Exploring surface charge dynamics: implications for AFM height measurements in 2D materials

• Mario Navarro-Rodriguez,
• Andres M. Somoza and
• Elisa Palacios-Lidon

Beilstein J. Nanotechnol. 2024, 15, 767–780, doi:10.3762/bjnano.15.64

• the dissipation. In this mode, the amplitude reduction may be due to (i) the tip–sample interaction (conservative or non-conservative), which shifts the resonance frequency and, therefore, makes the excitation go out of resonance, (ii) non-conservative interactions, which dissipate parts of the

• identify, in addition to the previously described interactions, an additional contribution to the tip–sample interaction due to the movement of charges on the surface induced by the oscillating tip. To understand and quantify this mechanism, we have proposed a very general model that solves Maxwell’s

• , GO is a hydrophilic insulating material [72], while rGO exhibits a hydrophobic and more conductive nature [69][73][74][75], both dependent on the degree of reduction. This stark contrast provides an ideal heterogeneous sample to study the tip–sample interaction of co-deposited GO and rGO on

Enhancing higher-order modal response in multifrequency atomic force microscopy with a coupled cantilever system

• Wendong Sun,
• Jianqiang Qian,
• Yingzi Li,
• Yanan Chen,
• Zhipeng Dou,
• Rui Lin,
• Peng Cheng,
• Xiaodong Gao,
• Quan Yuan and
• Yifan Hu

Beilstein J. Nanotechnol. 2024, 15, 694–703, doi:10.3762/bjnano.15.57

• beam. They are shown in Figure 1a. The Bode plots of the non-contact tip–sample interaction [12] and the contact tip–sample interaction [23] can be obtained through transfer function analysis. The results indicate that the higher-order modal response of the traditional rectangular cantilever gradually

Stiffness calibration of qPlus sensors at low temperature through thermal noise measurements

• Laurent Nony,
• Sylvain Clair,
• Daniel Uehli,
• Aitziber Herrero,
• Jean-Marc Themlin,
• Andrea Campos,
• Franck Para,
• Alessandro Pioda and
• Christian Loppacher

Beilstein J. Nanotechnol. 2024, 15, 580–602, doi:10.3762/bjnano.15.50

• to perform frequency shift spectroscopy to quantitatively evaluate the tip–sample interaction forces and potentials above individual atoms or molecules. The stiffness of the probe, k, is then required to perform the frequency shift-to-force conversion. However, this quantity is generally known with

Enhanced feedback performance in off-resonance AFM modes through pulse train sampling

• Mustafa Kangül,
• Navid Asmari,
• Santiago H. Andany,
• Marcos Penedo and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2024, 15, 134–143, doi:10.3762/bjnano.15.13

• vertical force changes during a defined time window of the tip–sample interaction. Through this, we use multiple samples in the proximity of the maximum force for the feedback loop, rather than only one sample at the maximum force instant. This method leads to improved topography tracking at a given ORT

• advantage of the tip–sample interaction between the first contact point and the maximum force instant. Here, we present a detailed analysis of how the sampling rate and delay in the conventional control method in ORT modes intrinsically limit the closed-loop control of the cantilever deflection and

• the proposed method, the reference curve is calculated by averaging multiple recorded waveforms to reduce the noise level. However, this reference only represents the tip–sample interaction for one given material, which can lead to over- or undercorrection of the interaction when the tip touches a

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

• with respect to the cutoff frequency fc of carrier transport between the bulk and interface states and measuring the difference in CPD by KPFM. In high–low KPFM, frequency modulation (FM) KPFM (FM-KPFM) combined with FM-AFM is used to detect the tip–sample interaction force. FM-KPFM has several

• amplitudes, but they can qualitatively explain the behavior of Δf–Vdc curves. Experimental Figure 4 shows the block diagram of AFM and high–low KPFS using AC bias voltages with high and low frequencies. The FM method was used to detect the tip–sample interaction force. The cantilever displacement signal

A cantilever-based, ultrahigh-vacuum, low-temperature scanning probe instrument for multidimensional scanning force microscopy

• Hao Liu,
• Zuned Ahmed,
• Sasa Vranjkovic,
• Manfred Parschau,
• Andrada-Oana Mandru and
• Hans J. Hug

Beilstein J. Nanotechnol. 2022, 13, 1120–1140, doi:10.3762/bjnano.13.95

• tip–sample interaction. However, because of the macroscopic size of the tuning fork, the high stiffness of the sensor goes together with a low resonance frequency typically around 30 kHz. This substantially limits the minimally measurable tip–sample interaction force gradients such that very small AFM

