Full data acquisition in Kelvin Probe Force Microscopy: Mapping dynamic electric phenomena in real space

Unraveling Spatiotemporal Transient Dynamics at the Nanoscale via Wavelet Transform-Based Kelvin Probe Force Microscopy

Mechanistic probing of surface potential changes arising from dynamic charge transport is the key to understanding and engineering increasingly complex nanoscale materials and devices. Spatiotemporal averaging in conventional heterodyne detection-based Kelvin probe force microscopy (KPFM) inherently limits its time resolution, causing an irretrievable loss of transient response and higher-order harmonics. Addressing this, we report a wavelet transform (WT)-based methodology capable of quantifying the sub-ms charge dynamics and probing the elusive transient response. The feedback-free, open-loop wavelet transform KPFM (OL-WT-KPFM) technique harnesses the WT's ability to simultaneously extract spatial and temporal information from the photodetector signal to provide a dynamic mapping of surface potential, capacitance gradient, and dielectric constant at a temporal resolution 3 orders of magnitude higher than the lock-in time constant. We further demonstrate the method's applicability to explore the surface-photovoltage-induced sub-ms hole-diffusion transient in bismuth oxyiodide semiconductor. The OL-WT-KPFM concept is readily applicable to commercial systems and can provide the underlying basis for the real-time analysis of transient electronic and electrochemical properties.

AC Kelvin Probe Force Microscopy Enables Charge Mapping in Water

Mapping charged chemical groups at the solid-liquid interface is important in many areas, ranging from colloidal systems to biomolecular interactions. However, classical methods to measure surface charges either lack spatial resolution or─like Kelvin-probe force microscopy (KPFM)─cannot be applied in aqueous solutions because a DC bias voltage is used. Here, we show that using AC Kelvin probe force microscopy (AC-KPFM), in which the DC bias is replaced with an AC voltage of sufficiently high frequency, the surface potential of spatially fixated, charged surface groups can be mapped in aqueous solution. We demonstrate this with micropatterned, functionalized alkanethiol layers which expose ionized amino- and carboxy-groups. These groups are representative of the charged groups of most biomolecules such as proteins. By adjusting the pH of the solution, the charge of the groups was reversibly altered, demonstrating the electrostatic nature of the measured signal. The influence of the electric double layer (EDL) on the measurement is discussed, and we, furthermore, show how charged, micropatterned layers can be used to spatially direct the deposition of nanoparticles of opposite charge.

Comparing the performance of single and multifrequency Kelvin probe force microscopy techniques in air and water

In this paper, we derive and present quantitative expressions governing the performance of single and multifrequency Kelvin probe force microscopy (KPFM) techniques in both air and water. Metrics such as minimum detectable contact potential difference, minimum required AC bias, and signal-to-noise ratio are compared and contrasted both off resonance and utilizing the first two eigenmodes of the cantilever. These comparisons allow the reader to quickly and quantitatively identify the parameters for the best performance for a given KPFM-based experiment in a given environment. Furthermore, we apply these performance metrics in the identification of KPFM-based modes that are most suitable for operation in liquid environments where bias application can lead to unwanted electrochemical reactions. We conclude that open-loop multifrequency KPFM modes operated with the first harmonic of the electrostatic response on the first eigenmode offer the best performance in liquid environments whilst needing the smallest AC bias for operation.

Open-loop amplitude-modulation Kelvin probe force microscopy operated in single-pass PeakForce tapping mode

