials in the megahertz to gigahertz regime, such as microwave impedance microscopy, where a sharp metallic tip extended from a high-frequency resonator was used as the antenna to emit and collect microwave photons104,105. In contrast to conventional near-field SPM, photo-induced force microscopy106 directly detects the near-field signal based on photo-induced dipolar forces, which efficiently suppress the overwhelming background signals.
SPM images are always acquired as a 2D matrix, whereas spectroscopic curves are saved in the form of arrays. The main steps for data analysis include image inspection, noise analysis, filtering and image reconstruction. For the curves of SPM spectra and the line profiles of topographic images, a fitting procedure is usually necessary for interpretation of the underlying quantities and parameters. In this section, we showcase several representative examples to discuss how to analyse SPM images and spectra. The popular software for processing the SPM data are briefly introduced.
SPM imaging provides pseudo-3D data. As a surface probing technique, it does not deliver information about the inside volume of the object under investigation but provides an x–y grid of data points to each of which a single z height is associated. SPM data are thus most often represented as an x–y 2D image, where a false-colour scale represents the z height107 (Fig. 5a). Sometimes, SPM data are represented as a 3D surface shown in perspective (Fig. 5b) that is visually attractive but scientifically less precise because at least one of the in-plane axes is skewed, the z height sometimes increased and some structural features obstructed by the perspective view. In the SPM field, unfortunately, no stringent standards have been established regarding the representation of SPM data in publications, and sometimes filters are used to display images. Specifically, the application of short-range median filters in the y dimension, which cancel lines from the fast scan axis (x dimension) of the image acquisition, is common.
Force–distance curves are acquired by recording the deflection signal of the AFM cantilever while controlling the tip–sample distance. For example, when the tip approaches the surface and interacts with the biomolecules, the interaction force is detected and used to describe the deformations of the sample33 (Fig. 5c). On the other hand, upon withdrawing the tip, the force–distance curve can be used to infer multi-mechanical parameters such as adhesion, Young’s modulus, plastic deformation and energy dissipation of the sample through fittings.
STS is suitable for investigating the local density of states of a sample. In Fig. 5d, a typical dI/dV curve acquired on a single pentacene molecule shows prominent peaks at both the positive and negative biases, which are attributed to the highest and lowest molecular orbitals (HOMO and LUMO, respectively)37. By fixing the bias at the LUMO or HOMO and spatially mapping out the dI/dV intensity, the frontier orbitals of the single pentacene molecule can be directly visualized in real space37 (Fig. 5f). Whereas the STM mode is only sensitive to the electronic states near the Fermi level, non-contact AFM working under the frequency modulation mode is able to probe the total electron density of the sample by entering into the region of short-range Pauli repulsion108. In Fig. 5g, a CO-functionalized tip clearly resolves the chemical skeleton of the single pentacene molecule, where the short-range Pauli repulsion dominates the tip–molecular interaction108. The sharp lines arise from the electron density build-up across the covalent bonds between the carbon atoms.
In some cases, inelastic electron tunnelling signals may be superimposed on the large background of elastic tunnelling conductance during STS measurements. For example, the dI/dV curve taken on the bilayer NaCl(001) film grown on Au(111) demonstrates a broad peak (grey), which corresponds to the interfacial electronic states109 (Fig. 5e). When the tip is positioned on the water molecule adsorbed on the surface, distinct kinks appear in addition to the interfacial electronic states (red). Such kinks are more clearly resolved as dips and peaks in d2I/dV2 spectra, which are point-symmetrical with respect to the zero bias. The energy positions of those features reflect the energies of different vibrational modes of the single water molecule.
Visualization and analysis software
The major problem of image visualization and image analysis originates from the fact that, so far, no common SPM file format has been established. Each SPM company has a specific proprietary file format and microscope-associated software for image data analysis. Among others, Gwyddion110, WSxM111 and ImageJ are free and open source software. They are likely the most powerful SPM data visualization and analysis platforms, as they provide a large number of data processing functions. These include standard statistical characterization, data correction, filtering and grain marking functions. Gwyddion and WSxM are compatible with most standard file formats (such as .dat, .txt and .sxm) acquired from commercial SPM programs such as Nanonis, Omicron and RHK. ImageJ has the advantage that it is widely used by the optical fluorescence microscopy community and, thus, features a large variety of functions that can be adapted for SPM data, and its capabilities are rapidly growing through contributions of analysis tools from a large scientific community.
Here, we take the application of AFM in biology as an example. When AFM is used for cellular imaging, either proprietary software is used for analysis or images are exported in various file formats such as .tiff, .raw, .png, .sxm and .gwy to be analysed by laboratory-written routines in the software packages mentioned above or in MATLAB112. Analysis of data from the above-described hybrid imaging/nanomechanical mapping modes113 is often done in proprietary application mode software; in this case, not only the data encoding but also the acquisition process is system-dependent. When AFM is used for molecular imaging and analysis of protein structures and conformations, AFM users often borrow methods from electron microscopy. The recent progress in electron microscopy to solve protein structures114 is directly associated with image analysis developments. To this end, there is a plethora of such programs for analysis of macromolecular structures, such as EMAN115, IMAGIC116, SPIDER117 and RELION118. Given that the contrast transfer function and the noise distribution of AFM are very different from those of electron microscopy, these programs must be adapted with care. SEMPER and MRC are most powerful to analyse 2D crystalline data58, and most other programs are adapted to analyse single particles119.
Analysis of biological data
When using AFM for the analysis of images of proteins, one particle is used for a cross-correlation search of all other molecules in the image. Next, cross-correlation-based lateral and rotational alignment of the particles is performed. Particle selection based on cross-correlation values can be performed to calculate an average of the most common particle structure120. During the averaging process, a standard deviation map can be calculated that highlights the most flexible parts in the molecule121. From the stack of particle images that one has extracted using cross-correlation searches, one can statistically assess any parameter of interest characterizing the molecule, such as the height and volume distribution of the particles122, or molecular symmetry123. For example, the complete perforin 2 rings shown in Fig. 5a can be distinguished from incomplete arcs using cross-correlation-based selection and laterally and rotationally aligned to calculate an ensemble average (Fig. 5a, insets). For the analysis of filamentous structures, such as DNA or filamentous proteins, automated particle detection based on the height above the background, followed by tracing of the filaments, allows direct extraction of the physical properties of the filament, such as its persistence length124. Unfortunately, structural analysis using automated programs is not utilized enough in the AFM field, and it is still rather common to place arrows on image panels to highlight features instead of calculating relevant molecular representations accompanied with statistical data, as is done in the electron microscopy field.
