Finite-size effect on the dynamic and sensing performances of graphene resonators: the role of edge stress

• Chang-Wan Kim,
• Mai Duc Dai and
• Kilho Eom

Beilstein J. Nanotechnol. 2016, 7, 685–696, doi:10.3762/bjnano.7.61

• of graphene are affected by the edge stress. Park and a coworker [29] investigated the role of edge stress on the dynamic behavior (e.g., Q-factor) of a graphene resonator by using atomistic simulations. Despite these previous studies [26][27][29], it has not been fully understood yet how the edge

• edge stress. It should be noted that this work based on the modified plate theory is restricted to studying only the resonant frequencies of graphene sheets, while this current work may not be applicable for understanding the Q-factor. Our model does not include the intrinsic (flaw) factors, which

• affect the Q-factor of a graphene resonator. In order to understand the effect of edge stress on the Q-factor of a graphene resonator [29], the theoretical model described in this work has to be modified by including the intrinsic damping factors such as clamping or support loss [47][48][49] and

Correlative infrared nanospectroscopic and nanomechanical imaging of block copolymer microdomains

• Benjamin Pollard and
• Markus B. Raschke

Beilstein J. Nanotechnol. 2016, 7, 605–612, doi:10.3762/bjnano.7.53

• modified commercial AFM (MultiMode 8, Bruker). We calibrate quantiative force values using measurements with the same tip on a Si sample and a rough TiO2 surface for measuring the deflection sensitivity and tip radius, respectively, as well as tuning curves for measuring the Q-factor using the Sader method

Contact-free experimental determination of the static flexural spring constant of cantilever sensors using a microfluidic force tool

• John D. Parkin and
• Georg Hähner

Beilstein J. Nanotechnol. 2016, 7, 492–500, doi:10.3762/bjnano.7.43

• was obtained with the Bruker software. The peak area, resonant frequency and Q-factor of the thermal noise spectra were determined with a self-coded MATLAB routine by fitting Lorentzian curves to the resonance peaks of the first flexural modes. Force curves, to calibrate the deflection sensitivity (σ1

• frequency and Q-factor Table 1 summarizes the geometrical dimensions, resonant frequency and Q-factor of the cantilevers studied. Here, “Nominal” refers to the information provided by the manufacturers. The actual plan view dimensions of all microcantilevers were determined with an Olympus optical

• humidity. Checking the quality factors Q and the resonance frequencies of the resonance peaks for very low flow speeds at the beginning of the measurements and at the end did not reveal significant differences. If there is some stress induced, it is certainly small and not revealed by the Q-factor or the

Length-extension resonator as a force sensor for high-resolution frequency-modulation atomic force microscopy in air

• Hannes Beyer,
• Tino Wagner and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2016, 7, 432–438, doi:10.3762/bjnano.7.38

• resonance frequency of about 1 MHz, a Q-factor of approximately 15,000 in air and an effective stiffness of keff = 1.08 MN/m. The effective stiffness amounts to twice the stiffness of a single beam (k = 540 kN/m) because the LER consists of two oscillating beams fixed at the center [9]. The very high

• resonance frequency and Q-factor, a problem also well-known for regular cantilevers. The problem is aggravated for the LER since the measured signal, i.e., the frequency shift Δf, is small due to the high stiffness of the LER (Δf f0/keff). Hence a controlled environment is essential for stable imaging

• et al. [19] and Fan et al. [21], applying a feedback based on the Q-factor to stabilise the tip–sample distance. In our implementation the ratio of excitation and amplitude of the first harmonic resonance, and thus the Q-factor, is held constant by a slow feedback to compensate for drift of the free

Efficiency improvement in the cantilever photothermal excitation method using a photothermal conversion layer

• Natsumi Inada,
• Hitoshi Asakawa,
• Taiki Kobayashi and
• Takeshi Fukuma

Beilstein J. Nanotechnol. 2016, 7, 409–417, doi:10.3762/bjnano.7.36

• coated cantilevers were corrected by subtracting the frequency-dependent phase delay caused by a phase-locked loop circuit. The dotted lines in the figures show ideal phase curves calculated with resonance frequency (f0) and Q-factor estimated from cantilever thermal vibration spectra as shown in Table 1

• coating of a PTC layer improves the phase response obtained by the photothermal excitation method. Table 1 and Table 2 show the physical properties of PPP-NCHAuD and AC55 cantilevers before and after coating with a PTC layer. The resonance frequency (f0), Q-factor and spring constant (k) of the

