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Introduction

Since the invention of atomic force microscopy (AFM) thirty years ago [1], scanning probe microscopies (SPM) have become an enabling technology for nanoscience and technology [2]. The collective effort of commercial, academic, and government institutions have created a fleet of SPM platforms over 50,000 units strong, enabling a broad range of studies from quantum transport imaging in low dimensional systems [3], functional magnetic [4, 5] and ferroelectric studies [6, 7], atomically resolved imaging in ultra-high vacuum (UHV) [811] and liquid environments [12], imaging active device structures [13, 14], single molecule reactions [15, 16] , biological recognition imaging [17, 18], and many others. Without exaggeration, SPM has become the key that unlocked the nanoworld for exploration and control.

The original SPMs, including scanning tunneling microscopy (STM) [19, 20] and contact mode atomic force microscopy (AFM) [21], were based on detection of static force or current signals, which imposed severe limitations on the detection limits. Modern dynamic SPMs typically use heterodyne signal processing to amplify weak periodic signals [22]. In this process, they compress the information stream from 10 MHz at the photodetector to ~1–10 kHz, as limited by the rate of the feedback operation and pixel acquisition. In this process the information on transients, non-linear interactions, etc., not captured by the excitations of harmonics, is essentially lost. Correspondingly, a number of groups have suggested approaches based on multiple excitations [2327], detection of intermodulation signals [26, 28], etc. [2931]. However, the decoding of this information and its transformation to material-specific properties remains complicated. Furthermore, these complex detection schemes do not provide information on the fundamental question of whether all available information is collected.

Here, we discuss opportunities offered by capturing the full data stream from the detector, referred to as General Mode (G-Mode) SPM. This approach allows exploration of the complex tip-surface interactions, spatial mapping of multidimensional variability of material properties and their mutual interactions, and imaging at the information channel capacity limit—providing a new paradigm for SPM detection. This approach circumvents limitations of heterodyne detection, and as a result unlocks capabilities such as simultaneous multi-resolution imaging at multiple frequencies, smart data compression, noise analysis, and novel spectroscopic methods. In this article, we explore the opportunities for comprehensive materials characterization that are now opened by G-Mode SPM, along with associated instrumental and mathematical challenges. The opportunities enabled by the G-Mode SPM as applied to structural and functional imaging are summarized in Table 1.

Table 1 Key imaging and spectroscopy modes in scanning probe microscopy (SPM).

Materials and Methods

Signal detection methods

In conventional SPM, a probe with a sharp tip is raster-scanned over the surface while the topography and material properties of the sample are measured by tracking changes in the tip-sample interaction. The vast majority of force-based SPM techniques use a laser-based photodetector system to track changes in the deflection of a cantilever as it interacts with the surface of a sample [32, 33]. Correspondingly, much of the SPM development traditionally targeted the instrument and probe functionality [34]. At the same time, the continuous development of the excitation and signal processing methods is less recognized. In order to achieve a high signal-to-noise ratio, traditional SPM techniques use the dynamic detection principle [35, 36]. In this method, either the probe or the sample is excited mechanically, electrically, magnetically, or thermally using a sinusoidal wave with known frequency, amplitude, and phase. A lock-in amplifier (LIA) isolates the probe response at the driving frequency or its harmonics that are used as the detected signal. Alternatively, phase-locked loops (PLL) are used to maintain the system at resonance by using the phase feedback between excitation and response signal.

Over the last decade it has been recognized that these single-frequency detection methods do not adequately capture the complete information from the tip-surface interactions [25]. This led to the development of multi-frequency SPMs in which the system is excited and measured at two or more frequencies. Passive [3740], intermodulation [26, 4144], and feedback-based [29] multi-frequency SPMs have provided considerably deeper insight into the physics of tip-surface interactions in force-based SPMs and have enabled high-resolution imaging and reconstruction of force-distance curves. From passive multi-frequency SPMs, the band excitation (BE) [45, 46] method allowed full characterization of linear tip-surface dynamics. Multi-frequency methods were recently reviewed by Garcia [25].

