Controllable physicochemical properties of WO_x thin films grown under glancing angle

• Rupam Mandal,
• Aparajita Mandal,
• Alapan Dutta,
• Rengasamy Sivakumar,
• Sanjeev Kumar Srivastava and
• Tapobrata Som

Beilstein J. Nanotechnol. 2024, 15, 350–359, doi:10.3762/bjnano.15.31

• uniformity. WSxM software was used to carry out AFM image analysis. Kelvin probe force microscopy (KPFM) was used to study the local work function of the WOx films. WOx samples were removed from the high-vacuum environment right before the KPFM measurements to avoid any contamination in air. For KPFM

• measurements, a conductive tip (Ti/Pt coated) having a resonance frequency of approx. 70 kHz, a stiffness of approx. 2 N·m−1, and a radius of curvature of approx. 30 nm was used for KPFM measurements. To examine the uniformity in work function values of each film, different regions on the sample surface were

• mapped. Also, variable scan angles and scan speeds (0.2 to 1 Hz) were used to avoid the undesired presence of artefacts in the measured data. A dry nitrogen atmosphere ensured a low humidity level of 8–10% during all the KPFM measurements [29]. Further, the I–V measurements on the WOx/p-Si

Dual-heterodyne Kelvin probe force microscopy

• Benjamin Grévin,
• Fatima Husainy,
• Dmitry Aldakov and
• Cyril Aumaître

Beilstein J. Nanotechnol. 2023, 14, 1068–1084, doi:10.3762/bjnano.14.88

• Benjamin Grevin Fatima Husainy Dmitry Aldakov Cyril Aumaitre Univ. Grenoble Alpes, CNRS, CEA, IRIG-SyMMES, 38000 Grenoble, France 10.3762/bjnano.14.88 Abstract We present a new open-loop implementation of Kelvin probe force microscopy (KPFM) that provides access to the Fourier spectrum of the

• achieved by using two numerical lock-in amplifiers configured in cascade. Dual-heterodyne KPFM (DHe-KPFM) can be used to map any harmonic (amplitude/phase) of the time-periodic surface potential at a standard scanning speed. The Fourier spectrum (series of harmonics) can also be recorded in spectroscopic

• mode (DHe-KPFM spectroscopy), and 2D dynamic images can be acquired in data cube mode. The capabilities of DHe-KPFM in terms of time-resolved measurements, surface photovoltage (SPV) imaging, and detection of weak SPV signals are demonstrated through a series of experiments on difference surfaces: a

Spatial mapping of photovoltage and light-induced displacement of on-chip coupled piezo/photodiodes by Kelvin probe force microscopy under modulated illumination

• Zeinab Eftekhari,
• Nasim Rezaei,
• Hidde Stokkel,
• Jian-Yao Zheng,
• Andrea Cerreta,
• Ilka Hermes,
• Minh Nguyen,
• Guus Rijnders and
• Rebecca Saive

Beilstein J. Nanotechnol. 2023, 14, 1059–1067, doi:10.3762/bjnano.14.87

• In this work, a silicon photodiode integrated with a piezoelectric membrane is studied by Kelvin probe force microscopy (KPFM) under modulated illumination. Time-dependent KPFM enables simultaneous quantification of the surface photovoltage generated by the photodiode as well as the resulting

• spatially map voltage-induced oscillation of various sizes of piezoelectric membranes without the photodiode to investigate their position- and size-dependent displacement. Keywords: Kelvin probe force microscopy (KPFM); light-driven micro/nano systems; piezoelectric membrane; surface photovoltage (SPV

• with atomic vertical resolution. In several studies, AFM has been used to determine photo-induced height/topography variation in organic–inorganic lead halide perovskites [15], nanosheets [16], and photosensitive polymers [17]. Kelvin probe force microscopy (KPFM), an electrostatic variant of AFM, can

Cross-sectional Kelvin probe force microscopy on III–V epitaxial multilayer stacks: challenges and perspectives