Current-induced runaway vibrations in dehydrogenated graphene nanoribbons

• Rasmus Bjerregaard Christensen,
• Jing-Tao Lü,
• Per Hedegård and
• Mads Brandbyge

Beilstein J. Nanotechnol. 2016, 7, 68–74, doi:10.3762/bjnano.7.8

• negative the mode is damped. The damping can be quantified by the inverse Q-factor giving the change in energy per period Thus, the run-away modes can be identified as the modes where Im(ω) > 0. The run-away modes are a linear combination of the non-perturbed normal modes. Normally, the runaway makes

Kelvin probe force microscopy for local characterisation of active nanoelectronic devices

• Tino Wagner,
• Hannes Beyer,
• Patrick Reissner,
• Philipp Mensch,
• Heike Riel,
• Bernd Gotsmann and
• Andreas Stemmer

Beilstein J. Nanotechnol. 2015, 6, 2193–2206, doi:10.3762/bjnano.6.225

• operation. In vacuum, this may require additional application of active Q control [44][45] to lower the Q-factor of the cantilever. Performance on a nanowire device To demonstrate the performance of our Kalman-KFM controller, we examine an active nanowire device as depicted in Figure 8 and Figure 9. Such

Development of a novel nanoindentation technique by utilizing a dual-probe AFM system

• Eyup Cinar,
• Ferat Sahin and
• Dalia Yablon

Beilstein J. Nanotechnol. 2015, 6, 2015–2027, doi:10.3762/bjnano.6.205

• approximately 34 kHz and a high Q factor in air that is over 1000. The instrument consists of four towers where each tower has lateral stepper motors for XYZ motion as shown in Figure 2 with a resolution of 21 nm. Each tower has also an upper piezo scanner integrated together with a pre-amplifier block, which

Improved atomic force microscopy cantilever performance by partial reflective coating

• Zeno Schumacher,
• Yoichi Miyahara,
• Laure Aeschimann and
• Peter Grütter

Beilstein J. Nanotechnol. 2015, 6, 1450–1456, doi:10.3762/bjnano.6.150

• damping of the cantilever, leading to a lower mechanical quality factor (Q-factor). In dynamic mode operation in high vacuum, a cantilever with a high Q-factor is desired in order to achieve a lower minimal detectable force. The reflective coating can also increase the low-frequency force noise. In

• coating at the tip end of the cantilever. The Q-factor, the detection and the force noise of fully coated, partially coated and uncoated cantilevers are compared and force distance curves are shown. Our results show an improvement in low-frequency force noise and increased Q-factor for the partially

• coated cantilevers compared to fully coated ones while maintaining the same reflectivity, therefore making it possible to combine the best of both worlds. Keywords: cantilever; force noise; partial coating; Q-factor; Introduction For cantilever based beam deflection atomic force microscope (AFM

Nanomechanical humidity detection through porous alumina cantilevers

• Olga Boytsova,
• Alexey Klimenko,
• Vasiliy Lebedev,
• Alexey Lukashin and
• Andrey Eliseev

Beilstein J. Nanotechnol. 2015, 6, 1332–1337, doi:10.3762/bjnano.6.137

• ). The amplitude–frequency profiles of rectangular cantilevers made of Si and porous anodic aluminium oxide are provided in Figure 2. Their characteristics are summarized in Table 1. The Q factor for both types of beams significantly increases after change air media to vacuum. Natural shifts to high

Influence of spurious resonances on the interaction force in dynamic AFM

• Luca Costa and
• Mario S. Rodrigues

Beilstein J. Nanotechnol. 2015, 6, 420–427, doi:10.3762/bjnano.6.42

• complicated. Moreover, it has already been observed that the motion of the cantilever base due to the acoustic excitation is not negligible in situations in which the Q factor is low – a typical situation when measuring in liquids. The same holds if the cantilever is not excited close to its resonance

• Equation 6 is still valid, because in that case the deflection is indeed proportional to the position. If the tip position is not measured and the cantilever is not directly excited, then Equation 6 does not hold, particularly away from the resonance frequency or when the Q factor is small. Coupling with

Dissipation signals due to lateral tip oscillations in FM-AFM

• Michael Klocke and
• Dietrich E. Wolf

Beilstein J. Nanotechnol. 2014, 5, 2048–2057, doi:10.3762/bjnano.5.213

• frequency ratio ωx/ωz for different systems. Dashed line indicates the lower bound of experimentally observed values. Dissipation rate is averaged over 300 cycles. Dissipation rate with respect to the variation of the Q-factor for nominal distances of d = 0.8 nm and d = 1.1 nm. Numerical simulation for 300