The open-loop (OL) variant of Kelvin probe force microscopy (KPFM) provides access to the voltage response of the electrostatic interaction between a conductive atomic force microscopy (AFM) probe and the investigated sample. The measured response can be analyzed a posteriori, modeled, and interpreted to include various contributions from the probe geometry and imaged features of the sample. In contrast to this, the currently implemented closed-loop (CL) variants of KPFM, either amplitude-modulation (AM) or frequency-modulation (FM), solely report on their final product in terms of the tip-sample contact potential difference. In ambient atmosphere, both CL AM-KPFM and CL FM-KPFM work at their best during the lift part of a two-pass scanning mode to avoid the direct contact with the surface of the sample. In this work, a new OL AM-KPFM mode was implemented in the single-pass scan of the PeakForce Tapping (PFT) mode. The topographical and electrical components were combined in a single pass by applying the electrical modulation only in between the PFT tip-sample contacts, when the AFM probe separates from the sample. In this way, any contact and tunneling discharges are avoided and, yet, the location of the measured electrical tip-sample interaction is directly affixed to the topography rendered by the mechanical PFT modulation at each tap. Furthermore, because the detailed response of the cantilever to the bias stimulation was recorded, it was possible to analyze and separate an average contribution of the cantilever to the determined local contact potential difference between the AFM probe and the imaged sample. The removal of this unwanted contribution greatly improved the accuracy of the AM-KPFM measurements to the level of the FM-KPFM counterpart.

Fingerprinting the Ammonia Synthesis Pathway Using Spatiotemporal Electrostatic Potential Distribution of Intermediates

It remains a research challenge in determining the catalytic reaction mechanisms primarily caused by the difficulty to experimentally identify active intermediates with current analytic characterizations. Although computational chemistry has provided an alternative approach to simulate the catalysis process and achieve insights into the reaction pathways, the simulation results would not be conclusive without experimental evidence. Herein, we investigate spatiotemporal electrostatic potential (ESP) distribution surrounding reacting molecules during the catalysis process and suggest its use as a fingerprint to help differentiate and identify active intermediates. Our ESP study of ammonia synthesis on the Ru surface shows a high spatial sensitivity of ESP distribution to molecular configuration and structure of intermediate species and only minor temporal ESP oscillation throughout the lifetime of the intermediates, which provides strong theoretical support to use ESP distribution as a new approach to characterize intermediates. With the ESP measurements at the microscale and in real-time, turning feasible, experimental identification of active intermediates and determination of reaction pathways would become possible by measuring the ESP surrounding the reacting molecules. We suggest developing ESP measurement tools to experimentally explore and unveil reaction mechanisms.

Nanoscale Charge Accumulation and Its Effect on Carrier Dynamics in Tri-cation Perovskite Structures

Nanoscale investigations by scanning probe microscopy have provided major contributions to the rapid development of organic-inorganic halide perovskites (OIHP) as optoelectronic devices. Further improvement of device level properties requires a deeper understanding of the performance-limiting mechanisms such as ion migration, phase segregation, and their effects on charge extraction both at the nano- and macroscale. Here, we have studied the dynamic electrical response of Cs0.05(FA0.83MA0.17)0.95PbI3-xBrx perovskite structures by employing conventional and microsecond time-resolved open-loop Kelvin probe force microscopy (KPFM). Our results indicate strong negative charge carrier trapping upon illumination and very slow (>1 s) relaxation of charges at the grain boundaries. The fast electronic recombination and transport dynamics on the microsecond scale probed by time-resolved open-loop KPFM show diffusion of charge carriers toward grain boundaries and indicate locally higher recombination rates because of intrinsic compositional heterogeneity. The nanoscale electrostatic effects revealed are summarized in a collective model for mixed-halide CsFAMA. Results on multilayer solar cell structures draw direct relations between nanoscale ionic transport, charge accumulation, recombination properties, and the final device performance. Our findings extend the current understanding of complex charge carrier dynamics in stable multication OIHP structures.