Information compression

Until recently all dynamic SPM methods universally used the lock-in method of processing to compress the information stream from 10 MHz as limited both by the bandwidth of the photodetector and fundamental physics of the cantilever, to the ~1–10 kHz rate of feedback operation and pixel acquisition. Though these signal streams can be multimodal (for example, intermodulation signals or harmonics), the data flow is still extremely compressed. In the same vein, BE can be represented as a set of parallel lock-ins that compress the data flow to ~100 kHz. Even in this case, the data is compressed to about 1% of the initial data volume. Overall, these approaches restrict the analysis to a-priori postulated physical models (for example harmonic response) and ignore information on transients, single events, and incommensurate harmonics appearing in the response. In general, we note there is a direct benefit in increasing the amount of information that can be generated by an imaging tool, as illustrated in Figure 1.

Figure 1 The information in any imaging method can be represented as a combination of the spatial resolution, time resolution, and chemical/functional resolution. Correspondingly, increasing data flow in microscopy can be translated into increased spatial, time, or functional resolution, with the associated conversion factors dependent on technique.

General Mode SPM

In this section we provide an overview of the progress and opportunities for dynamic AFM imaging and analysis based on capturing and analyzing the full data stream from the detector, referred to as General Mode (G-Mode) SPM [47]. The G-Mode SPM concept allows full exploration of complex tip-surface interactions, spatial mapping of multi-dimensional variability of material properties and their mutual interactions, and imaging at the full capacity of the information channel. This approach circumvents limitations of heterodyne detection and, as a result, unlocks capabilities such as simultaneous multi-resolution imaging at multiple frequencies, smart data compression, noise analysis, and spectroscopic methods, which often lead to multiple orders of magnitude improvements in speed compared to classical SPM techniques. Importantly, this approach facilitates the application of a broad set of machine learning tools to the measured responses, thereby taking advantage of existing big data infrastructure and overcoming the limitations imposed by preselected physical model-based analysis [4850].

Principles of the G-Mode SPM

Figure 2 illustrates the fundamental paradigm of G-Mode SPM, which is the information-theory-based analysis of the full information flow from the detector. The cantilever is driven by a suitably chosen excitation signal corresponding to conventional single frequency, dual frequency, band excitation, or more complex excitation modes. However, unlike the heterodyne or parallel heterodyne processing in the classical and band excitation SPM (BE-SPM), G-Mode SPM captures the full time-dependent response of the cantilever and (temporarily) stores it for the whole image. The raw data is subsequently analyzed and compressed for long-term storage. Multiple information channels such as vertical response, lateral response, and collected current can be captured simultaneously. The stored data are then de-correlated, simplified, and processed using appropriate statistical and physical methods for visualization and interpretation. In this manner, G-Mode is an alternative to lock-in, PLL, or BE detection schemes. Similar to classic detection schemes, measuring the response as a function of local or global stimuli facilitates construction of spectroscopic imaging modes [48, 51].

Figure 2 Principles of G-Mode SPM. On the right side, G-Mode captures the complete raw signal from the photodetector thereby adding the time dimension for each spatial pixel. In contrast, the traditional lock-in paradigm (lower left) integrates the product of the excitation and response signals over the time constant and produces a single pair (amplitude and phase) of values at each spatial pixel.

SPM via G-Mode provides several unique advantages over classical detection schemes that cannot be enabled in other multi-frequency detection schemes. First, the availability of the complete, broadband data stream provides knowledge about the AFM tip-sample interaction for multiple resonance peaks, harmonics, mode mixing, and other non-linear phenomena. Furthermore, the complete data also facilitates adaptive and data-driven signal filtering in the frequency domain instead of using predefined filters as in conventional AFM modes. Second, G-Mode enables multi-resolution imaging, which allows the same data to be represented as a 512 × 512 image with a low noise level or a 512 × 4096 image with higher noise level. This advantage is ideal for measurements requiring precise lateral positioning or imaging of large areas containing small features. Third, G-Mode enables high veracity separation of surface regions with different mechanical, chemical, and electrostatic properties within a single experiment. Below, we illustrate G-Mode implementation for electrostatic force microscopy (EFM), Kelvin probe force microscopy (KPFM) [52, 53], and piezoresponse force microscopy (PFM) [54] in the switching and non-switching regimes. For these techniques, we demonstrate physics and information-theory-based analyses, as well as the reduction to classical SPM methods. Finally, we discuss new SPM spectroscopic imaging modalities that are enabled by G-Mode.