SPM has found a multitude of applications in the natural sciences. In the following, we divide those applications into physics, chemistry, materials science and biology, although they are often closely linked to each other and have strong overlap.
Examples from physics
The initial application for STM was in the field of surface science, where atomic-scale arrangement as well as the electronic properties of materials needed investigation. The key initial experimental evidence for the power of STM in this regard was the atomic-scale imaging of the Si(111) 7 × 7 reconstructed surface125. Here, STM was able to offer insight that was hard to gain from reciprocal space tools such as low-energy electron deflection (LEED). In particular, the surface reconstruction containing multiple atoms within a unit cell yields a very complicated diffraction pattern when using LEED, from which it is difficult to deduce the exact atomic arrangement. In other words, different atomic-scale models could give rise to the same LEED pattern. By contrast, STM directly images atoms in real space and eliminates the uncertainties of structural determination through model building.
In contrast to reciprocal space tools such as LEED, STM is able to measure individual defects in materials, one at a time. This is beautifully exemplified by the imaging of dopant atoms in semiconductors126,127. STM allows the imaging of embedded dopants for up to about ten atomic layers below the surface128, showing an intricate shape that depends on the band structure of the material as well as the electron scattering properties of the defect126,127. Great care has to be taken with the interpretation of conductance spectra in these systems as the presence of the metallic tip over a semiconductor or thin insulator can dramatically change the electronic band structure, an effect referred to as tip-induced band bending129. When combined with femtosecond or nanosecond laser pulses, ultra-fast charge dynamics of defects can be mapped out in real space at nanoscales63,130.
Scanning probes can also modify materials on the atomic scale. In semiconductors, STM can be used to desorb individual hydrogen atoms from a hydrogen-saturated silicon surface131. The resulting reactive dangling bonds can then be used to incorporate dopants at precisely defined positions. When such a sample is then overgrown with more silicon, it becomes possible to place dopants underneath a silicon surface with atomic-scale spatial precision. This, in turn, offers the possibility to use them as quantum bits for quantum information studies132 (Fig. 6a).
Atoms on surfaces
Perhaps the prototypical application of STM and AFM in physics is the investigation of individual atoms on surfaces of various materials. The equally important area of molecules on surfaces will be discussed below. If atoms are deposited onto cold (<20 K) metal surfaces, such as Cu(111), then they will absorb in random positions. However, atoms can be moved with atomic-scale precision to any desired binding site11. This approach was used to build quantum corrals10 (Fig. 6b), computing devices with molecule cascades133 and artificial quantum materials134. AFM has been used to measure the atomic forces involved in these manipulations45, and AFM at UHV and low temperature now has better spatial resolution than STM by probing the short-range forces with functionalized tips108. The combination of AFM (which is sensitive to the atomic configuration) with STM (which is sensitive to the electronic structure) can combine electronic, magnetic and structural information in a single measurement tool — often enabled through the qPlus sensor28.
Spins on surfaces
Magnetic atoms on surfaces were first investigated in thin films71 where STM and AFM can be converted into spin-polarized variants, which are sensitive to the magnetic orientation of the atoms. Because of the real-space power of these techniques, intriguing spin textures such as spin spirals and skyrmions were imaged and manipulated135 (Fig. 6d). Interestingly, when single atoms retain a spin character on a metal surface, they enter a strongly correlated electronic state with the underlying conduction electrons, called a Kondo effect136, with a typical interaction energy of tens of millielectronvolts. This interaction can be weakened dramatically by replacing the normal metal with a superconductor. The magnetic interaction can then be observed as Yu–Shiba–Rusinov excitations within the band gap of the superconductor (less than 1 meV)137. This was extended to spin chains on non-trivial superconductors, in search of the elusive Majorana mode, which is supposed to localize at the ends of chains138 (Fig. 6e).
The spin character of magnetic atoms38 or chains of atoms139 can be preserved when decoupling the spins from a metal by a thin insulating film. This allowed a development of fast STM by means of all-electrical pump-probe spectroscopy62 with a time resolution of 1 ns, to probe the spin dynamics of single atoms. There is a strong urge to utilize quantum-coherent functionality in nanoscale structures, materials and devices. STM has only recently entered the field of coherent manipulation of spins by combining the high spatial resolution of STM with the high energy resolution of ESR75. Such a system needs to incorporate gigahertz microwave excitations into low-temperature STM. In practice, the DC bias voltage of STM is preplaced by a gigahertz-frequency AC field possibly added on top of a DC voltage. This high-frequency voltage converts to an oscillating electric field in the tunnel junction, where it can drive coherent spin manipulation. Figure 6c shows an example of the applications of ESR-STM to probe the spin of titanium atoms (with an attached hydrogen) on magnesium oxide, where most atoms show a single ESR line, whereas some show six lines and others eight lines. The different spin energy structures between those titanium hydride atoms stem from a different nuclear isotope that has a strong hyperfine interaction with the electron spin76.
Examples from chemistry
The birth of SPM has opened up a fascinating opportunity of probing and controlling chemistry at the single-molecule level43,140. The frontier orbitals of molecules play an important role in chemical reactions, and can be selectively imaged at the submolecular level by the tunnelling electrons of STM37,56. Remarkably, orbital imaging has been applied to capture the proton-transfer reaction in real time, even if the reaction-induced change in the STM image is very subtle141. In addition to real-space imaging, vibrational spectroscopy based on STM-IETS was successful for the chemical identification of different isotopes142,143 (Fig. 7D), quantitative determination of the intermolecular interaction109 and exploring the fundamental effects of molecular vibration on surface chemical reactions144. The tunnelling electrons of STM are not only probes but also act as powerful handles for triggering chemical reactions (Fig. 7A), such as selective bond formation/breaking42,44,140, diffusion/desorption145,146 and reduction/oxidation147, through vibrational and electronic excitation. STM has become a routine tool to identify the active sites on metallic148 or semiconducting149,150 catalytic materials, which is vital for unveiling the underlying mechanism in surface catalysis. Ultra-fast dynamics such as coherent molecular vibrations could be approached by incorporating terahertz66 or femtosecond151 optical pulses in STM systems.