Dynamic Manipulation in Piezoresponse Force Microscopy: Creating Nonequilibrium Phases with Large Electromechanical Response

Domain walls and topological defects in ferroelectric materials have emerged as a powerful tool for functional electronic devices including memory and logic. Similarly, wall interactions and dynamics underpin a broad range of mesoscale phenomena ranging from giant electromechanical responses to memory effects. Exploring the functionalities of individual domain walls, their interactions, and controlled modifications of the domain structures is crucial for applications and fundamental physical studies. However, the dynamic nature of these features severely limits studies of their local physics since application of local biases or pressures in piezoresponse force microscopy induce wall displacement as a primary response. Here, we introduce an approach for the control and modification of domain structures based on automated experimentation, whereby real-space image-based feedback is used to control the tip bias during ferroelectric switching, allowing for modification routes conditioned on domain states under the tip. This automated experiment approach is demonstrated for the exploration of domain wall dynamics and creation of metastable phases with large electromechanical response.

Measurement of electrostatic tip-sample interactions by time-domain Kelvin probe force microscopy

Kelvin probe force microscopy is a scanning probe technique used to quantify the local electrostatic potential of a surface. In common implementations, the bias voltage between the tip and the sample is modulated. The resulting electrostatic force or force gradient is detected via lock-in techniques and canceled by adjusting the dc component of the tip-sample bias. This allows for an electrostatic characterization and simultaneously minimizes the electrostatic influence onto the topography measurement. However, a static contribution due to the bias modulation itself remains uncompensated, which can induce topographic height errors. Here, we demonstrate an alternative approach to find the surface potential without lock-in detection. Our method operates directly on the frequency-shift signal measured in frequency-modulated atomic force microscopy and continuously estimates the electrostatic influence due to the applied voltage modulation. This results in a continuous measurement of the local surface potential, the capacitance gradient, and the frequency shift induced by surface topography. In contrast to conventional techniques, the detection of the topography-induced frequency shift enables the compensation of all electrostatic influences, including the component arising from the bias modulation. This constitutes an important improvement over conventional techniques and paves the way for more reliable and accurate measurements of electrostatics and topography.

High-speed digitization of the amplitude and frequency in open-loop sideband frequency-modulation Kelvin probe force microscopy

A more inclusive and detailed measurement of various physical interactions is enabled by the advance of high-speed data digitization. For surface potential characterization, this was demonstrated recently in terms of open-loop amplitude modulation Kelvin probe force microscopy (OL AM-KPFM). Its counterpart, namely open-loop frequency modulation Kelvin probe force microscopy (OL FM-KPFM), is examined here across different materials and under various bias voltages in the form of OL sideband FM-KPFM. In this implementation the changes in the amplitude and resonance frequency of the cantilever were continuously tracked as a conductive AFM probe was modulated by a 2 kHz AC bias voltage around the first eigenmode frequency of the cantilever. The contact potential difference (CPD) between the AFM probe and sample was determined from the time series analysis of the high-speed 4 MHz digitized amplitude and frequency signals of the OL sideband FM-KPFM mode. This interpretation is demonstrated to be superior to the analysis of the parabolic bias dependent response, which is more commonly used to extract the CPD in OL KPFM modes. The measured OL sideband FM-KPFM amplitude and frequency responses are directly related to the electrostatic force and force-gradient between the AFM probe and sample, respectively. As a result, clear distinction was observed for the determined CPD in each of these cases across materials of different surface potentials, with far superior spatial resolution when the force-gradient detection was used. In addition, the CPD values obtained from OL sideband FM-KPFM amplitude and frequency measurements perfectly matched those determined from their closed-loop AM-KPFM and FM-KPFM counterparts, respectively.

Correlation of Spatiotemporal Dynamics of Polarization and Charge Transport in Blended Hybrid Organic-Inorganic Perovskites on Macro- and Nanoscales

Progress in flexible organic electronics necessitates a full understanding of how local inhomogeneities impact electronic and ionic conduction pathways and underlie macroscopic device characteristics. We used frequency- and time-resolved macro- and nanoprobe measurements to study spatiotemporal characteristics of multiscale charge transport dynamics in a series of ternary-blended hybrid organic inorganic perovskites (HOIPs) (MA_0.95-xFA_xCs_0.05PbI₃). We show that A-site cation composition defines charge transport mechanisms across broad temporal (10²-10^-6 s) and spatial (millimeters-picometers) scales. Ab initio molecular dynamic simulations suggest that insertion of FA results in a dynamic lattice, improved ion transport, and dipole screening. We demonstrate that correlations between macro- and nanoscale measurements provide a pathway for accessing distribution of relaxation in nanoscale polarization and charge transport dynamics of ionically conductive functional perovskites.

