Full Information Acquisition
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 spectro- scopic 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 diff erences (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 [ 57 – 60 ]. Classical KPFM uses heterodyne detection and closed-loop-bias feedback to determine the CPD by compensating the potential diff erence and hence nullifying the electrostatic force between the probe and the sample [ 55 ]. T is 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 aff ect the measurement [ 61 – 63 ].
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. T e parabolic dependence of the electrostatic force can
be recovered directly by plotting the cantilever response versus the applied voltage as seen in Figure 3 . T is 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 ]. T is 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. In contrast to the KPFS paradigm, which involves long integration times (100 μ s to 10 ms) and requires signifi cant 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. T is 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. T e graphene fl akes 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 = ax2 + bx + c, is performed to determine several electronic properties including CPD (for exmaple, equal to fi tting coeffi cients – b / a ) and the capacitance gradient, which is proportional to a .
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 fi rst 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.
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