• constant is generally much smaller than the measured derivative of the tip–sample interaction force [61]. The force constant of a rectangular cantilever and its first flexural mode stiffness, respectively, are given by: where ρSi = 2331 kg/m3 and ESi = 1.69 × 1011 N/m2 are the density and the elastic

• measurement of small magnetic forces and for MFM with optimized lateral resolution. To obtain atomic resolution, cantilevers with a higher stiffness are required to meet the stability criteria: or where Fts is the tip–sample interaction force. From Equation 9, the cantilever stiffness must surpass the highest

Quantitative dynamic force microscopy with inclined tip oscillation

• Philipp Rahe,
• Daniel Heile,
• Reinhard Olbrich and
• Michael Reichling

Beilstein J. Nanotechnol. 2022, 13, 610–619, doi:10.3762/bjnano.13.53

• force represents the component of the tip–sample force along this direction. Despite the formal and quantitative difference from the commonly considered vertical component the component along w delivers identical physical insights into the tip–sample interaction. Appendix: Mathematical Derivations AFM

Cantilever signature of tip detachment during contact resonance AFM

• Devin Kalafut,
• Ryan Wagner,
• Maria Jose Cadena,
• Anil Bajaj and
• Arvind Raman

Beilstein J. Nanotechnol. 2021, 12, 1286–1296, doi:10.3762/bjnano.12.96

• defined as: where u(L1,t) is the deflection of the cantilever about the equilibrium at the location of the probe tip. The tip–sample interaction FTS is rooted in the Derjaguin, Muller, and Toporov (DMT) model of adhesive contact between particles [34], but modified via works by Shaik et al. [35] to

Two dynamic modes to streamline challenging atomic force microscopy measurements

• Alexei G. Temiryazev,
• Andrey V. Krayev and
• Marina P. Temiryazeva

Beilstein J. Nanotechnol. 2021, 12, 1226–1236, doi:10.3762/bjnano.12.90

• and sharp probes in the attraction regime means that the contact area is small and the tip–sample interaction is negligible. On the one hand, this allows for high-quality imaging of loosely attached and soft objects, even if they have a high aspect ratio. For example, Figure 2d shows a film of single

• change in the resonant frequency. It depends on the strength of the tip–sample interaction and often has a better (compared to topography) contrast. Figure 4 shows an example of the use of DM. We investigated the lamellar structure of a self-assembled layer of palmityl palmitate on the surface of highly

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

• 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

• -KPFM [27][28]. The benefit of a CL KPFM method is that the CPD is readily obtained in the form of a final product that is assembled in a map over the scanned area. However, the detailed response of the electrostatic tip–sample interaction is not available in CL KPFM, so post-processing and modeling of

• the proximity of the surface, might inadvertently include contributions from the van der Waals tip–sample interaction to the measured CPD. In the current OL KPFM-PFT implementation, all these impediments are avoided by precisely controlling the synchronization of the bias modulation with the PFT

Reducing molecular simulation time for AFM images based on super-resolution methods

• Zhipeng Dou,
• Jianqiang Qian,
• Yingzi Li,
• Rui Lin,
• Jianhai Wang,
• Peng Cheng and
• Zeyu Xu

Beilstein J. Nanotechnol. 2021, 12, 775–785, doi:10.3762/bjnano.12.61

• distance). The cut-off distance for the C–C interaction is 1.19 nm. The cut-off distance for the Si–C interaction is changed to observe the impact on the simulation. Increasing the cut-off distance increases the number of atoms in the tip–sample interaction but the result is more accurate. For the gold

• . In the scan, the tip is parallel to the sample surface in steps of 0.1 Å. After scanning 51 points, the tip turns to the next line until all are scanned. Then, the average energy map of the tip–sample interaction is obtained. In a quasi-static simulation, the tip is not excited and the conical tip is

• simulated image [35]. Filters of spatial sizes of 9 × 9, 5 × 5, and 5 × 5 were used. The flow chart of the proposed SRCNN reconstruction method is shown in Figure 4. First, we use molecular dynamics simulation to obtain energy maps of the tip–sample interaction with low-resolution. Different from the full

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

• at different areas of the Moiré superstructure [23]. Additionally, such a set of data enables us to obtain maps of constant tip–sample interaction forces that allow for the quantification of the corrugation of the Moiré superstructure. To obtain such data we map the Δf signal at constant oscillation

Application of contact-resonance AFM methods to polymer samples

• Sebastian Friedrich and
• Brunero Cappella

Beilstein J. Nanotechnol. 2020, 11, 1714–1727, doi:10.3762/bjnano.11.154

• b, density ρ, and Young’s modulus Et. The tip mass, being typically much smaller than the cantilever mass, is neglected. The tip is located at a distance L1 < L from the clamped end of the cantilever. The flexural spring constant of the cantilever is [2]. The tip–sample interaction can be modeled