Toward Electrochemical Studies on the Nanometer and Atomic Scales: Progress, Challenges, and Opportunities

Electrochemical reactions and ionic transport underpin the operation of a broad range of devices and applications, from energy storage and conversion to information technologies, as well as biochemical processes, artificial muscles, and soft actuators. Understanding the mechanisms governing function of these applications requires probing local electrochemical phenomena on the relevant time and length scales. Here, we discuss the challenges and opportunities for extending electrochemical characterization probes to the nanometer and ultimately atomic scales, including challenges in down-scaling classical methods, the emergence of novel probes enabled by nanotechnology and based on emergent physics and chemistry of nanoscale systems, and the integration of local data into macroscopic models. Scanning probe microscopy (SPM) methods based on strain detection, potential detection, and hysteretic current measurements are discussed. We further compare SPM to electron beam probes and discuss the applicability of electron beam methods to probe local electrochemical behavior on the mesoscopic and atomic levels. Similar to a SPM tip, the electron beam can be used both for observing behavior and as an active electrode to induce reactions. We briefly discuss new challenges and opportunities for conducting fundamental scientific studies, matter patterning, and atomic manipulation arising in this context.

Time-Resolved Electrical Scanning Probe Microscopy of Layered Perovskites Reveals Spatial Variations in Photoinduced Ionic and Electronic Carrier Motion

We study light-induced dynamics in thin films comprising Ruddlesden-Popper phases of the layered 2D perovskite (C₄H₉NH₃)₂PbI₄. We probe ionic and electronic carrier dynamics using two complementary scanning probe methods, time-resolved G-mode Kelvin probe force microscopy and fast free time-resolved electrostatic force microscopy, as a function of position, time, and illumination. We show that the average surface photovoltage sign is dominated by the band bending at the buried perovskite-substrate interface. However, the film exhibits substantial variations in the spatial and temporal response of the photovoltage. Under illumination, the photovoltage equilibrates over hundreds of microseconds, a time scale associated with ionic motion and trapped electronic carriers. Surprisingly, we observe that the surface photovoltage of the 2D grain centers evolves more rapidly in time than at the grain boundaries. We propose that the slower evolution at grain boundaries is due to a combination of ion migration occurring between PbI₄ planes, as well as electronic carriers traversing grain boundary traps, thereby changing the time-dependent band unbending at grain boundaries. These results provide a model for the photoinduced dynamics in 2D perovskites and are a useful basis for interpreting photovoltage dynamics on hybrid 2D/3D structures.

Nanoscale dipole dynamics of protein membranes studied by broadband dielectric microscopy

We investigate the nearfield dipole mobility of protein membranes in a wide frequency range from 3 kHz to 10 GHz. The results of our nanoscale dielectric images and spectra of bacteriorhodopsin (bR) reveal Debye relaxations with time constants of τ ∼ 2 ns and τ ∼ 100 ns being characteristic of the dipole moments of the bR retinal and α-helices, respectively. However, the dipole mobility and therefore the protein biophysical function depend critically on the amount of surface water surrounding the protein, and the characteristic mobility in the secondary structure is only observed for humidity levels <30%. Our results have been achieved by adding the frequency as a second fundamental dimension to quantitative dielectric microscopy. The key elements for the success of this advanced technique are the employed heterodyne detection scheme, the broadband electrical signal source, a high frequency optimized cabling, development of calibration procedures and precise finite element modelling. Our study demonstrates the exciting possibilities of broadband dielectric microscopy for the investigation of dynamic processes in cell bioelectricity at the individual molecular level. Furthermore, the technique may shed light on local dynamic processes in related materials science applications like semiconductor research or nano-electronics.