• Mattia da Lisca,
• José Alvarez,
• James P. Connolly,
• Nicolas Vaissiere,
• Karim Mekhazni,
• Jean Decobert and
• Jean-Paul Kleider

Beilstein J. Nanotechnol. 2023, 14, 725–737, doi:10.3762/bjnano.14.59

• technique for the analysis of an InP/GaInAs(P) multilayer stack. KPFM reveals a strong dependence on the local doping concentration, allowing for the detection of the surface potential of layers with a resolution as low as 20 nm. The analysis of the surface potential allowed for the identification of space

• charge regions and, thus, the presence of several junctions along the stack. Furthermore, a contrast enhancement in the surface potential image was observed when KPFM was performed under illumination, which is analysed in terms of the reduction of surface band bending induced by surface defects by

• photogenerated carrier distributions. The analysis of the KPFM data was assisted by means of theoretical modelling simulating the energy bands profile and KPFM measurements. Keywords: FM-KPFM; frequency-modulated Kelvin probe force microscopy; III–V multilayer stack; Kelvin probe modelling; KP modelling; SPV

High–low Kelvin probe force spectroscopy for measuring the interface state density

• Ryo Izumi,
• Masato Miyazaki,
• Yan Jun Li and
• Yasuhiro Sugawara

Beilstein J. Nanotechnol. 2023, 14, 175–189, doi:10.3762/bjnano.14.18

• Ryo Izumi Masato Miyazaki Yan Jun Li Yasuhiro Sugawara Department of Applied Physics, Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan 10.3762/bjnano.14.18 Abstract The recently proposed high–low Kelvin probe force microscopy (KPFM) enables evaluation

• [1][2][3]. Therefore, direct observation of semiconductor surfaces with nanoscale spatial resolution will become even more important for understanding and controlling the effects of these properties on devices and for evaluating semiconductor device operation. Kelvin probe force microscopy (KPFM) is

• known as a method that can measure the contact potential difference (CPD) between a tip and a sample with high spatial resolution [4][5]. KPFM is based on the detection of the electrostatic force between a tip and a sample using atomic force microscopy (AFM) [6][7][8]. CPD and topographic measurements

Utilizing the surface potential of a solid electrolyte region as the potential reference in Kelvin probe force microscopy

• Nobuyuki Ishida

Beilstein J. Nanotechnol. 2022, 13, 1558–1563, doi:10.3762/bjnano.13.129

• electrodes. In Kelvin probe force microscopy (KPFM) measurements on electrochemical cells, the surface potential is generally measured relative to electrical ground instead of a stable reference. Here, we show that the changes in the surface potential, measured using KPFM relative to the surface potential in

• the electrolyte region, is consistent with the changes in the electrode potential measured using a voltmeter relative to a reference electrode. These results demonstrate that the surface potential in the electrolyte region can be utilized as a stable potential reference when analyzing KPFM data

• . Keywords: electrochemistry; Kelvin probe force microscopy (KPFM); reference electrode; solid electrolyte; Introduction Kelvin probe force microscopy (KPFM) is a scanning probe technique for imaging surface potentials on the nanometer scale [1][2][3][4]. Its operating principle is based on detecting the

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

• Jason I. Kilpatrick,
• Emrullah Kargin and
• Brian J. Rodriguez

Beilstein J. Nanotechnol. 2022, 13, 922–943, doi:10.3762/bjnano.13.82

• 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

Direct measurement of surface photovoltage by AC bias Kelvin probe force microscopy

• Masato Miyazaki,
• Yasuhiro Sugawara and
• Yan Jun Li

Beilstein J. Nanotechnol. 2022, 13, 712–720, doi:10.3762/bjnano.13.63

• photocatalytic semiconductors. The local SPV is generally measured consecutively by Kelvin probe force microscopy (KPFM) in darkness and under illumination, in which thermal drift degrades spatial and energy resolutions. In this study, we propose the method of AC bias Kelvin probe force microscopy (AC-KPFM

• ), which controls the AC bias to nullify the modulated signal. We succeeded in directly measuring the local SPV by AC-KPFM with higher resolution, thanks to the exclusion of the thermal drift. We found that AC-KPFM can achieve a SPV response faster by about one to eight orders of magnitude than classical