Results

Kelvin probe force microscopy

KPFM [55] is an extension of the century-old Kelvin probe technique that allows measurement of the electrochemical or contact potential differences (CPD) between a conductive probe and sample under test. Leveraging the high resolution and force sensitivity of the AFM enables lateral resolution of electronic surface properties on the nanometer [56], and even atomic, scales [5760]. Classical KPFM uses heterodyne detection and closed-loop-bias feedback to determine the CPD by compensating the potential difference and hence nullifying the electrostatic force between the probe and the sample [55]. This limits the KPFM measurement in terms of channels of information available (that is, CPD is the only channel available) and the time resolution of the measurement (for example, ~1–10 MHz photodetector stream is downsampled to a single readout of CPD per pixel corresponding to ~100 Hz). Furthermore, the feedback loop itself can affect the measurement [6163].

In contrast, G-Mode KPFM allows the full electrostatic force–bias relationship to be reconstructed with high temporal resolution (~1–3 µs of single cantilever oscillation) for each spatial location of the sample [64, 65]. In G-Mode KPFM, the tip (or sample) only needs the application of an AC voltage, and no bias feedback loop is required. The parabolic dependence of the electrostatic force can be recovered directly by plotting the cantilever response versus the applied voltage as seen in Figure 3. This measurement can be compared with conventional Kelvin probe force spectroscopy (KPFS), in which a linear DC bias sweep is applied to either the tip or the sample, over a single sample location while monitoring the electrostatic force (or force gradient) response using heterodyne detection [66]. This approach avoids many of the complications associated with typical closed-loop KPFM [62] and has even been used to image a single molecular charge under UHV.

Figure 3 G-Mode KPFM. (a) Topography image of an HOPG sample. (b) Single-point parabolas (averaged over the 4 ms pixel time) for two different locations (indicated via the red and blue squares on (a)) showing a 49 mV offset in the CPD between positions. (c) Second and (d) first order fitting coefficient determined from fitting the parabola at each spatial location for the first period of oscillation. (e) The CPD determined from fitting parameters for the first period of oscillation. Reprinted with permission from L Collins et al., Scientific Reports 6 (2016) 30557.

In contrast to the KPFS paradigm, which involves long integration times (100 μs to 10 ms) and requires significant amounts of time to collect high-resolution spectroscopic images (for example, several hours) [58], G-Mode KPFM provides the same information, for every oscillation of the AC voltage. In other words, rather than a two-stage detection scheme where an AC response is detected at each voltage of a slow DC waveform, here the force-bias dependence is detected directly. This allows G-Mode KPFM to collect high-resolution maps at regular imaging speeds, as well as retaining high temporal information at every pixel. In Figure 3, the imaging capabilities of G-Mode KPFM are demonstrated on freshly cleaved, highly ordered pyrolytic graphite (HOPG) with a partial delamination of the substrate, exposing graphene layers. The graphene flakes become electronically decoupled from the graphite surface, demonstrating variation in electronic properties across the sample surface. Fitting the bias dependence of the electrostatic force to a second-order polynomial curve, described by $y{\equals}ax^{2} {\plus}bx{\plus}c,$ , is performed to determine several electronic properties including CPD (for exmaple, equal to fitting coefficients –b/a) and the capacitance gradient, which is proportional to a. Furthermore, G-Mode overcomes the requirement for application of a DC bias [63], which can be problematic for voltage-sensitive materials [67] or operation in liquid [6870].