As STM is only sensitive to frontier molecular orbitals near the Fermi level, resolving atoms within the molecules is not so straightforward. Thanks to the high sensitivity of qPlus-based non-contact AFM to the atom position by probing the short-range Pauli repulsion forces108 and high-order electrostatic forces54, the chemical structure and chemical bonds of a single molecule can be directly visualized in real space with a CO-functionalized tip (Fig. 7C). This technique allows the identification of both the metastable states and the by-products along the reaction coordinates152. When combined with STM, non-contact AFM provides an unprecedented chance for identification and control of multiple charge states of single molecules on insulating films153,154, which are key steps during chemical reactions. Furthermore, the force versus distance curves contain characteristic fingerprints arising from the complex interplay between the van der Waals, electrostatic, chemical and repulsive forces, which can be further harnessed for elemental recognition155 and structure analysis108. STM, non-contact AFM and TERS have been combined to achieve the univocal characterization of the structural and chemical heterogeneities of single molecules with single-bond resolution156.
Chemical reaction at liquid–solid interfaces
Many heterogeneous chemical reactions occur at liquid–solid interfaces, which are quite different from the vacuum condition or gas phase for single-molecule chemistry as described in the previous section. Molecular and nanoscale information of various electrochemical processes such as the formation of an electrochemical double layer157, metal corrosion158 and electrodeposition159 can be obtained by EC-STM at solid–electrolyte interfaces. Recently, the catalytically active sites at solid–electrolyte interfaces have been successfully identified by monitoring the noise of the tunnelling current17. In addition, EC-STM also allows imaging of the structural phase transition induced by electrode potential or redox-induced charge state variation160. Characterizing liquid–solid interfaces is ideal with non-contact AFM, as it removes the need for imaging on conductive substrates. Both soft cantilever-based89,161 and qPlus-based162,163 systems work well in aqueous conditions to achieve atomic resolution. Various substrates ranging from inorganic crystals164 to interfacial organic molecules165,166 were extensively investigated by non-contact AFM in solutions. Furthermore, non-contact AFM can also probe the atomic-scale interaction between substrates and solvent/solute molecules by mapping the tip–surface force in a 3D manner90,165,166. Using such a technique, the 3D periodicity of hydration layers on mica90,167 and the specific atomic-scale patterns on calcite substrates168 were visualized. Exotic laser-combined SPM techniques also provide new insights into the field of chemistry at solid–liquid interfaces. For example, by applying a sharp plasmonic tip and the TERS technique, redox reaction processes49 and catalytical sites169 have been visualized with nanoscale resolution.
Chemistry at liquid–solid interfaces can also be investigated ex situ under UHV conditions. In such experiments, the solid substrates are immersed in solution or topped by a droplet outside the UHV chamber170,171,172. The interfacial solution layer may survive after transferring the sample to the vacuum environment, allowing for high-resolution SPM characterization. To avoid unwanted contaminants in the air, preparation of the ultra-pure water droplet on solid surfaces can be done directly inside the UHV chamber173. Using this method, hydration structures on various metal oxide surfaces could be investigated with atomic resolution174. For the chemical reactions at liquid–solid interfaces, the structure and dynamics of hydrates play an important role, but have been poorly understood until very recently. SPM has been used to construct individual sodium hydrates at a salt surface containing different quantities of water molecules175, which revealed correlation between ion transport and hydration numbers (Fig. 7E).
Molecular self-assembly on surfaces
On-surface synthesis of molecular networks and nanoarchitectonics based on surface self-assembly has received increasing attention in the past few decades176. The detailed topology of the molecular networks can be distinguished by high-resolution SPM. For example, high-quality imaging at the solid–liquid interface between non-ionic organic liquids and atomically flat conductive substrates has been achieved by both STM85,86,87 and AFM177,178. Also, intermolecular interactions have been extensively investigated by STM in both vacuum–solid179,180 and liquid–solid181 interfaces. In particular, the covalent-bonding180,182, coordinate-bonding183, hydrogen-bonding184,185 and halogen-bonding186,187 structures of molecular assemblies were resolved at the single-bond level. In addition to imaging, the SPM tip can be used to construct or modify the supramolecular phase through precise manipulation42,140, ranging from synthesizing individual molecular units140 to establishing 1D (ref.188) or even 2D (ref.189) molecular networks.
One representative application of on-surface assembly based on covalent coupling is the synthesis and engineering of graphene nanoribbons with atomic precision in a bottom-up manner182,190 (Fig. 7B). The precise control of the width and edge structure of graphene nanoribbons was achieved by depositing appropriate precursors, followed by the on-surface reactions finely tuned through the annealing temperature. Notably, the intermediate polymer structures and the final products with a flatter geometry after cyclodehydrogenation were identified by AFM. In addition to obtaining the geometric structure, STS measurements also yield valuable information on the electronic structure of graphene nanoribbon-based heterojunction191, spin polarization192 and the topological properties193,194 of edge states.
Examples from materials science
STM is an ideal tool for exploring the microscopic origin of superconductivity, owing to its ability to probe the electronic and vibrational states at the atomic scale both in real and momentum space. Indeed, STM-IETS was used to unveil the correlations between electronic properties and lattice vibrations of superconductors in real space195. The energy resolution of STM can be greatly enhanced (up to 10 μeV) by using a superconducting tip, which allows precise determination of the superconducting gap arising from the formation of Cooper pairs in dI/dV spectra22 (Fig. 8A). Meanwhile, through mapping the dI/dV signals under zero-bias voltage, the local magnetic vortices, which are the characteristic features of type II superconductors in a magnetic field, were directly visualized196. Spectroscopic mapping at different bias voltages is also a powerful tool for obtaining the momentum-space information based on quasiparticle interference (QPI), where the wavevectors of resulting standing waves can be obtained by Fourier transformation of dI/dV images197,198 (Fig. 8B). QPI imaging allows extraction of intriguing electronic properties such as band structure197,198, non-dispersive periodic electronic modulation199 and pairing symmetry200. Particularly, it is possible to visualize the local charge ordering in superconducting201, pseudogap199 and Mott states202. Both cuprate-based201 and iron-based200,203 high-temperature superconductors have been extensively investigated with this method, where the spatial correlation between charge and/or magnetic order and superconductivity was revealed. The proposed underlying mechanisms include the stripe order204, Fermi surface nesting205, Fermi arc instability206 and Cooper pair density wave207.