• KPFM. Moreover, AC-KPFM is applicable in both amplitude modulation and frequency modulation mode. Thus, it contributes to advancing SPV measurements in various environments, such as vacuum, air, and liquids. This method can be utilized for direct measurements of changes in surface potential induced by

Measurement of polarization effects in dual-phase ceria-based oxygen permeation membranes using Kelvin probe force microscopy

• Kerstin Neuhaus,
• Christina Schmidt,
• Liudmila Fischer,
• Wilhelm Albert Meulenberg,
• Ke Ran,
• Joachim Mayer and
• Stefan Baumann

Beilstein J. Nanotechnol. 2021, 12, 1380–1391, doi:10.3762/bjnano.12.102

• was used as a model to demonstrate that a combination of polarization relaxation measurements and Kelvin probe force microscopy (KPFM)-based mapping of the Volta potential before and after the end of polarization can be used to determine the chemical diffusion coefficient of the ceria component of the

• composite. The KPFM measurements were performed at room temperature and show diffusion coefficients in the range of 3 × 10−13 cm2·s−1, which is comparable to values measured for single-phase Gd-doped ceria thin films using the same method. Keywords: ceria; diffusion coefficient; Kelvin probe force

• |ceria, ceria|electron conductor, and electron conductor|electron conductor). Kelvin probe force microscopy (KPFM) is an atomic force microscopy (AFM)-based measurement method that can measure the local surface potential (or Volta potential) of the sample [18][19]. The surface potential is a sensitive

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

• Gheorghe Stan and
• Pradeep Namboodiri

Beilstein J. Nanotechnol. 2021, 12, 1115–1126, doi:10.3762/bjnano.12.83

• (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

The role of convolutional neural networks in scanning probe microscopy: a review

• Ido Azuri,
• Irit Rosenhek-Goldian,
• Neta Regev-Rudzki,
• Georg Fantner and
• Sidney R. Cohen

Beilstein J. Nanotechnol. 2021, 12, 878–901, doi:10.3762/bjnano.12.66

• -topographical SPM technique is the study of ferroelectric switching [135]. This switching is a function of both reading and writing voltages, and can vary with experimental conditions such as time and temperature, and is further complicated by competing processes. The measurement technique was contact KPFM

Local stiffness and work function variations of hexagonal boron nitride on Cu(111)

• Abhishek Grewal,
• Yuqi Wang,
• Matthias Münks,
• Klaus Kern and
• Markus Ternes

Beilstein J. Nanotechnol. 2021, 12, 559–565, doi:10.3762/bjnano.12.46

• –4.5 V is due to varying contributions from the two interfaces of the dielectric layer. We therefore evaluate the unambiguous shift of the second peak at around 5.6–6.0 V as a measure for the local Φ variation. Our nc-AFM allows us to employ with Kelvin probe force microscopy (KPFM) a second

• , however, we find a significantly smaller average difference between valley and rim regions of only ΔΦ = 86 ± 16 meV when analysing the contact potential difference (CPD) data. This hints toward a lower lateral resolution of the KPFM measurement compared to the FER map. The Δf signal in KPFM originates

• corroborate that the h-BN monolayer is only weakly coupled to the Cu(111) surface as is evidenced by the large angular range of Moiré superstructures observed, which in turn leads to work function patterning. Using FER and KPFM maps we report a work function variation of 148 ± 17 and 86 ± 16 meV, respectively

Reconstruction of a 2D layer of KBr on Ir(111) and electromechanical alteration by graphene

• Zhao Liu,
• Antoine Hinaut,
• Stefan Peeters,
• Sebastian Scherb,
• Ernst Meyer,
• Maria Clelia Righi and
• Thilo Glatzel

Beilstein J. Nanotechnol. 2021, 12, 432–439, doi:10.3762/bjnano.12.35

• reduced by the decoupling effect of graphene, thus yielding different electrical and mechanical properties of the top KBr layer. Keywords: DFT; graphene; Ir(111); KBr; KPFM; nc-AFM; surface reconstruction; Introduction Many two-dimensional (2D) materials have excellent optical, mechanical