• by a vertical and a horizontal spring and a dashpot accounting for dissipative forces [16][26]. Yet, these sophisticated models lead to rather complex equations with a large number of parameters. In the simplest model, the tip–sample interaction is completely elastic and along a direction normal to

An atomic force microscope integrated with a helium ion microscope for correlative nanoscale characterization

• Santiago H. Andany,
• Gregor Hlawacek,
• Stefan Hummel,
• Charlène Brillard,
• Mustafa Kangül and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2020, 11, 1272–1279, doi:10.3762/bjnano.11.111

• vacuum. The scanning electron microscope (SEM) was first combined with scanning tunneling microscopy (STM) [2][3], allowing for the visual observation at the tip–sample interaction point with the SEM. Later, Ermakov et al. [4] successfully integrated an AFM into an SEM for the first time, enabling

Revealing the local crystallinity of single silicon core–shell nanowires using tip-enhanced Raman spectroscopy

• Marius van den Berg,
• Ardeshir Moeinian,
• Arne Kobald,
• Yu-Ting Chen,
• Anke Horneber,
• Steffen Strehle,
• Alfred J. Meixner and
• Dai Zhang

Beilstein J. Nanotechnol. 2020, 11, 1147–1156, doi:10.3762/bjnano.11.99

• excited stronger by the evanescent electromagnetic near field at the tip apex. The highly improved optical resolution achieved with TERS depends strongly on the tip–sample interaction. When the sample is positioned within close proximity of the excited tip apex, the substrate material gains influence via

Extracting viscoelastic material parameters using an atomic force microscope and static force spectroscopy

• Cameron H. Parvini,
• M. A. S. R. Saadi and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2020, 11, 922–937, doi:10.3762/bjnano.11.77

• choices available for viscoelastic models in AFM indentation problems, it is helpful to begin with the viscoelastic correspondence principle framework mentioned above. An AFM tip–sample interaction involves measuring force and deformation, which can then be compared to the solution of a contact problem

• exposed to an instantaneous constant stress [17][18]. While applicable for this type of study, the tip–sample interaction during AFM experiments does not apply a constant force (i.e., stress) as a function of the time. The load history is more reminiscent of a discrete impulse function in which the

Quantitative determination of the interaction potential between two surfaces using frequency-modulated atomic force microscopy

• Nicholas Chan,
• Carrie Lin,
• Tevis Jacobs,
• Robert W. Carpick and
• Philip Egberts

Beilstein J. Nanotechnol. 2020, 11, 729–739, doi:10.3762/bjnano.11.60

• control of environment and probe/sample materials [36][37]. Therefore, we seek to leverage these advances to create a methodology for better validation of empirical pair potentials. In particular, we will do this by combining measurements of tip–sample interaction forces and experimental tip apex

• microscopy FM-AFM is a mode of AFM that allows for the probing of tip–sample interaction forces with the possibility of atomic resolution [41]. In this method, the probe is oscillated at its fundamental flexural resonance frequency (i.e., normal to the sample) and at a constant amplitude, while it is scanned

• laterally relative to the sample. A piezoactuator acting in the z-direction brings the probe closer or further from the sample. Due to non-linear tip–sample interaction forces, the resonance frequency of the oscillating cantilever will shift. This shift can be used as a feedback signal to measure the sample

Stochastic excitation for high-resolution atomic force acoustic microscopy imaging: a system theory approach

• Edgar Cruz Valeriano,
• José Juan Gervacio Arciniega,
• Christian Iván Enriquez Flores,
• Susana Meraz Dávila,
• Joel Moreno Palmerin,
• Martín Adelaido Hernández Landaverde,
• Yuri Lizbeth Chipatecua Godoy,
• Aime Margarita Gutiérrez Peralta,
• Rafael Ramírez Bon and
• José Martín Yañez Limón

Beilstein J. Nanotechnol. 2020, 11, 703–716, doi:10.3762/bjnano.11.58

• that gives a qualitative relationship between a set of contact resonance frequencies and the indentation modulus. It is based on white-noise excitation of the tip–sample interaction and uses system theory for the extraction of the resonance modes. During conventional scanning, for each pixel, the tip

• to tip–sample interaction. The frequency shifts can be used with a suitable model to calculate the mechanical properties of the sample material. This can be achieved by an external actuator or by an actuator attached to the cantilever holder chip [1][6][7][8][9][10][11]. The methods that use the

• ]. Here, a mathematical model that describes the resonance frequencies for a free cantilever and a cantilever at contact with the sample is calculated for stochastic perturbations of the tip–sample interaction. For this reason, the technique is referred to as stochastic atomic force acoustic microscopy (S