Topological insulators are insulating in the bulk while processing metallic states on the surface, which are called topological surface states. Such gapless states connecting the bulk band gap are topologically protected and robust against external disturbances208, leading to great potential in various applications such as non-dissipative electronics. As a surface-sensitive electronic probe, STM is suitable for investigating topological surface states and its response to local atomic-size impurities. Both the discrete Landau levels of topological surface states under a magnetic field209 and the band structure evolution along with electric gating can be resolved by STS measurements210. The forbidden backscattering of the quasiparticles, which is a key feature of topological surface states, was confirmed through analysis of the QPI patterns around individual non-magnetic scattering centres such as adsorbed atoms208 or defects211 (Fig. 8C). The influence of charged and magnetic impurities on electron mobility has also been investigated212. So far, STM has shown unique ability to provide atomic-scale insights into various quantum materials with topological protection, such as topological superconductors213, topological crystalline insulators214, topological semimetals215 and Majorana fermions138,216,217. Based on the advanced molecular manipulation techniques of STM, scientists are able to build artificial 2D topological materials from CO molecules218,219 (Fig. 8D) or create vacancies in chlorine monolayers220, which provide new possibilities for engineering topological states and exploring new exotic quantum phases.
The electronic, optical and magnetic properties of atomically thin 2D materials are extremely susceptible to local corrugations, ripples, boundaries and reconstructions, which can be perfectly probed by STM and AFM with atomic resolution221,222. Characteristic electronic properties of graphene such as Dirac points221, phonon-assisted tunnelling221, electronic chirality223, pseudospin223 and inter/intra-valley scattering224 have been revealed by STM and QPI measurements. It is also possible to probe the edge states and local band structure of both single-layer225 and bilayer226 heterojunctions or the heterophase227,228 of transition metal dichalcogenides. More recently, increasing efforts have been made to locally probe strongly correlated quantum phenomena such as superconducting phases229 and cascade phase transition230,231 on twisted bilayer 2D materials using exotic SPM techniques such as scanning SQUID and scanning single-electron transistor microscopy. Another unique application of SPM is using a conductive tip for local electric gating to achieve charge state control of single defects232 and local tip-induced phase transitions233.
In order to probe the optical properties of 2D materials at the nanoscale, scattering-type SNOM has been used because of its high spatial resolution beyond the optical diffraction limit102, where the metallic tip eliminates the momentum mismatch between the free space photon and confined surface plasmon polaritons234. Hence, it is possible to probe both the local properties and the propagating behaviour of surface plasmon polaritons in 2D materials by analysing the interference patterns in real space235. SPM is also ideal for probing magnetism and ferroelectricity of 2D materials. For example, the atomic magnetic structure of 2D ferromagnetic materials such as chromium bromide has been unveiled by spin-polarized STM236, which clarified the relation between the stacking order and magnetism. In addition, local electric and structural analyses of 2D ferroelectric materials have also been correlated by AFM and PFM237.
In addition to the static properties, the real-time monitoring of the growing process of graphene on nickel substrates has been achieved using video-rate STM15, which captured the catalytic action of a single adjacent nickel atom at the edges of growing graphene flakes. Very recently, the CO tip of qPlus-AFM was used to resolve highly fragile edge structures of 2D ice, thanks to the weakly perturbative nature of the tip184. Notably, various metastable and/or intermediate edge structures involved in ice growth were frozen and imaged, allowing reconstruction of the ice growth process (Fig. 8E).
To date, SPM has been successfully used to image the surface of photovoltaic and optoelectronic materials, such as the perovskite-based materials. For example, STM and AFM has been applied to investigate halide perovskite238,239 with atomic resolution. The alignment of organic and inorganic atoms in halide perovskites, as well as the domain structures240, could be clearly resolved. SPM has also found wide applications in ion batteries, by quantitively characterizing the topographic, mechanical and electrochemical properties at the electrolyte–electrode interface with nanoscale resolution. One prominent example is the in situ AFM observation of the growth of the solid–electrolyte interface layer on the electrode in a lithium ion battery241, which results from the decomposition of the electrolyte during an electrochemical process. In addition, the insertion/de-insertion of lithium ions during the charging and discharging processes can also be sensed by conductive AFM, owing to the changes in the electrical properties of the electrode materials242. However, the spatial resolution in such materials is still far from the atomic scale.
Meanwhile, other kinds of functional materials such as multiferroic materials have also been extensively investigated through SPM. Multiferroic materials possess both ferroelectric and magnetic orders243. The spontaneous polarization and magnetization orderings of multiferroics either arise independently or appear under mutual induction through magnetoelectric couplings. A powerful method for multiferroic research is PFM, which can probe and manipulate multiple ferroelectric properties in real space with nanometre precision83. Both the relative polarization strength and the direction of static domain structures244,245 have been imaged by PFM with nanoscale resolution. The electrically biased tip in PFM can also be used to manipulate ferroelectric properties, such as local polarization, with high precision246,247. By tuning the tip bias, multiple parameters such as the piezo coefficients, disorder potential, energy dissipation, nucleation bias and coercive bias can be locally inferred from hysteresis loops248. In order to track the dynamics of the ferroelectric domain structure, stroboscopic PFM was developed to measure fast snapshots with nanosecond time resolution, from which the nucleation rate or the mobile velocity of domain walls were extracted249. As PFM is only sensitive to the strength of electric fields, the combination of PFM with magnetic force microscopy250 or scanning magnetometry251 opens up the possibility of simultaneous imaging of ferroelectric and ferromagnetic ordering, which provides microscopic insight into the coupling of ferroelectric and non-collinear antiferromagnetic domains.
Examples from biology
Imaging biological systems at work
AFM is most often used in biology as an imaging technique24, widely applied to various biological systems ranging from organs, tissues, cells, organelles and membranes to proteins and nucleic acids. The (sub)structural details of single native proteins or nucleic acids can be directly imaged at (sub)nanometre resolution24,252,253,254 (Fig. 9a–c). Because cells, bones, tissues and organs have rough surfaces that are softer than the silicon nitride tip used in AFM, they deform easily and interact with larger areas of the tip apex and side. Such samples are imaged at lower resolution, approaching a few tens of nanometres, with the topographies often showing imaging artefacts24,255 (Fig. 9d–f).