• Kelvin probe force microscopy (KPFM), as can be seen in Supporting Information File 1, Figure S3. To be able to tune this corrugated structure, a monolayer of graphene was prepared on Ir(111) before KBr deposition. Figure 4a shows a large-area topography of the Ir(111) surface, half of which is covered

• contamination and averaging effects in KPFM [51]. Conclusion In conclusion, a novel corrugated reconstruction of KBr was observed on Ir(111) by nc-AFM and confirmed by DFT simulations. It is attributed to the lattice symmetry of KBr with respect to the iridium substrate in one direction and a self-adjustment in

Fusion of purple membranes triggered by immobilization on carbon nanomembranes

• René Riedel,
• Natalie Frese,
• Fang Yang,
• Martin Wortmann,
• Raphael Dalpke,
• Daniel Rhinow,
• Norbert Hampp and
• Armin Gölzhäuser

Beilstein J. Nanotechnol. 2021, 12, 93–101, doi:10.3762/bjnano.12.8

• was used for topographical pictures with a smaller field of view as well as for electrostatic measurements. For PeakForce Kelvin probe force microscopy (PF-KPFM), a line is first scanned in PeakForce mode. In a second scan the same line is scanned with an adjustable height offset and using the

• sedimentation: (a, b) initial drop-casting experiments showing a low substrate coverage of approx. 35% and/or cluster formation. (c–f) Sedimentation in an electric field: (c, e) AFM image at different magnifications, (d) SEM image and (f) PF-KPFM image showing the uniform orientation of the PM fragments with

Atomic defect classification of the H–Si(100) surface through multi-mode scanning probe microscopy

• Jeremiah Croshaw,
• Thomas Dienel,
• Taleana Huff and
• Robert Wolkow

Beilstein J. Nanotechnol. 2020, 11, 1346–1360, doi:10.3762/bjnano.11.119

• also shown to have no effect on the contact potential difference of the surface as measured with KPFM (Figure 1 of [9]). We now move to a discussion of defects that affect a whole dimer, starting with dihydride pairs (Figure 2d) and single dihydrides (Figure 2e). Instead of a silicon bonding with its

Comparison of fresh and aged lithium iron phosphate cathodes using a tailored electrochemical strain microscopy technique

• Matthias Simolka,
• Hanno Kaess and
• Kaspar Andreas Friedrich

Beilstein J. Nanotechnol. 2020, 11, 583–596, doi:10.3762/bjnano.11.46

• solid electrolyte interface (SEI) on graphite anodes and HOPG [14][15][16], Li metal [17] and on cathode materials [18][19] as well as the changes in particle size during ageing [19][20]. Other AFM modes used for the analysis of ageing are, for example, Kelvin probe force microscopy (KPFM) and

• conductive AFM (CAFM). Luchkin et al. used KPFM to analyse the Li-ion distribution in graphite anodes and found a core–shell structure in aged graphite particles [21]. Wu et al. used KPFM to track the changes in the surface potential of LiCoO2 cathodes during ageing and found a decrease of the surface

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

• Berkin Uluutku and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 453–465, doi:10.3762/bjnano.11.37

• with a flat surface [42]. The imaging parameters are selected to resemble day-to-day large-amplitude experiments. The cantilever properties are similar to those of commercial cantilevers (e.g., BudgetSensors, ElectriMulti75-G conductively coated KPFM cantilevers). The Hamaker constant is chosen within

Implementation of data-cube pump–probe KPFM on organic solar cells

• Benjamin Grévin,
• Olivier Bardagot and
• Renaud Demadrille

Beilstein J. Nanotechnol. 2020, 11, 323–337, doi:10.3762/bjnano.11.24

• Benjamin Grevin Olivier Bardagot Renaud Demadrille Univ. Grenoble Alpes, CNRS, CEA, IRIG-SyMMES, 38000 Grenoble, France 10.3762/bjnano.11.24 Abstract An implementation of pump–probe Kelvin probe force microscopy (pp-KPFM) is reported that enables recording the time-resolved surface potential in