Noncontact Imaging of Ion Dynamics in Polymer Electrolytes with Time-Resolved Electrostatic Force Microscopy

Ionic-transport processes govern performance in many classic and emerging devices, ranging from battery storage to modern mixed-conduction organic electrochemical transistors (OECT). Here, we study local ion-transport dynamics in polymer films using time-resolved electrostatic force microscopy (trEFM). We establish a correspondence between local and macroscopic measurements using local trEFM and macroscopic electrical impedance spectroscopy (EIS). We use polymer films doped with lithium bis(trifluoromethane)sulfonimide (LiTFSI) as a model system where the polymer backbone has oxanorbornenedicarboximide repeat units with an oligomeric ethylene oxide side chain of length n. Our results show that the local polymer response measured in the time domain with trEFM follows stretched-exponential relaxation kinetics, consistent with the Havriliak-Negami relaxation we measure in the frequency-domain EIS data for macroscopic samples of the same polymers. Furthermore, we show that the trEFM results capture the same trends as the EIS results-changes in ion dynamics with increasing temperature, increasing salt concentration, and increasing volume fraction of ethylene oxide side chains in the polymer matrix evolve with the same trends in both measurement techniques. We conclude from this correlation that trEFM data reflect, at the nanoscale, the same ionic processes probed in conventional EIS at the device level. Finally, as an example application for emerging materials syntheses, we use trEFM and infrared photoinduced force microscopy (PiFM) to image a diblock copolymer electrolyte for next-generation solid-state energy storage applications.

Materials Science in the AI age: high-throughput library generation, machine learning and a pathway from correlations to the underpinning physics

The use of advanced data analytics and applications of statistical and machine learning approaches ('AI') to materials science is experiencing explosive growth recently. In this prospective, we review recent work focusing on generation and application of libraries from both experiment and theoretical tools, across length scales. The available library data both enables classical correlative machine learning, and also opens the pathway for exploration of underlying causative physical behaviors. We highlight the key advances facilitated by this approach, and illustrate how modeling, macroscopic experiments and atomic-scale imaging can be combined to dramatically accelerate understanding and development of new material systems via a statistical physics framework. These developments point towards a data driven future wherein knowledge can be aggregated and used collectively, accelerating the advancement of materials science.

Quantitative comparison of closed-loop and dual harmonic Kelvin probe force microscopy techniques

Kelvin probe force microscopy (KPFM) is a widely used technique to map surface potentials at the nanometer scale. In traditional KPFM, a feedback loop regulates the DC bias applied between a sharp conductive probe and a sample to nullify the electrostatic force (closed-loop operation). In comparison, open-loop techniques such as dual harmonic KPFM (DH-KPFM) are simpler to implement, are less sensitive to artefacts, offer the unique ability to probe voltage sensitive materials, and operate in liquid environments. Here, we directly compare the two techniques in terms of their bandwidth and sensitivity to instrumentation artefacts. Furthermore, we introduce a new correction for traditional KPFM termed "setpoint correction," which allows us to obtain agreement between open and closed-loop techniques within 1%. Quantitative validation of DH-KPFM may lead to a wider adoption of open-loop KPFM techniques by the scanning probe community.

Time resolved surface photovoltage measurements using a big data capture approach to KPFM

Optoelectronic behavior in materials such as organic/inorganic hybrid perovskites depend on a complex interplay between fast (electronic) and slower (ionic) processes. These processes are thought to be influenced by structural inhomogeneities (e.g. interfaces and grain boundaries) bringing forward the necessity for development of techniques capable of correlating nanostructure and photo-transport behavior. While Kelvin probe force microscopy (KPFM) is ideally suited to map surface potentials on relevant length scales, it lacks sufficient temporal resolution to extract the meaningful system dynamics. Here, we develop a time resolved surface photovoltage (SPV) measurement based on full information capture of the photodetector stream during open loop KPFM operation. G-Mode, or G-KPFM allows quantification of SPV with microsecond temporal and nanoscale spatial resolution. Using this technique, we observe concurrent spatial and fast temporal variations in the SPV generated across a methylammonium lead bromide (MAPbBr3) thin film, a possible indicator relating microstructure with heterogenous photo-transport behavior. We further demonstrate the advantage of adopting big data analytics including unsupervised clustering methods to quickly discern spatial variability in the information rich SPV dataset. Beyond G-KPFM, such clustering methods will be useful for interpretation of the multidimensional datasets arising from the growing number of time resolved KPFM approaches now available.