Imaged in time-lapse mode, biosystems can be observed at work256, including migrating and dividing cells257, assembly of actin filaments or collagen fibrils258, chaperones259, human communication channels260, ion channels261 or uncoiling DNA molecules253,262,263 (Fig. 9g,h). High-speed AFM allows the monitoring of biological systems at millisecond time resolution, as well as to directly film, for example, dividing bacteria264, light-driven proton pumps265, motor proteins263, immunoglobulins266, ATP-driven enzymes267, endosomal sorting complexes268, nuclear pore complexes269, channels119, transporters270 or CRISPR–Cas9 (ref.271) at work. Reducing the high-speed AFM image acquisition to a single position, biomolecular dynamics can be detected at microsecond time resolution272. However, the force applied by the AFM tip while contouring the biological system has to be carefully controlled as the imaging process can quickly (ir)reversibly deform the sample. Nevertheless, a precisely controlled AFM tip can be used to observe force-induced conformational changes of membrane proteins256,273,274, to dissect DNA275 or protein276 complexes, or even to manipulate and design biological systems277. Such force control of the AFM tip is made easy by a wide variety of AFM imaging modalities, force-feedback controls, and soft and fast-reacting AFM cantilevers24,29,278,279.
Manipulation and spectroscopy
The ability to mechanically manipulate biological samples by the AFM tip has raised the issues of measuring the forces interacting between the AFM tip and sample and those interacting between biological samples280. Force–distance curves can be used to quantify the hydrophobic, hydrophilic, electrostatic, van der Waals, Young’s modulus, energy dissipation and many other physical properties of the sample surface, provided that the properties of the AFM tip have been defined by, for example, characterizing a reference sample. Sometimes, the tip is replaced by a micrometre-sized bead to probe the mechanical properties of larger surface areas of cells or tissues281. Examples encompass measuring the elastic properties of the cell cortex, neuronal tissues or even organs of living animals34. However, to properly analyse the elastic properties of a soft heterogeneous sample indented by a sharp tip requires the application of theoretical models such as Hertz theory or similar models, which have limitations and must be applied with care34,282. One way to circumvent such limitations is to use a bare AFM cantilever without the tip in a parallel plate assay, which has shown that mammalian cells measure confining distances of their surrounding environment283 and round up for mitosis by generating hydrostatic pressure284,285. The physical properties, measured as force–distance or force–time curves, depend on the speed or time at which they are probed by AFM34. Consequently, the elastic properties of biological systems probed at various speeds can differ considerably286,287. To properly describe the mechanical properties of a biological sample relies on the characterization of these properties over a wide range of speeds, which leads towards describing the free-energy landscape of biomolecular bonds or the rheological properties of cells34. Approaches that probe the time dependency of mechanical properties can provide detailed insight into the non-linear active and passive viscoelastic response of biological systems to mechanical stimuli257,287 or the non-linear characteristic behaviour of biological bonds288,289.
Using single-molecule force spectroscopy to measure specific forces between an AFM tip and a biological system or between two biological systems requires tip functionalization31 (Box 2). Single-molecule force spectroscopy is currently used as a tool to characterize the binding of many different receptor–ligand interactions, the stretching of polypeptides, nucleic acids or sugars, or the unfolding of water-soluble and membrane proteins. Single-molecule force spectroscopy has been used to characterize biochemical bonds or interactions in and out of equilibrium290,291.
In single-cell force spectroscopy, the tip of the AFM cantilever is replaced by a living cell to probe cellular interactions with the environment292. Single-cell force spectroscopy is particularly fascinating to learn how cells initiate and strengthen adhesion to their environment, including extracellular molecules, viruses, cells, tissues, bones, organs or biomaterials293. Taking the force spectra at every pixel during scanning enables simultaneous measurement of sample topography and related maps of mechanical adhesion, deformation, elasticity and dissipation294 (Fig. 9i–l).
Beyond imaging, cantilever array technologies are excellent chemical and biomedical nanosensors, which can convert the specific or unspecific adsorption of molecules to the cantilever into nanomechanical motion295. Applications of nanosensors include detecting DNA hybridization with single point mutation sensitivity, recognizing proteins and antibodies, assessing patient eligibility for cancer treatment or detecting multidrug-resistant bacteria, which cause considerable morbidity, mortality and health-care costs32,296.
The dysregulation of size, volume and mass in living cells gives rise to many diseases. Several microcantilever-based technologies have been developed to monitor the mass of single cells with unprecedented accuracy. In one approach, suspended cells are floating through a hollow cantilever exposed to a vacuum and, upon passing the free cantilever end, their buoyant mass is measured. The high mass resolution approaching several femtograms makes this approach particularly suitable to monitor small cells such as yeast at repeating time points297. In another approach, the cantilever immersed in buffer solution and exposed to cell culture conditions continuously monitors the total (inertial) mass of larger mammalian cells adhering to the free cantilever end at millisecond time resolution over the course of days298. The combination of both approaches with modern light microscopy enables optical imaging of biological processes inside the cell and monitoring their link to cell volume regulation and growth.
Reproducibility and data deposition
For SPM applied across physics, chemistry and material sciences, the results are relatively easy to reproduce, especially for those under the UHV condition, owing to well-controlled tip and surface conditions. However, in ambient and liquid conditions, reproducibility is unfortunately poorer, likely owing to noise in liquid and at room temperature, uncertainties of the tip apex and possible contamination of the tip and the surface. Such problems are probably most prominent for the adoption of SPM in biology, which has very complicated environment and deals with sophisticated biological samples, and lead to a lag in establishing reproducibility, field standards and data sharing.
SPM is a young technique and, thus, is still technically improving a lot. Therefore, wider reproducibility would require many users to have access to state-of-the-art machines, which is difficult to achieve in a field where many laboratories operate prototype devices and customized variations. Specifically, in different prototypes from different laboratories, the routines for operation, the techniques for data acquisition, the treatments for the tip apex and surface, and the post-process and analysis strategies for raw data have big discrepancies, leading to limited reproducibility for general users. Another related problem is that acquiring state-of-the-art data still demands technical insights and the skills of a specialist, because users should have the requisite experience and critical understanding to recognize tip and surface quality, to choose the appropriate imaging parameters and to rule out imaging artefacts. Over recent years, we have seen the emergence of several operational modes that alleviate manual operation problems and automatically propose operational parameters, such as ScanAsyst and similar modes. Unfortunately, these modes are manufacturer-specific and the resulting data are not reproducible with different devices.