• single-point mode or over a 2D grid. The spectroscopic data are acquired in open z-loop configuration, which simplifies the pp-KPFM operation. The validity of the implementation is probed by measurements using electrical pumping. The dynamical photoresponse of a bulk heterojunction solar cell based on

• PTB7 and PC71BM is subsequently investigated by recording point-spectroscopy curves as a function of the optical power at the cathode and by mapping 2D time-resolved images of the surface photovoltage of the bare organic active layer. Keywords: bulk heterojunctions; Kelvin probe force microscopy (KPFM

Kelvin probe force microscopy work function characterization of transition metal oxide crystals under ongoing reduction and oxidation

• Dominik Wrana,
• Karol Cieślik,
• Wojciech Belza,
• Christian Rodenbücher,
• Krzysztof Szot and
• Franciszek Krok

Beilstein J. Nanotechnol. 2019, 10, 1596–1607, doi:10.3762/bjnano.10.155

• future energy production and storage. As the majority of applications involve the use of heterostructures, the most suitable characterization technique is Kelvin probe force microscopy (KPFM), which provides excellent energetic and lateral resolution. In this paper, we demonstrate precise

• significant variations among the different crystallographic facets were also observed. Despite the remarkable height of the TiO nanowires, KPFM was implemented to achieve a high lateral resolution of 15 nm, which is close to the topographical limit. In this study, we also show the unique possibility of

• method employing KPFM and local conductivity AFM for the characterization of the work function of transition metal oxides may help in understanding the impact of reduction and oxidation on electronic properties, which is of high importance in the development of effective sensing and catalytic devices

Kelvin probe force microscopy of the nanoscale electrical surface potential barrier of metal/semiconductor interfaces in ambient atmosphere

• Petr Knotek,
• Tomáš Plecháček,
• Jan Smolík,
• Petr Kutálek,
• Filip Dvořák,
• Milan Vlček,
• Jiří Navrátil and
• Čestmír Drašar

Beilstein J. Nanotechnol. 2019, 10, 1401–1411, doi:10.3762/bjnano.10.138

• nanosheets through the reaction with the Bi2Se3. The Schottky barrier formed by the 1D and 2D nanoinclusions was characterized by means of atomic force microscopy (AFM). We used Kelvin probe force microscopy (KPFM) in ambient atmosphere at the nanoscale and compared the results to those of ultraviolet

• photoelectron spectroscopy (UPS) in UHV at the macroscale. The existence of the Schottky barrier was demonstrated at +120 meV for the Mo layer and −80 meV for the Au layer reflecting the formation of MoSe2 and Au/Bi2Se3 alloy, respectively. The results of both methods (KPFM and UPS) were in good agreement. We

• material [19][20][21]; ii) by mapping of the different surface contact potential values by Kelvin probe force microscopy (KPFM) in the semicontact mode [19][22][23][24][25], or iii) by measuring the differences in thermal conductivity by scanning thermal microscopy (SThM) [19][20][26]. Shape, size

Imaging the surface potential at the steps on the rutile TiO₂(110) surface by Kelvin probe force microscopy

• Masato Miyazaki,
• Huan Fei Wen,
• Quanzhen Zhang,
• Yuuki Adachi,
• Jan Brndiar,
• Ivan Štich,
• Yan Jun Li and
• Yasuhiro Sugawara

Beilstein J. Nanotechnol. 2019, 10, 1228–1236, doi:10.3762/bjnano.10.122

• observed with a lateral resolution of several nanometers by Kelvin probe force microscopy (KPFM) [29][30]. However, the dependence of surface potential on direction and structure of steps such as [001], and has not yet been clarified. In scanning tunneling microscopy (STM) [31] studies, three typical

• preparation. The steps showed a higher photodegradation activity than the steps for aqueous solutions of methylene blue [23], indicating that the different step structures have different catalytic activities. KPFM measures the contact potential difference (CPD), corresponding to the difference in work