It is important to note that despite the popularity of KPFM measurements, the level of information available (that is, CPD) is not sufficient for systems such as electroactive materials, devices, or solid-liquid interfaces, involving nonlinear lossy dielectrics. In such cases it is not enough to know the bias dependence of the electrostatic force (or to be more precise, apex of the parabola); it is imperative that the time dependence of the electrostatic force is also known [70]. In G-Mode KPFM, for every period of AC voltage, the parabolic bias dependence of the electrostatic force, and hence the electronic properties, can be determined [64]. Since the probe raster motion is much slower than the electrical excitation, several 10s–100s of readouts can be performed at each pixel. In this way, G-Mode KPFM provides a measure of the transient changes in electronic properties of the sample at each spatial location, where the temporal resolution of the measurement is on the order of the AC voltage period. This dynamic aspect will be particularly useful for probing surface photovoltage in photovoltaics [71], ion transport in materials and devices [72], and even screening processes at the solid-liquid interface [64]. G-Mode KPFM can potentially enable multi-frequency open-loop KPFM measurements, allow reliable measurements in liquid to probe nonlinear interactions, and improve the measurement rate of KPFM by 1,000 times via direct force-voltage curve reconstructions.

Piezoresponse force microscopy

The PFM technique is used for probing electromechanical activity at the nanoscale and provides insight into localized functionality of ferroelectric and multiferroic materials [6, 7380]. In PFM, an electric bias is applied to a conductive AFM tip in contact with the sample. The bias results in surface deformation because of the converse piezoelectric effect and/or strain-coupled electrochemical phenomena, as well as an electrostatic force at the tip-surface junction. These surface deformations induce vibrations in the cantilever, which are measured at the AFM photodetector. In spectroscopic modes of PFM, the ferroelectric properties of a material are explored via local hysteresis loop measurements, where the electromechanical response is measured as a function of applied DC bias.

In classical, single-frequency PFM (S-PFM), the cantilever is excited with a sinusoidal bias (typically 10–500 kHz), and the resultant cantilever response is measured using a lock-in amplifier. Consequently, PFM images only contain phase and amplitude information at the excitation frequency at each spatial pixel. In G-Mode PFM (G-PFM) [54] the complete cantilever response at each pixel is stored for later analysis for the same sinusoidal excitation. Similar to KPFM, G-PFM data can be analyzed either by applying digital lock-ins at any frequency or through multivariate statistical analysis methods such as principal component analysis (PCA). Figure 4 compares information from S-PFM, digital lock-in, and PCA applied to an example G-PFM dataset acquired on a polycrystalline Pb(Zr0.2Ti0.8)O3 (PZT) ceramic. Here, the loading maps of the first two PCA components show strong contrast between oppositely oriented domains and are similar to the amplitude and phase images from traditional PFM images. Correspondingly, the eigenvectors of the first two components show almost identical harmonic content and correspond to the phase-shifted (by 90 degrees) periodic components of the response. Note that unlike lock-in detection, each PCA component contains multiple harmonics. The third eigenvector is dominated by the intrinsic cantilever resonance, and the corresponding loading map shows characteristics of the transient cantilever response induced by the edges of topographical features, resembling the error signal in the force feedback loop. Appropriate signal de-mixing algorithms can be used to decouple domain contrast from topographic information. These G-PFM data can also be analyzed using clustering algorithms, independent component analysis, Bayesian linear unmixing methods, and correlational analysis techniques [48, 8186].

Figure 4 G-Mode PFM imaging. (a) Topography, amplitude, and phase images of a ceramic perovskite obtained from traditional single frequency PFM (S-PFM). (b) Digital lock-ins applied at 435 kHz and 1036 kHz to the G-PFM dataset and the corresponding amplitude and phase maps. (c) Results of principal component analysis (PCA) applied to G-PFM: the first three loading maps and corresponding eigenvectors in frequency-space and real-space (insets). Reprinted from S Somnath et al., App Phys Lett 107 (2015) 263102 with permission of AIP Publishing.