The cleanness and robustness of sample surfaces are very important to achieve good reproducibility. Under the UHV environment, a clean surface of the sample can be easily obtained and maintained by cycles of ion sputtering and thermal annealing. By contrast, the surface under liquid and ambient conditions can easily be contaminated or chemically changed. So far, there is almost no efficient and reversible control of the sample state, which can change during sample preparation or SPM imaging. In the worst case, it may be difficult to determine which topography corresponds to which cell state.
Several challenges had to be overcome to enable the imaging of biological systems in their native state. First, AFM sample preparation procedures had to be developed to ensure the native state of the biological system. The challenge was achieved by, for example, adsorbing biological samples in physiologically relevant buffer solutions and temperatures to chemically inert supports such as hydrophilic mica that would not impair their functionality. Second, the native state of the sample had to be maintained during AFM measurement, which mostly is provided by buffer solution and controlled environmental systems (temperature, humidity and gas). Third, AFM technology and imaging conditions had to be developed to avoid unwanted perturbation of the soft biological system contoured by the mechanically scanning AFM tip. Structurally and functionally well-characterized reference samples served valuably to optimize AFM set-up and imaging conditions such as cantilever properties, tip radius and material, imaging force and other imaging parameters.
Finally, and likely most importantly, SPM reproducibility relies a lot on tip qualities such as the sharpness, aspect ratio and symmetry of the tip apex, directly affecting the surface contouring accuracy and, thus, the imaging result. Finding ways to reproducibly generate high-quality tips is thus a prerequisite for data reproducibility in the field. For UHV experiments, an atomically sharp tip can be readily obtained by in situ tip treatments such as controlled poking and field emission during the scanning. The tip condition is usually judged by the characteristic features of known atoms, molecules or surface reconstructions. The ways to functionalize the tip by single atoms or molecules and to manipulate single atoms or molecules are also well established. Such mature procedures mentioned above are popularly applied for obtaining the atomically resolved images and STS on surfaces of different single crystals such as Au(111), Si(111) and graphite, all of which are standard samples for characterizing SPM function and to ensure the acquisition of high-quality images and STS spectra.
Field standards on open data
In both the electron microscopy and X-ray crystallography fields, data acquisition tables and data processing methods are published alongside structures. This is unfortunately not the case for the SPM field. Establishing general standards such as data formats and the strategies of data processing and image reconstruction should be a major ambition. In AFM-based force spectroscopy, standardization of methods to characterize and calibrate the cantilever and the sensitivity of the optical lever system, the ensemble signal response of the laser and the optical path that documents the cantilever deflection has been established299,300. In imaging, the multitude of operational modes makes establishing generalizable field standards difficult. Although individual companies and laboratories have evolved powerful methods for image acquisition, raw data are not easily shareable within the community and the analysis tools and data representation are today not standardized. Images and derived AFM structures could and should be encoded in a common file format such as .dat, which would allow efficient database deposition, interchange, cross-evaluation, comparison and model-based validation of data.
Minimum reporting standards
Researchers should provide in their methods section a clear description of the AFM set-up used, the AFM mode applied and the operation details of the applied mode. Basic details regarding the cantilevers of use are also expected, such as the geometrical dimensions, shape, material, spring constant resonance frequency and quality factor. Finally, knowledge about the tip shape should be provided. For biological applications, the environmental conditions, precise buffer conditions, temperature and how the sample was treated before and throughout the experiment are of equal importance.
Limitations and optimizations
One common intrinsic limitation of all SPM is that the tip will inevitably perturb the surface as well as any adsorbates; this is due to the excitation of the tunnelling current and the interaction force between the tip and the surface. Therefore, the acquired images may not reflect the real structure and dynamics. This problem becomes particularly serious for weakly bonded systems and under high-resolution imaging conditions, where the tip is usually brought very close to the surface. One straightforward way to reduce tip disturbance is by enhancing detection sensitivity and using only a small current and force for imaging. In SPM under UHV conditions, the CO-terminated tip allows the imaging of metastable structures in a nearly non-invasive manner owing to the ultra-high flexibility of the tip apex and the weak higher-order electrostatic force54. Recently, a single nitrogen vacancy centre in proximity to the surface of a high-quality diamond tip is promising to sense extremely weak magnetic fields through magnetic dipole interactions, such as proton spin fluctuations301. Nevertheless, tip disturbance is not always unfavourable and does not always need to be avoided. It can be used as a stimulus to measure the mechanical, magnetic, optical and electrical responses of the surface or to manipulate the sample. In biological AFM, improved FM-AFM and amplitude modulation AFM and non-resonant modes with faster and more sensitive feedback operation enable sufficient control of applied force to image biological samples. Researchers have used comparison with molecular structures and internal molecular symmetry (if present) to assess the non-invasiveness of AFM scanning120.
Limited temporal resolution
Despite unprecedented spatial resolution down to the atomic scale, the traditional temporal resolution of SPM is limited by the bandwidth of electronics for signal acquisition and the resonance frequency of the scanner head, typically in the order of microseconds. It is possible to improve the temporal resolution by using wideband preamplifiers, fast analogue to digital converters, small and rigid scanners, and fast feedback systems61,302. In this way, the scanning speed can be increased above 100 frames per second, which is video-rate SPM15. In order to further push the temporal resolution of signal detection to picoseconds or even femtoseconds, SPM must be combined with ultra-fast pump-probe technology, by coupling the tip–surface junction with pulsed electric waves, terahertz pulses and near-infrared and visible lasers63,64,65,66,130. The key feature is that the optical or electric pulses are employed to pump the electronic states of sample to a higher energy level, whereas the response and the relaxation dynamics are locally probed by the tip–surface interactions, either pulsed or continuous, to ensure the atomic spatial resolution. The temporal resolution is basically given by the delay time between the optical or electric pulses, thus defeating the intrinsic limitation from the SPM electronics and mechanics. Tracking and control of the ultra-fast electronic processes on the atomic scale even with attosecond resolution has recently been demonstrated303.