Tuning Oxygen Vacancy Diffusion through Strain in SrTiO3 Thin Films

Understanding diffusion of oxygen vacancies in oxides under different external stimuli is crucial for the design of ion-based electronic devices, improvement of catalytic performance, and so forth. In this manuscript, using an external electric field produced by an atomic force microscopy tip, we obtain the room-temperature diffusion coefficient of oxygen-vacancies in thin films of SrTiO₃ under compressive/tensile epitaxial strain. Tensile strain produces a substantial increase of the diffusion coefficient, facilitating the mobility of vacancies through the film. Additionally, the effect of tip bias, pulse time, and temperature on the local concentration of vacancies is investigated. These are important parameters of control in the production and stabilization of nonvolatile states in ion-based devices. Our findings show the key role played by strain for the control of oxygen vacancy migration in thin-film oxides.

Mapping intrinsic electromechanical responses at the nanoscale via sequential excitation scanning probe microscopy empowered by deep data

Ever-increasing hardware capabilities and computation powers have enabled acquisition and analysis of big scientific data at the nanoscale routine, though much of the data acquired often turn out to be redundant, noisy and/or irrelevant to the problems of interest, and it remains nontrivial to draw clear mechanistic insights from pure data analytics. In this work, we use scanning probe microscopy (SPM) as an example to demonstrate deep data methodology for nanosciences, transitioning from brute-force analytics such as data mining, correlation analysis and unsupervised classification to informed and/or targeted causative data analytics built on sound physical understanding. Three key ingredients of such deep data analytics are presented. A sequential excitation scanning probe microscopy (SE-SPM) technique is first developed to acquire high-quality, efficient and physically relevant data, which can be easily implemented on any standard atomic force microscope (AFM). Brute-force physical analysis is then carried out using a simple harmonic oscillator (SHO) model, enabling us to derive intrinsic electromechanical coupling of interest. Finally, principal component analysis (PCA) is carried out, which not only speeds up the analysis by four orders of magnitude, but also allows a clear physical interpretation of its modes in combination with SHO analysis. A rough piezoelectric material has been probed using such a strategy, enabling us to map its intrinsic electromechanical properties at the nanoscale with high fidelity, where conventional methods fail. The SE in combination with deep data methodology can be easily adapted for other SPM techniques to probe a wide range of functional phenomena at the nanoscale.

Towards nanoscale electrical measurements in liquid by advanced KPFM techniques: a review

Fundamental mechanisms of energy storage, corrosion, sensing, and multiple biological functionalities are directly coupled to electrical processes and ionic dynamics at solid-liquid interfaces. In many cases, these processes are spatially inhomogeneous taking place at grain boundaries, step edges, point defects, ion channels, etc and possess complex time and voltage dependent dynamics. This necessitates time-resolved and real-space probing of these phenomena. In this review, we discuss the applications of force-sensitive voltage modulated scanning probe microscopy (SPM) for probing electrical phenomena at solid-liquid interfaces. We first describe the working principles behind electrostatic and Kelvin probe force microscopies (EFM & KPFM) at the gas-solid interface, review the state of the art in advanced KPFM methods and developments to (i) overcome limitations of classical KPFM, (ii) expand the information accessible from KPFM, and (iii) extend KPFM operation to liquid environments. We briefly discuss the theoretical framework of electrical double layer (EDL) forces and dynamics, the implications and breakdown of classical EDL models for highly charged interfaces or under high ion concentrations, and describe recent modifications of the classical EDL theory relevant for understanding nanoscale electrical measurements at the solid-liquid interface. We further review the latest achievements in mapping surface charge, dielectric constants, and electrodynamic and electrochemical processes in liquids. Finally, we outline the key challenges and opportunities that exist in the field of nanoscale electrical measurements in liquid as well as providing a roadmap for the future development of liquid KPFM.