The G-PFM approach can also be extended to study polarization switching in ferroelectric materials, as implemented in G-Mode voltage spectroscopy (G-VS) [87]. In G-VS, the amplitude of the G-PFM excitation signal is increased beyond the coercive bias of the sample. G-VS uses data-driven adaptive signal filtering techniques to reveal strain loops that are indicative of polarization switching in ferroelectric materials, as shown in Figure 5a. The raw data itself is used to calculate an appropriate noise-floor for the signal at each pixel. A band-pass filter only retains the signal from the excitation frequency to 10–12 harmonics of the drive frequency, and any signal below the calculated noise floor is rejected. The filtered signal reveals numerous bias-induced strain loops. Such extraction of hysteresis loops would not be possible without the complete data or by using the traditional heterodyne detection schemes since the response frequencies are not known a priori. Compared to the current state-of-art technique, band excitation polarization switching (BEPS) that uses a slow (0.25–2 Hz) polarization switching waveform, the ultrafast excitation waveform of G-VS (10–60 kHz) results in a 3,500-fold improvement in measurement speed over BEPS. The sheer speed of the polarization switching waveform enables G-VS to enjoy high spatial resolution, minimal drift, and short measurement durations typical of imaging modes such as S-PFM, while having the polarization switching capability of spectroscopy techniques. Once the data are filtered, relevant material-specific properties may be extracted from the shape of the strain loops. Alternatively, statistical methods may be applied to analyze the data. Figure 5b compares the spatial resolutions of S-PFM, BEPS, and G-VS for measurements on a Pb(Zr0.2Ti0.8)O3 (PZT) thin film sandwiched between gold nanocapacitor discs and a SrRuO3 bottom electrode on a SrTiO3 substrate. The S-PFM and G-VS measurements resulted in high-resolution 256 × 256 pixel images acquired in 8.5 and 17 minutes, respectively, while the BEPS measurement resulted in a 40 × 40 pixel image acquired in 77 minutes.

Figure 5 G-Mode voltage spectroscopy (G-VS): a technique for ultrafast imaging of polarization switching in ferroelectric materials. (a) Raw G-VS data filtered in the frequency domain using adaptive noise thresholding and a band-pass filter to reveal multiple material bias-induced strain loops that are characteristic of the hysteretic response shown by ferroelectric materials. (b) Spatial maps of single frequency PFM (S-PFM) amplitude and phase signals, area of the piezoresponse loop from band excitation polarization switching (BEPS), the current state-of-art method for spectroscopic studies on ferroelectric materials, area of the mean strain loops in G-VS. S-PFM and G-VS show high-resolution maps with 256 × 256 spatial pixels acquired in 8.5 and 17 minutes respectively, while BEPS acquired a 40 × 40 pixel image in 77 minutes illustrating that G-VS is 3–4 orders of magnitude faster than BEPS. Reprinted with permission from S Somnath et al., Nature Communications 7 (2016) 13290.

New SPM modes enabled by full data acquisition

Besides adaptations to traditional imaging techniques, G-Mode also can give rise to fundamentally new modes of SPM operation [88]. For example, in order to completely characterize any system, it is important to study the dynamic behavior of the system to identify and isolate the contributions of different phenomena with respect to the system’s response.

Figure 6a illustrates general dynamic mode (GDM), which applies the G-Mode methodology to frequency sweeps such that the result at each spatial location is a two-dimensional dataset with excitation frequency (ωE) on one axis and the response frequency (ωR) on the other. GDM can be extended to imaging on a grid of points or spectroscopic measurements, where one or more system parameters are varied, to generate datasets with 3 or more dimensions and data sizes that can range from 10 GB to 1000 GB. Such GDM spectroscopic or imaging datasets can be analyzed using PCA or established physical models. Figures 6b and 6c illustrate the results from PCA applied to a four-dimensional (x, y, ωE, ωR) GDM imaging dataset acquired for a model system of a purely capacitively actuated cantilever over a silicon sample with gold and aluminum electrodes. The Eigenvectors from PCA are GDM spectrograms that show prominent peaks at the first two resonant modes of the cantilever as well as their first harmonic. The first PCA component shows the mean response over the entire dataset. The eigenvector from the second component is dominated by response from the resonance peaks, and the corresponding loading map shows a distinct response from each phase in the sample. The third component resembles the capacitance gradient, which is dependent on the dielectric properties of the sample and the tip-surface geometry. The loading map from the fourth component appears to be sensitive to the topography edges only, and the subsequent PCA components mainly contain noise. GDM reveals vital information such as mode-mixing, harmonics, and other non-linear behaviors of systems that are impossible to visualize using other techniques [88]. GDM could also be applied to measurements such as contact resonance to extract more information about the viscoelastic properties of materials.