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

• the work of Hembacher and co-workers [37], the an values correspond to higher harmonics of the cantilever oscillation, as indicated in Equation 10, where the tip–sample interaction force exhibits short range compared to the full cantilever oscillation: The an values decrease rapidly with increasing n

• second case, we performed a numerical simulation for a dynamic AFM experiment that operates in the attractive tip–sample interaction regime. For this we have integrated the equation of motion of a spring–mass–dashpot model (Equation 21), customarily used to model dynamic AFM [45], where meff is the

• effective mass of the cantilever, f0 its natural frequency, k its stiffness and Q its quality factor: Fexcitation is the sinusoidal driving force and the tip–sample interaction force, Finteraction, is based on the Hamaker equation [42]. The simulation parameters are provided in Table 1. In the power

Atomic force acoustic microscopy reveals the influence of substrate stiffness and topography on cell behavior

• Yan Liu,
• Li Li,
• Xing Chen,
• Ying Wang,
• Meng-Nan Liu,
• Jin Yan,
• Liang Cao,
• Lu Wang and
• Zuo-Bin Wang

Beilstein J. Nanotechnol. 2019, 10, 2329–2337, doi:10.3762/bjnano.10.223

• describe the vibrations of the cantilever, the contact stiffness of the tip–sample interaction can be estimated [27][28]. For one-phase homogeneous materials, the detected vibrations will remain relatively uniform, while for inhomogeneous materials, the vibrational amplitude depends on the elastic

Ion mobility and material transport on KBr in air as a function of the relative humidity

• Dominik J. Kirpal,
• Korbinian Pürckhauer,
• Alfred J. Weymouth and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2019, 10, 2084–2093, doi:10.3762/bjnano.10.203

• important. AFM enables high lateral resolution, although the imaging of structures with rough topographies is challenging. When scanning rugged surfaces the back structure of the tip apex becomes more important. As the tip follows the surface while keeping the tip–sample interaction constant, side effects

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

• Schottky barrier in ambient atmosphere to stable materials. KPFM is an alternative way for mapping the changes in the surface contact potential [19][20][26] and reduces force and time of the tip–sample interaction, which in turn reduces the oxidation of the material. The NIs were embedded by local Au

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

• surface potentials [14][15][16][17][18], and other techniques that exploit non-linear signal mixing or heterodyning to extract the time evolution of the tip–sample interaction [19][20]. All of these techniques share a common goal of furthering the understanding of charge generation and transport processes

• : with the integral taken over one cycle (1/f0). Thus far we have only made an assumption regarding the functional form of the tip–sample capacitance. This relation (Equation 8) is thus valid for arbitrary oscillation amplitudes and timescales as long as the tip–sample interaction remains a small

• time-dependent tip–sample interaction. Application to ionic transport measurements To accurately quantify ionic transport requires the capability to fully resolve the functional form of a stretched exponential response to extract the two main parameters of interest, τ and β. To test the suitability of

Investigation of CVD graphene as-grown on Cu foil using simultaneous scanning tunneling/atomic force microscopy

• Majid Fazeli Jadidi,
• Umut Kamber,
• Oğuzhan Gürlü and
• H. Özgür Özer

Beilstein J. Nanotechnol. 2018, 9, 2953–2959, doi:10.3762/bjnano.9.274

• topography in this work resulted in maxima in between the two C atoms, which is supported by theoretical calculations. Such an observation would not be possible without simultaneous acquisition of tunnel current and force interaction. Under the typical STM imaging conditions of graphene, the tip–sample

• interaction force is in repulsive regime. This behavior, which has been observed ever since the very early STM results of the HOPG surface, is shown to be the case in graphene surface as well. Hence atomic relaxations might be quite influential in STM imaging of graphene. The contrast mechanisms could be

In situ characterization of nanoscale contaminations adsorbed in air using atomic force microscopy

• Jesús S. Lacasa,
• Lisa Almonte and
• Jaime Colchero

Beilstein J. Nanotechnol. 2018, 9, 2925–2935, doi:10.3762/bjnano.9.271

• contamination; tip cleaning; tip–sample interaction; van der Waals interaction; Introduction Surface science is fundamental to understand many processes in industrial applications, environmental science, biology, medicine and phenomena such as self-assembly [1], friction [2][3] and wetting [4]. In any study

• approach [37][38][39][40]. As discussed above, AFM is fundamentally based on tip–sample interaction. In this context, we may interpret that the tip is one half of the system, the sample being the other half. Unfortunately, the tip is the half of the system that is not directly seen, making tip

• the other (described by the surface energy w(d)). In the context of the present work we note that Equation 1 may be understood in the following way: it separates the tip–sample interaction into a term describing the geometry (radius R) and a term w(d) describing the chemistry of the system. In the