Breaking the Time Barrier in Kelvin Probe Force Microscopy: Fast Free Force Reconstruction Using the G‑Mode Platform Liam Collins,*,†,‡ Mahshid Ahmadi,§ Ting Wu,§ Bin Hu,§ Sergei V. Kalinin,†,‡ and Stephen Jesse*,†,‡ †
Center for Nanophase Materials Sciences and ‡Institute for Functional Imaging of Materials, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States § Joint Institute for Advanced Materials, Department of Materials Science and Engineering, University of Tennessee, Knoxville 37996, United States S Supporting Information *
ABSTRACT: Atomic force microscopy (AFM) offers unparalleled insight into structure and material functionality across nanometer length scales. However, the spatial resolution afforded by the AFM tip is counterpoised by slow detection speeds compared to other common microscopy techniques (e.g., optical, scanning electron microscopy, etc.). In this work, we develop an ultrafast AFM imaging approach allowing direct reconstruction of the tip-sample forces with ∼3 order of magnitude higher time resolution than is achievable using standard AFM detection methods. Fast free force recovery (F3R) overcomes the widely viewed temporal bottleneck in AFM, that is, the mechanical bandwidth of the cantilever, enabling time-resolved imaging at subbandwidth speeds. We demonstrate quantitative recovery of electrostatic forces with ∼10 μs temporal resolution, free from influences of the cantilever ring-down. We further apply the F3R method to Kelvin probe force microscopy (KPFM) measurements. F3R-KPFM is an open loop imaging approach (i.e., no bias feedback), allowing ultrafast surface potential measurements (e.g., 10 μs), free from influences of the cantilever ring-down effects. We then leverage ultrafast F3R detection for KPFM measurements, operated in open loop, performed at regular scan rates (∼0.5 Hz) and without the need for complex triggering circuits30,47 or the reliance on a precise impulse50,51 applied to the sample. Finally, F3R-KPFM imaging is shown to allow ultrafast (1) may require additional consideration.70 On the right-hand side of eq 1, two terms representing the time-dependent driving force, FD, and the nonlinear tip−sample interaction force, Fts, are included. As has been mentioned previously, in the case of capacitive actuation, the driving force and tip−sample interaction force coincide.71 For example, in KPFM, the tip is held far from the surface (>10 nm) and the system is driven capactively (i.e., no mechanical drive) using a voltage-modulated probe (or sample) Vtip = Vdc + Vac cos(ωt). In this case, the electrostatic force, established between the grounded sample and conductive probe, is written as Fts =
1 C′(Vtip − Vcpd)2 2
Y (ω) =
1 1 F(ω) kn ( −iω/ωn)2 + iω/Q nωn + 1
= H(ω)F(ω)
(3)
where Y(ω) is the Fourier transform of the time-dependent tip displacement (i.e., Y (ω) = {y(t )}), F(ω) = {Fts(t )}, H(ω) is the frequency-dependent cantilever transfer function, and Y, H, and F are all complex parameters having both in-phase and quadrature components. Clearly, after Fourier transformation, the measured deflection is related to the product of the specific tip−surface interaction forces and the intrinsic cantilever dynamics. Unfortunately, the established sensing and detection platforms in traditional dynamic AFM approaches (Figure 1a) preclude the separation of both influences and hence do not allow for the extraction of the real-time tip−sample forces. Further, the adoption of LIA/ PLL detection, which operates by integrating the response over many periods of the excitation waveform (in the time domain), effectively attenuates any/all responses outside the single (or sometimes multiple harmonic) frequency detection bins, ultimately leading to a loss of temporal information (in favor of perceived improvements in signal/noise). In the context of
(2)
where C′ is the tip−sample capacitance gradient, Vcpd is the contact potential difference (CPD). Fourier transforming eq 1 for the case of capacitive driving yields a general linear equation 8720
DOI: 10.1021/acsnano.7b02114 ACS Nano 2017, 11, 8717−8729
Article
ACS Nano