High-veracity functional imaging in scanning probe microscopy via Graph-Bootstrapping

The key objective of scanning probe microscopy (SPM) techniques is the optimal representation of the nanoscale surface structure and functionality inferred from the dynamics of the cantilever. This is particularly pertinent today, as the SPM community has seen a rapidly growing trend towards simultaneous capture of multiple imaging channels and complex modes of operation involving high-dimensional information-rich datasets, bringing forward the challenges of visualization and analysis, particularly for cases where the underlying dynamic model is poorly understood. To meet this challenge, we present a data-driven approach, Graph-Bootstrapping, based on low-dimensional manifold learning of the full SPM spectra and demonstrate its successes for high-veracity mechanical mapping on a mixed polymer thin film and resolving irregular hydration structure of calcite at atomic resolution. Using the proposed methodology, we can efficiently reveal and hierarchically represent salient material features with rich local details, further enabling denoising, classification, and high-resolution functional imaging.

Identifying Nanoscale Structure-Function Relationships Using Multimodal Atomic Force Microscopy, Dimensionality Reduction, and Regression Techniques

Correlating nanoscale chemical specificity with operational physics is a long-standing goal of functional scanning probe microscopy (SPM). We employ a data analytic approach combining multiple microscopy modes using compositional information in infrared vibrational excitation maps acquired via photoinduced force microscopy (PiFM) with electrical information from conductive atomic force microscopy. We study a model polymer blend comprising insulating poly(methyl methacrylate) (PMMA) and semiconducting poly(3-hexylthiophene) (P3HT). We show that PiFM spectra are different from FTIR spectra but can still be used to identify local composition. We use principal component analysis to extract statistically significant principal components and principal component regression to predict local current and identify local polymer composition. In doing so, we observe evidence of semiconducting P3HT within PMMA aggregates. These methods are generalizable to correlated SPM data and provide a meaningful technique for extracting complex compositional information that is impossible to measure from any one technique.

Deep data analysis via physically constrained linear unmixing: universal framework, domain examples, and a community-wide platform

Many spectral responses in materials science, physics, and chemistry experiments can be characterized as resulting from the superposition of a number of more basic individual spectra. In this context, unmixing is defined as the problem of determining the individual spectra, given measurements of multiple spectra that are spatially resolved across samples, as well as the determination of the corresponding abundance maps indicating the local weighting of each individual spectrum. Matrix factorization is a popular linear unmixing technique that considers that the mixture model between the individual spectra and the spatial maps is linear. Here, we present a tutorial paper targeted at domain scientists to introduce linear unmixing techniques, to facilitate greater understanding of spectroscopic imaging data. We detail a matrix factorization framework that can incorporate different domain information through various parameters of the matrix factorization method. We demonstrate many domain-specific examples to explain the expressivity of the matrix factorization framework and show how the appropriate use of domain-specific constraints such as non-negativity and sum-to-one abundance result in physically meaningful spectral decompositions that are more readily interpretable. Our aim is not only to explain the off-the-shelf available tools, but to add additional constraints when ready-made algorithms are unavailable for the task. All examples use the scalable open source implementation from https://github.com/ramkikannan/nmflibrary that can run from small laptops to supercomputers, creating a user-wide platform for rapid dissemination and adoption across scientific disciplines.