Insensitivity to the buried interface
As a surface-sensitive technique, SPM cannot readily access the buried interfaces. This is because low-energy tunnelling electrons cannot penetrate through thick layers, and high spatial resolution usually relies on the short-range tip–surface interaction. Cross-section SPM provides a solution to access interfacial information, by breaking the sample apart and positioning the tip on the cross-section of the sample304. Such a technique can only gain spatial information along the surface; lateral information is not measured. Scanning gate microscopy has been used to probe the 2D electron gas located at the interface of semiconductor devices97. Owing to their excellent penetrability, microwaves emitted by the SPM tip are used to map out the dielectric response of interfacial materials by detecting the S/T parameters of near-field microwaves105. However, the spatial resolution of these methods is limited because of the large distance between the tip and the target interface, as well as the slow decay of the microwave and electric fields on the tip. Integration of a super lens to SNOM allows the investigation of buried interfaces as deep as hundreds of nanometres while still maintaining the nanoscale spatial resolution305.
Coherent detection and control
Imaging by SPM methods relies on various tip–surface interactions. However, the quantum coherence could be easily destroyed by such interactions as the tunnelling current, force, electron and/or phonon scattering, and charge and/or spin noise. In addition, many coherent processes occur at ultra-fast timescales, beyond the temporal resolution of conventional SPM. Therefore, most of the results obtained by SPM reflect only incoherent processes. Following coherent evolution and achieving coherent control on various quantum processes is one of most challenging but fascinating future directions for SPM. SPM combined with nitrogen vacancy technology provides a possible solution79. The spin triplet states of the nitrogen vacancy could be excited and coherently manipulated through microwave pulses. The magnetic information near the nitrogen vacancy can be stored during the coherent evolution of nitrogen vacancy states through dipolar interaction, and finally read out by spin-dependent fluorescence306. Because of its inert host and long coherence time, the nitrogen vacancy could be powerful even under an ambient environment307. Integrating SPM with a nitrogen vacancy quantum sensor (nitrogen vacancy-based SPM) is able to quantitatively image and precisely control the coherent behaviours of target spins with nanoscale resolution. The detection is non-perturbative because of the weak coupling strength between the nitrogen vacancy and the sample308,309. Choosing qPlus-based non-contact AFM will further optimize the coherence and sensitivity of such a quantum sensor in nitrogen vacancy-based SPM310. The coupling of STM with different electromagnetic waves also provides unique opportunities to detect the coherent spin, electron and phonon dynamics at different timescales. Indeed, imaging and coherent control of electron spins with atomic resolution has been achieved by ESR-STM77, where the spin dynamics is driven by radio-frequency bias. In addition, the coherent vibration dynamics of single molecules at the picosecond scale can be monitored through terahertz STM66. By coupling a femtosecond laser with STM, it has been possible to track ultra-fast dynamics such as the temperature-transient charge carrier63, dependent spin relaxations in gallium arsenide64 and the coherent vibration-driven conformational changes of single molecules151. Very recently, coherent control of electrons even at attosecond resolution has also been demonstrated303.
SPM has been very successful in imaging samples in two dimensions, where the sample surface needs to be atomically flat to ensure high-resolution and stable imaging. However, when the target objects have a relatively rough surface, the imaging resolution and quality usually decline311. Unfortunately, atomically flat surfaces are only available for simple model systems, whereas 3D samples are more ubiquitous. These include large biomolecules, clusters, porous materials, nanostructured surfaces and so on. It is therefore imperative to develop new SPM techniques capable of atomic imaging in 3D.
One avenue for achieving 3D imaging is measuring height-dependent current and force curves at every pixel and plotting the current and force data in xyz directions. For example, the 3D force mapping of water–solid interfaces by FM-AFM provides microscopic insight into the interfacial structure of hydration layers90,167,312. Other examples contour the rather rough surfaces of complex biological systems in 3D and at the same time map their mechanical properties. However, such approaches are time-consuming and suffer from thermal drift because of the need for long-term data acquisition. A simpler method — which also improves resolution — is to apply height compensation either by opening the current feedback loop simultaneously during the signal acquisition or by automatically adjusting the tip height according to pre-acquired tomography information to make the tip follow the geometric contour of the 3D objects313. With such methods, the step structure of semiconductor surfaces, C60 (ref.313) and other non-planar molecules with complex 3D geometry314 have been visualized with submolecular resolution.
Recently, a remarkable achievement was made in molecular 3D structure reconstruction from 3D SPM data sets using machine learning based on convolutional neural networks315, which can learn an approximation for image inversion efficiently using such a universal fitting scheme. However, one of the biggest challenges lies in the insufficient amounts of data sets from realistic SPM experiments needed for image inversion of 3D molecular structure processes. Another way to image 3D structure is similar to the idea of magnetic resonance imaging316. The SPM tip with a high field gradient may be used to select a certain thin slice of the 3D samples, such that the electronic, vibrational or spin signals within this specific slice can be read out by far-field photons. The combination of optical microcavity with SPM may also provide new possibilities of sensing the internal information in 3D structure using an optomechanical response, such as ultrasonic measurements317.
SPM under extreme conditions
Under extreme conditions, such as ultra-low and ultra-high temperatures, strong magnetic fields and ultra-high pressure, many interesting and unexpected phenomena will emerge, beyond our conventional knowledge of more standard conditions. To date, the atomic or nanoscale understanding of material properties under various extreme conditions is far from complete, calling for the development of SPM that is compatible with various extreme conditions.
STM has been successfully combined with a dilution fridge, which can lower the base temperature to 10 mK (ref.13) and provide an ultra-high magnetic field up to 30 T (ref.14). The highest electronic energy resolution could achieve ~10 μeV (refs13,22), which is limited by the efficient electron temperature instead of the absolute base temperature. The key issues are how to isolate the vibration from the dilution fridge and to lower the electronic temperature by proper radio-frequency shielding. Recently, qPlus-AFM was also incorporated into a dilution fridge with magnetic field up to 7 T, which opens up new capabilities in studying electronic devices22. SPM working at ultra-low temperature and ultra-high magnetic field is expected to address exotic quantum effects with unprecedented details in both real space and energy space, such as superconductivity, the quantum Hall effect and strongly correlated physics.
