Control theory for scanning probe microscopy revisited

• Julian Stirling

Beilstein J. Nanotechnol. 2014, 5, 337–345, doi:10.3762/bjnano.5.38

• higher harmonics of frequencies present in D(t) being generated by the exponential dependence in the tunnel junction. Conclusion We have derived an appropriate updated model to understand SPM feedback in the context of control theory. This model shows the intrinsic stability of the SPM feedback

Unlocking higher harmonics in atomic force microscopy with gentle interactions

• Sergio Santos,
• Victor Barcons,
• Josep Font and
• Albert Verdaguer

Beilstein J. Nanotechnol. 2014, 5, 268–277, doi:10.3762/bjnano.5.29

• (Barcelona), Spain CSIC - Consejo Superior de Investigaciones Cientificas, ICN2 Building ,08193 Bellaterra (Barcelona), Spain 10.3762/bjnano.5.29 Abstract In dynamic atomic force microscopy, nanoscale properties are encoded in the higher harmonics. Nevertheless, when gentle interactions and minimal

• invasiveness are required, these harmonics are typically undetectable. Here, we propose to externally drive an arbitrary number of exact higher harmonics above the noise level. In this way, multiple contrast channels that are sensitive to compositional variations are made accessible. Numerical integration of

• absence of an external excitation of higher harmonics. Higher harmonic phase shifts further provide the means to directly decouple the true topography from that induced by compositional heterogeneity. Keywords: atomic force microscopy; chemistry; composition; heterogeneity; higher harmonics; phase

Noise performance of frequency modulation Kelvin force microscopy

• Heinrich Diesinger,
• Dominique Deresmes and
• Thierry Mélin

Beilstein J. Nanotechnol. 2014, 5, 1–18, doi:10.3762/bjnano.5.1

• the probe–sample capacity is used, it is expected to be more sensitive to the very extremity of the tip [4], or because the use of probes with an increased fundamental resonance frequency makes the use of higher harmonics for simultaneous surface potential imaging inaccessible to the bandwidth of the

Peak forces and lateral resolution in amplitude modulation force microscopy in liquid

• Horacio V. Guzman and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2013, 4, 852–859, doi:10.3762/bjnano.4.96

• interaction force. The point-mass model is suitable if the contribution of higher modes to the cantilever motion is negligible [37]. This could be the case in liquid for small free amplitudes, say below 1.5 nm [38]. At higher amplitudes, the tip–surface force generates higher harmonics components, which could

Dynamic nanoindentation by instrumented nanoindentation and force microscopy: a comparative review

• Sidney R. Cohen and
• Estelle Kalfon-Cohen

Beilstein J. Nanotechnol. 2013, 4, 815–833, doi:10.3762/bjnano.4.93

• for [84]. The bandwidth advantage has been extended to the MHz range, allowing an access to higher harmonics [85][86][87][88][89]. This provides several advantages: Higher harmonics can be exploited to separate the mechanical measurement from the topographic feedback, the signal-to-noise ratio can be

Polynomial force approximations and multifrequency atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 352–360, doi:10.3762/bjnano.4.41

• , which is PS-rich and is a factor of two softer than the PMMA-domains. Similar results on the same model polymer system have been obtained with methods employing higher harmonics [15][29] and by ADFS [20]. Polynomial reconstruction from force quadrature data Polynomial force reconstruction is an

High-resolution nanomechanical analysis of suspended electrospun silk fibers with the torsional harmonic atomic force microscope

• Mark Cronin-Golomb and
• Ozgur Sahin

Beilstein J. Nanotechnol. 2013, 4, 243–248, doi:10.3762/bjnano.4.25

• -interaction forces twist the cantilever by a detectible amount. The high bandwidth of torsional motion allows accessing higher harmonics of the tip–sample-interaction forces to reconstruct tip–sample-force waveforms. This process involves calibration of the frequency response of the torsional mode by

High-resolution dynamic atomic force microscopy in liquids with different feedback architectures

• John Melcher,
• David Martínez-Martín,
• Miriam Jaafar,
• Julio Gómez-Herrero and
• Arvind Raman

Beilstein J. Nanotechnol. 2013, 4, 153–163, doi:10.3762/bjnano.4.15

• oscillations of the probe are strongly influenced by the presence of tip–sample forces in vacuum. On the other hand, ets and vts are on the order of unity in air and small compared to unity in liquid. Before proceeding, we will briefly address the issue of higher harmonics in liquids. Early work on dAFM in

• liquids showed that significant higher harmonic distortions in the oscillation waveform could provide additional channels for compositional mapping [35]. More recently, it was discovered that the use of soft microcantilevers (≤1 N/m) with quality factors close to unity resulted in higher harmonics from

• higher eigenmodes [36][37]. The present theory does not extend to soft microcantilevers in liquids. However, from prior work, we can expect that the primary difference for soft microcantilevers is that the dissipation reflects the energy lost to higher harmonics [38][39]. Performance metrics for high

Interpreting motion and force for narrow-band intermodulation atomic force microscopy