Postprocessing Procedures. Because F3R aims to recover, and retain, the real-time tip−sample interaction force, it is not possible to rely on traditional processing techniques involving averaging or demodulation of the signal in the time domain (e.g., homodyne/heterodyne detection). Noteworthy, in most AFM measurements, filter settings are configured prior to the measurement, often without any real consideration into the noise levels in the system, and remain constant throughout the experiment. On the contrary, in G-Mode, multiple filtering routes can be applied to the stored signal either in series or parallel, allowing significant flexibility and better information extraction without corrupting the original photodetector signal. In Figure 3, we illustrate distinct preprocessing steps involving Fourier filtering and principal component analysis (PCA) denoising. In this experiment, F3R was performed in lift mode (∼50 nm lift height) above a freshly cleaved HOPG sample (grounded) while the tip voltage was modulated using a square wave voltage (amplitude = 0−3 V, frequency ≈ 250 Hz). The full experimental data set contained 4 × 128 pixels, with ∼4 ms of data captured at 4 MHz sample rate, corresponding to a file size of 65.5 Mb. Figure 3a shows the frequency spectrum for a single line (1 × 128 pixels) of data after an FFT operation has been performed on the raw time domain signal. The amplitude spectrum represents the level of signal present in each frequency bin. From inspection of Figure 3a, the majority of the signal is confined to frequency bins 50 μs.
below the 95th percentile of the expected contrast. Figure 5e depicts the mean and standard deviations for both on and off states as a function of pulse width. To eliminate complications arising from overshooting of the square wave voltage, only the central 80% of the pulse width was considered in calculating Dcontrast. The expected Dcontrast was calculated as the mean difference between on and off states for pulse widths >50 μs. Under these criteria, and from inspection of Figure 5f, the temporal resolution (within 95th percentile) corresponds to ∼9 μs for this particular cantilever. At the same time, signal contrast is still detected beyond this time scale, as the on and off states can be distinguished from each other up until approximately 5 μs (see Figure 5e). Beyond this time scale, the signal levels fall below the noise level, and no additional information (even qualitative information) can be obtained (i.e., the information limit). Note that both parameters, the time resolution and the information limit, will depend on the reconstruction error, the ratio of the signal strength, as well as the noise level in the system. However, even simple models and procedures, as employed here, are demonstrated to allow reconstruction of the forces within sufficiently acceptable error limits but with ∼3 orders of magnitude faster response rate
bias, free from the influences of the cantilever dynamics, and furthermore, the magnitude matches well with the modeled force. Noise Limits and Time Resolution. In Figure 5, we investigate the temporal resolution of the F3R approach. To do this, a similar measurement as shown in Figure 4 was performed, but this time the pulse width was varied linearly from ∼0.66 ms to ∼25 μs over a period of ∼8 ms. In Figure 5a, the applied bias is presented along with the recovered displacement. Unlike the observed response (see Supplementary Figure S4), the recovered force tracks the applied bias extremely well, and the overall magnitude remains stable for the entire duration of the measurement. On closer inspection (Figure 5b−d), even for relatively short pulses (100 compared to classical approaches.9 Next, we demonstrate the imaging capabilities of F3R-KPFM. As a model system of interest, we choose OIHP, a class of materials that are promising for a range of applications including high-performance and low-cost solar cells,82−84 light-emitting diodes,84,85 photodetectors,86 and high-energy radiation detectors.87,88 While high-performance OIHP-based devices are being intensively investigated,89 many factors still remain if these materials are to be commercially viable and stable. In particular, the role of intrinsic ion migration needs to be fully understood.90,91 Indeed, ion migration has been largely established90,92 as a mechanism involved in observations of unusual electronic behavior including hysteretic current− voltage93 and switchable photovoltaic94 effects. Whereas classical KPFM has proven to be extremely useful in the microscopic exploration of both optical and electric-field-driven ion migration in OIHP single crystals and thin films,25,94−97 a full understanding of the role ion migration plays in OIHPs would benefit greatly from KPFM measurements capable of capturing fast ion dynamics (