Ultrafast current imaging by Bayesian inversion

Spectroscopic measurements of current–voltage curves in scanning probe microscopy is the earliest and one of the most common methods for characterizing local energy-dependent electronic properties, providing insight into superconductive, semiconductor, and memristive behaviors. However, the quasistatic nature of these measurements renders them extremely slow. Here, we demonstrate a fundamentally new approach for dynamic spectroscopic current imaging via full information capture and Bayesian inference. This general-mode I–V method allows three orders of magnitude faster measurement rates than presently possible. The technique is demonstrated by acquiring I–V curves in ferroelectric nanocapacitors, yielding >100,000 I–V curves in <20 min. This allows detection of switching currents in the nanoscale capacitors, as well as determination of the dielectric constant. These experiments show the potential for the use of full information capture and Bayesian inference toward extracting physics from rapid I–V measurements, and can be used for transport measurements in both atomic force and scanning tunneling microscopy.

Scanning probe microscopy is widely used to characterize material properties with atomic resolution, yet electronic property mapping is normally constrained by slow data acquisition. Somnath et al. show a current–voltage method, which enables fast electronic spectroscopy mapping over micrometer-sized areas.

Breaking the Time Barrier in Kelvin Probe Force Microscopy: Fast Free Force Reconstruction Using the G-Mode Platform

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 sub-bandwidth 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., <20 μs) to be performed at regular KPFM scan speeds. F³R-KPFM is demonstrated for exploration of ion migration in organometallic halide perovskite materials and shown to allow spatiotemporal imaging of positively charged ion migration under applied electric field, as well as subsequent formation of accumulated charges at the perovskite/electrode interface. In this work, we demonstrate quantitative F³R-KPFM measurements-however, we fully expect the F³R approach to be valid for all modes of noncontact AFM operation, including noninvasive probing of ultrafast electrical and magnetic dynamics.

Recent advances in hybrid measurement methods based on atomic force microscopy and surface sensitive measurement techniques

This review summaries the recent progress of the combination of optical and non-optical surface sensitive techniques with the atomic force microscopy.

Rapid mapping of polarization switching through complete information acquisition

Polarization switching in ferroelectric and multiferroic materials underpins a broad range of current and emergent applications, ranging from random access memories to field-effect transistors, and tunnelling devices. Switching in these materials is exquisitely sensitive to local defects and microstructure on the nanometre scale, necessitating spatially resolved high-resolution studies of these phenomena. Classical piezoresponse force microscopy and spectroscopy, although providing necessary spatial resolution, are fundamentally limited in data acquisition rates and energy resolution. This limitation stems from their two-tiered measurement protocol that combines slow (∼1 s) switching and fast (∼10 kHz-1 MHz) detection waveforms. Here we develop an approach for rapid probing of ferroelectric switching using direct strain detection of material response to probe bias. This approach, facilitated by high-sensitivity electronics and adaptive filtering, enables spectroscopic imaging at a rate 3,504 times faster the current state of the art, achieving high-veracity imaging of polarization dynamics in complex microstructures.

Imaging via complete cantilever dynamic detection: general dynamic mode imaging and spectroscopy in scanning probe microscopy

We develop and implement a multifrequency spectroscopy and spectroscopic imaging mode, referred to as general dynamic mode (GDM), that captures the complete spatially- and stimulus dependent information on nonlinear cantilever dynamics in scanning probe microscopy (SPM). GDM acquires the cantilever response including harmonics and mode mixing products across the entire broadband cantilever spectrum as a function of excitation frequency. GDM spectra substitute the classical measurements in SPM, e.g. amplitude and phase in lock-in detection. Here, GDM is used to investigate the response of a purely capacitively driven cantilever. We use information theory techniques to mine the data and verify the findings with governing equations and classical lock-in based approaches. We explore the dependence of the cantilever dynamics on the tip-sample distance, AC and DC driving bias. This approach can be applied to investigate the dynamic behavior of other systems within and beyond dynamic SPM. GDM is expected to be useful for separating the contribution of different physical phenomena in the cantilever response and understanding the role of cantilever dynamics in dynamic AFM techniques.