Figure 6 General dynamic mode (GDM) applies G-Mode to frequency sweeps. (a) In GDM, the complete response from the AFM is recorded for a sequence of excitation waveforms of increasing frequency to generate a 2D spectrogram with the excitation frequency on one axis and the response frequency on the other for each spatial location. (b-c) Results of PCA applied to a GDM imaging dataset on a silicon substrate with gold and aluminum electrodes. The first four PCA loading maps (b) and eigenvectors (c), which are GDM spectrograms. Reprinted from S Somnath et al., Nanotechnology 27 (2016) 414003 with permission of IOP Publishing.

In addition, G-Mode also can be applied to other SPM modes such as magnetic force microscopy (MFM) [53] and intermittent contact mode imaging [47], in many cases offering several orders of magnitude greater speed in imaging. Since G-Mode captures several data points for each oscillation of the AFM cantilever, force-distance curves can be extracted from G-Mode intermittent contact mode measurements to enable rapid acquisition of dense 3D grids of the tip-sample forces. Much like G-VS, these measurements would be at least 3 orders of magnitude faster than classical force-mapping measurements that use heterodyne detection methods. However, the key challenge is the inversion of data to extract the force-distance curves. Similarly, applying G-Mode to current-voltage (IV) measurements can decrease measurement time by 2–3 orders of magnitude and facilitate the capturing of materials physics that is not possible with conventional methods. Yet again, the inversion of data to extract the local resistance as a function voltage via methods such as Bayesian inference will be a challenge. In addition, G-Mode applied to MFM enables the measurement of magnetic domains, average dissipation, and single dissipation events from a single experiment. Furthermore, it is possible to deconvolute electronic effects, and probe the non-linearities and frequency-dependent mixing phenomena in G-Mode MFM.

Discussion

The (temporary) capture of the complete information stream and subsequent analysis requires advanced computational capabilities, as summarized in Table II. However, the explosive growth of cloud-enabled computing technologies makes these calculations highly feasible [4850]

Table 2 G-Mode Limitations

The potential of G-Mode SPM to attain the ultimate goal for an SPM experiment, that is, quantitative probing of local material functionality, has two stages, namely reconstruction of the force-distance (FD) curve (for dynamic measurements) or force-voltage curve (for voltage modulated measurements) from the measured signals and the physics-based analysis to extract local functionalities. Indeed, the FD curves contain the full information about the tip-surface interactions and represent the maximum amount we can extract from SPM measurements without additional information on the tip-geometry and properties. Correspondingly, the next step of G-Mode SPM is the introduction of mathematical frameworks and modulation modes that allow reconstruction of local FD curves from the dynamic data. Once available, this will open a pathway for physics-based analysis. Furthermore, the linearity of FD interactions in terms of relevant contributions suggests a tremendous potential for blind linear unmixing methods to separate local contributions, giving rise to new SPM imaging paradigms.

Conclusion

This article describes a new scanning probe microscopy method called General Mode (G-Mode) SPM, which allows exploration of the entire signal resulting from complex tip-surface interactions. Typical G-Mode SPM allows spatial mapping of the multi-dimensional variability in material properties and their interactions on a pixel-by-pixel basis. Imaging and spectroscopy with this method uses the entire capacity of the available information channels.

Acknowledgements

This research was funded by the Center for Nanophase Materials Sciences, which is a U. S. Department of Energy Office of Science User Facility.

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