Noncontact Atomic Force Microscopy

doi:10.1007/978-3-319-15588-3

Cited by 74 publications

(6 citation statements)

References 7 publications

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“…A stiff qPlus cantilever design [49] (k 0 = 1800 N•m −1 , f 0 = 29077 Hz, Q = 60000) at an oscillation amplitude A osc = 50 pm enables the nc-AFM functionality. We calibrated the amplitude prior to the measurement atop the bare Cu(111) substrate [50]. The bias voltage V is applied to the substrate and the tunnelling current I is measured at the virtually grounded tip.…”

Section: Methodsmentioning

confidence: 99%

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

Grewal¹,

Wang²,

Münks³

et al. 2021

Beilstein J. Nanotechnol.

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Combined scanning tunnelling and atomic force microscopy using a qPlus sensor enables the measurement of electronic and mechanic properties of two-dimensional materials at the nanoscale. In this work, we study hexagonal boron nitride (h-BN), an atomically thin 2D layer, that is van der Waals-coupled to a Cu(111) surface. The system is of interest as a decoupling layer for functional 2D heterostructures due to the preservation of the h-BN bandgap and as a template for atomic and molecular adsorbates owing to its local electronic trapping potential due to the in-plane electric field. We obtain work function (Φ) variations on the h-BN/Cu(111) superstructure of the order of 100 meV using two independent methods, namely the shift of field emission resonances and the contact potential difference measured by Kelvin probe force microscopy. Using 3D force profiles of the same area we determine the relative stiffness of the Moiré region allowing us to analyse both electronic and mechanical properties of the 2D layer simultaneously. We obtain a sheet stiffness of 9.4 ± 0.9 N·m−1, which is one order of magnitude higher than the one obtained for h-BN/Rh(111). Using constant force maps we are able to derive height profiles of h-BN/Cu(111) showing that the system has a corrugation of 0.6 ± 0.2 Å, which helps to demystify the discussion around the flatness of the h-BN/Cu(111) substrate.

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Section: Methodsmentioning

confidence: 99%

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

Grewal¹,

Wang²,

Münks³

et al. 2021

Beilstein J. Nanotechnol.

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“…(5) (6) where α i = {1.8750, 4.6941, 7.8548, … } are coefficients defined by the characteristic equation of an oscillating rectangular cantilever with one free end [60]. Note that for a typical non-contact AFM experiment, the tip end of the cantilever can be considered as free because the cantilever force 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: (7) where ρ Si = 2331 kg/m 3 and E Si = 1.69 × 10 11 N/m 2 are the density and the elastic modulus of silicon, respectively; L, w, and t are the length, width, and thickness of the cantilever, respectively.…”

Section: Performance Of the Spm Relevant Afm Noise Sourcesmentioning

confidence: 99%

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

Liu¹,

Ahmed²,

Vranjkovic³

et al. 2022

Beilstein J. Nanotechnol.

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Cantilever-based atomic force microscopy (AFM) performed under ambient conditions has become an important tool to characterize new material systems as well as devices. Current instruments permit robust scanning over large areas, atomic-scale lateral resolution, and the characterization of various sample properties using multifrequency and multimodal AFM operation modes. Research of new quantum materials and devices, however, often requires low temperatures and ultrahigh vacuum (UHV) conditions and, more specifically, AFM instrumentation providing atomic resolution. For this, AFM instrumentation based on a tuning fork force sensor became increasingly popular. In comparison to microfabricated cantilevers, the more macroscopic tuning forks, however, lack sensitivity, which limits the measurement bandwidth. Moreover, multimodal and multifrequency techniques, such as those available in cantilever-based AFM carried out under ambient conditions, are challenging to implement. In this article, we describe a cantilever-based low-temperature UHV AFM setup that allows one to transfer the versatile AFM techniques developed for ambient conditions to UHV and low-temperature conditions. We demonstrate that such a cantilever-based AFM offers experimental flexibility by permitting multimodal or multifrequency operations with superior force derivative sensitivities and bandwidths. Our instrument has a sub-picometer gap stability and can simultaneously map not only vertical and lateral forces with atomic-scale resolution, but also perform rapid overview scans with the tip kept at larger tip–sample distances for robust imaging.

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“…Commercial AFMs mostly use proportional-integral (PI) or proportional-integral-derivative (PID)-type controllers. 1,29,39 To assess the performance of the proposed I&I controller in comparison with the classic control methods, we conducted comparative simulation using a PID controller of the form…”

Section: Comparison With Pid Controlmentioning

confidence: 99%

“…Since the AFM tip in tapping mode is under attractive nonlinear force, behavioral instability and chaos may occur in the tapping mode near the sample. 1 This instability creates hysteresis and jump phenomenon in the system, which causes some errors in the test results. 2 Chaos is commonly found in nonlinear dynamical systems, which is calamitous and can cause fatigue or damage to the system.…”

mentioning

confidence: 99%

Robust nonlinear control of atomic force microscope via immersion and invariance

Keighobadi

Hosseini-Pishrobat

Faraji

et al. 2018

Intl J Robust & Nonlinear

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This paper reports an immersion and invariance (I&I)-based robust nonlinear controller for atomic force microscope (AFM) applications. The AFM dynamics is prone to chaos, which, in practice, leads to performance degradation and inaccurate measurements. Therefore, we design a nonlinear tracking controller that stabilizes the AFM dynamics around a desired periodic orbit. To this end, in the tracking error state space, we define a target invariant manifold, on which the system dynamics fulfills the control objective. First, considering a nominal case with full state measurement and no modeling uncertainty, we design an I&I controller to render the target manifold exponentially attractive. Next, we consider an uncertain AFM dynamics, in which only the displacement of the probe cantilever is measured. In the framework of the I&I method, we recast the robust output feedback control problem as the immersion of the output feedback closed-loop system into the nominal full state one. For this purpose, we define another target invariant manifold that recovers the performance of the nominal control system. Moreover, to handle large uncertainty/disturbances, we incorporate the method of active disturbance rejection into the I&I output feedback control. Through Lyapunov-based analysis of the closed-loop stability and robustness, we show the semiglobal practical stability and convergence of the tracking error dynamics. Finally, we present a set of detailed, comparative software simulations to assess the effectiveness of the control method. KEYWORDSatomic force microscope, chaos, disturbance rejection control, immersion and invariance, output feedback control INTRODUCTIONAtomic force microscopes (AFMs) are useful tools for measuring intermolecular forces in electronics, identification of biological materials, materials science, and semiconductors. The main component of an AFM is a microcantilever with a sharp tip, which is connected to a piezoelectric. A photodiode sensor, which is sensitive to the microcantilever's end position, determines the tip displacement. When the tip approaches the sample substrate, the atomic force interaction changes the dynamics of the AFM tip and, consequently, the whole microscope. The AFMs can operate in different modes including contact, noncontact, and tapping modes. In the contact mode, the tip operates within the range of the repulsive Int J Robust Nonlinear Control. 2019;29:1031-1050.wileyonlinelibrary.com/journal/rnc

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Noncontact Atomic Force Microscopy

Cited by 74 publications

References 7 publications

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

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

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

Robust nonlinear control of atomic force microscope via immersion and invariance

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