• Daniel Platz,
• Daniel Forchheimer,
• Erik A. Tholén and
• David B. Haviland

Beilstein J. Nanotechnol. 2013, 4, 45–56, doi:10.3762/bjnano.4.5

• frequencies close to a cantilever resonance, and those that use off-resonance components. Off-resonance techniques typically measure higher harmonics of the tip motion, which allows for a reconstruction of time-dependent surface forces acting on the tip. Due to the lack of transfer gain off resonance, these

Thermal noise limit for ultra-high vacuum noncontact atomic force microscopy

• Jannis Lübbe,
• Matthias Temmen,
• Sebastian Rode,
• Philipp Rahe,
• Angelika Kühnle and
• Michael Reichling

Beilstein J. Nanotechnol. 2013, 4, 32–44, doi:10.3762/bjnano.4.4

• modulation index Δfm/fm producing an infinite number of higher harmonics with rapidly decreasing power [4]. How many of these side peaks can be detected depends on the modulation index of the signal and the noise characteristics of the measurement system. For the hypothetical measurement illustrated in

• Section 2 of Supporting Information File 1 can be represented as: Here, is calculated only for the fundamental cantilever oscillation mode with eigenfrequency f0, stiffness k0 and Q-factor Q0 as the contribution of higher harmonics to the total noise power spectral density is small; the fundamental mode

• contains 97% or more of the total power extracted by the cantilever from the thermal bath. For the investigation of noise at higher harmonics, f0, k0 and Q0 would have to be replaced by the respective modal values fn, kn and Qn (see Section 2 of Supporting Information File 1). The noise spectral density

Mapping mechanical properties of organic thin films by force-modulation microscopy in aqueous media

• Jianming Zhang,
• Zehra Parlak,
• Carleen M. Bowers,
• Terrence Oas and
• Stefan Zauscher

Beilstein J. Nanotechnol. 2012, 3, 464–474, doi:10.3762/bjnano.3.53

• linearization of the contact models. For this case of soft contact, the sinusoidal force modulation at a single frequency yields a nonlinear (distorted sinusoidal) cantilever deflection response, which reflects the contact nonlinearity and gives rise to higher harmonics, as shown in Equation 3 (see also

Simultaneous current, force and dissipation measurements on the Si(111) 7×7 surface with an optimized qPlus AFM/STM technique

• Zsolt Majzik,
• Martin Setvín,
• Andreas Bettac,
• Albrecht Feltz,
• Vladimír Cháb and
• Pavel Jelínek

Beilstein J. Nanotechnol. 2012, 3, 249–259, doi:10.3762/bjnano.3.28

• tunneling current depends exponentially on the tip–surface separation z as It(z)=I0e−2κz, the harmonic modulation produces sharp peaks in the current signal (Figure 1B). As a consequence, the frequency spectrum of the tunneling current shows higher harmonics of the modulation signal (Figure 1C). The

• amplitude leading to the appearance of a “dissipation” signal. This can take both positive and negative values. Finally, special attention has to be paid when the tuning fork is used at higher harmonics or higher flexural modes, because the harmonic modulation of the tunneling current can appear in the

Analysis of force-deconvolution methods in frequency-modulation atomic force microscopy

• Joachim Welker,
• Esther Illek and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2012, 3, 238–248, doi:10.3762/bjnano.3.27

• frequency shift to force have been suggested. Iterative methods were proposed by Gotsmann [8] and Dürig [9]. The higher harmonics of the cantilever oscillation can be exploited to recover the force instantaneously [10]. Hölscher showed that a deconvolution is possible if the amplitude dependence of the

Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus

• Elena T. Herruzo and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2012, 3, 198–206, doi:10.3762/bjnano.3.22

• microscopy (SPAM) [8][28], or by making use of higher harmonics of the oscillation in order to relate the force with the observable quantity through its transfer function [11]. In particular, the torsional-harmonic cantilevers introduced by Sahin et al. allowed the reconstruction of the effective elastic

Direct monitoring of opto-mechanical switching of self-assembled monolayer films containing the azobenzene group

• Einat Tirosh,
• Enrico Benassi,
• Silvio Pipolo,
• Marcel Mayor,
• Michal Valášek,
• Veronica Frydman,
• Stefano Corni and
• Sidney R. Cohen

Beilstein J. Nanotechnol. 2011, 2, 834–844, doi:10.3762/bjnano.2.93

• ]diazene organized in a self-assembled film on Au islands, using atomic force microscopy. Analysis of higher harmonics by means of a torsional harmonic cantilever allowed real-time extraction of mechanical data. Quantitative analysis of elastic modulus maps obtained simultaneously with topographic images

• and reliable referencing to the substrate must be made. The method applied here is time-resolved tapping force imaging, in which force–deformation curves are reconstructed from the amplitudes of the higher harmonics of oscillation of the flexural mode of the cantilever, spring-coupled to the torsional

• acquisition of the tapping-mode image. This is done by analysis of higher harmonics in the oscillating cantilever signal in order to extract full force versus distance curves. A full description of the technique can be found in the literature [19][25]. Since the force curves and stiffness data are derived