• function between the tip and the sample, on the basis of atomic force microscopy (AFM) [39][40]. Since the CPD strongly depends on the charge distribution on the surface, KPFM allows us to investigate the electrostatic properties of surfaces [41][42][43]. In this study, we measured the CPD around the steps

Influence of dielectric layer thickness and roughness on topographic effects in magnetic force microscopy

• Alexander Krivcov,
• Jasmin Ehrler,
• Marc Fuhrmann,
• Tanja Junkers and
• Hildegard Möbius

Beilstein J. Nanotechnol. 2019, 10, 1056–1064, doi:10.3762/bjnano.10.106

• tip bias. Kim et al. [11] used a capacitive coupling of electrostatic force modulation to separate the magnetic from the topographic signal. In our previous paper [14], we demonstrated that Kelvin force probe microscopy (KPFM) measurements as proposed by Jaafar et al. [13] show no difference between

• measurements above SPIONs and measurements above the substrate. The combination of KPFM and MFM can only eliminate the electrostatic contributions for structures larger than the tip size [13]. Measuring structures with dimensions similar or smaller than the tip size KPFM does not reduce the capacitive coupling

Comparing a porphyrin- and a coumarin-based dye adsorbed on NiO(001)

• Sara Freund,
• Antoine Hinaut,
• Nathalie Marinakis,
• Edwin C. Constable,
• Ernst Meyer,
• Catherine E. Housecroft and
• Thilo Glatzel

Beilstein J. Nanotechnol. 2019, 10, 874–881, doi:10.3762/bjnano.10.88

• investigated by Kelvin probe force microscopy (KPFM) [25]. This technique is used to observe and quantify the contact potential difference (CPD) changes between the metal oxide surface and the molecular layers and to determine the corresponding dipole moments. Results and Discussion Atomically clean NiO

• to the experimental results in Table 2. The data demonstrate that the parameters correspond nicely, highlighting the accuracy of the model. Charge-transfer direction studied by KPFM KPFM is an analytical method that can be applied to examine the change of the work function induced by the adsorption

• to facilitate the comparison between Cu-TCPP and C343, the CPD of NiO was set as reference (0 V) and all CPD values given below are relative values. The values of the CPD between the surface and the molecular islands measured by using KPFM [25] are given in Figure 5a and Figure 5b. These large-scale

Novel reversibly switchable wettability of superhydrophobic–superhydrophilic surfaces induced by charge injection and heating

• Xiangdong Ye,
• Junwen Hou and
• Dongbao Cai

Beilstein J. Nanotechnol. 2019, 10, 840–847, doi:10.3762/bjnano.10.84

• -contact area in the coating. The surface potential was measured at five points in each sample area. The results are shown in Table 1. Because there are many KPFM images (CPD) for the whole data set in Table 1, as an example, we have only shown the KPFM image for the point 1 to show the contact potential

Review of time-resolved non-contact electrostatic force microscopy techniques with applications to ionic transport measurements

• Aaron Mascaro,
• Yoichi Miyahara,
• Tyler Enright,
• Omur E. Dagdeviren and
• Peter Grütter

Beilstein J. Nanotechnol. 2019, 10, 617–633, doi:10.3762/bjnano.10.62

• -domain EFM to measure ionic transport [7][12], time-resolved electrochemical strain microscopy (ESM) to measure ionic transport [8][13], various time-resolved Kelvin probe force microscopy (KPFM) techniques that utilize either optical pump-probe or advanced signal processing to measure time-resolved

• implementations and analyses, we have restricted our review to exclude all pump–probe and KPFM techniques as these are generally unsuitable for probing ionic transport. For a recent review of all KPFM and related techniques, we refer the reader to [21]. We begin by describing the direct time-domain method and its

• . One example of this is in time-resolved Kelvin probe force microscopy (KPFM) experiments that measure the surface photovoltage of a sample as a function of time after a light source is pulsed. This was first implemented by Takihara et al. to measure the photovoltage dynamics of a sample at time scales