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it is important to study the dynamic behavior of the system to identify and isolate the contributions of diff erent 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 (ω E ) on one axis and the response frequency (ω R ) 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 6 b and 6 c illustrate the results from PCA applied to a four-dimensional ( x , y , ω E , ω R ) GDM imaging dataset acquired for a model system of a purely capacitively actuated cantilever over a silicon sample with gold and aluminum electrodes. T e Eigenvectors from PCA are GDM spectrograms that show prominent peaks at the fi rst two resonant modes of the cantilever as well as their fi rst harmonic. T e fi rst PCA component shows the mean response over the entire dataset. T e 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. T e third component resembles the capacitance gradient, which is dependent on the dielectric properties of the sample and the tip-surface geometry. T e 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. 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 off ering 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 measure- ments 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 eff ects, and probe the non-linearities and frequency-dependent mixing phenomena in G-Mode MFM.


44


Discussion T e (temporary) capture of the complete information stream and subsequent analysis requires advanced computa- tional capabilities, as summarized in Table II . However, the explosive growth of cloud-enabled computing technologies makes these calculations highly feasible [ 48 – 50 ] T e 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 measure- ments 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 interac- tions 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 T is 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 T is research was funded by the Center for Nanophase Materials Sciences, which is a U. S. Department of Energy Offi ce of Science User Facility.


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[5] P Grutter et al ., Appl Phys Lett 71 ( 2 ) ( 1997 ) 279 – 81 . [6] DA Bonnell et al ., MRS Bull 34 ( 9 ) ( 2009 ) 648 – 657 . [7] SV Kalinin et al. , Rep Prog Phys 73 ( 5 ) ( 2010 ) 056502 . [8] G Binnig et al. , “ 7 × 7 Reconstruction on Si(111) Resolved in Real Space” in Scanning Tunneling Microscopy ed. H Neddermeyer, Springer , New York , ( 1993 ) 36 – 39 .


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