Many chemical reactions and material growth reactions occur at elevated temperatures. High-temperature SPM is a useful operando technique to monitor those dynamic processes with atomic resolution318. The most challenging problems remaining for high-temperature SPM are thermal drift and mechanical stability. In addition, the rapid degradation of the tip and scanner materials at high temperature under a high-pressure gas environment also limits its performance. Recently, some new techniques have been introduced to suppress drifting and enhance stability. One of the efficient solutions is developing video-rate SPM systems where the fast dynamics in chemical reactions are captured within milliseconds with little impact from temperature fluctuations15. For example, real-time monitoring of the atomic growth of graphene has been realized by video-rate STM at 710 K (ref.15).
SPM of living systems
Compared with most optical microscopies, SPM-based approaches can image living biological systems with an unprecedentedly low signal to noise ratio. However, owing to the increasing complexity of such living systems, the user is often challenged to identify specific cellular features and must either compare the sample topography with known morphologies (for example, structural references) or combine SPM with fluorescence microscopy, where a subset of structural details has been fluorescently labelled. AFM-based functional imaging may be the answer; this technique uses the AFM tip as a nanoscopic tool that can simultaneously image, quantify, morphologically map and manipulate specific interactions of biological moieties24,31. Biological systems are highly dynamic and can actively or passively change state within milliseconds to minutes. Thus, the state of complex biosystems imaged by SPM must be monitored and should not be altered by, for example, the sample preparation procedure, including features such as drying, adsorption of a 3D object onto a support, non-physiological temperature or a buffer solution. If all of the SPM parameters are adjusted properly, biological systems can be observed at work by time-lapse or high-speed video SPM. However, other microscopic approaches such as cryogenic transmission electron microscopy can provide snapshots of biological systems at work in 3D at atomistic resolution. Thus, SPM as a surface technique may be a tool for examining niches not addressable by any other technique, such as simultaneously imaging biological systems at work at nanometre resolution and characterizing their various mechanical, chemical and biological properties24,34,277.
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K.B. and Y.J. acknowledge support from the National Key R&D Program (Grant Nos 2016YFA0300901 and 2017YFA0205003), the National Natural Science Foundation of China (Grant Nos 11888101, 11634001 and 21725302), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB28000000) and Beijing Municipal Science & Technology Commission (Grant No. Z181100004218006). C.G. acknowledges support from Swiss Nanoscience Institute (SNI), University of Basel. A.J.H. acknowledges support from the Institute for Basic Science (IBS) (Grant No. R027-D1). D.J.M. acknowledges support from the Swiss National Science Foundation (NCCR Molecular Systems Engineering) and the ETH Zurich (Grant ETH-20 17-2). S.S acknowledges the support from a National Institutes of Health (NIH) Director’s Pioneer Award (DP1AT010874 from the National Center for Complementary and Integrative Health (NCCIH)) and a NIH Research Project Grant (RO1NS110790 from the National Institute of Neurological Disorders and Stroke (NINDS)).
The authors declare no competing interests.
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- Tunnelling current
The current created from electrons tunnelling through a finite barrier that is forbidden in the classic regime.
A rectangular pattern of image capture and reconstruction.
- Tip–sample junction
The tunnelling junction between the tip and the sample where electrons tunnel through a finite barrier in between.
- Piezoelectric effect
The effect showing a finite induced voltage on both sides of a material when a specific pressure is applied on it.
- Biased voltage
The DC voltage applied to the tunnelling junction, either on the sample or on the tip.
- Eddy current
Loops of electrical current induced within a conductor by changing the magnetic field through this conductor based on Faraday’s law of induction.
- Mechanical resonance frequency
The frequency at which a mechanical system vibrates with greater amplitude than it does at other frequencies, generally determined by the stiffness and mass of this mechanical system.
- Quantum corrals
The barriers constructed by individually positioning the iron adatom through the scanning tunnelling microscopy tip.
- Local force
The local interaction between the atoms on the tip apex and the surface within a volume of several cubic nanometres.
- Dynamical AFM
A type of atomic force microscopy (AFM) where an oscillator (for example, cantilever, tuning fork) works at its resonance frequency, detecting interactions between the tip and the sample through the changes of frequency, amplitude and energy compensation of this oscillator.
- Temporal resolution
The duration of time for acquisition or capture of a single event in measurements.
- Functionalized tips
Modified tips with a single molecule or specific clusters in order to make the tip adapted for specific applications.
- Quality factor
The dimensionless factor describing the dissipation and damping of the mechanical oscillator during a single oscillating cycle.
- Thermal drift
The steady and monotonic changes of the specific location or parameter with time resulting from the changed temperature.
- Young’s modulus
A mechanical property that quantifies the relationship between tensile stress and axial strain, which reflects the tensile stiffness of a solid material.
- CO-functionalized tip
Modification of the tip with a single CO molecule in order to enhance the spatial resolution of scanning probe microscopy.
- Hall probe
A micron-sized device for detecting the external magnetic field through the Hall effect.
An electronic system capable of controlling two potentiostats, which include two working electrodes, one shared reference electrode and one shared counter electrode for electrochemical measurements.
- Scanning gate microscopy
A kind of scanning probe microscopy capable of probing electrical transport at the nanoscale, where a conductive tip is used as the local gate capacitively coupled to the sample.
- Kondo effect
An effect describing the scattering of conduction electrons caused by the magnetic impurities within a tunnelling junction, leading to a characteristic change in the electric conductivity at low temperature.
- Yu–Shiba–Rusinov excitations
A pair of bound states inside the superconducting energy gap caused by the coupling between the superconductor and a magnetic impurity.
- Cooper pairs
Pairs of electrons bound together through electron–phonon couplings, which are responsible for explaining superconductivity.
- Quasiparticle interference
(QPI). Interference caused by the coherence of quasiparticles, inherently a kind of collective disturbance that behaves as a single particle.
- QPI imaging
Imaging showing the quasiparticle interference (QPI).
- Cantilever array technologies
Technologies using arrays of cantilevers for detecting the chemical reactions and nanomechanical motion of biomolecules with high sensitivity.
- S/T parameters
Scattering/scattering transfer parameters describing the behaviours of incident and reflected waves during propagation through microwave electronics.
- Quantum coherence
The status of a quantum state or wave function that has well-defined amplitude and phase, resulting from the principle of superposition.
- Universal fitting scheme
A fitting scheme universally applied for analysing and processing all of the relative data sets during automated structure discovery.
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Bian, K., Gerber, C., Heinrich, A.J. et al. Scanning probe microscopy. Nat Rev Methods Primers 1, 36 (2021). https://doi.org/10.1038/s43586-021-00033-2