Resonance of graphene nanoribbons doped with nitrogen and boron: a molecular dynamics study

• Ye Wei,
• Haifei Zhan,
• Kang Xia,
• Wendong Zhang,
• Shengbo Sang and
• Yuantong Gu

Beilstein J. Nanotechnol. 2014, 5, 717–725, doi:10.3762/bjnano.5.84

• of dopant atoms ranging from 0.26% to 2.78%, in which B and N share the same density, namely half of the total percentage. Strikingly, the GNR with 0.26% of B- and N-dopants appear to have an enhanced Q-factor of about 9050, which is twice of that observed from the pristine GNR. Except this case, the

• for the case with 2.40% dopant density. As shown in Figure 11a, no obvious energy dissipation is found, which results in a Q-factor as high as 79020. The corresponding frequency spectrum reveals that there are two resonance modes existing. Close inspection of the atomic configurations of the sample

• concluded that for the GNR with four vacancies, a higher density of dopants will make the translational vibration mode much easier to be excited. Before concluding, we compare the resonance frequencies and Q-factor among all testing samples. As seen in Figure 12a, the resonance frequency usually decreases

Frequency, amplitude, and phase measurements in contact resonance atomic force microscopies

• Gheorghe Stan and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2014, 5, 278–288, doi:10.3762/bjnano.5.30

• , the quality factor is directly associated with the damping response of the system. However, as it can be seen in Figure 7d and 7h, it depends on both the contact stiffness and contact damping. The Q-factor is almost independent of contact stiffness for the second UAFM and AFAM eigenmodes, in which

• and Figure 8h are in agreement, within the common range of contact stiffness, with the Q-factor versus contact damping dependences shown in Figure 2 of [37] for the first two eigenmodes. Phase-locked loop detection By considering their specific dependences in either UAFM or AFAM configurations, the

Exploring the retention properties of CaF₂ nanoparticles as possible additives for dental care application with tapping-mode atomic force microscope in liquid

• Matthias Wasem,
• Joachim Köser,
• Sylvia Hess,
• Enrico Gnecco and
• Ernst Meyer

Beilstein J. Nanotechnol. 2014, 5, 36–43, doi:10.3762/bjnano.5.4

• manipulated particles adsorbed on mica. The amplitude was A = 23 nm, the Q-factor = 7 and A0 = 1.2A. SEM images of the three morphologies of nanoparticles explored in this work. A certain size distribution of the particles was achieved with the synthesis method described in the text. The diameters vary from

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 exponents of k higher than 1/2 in the denominator yield increasing merit factors for decreasing stiffness. Both merit factors cannot be increased infinitely because downsizing the probe beyond a certain limit will decrease the Q-factor and increase sensor noise. A table of merit factors for

• where it dominates becomes smaller, as can be seen in Figure 9. Mass and spring constant cannot be reduced infinitely without reducing the Q-factor. Furthermore, increasing the merit factor in the thermally dominated case is a simple downsizing of the detector, and with the same type of sensor, would

• increase the sensor noise or decrease the Q-factor of the oscillator by sensor back-action (e.g., radiation pressure). Similarly, all attempts of improving the detector have a trend to increase invasiveness and to reduce the Q-factor. As long as one type of noise is clearly dominant, the remedy is to

Optimal geometry for a quartz multipurpose SPM sensor

• Julian Stirling

Beilstein J. Nanotechnol. 2013, 4, 370–376, doi:10.3762/bjnano.4.43

• excited at or near one of its eigenfrequencies, properties such as the Q factor, eigenfrequencies, effective spring constant [1] and other geometrical properties [2] of the eigenmodes become important. AFM and LFM sensors have evolved from gold foil with diamond tip [3] and bent tungsten wires [4

Determining cantilever stiffness from thermal noise

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

Beilstein J. Nanotechnol. 2013, 4, 227–233, doi:10.3762/bjnano.4.23

• demonstrate that the latter method is in particular useful for noncontact atomic force microscopy (NC-AFM) where the required simple instrumentation for spectral analysis is available in most experimental systems. Keywords: AFM; cantilever; noncontact atomic force microscopy (NC-AFM); Q-factor; thermal

• of the cantilever is small, is given by where kn and Qn are the modal stiffness [4] and Q-factor of the nth cantilever eigenmode [5], respectively. The relation is of relevance for any practical application involving microcantilevers and specifically important for high-resolution noncontact atomic

• thermal frequency-shift noise spectral density (fm) [6]. Results and Discussion Stiffness from displacement thermal noise In a displacement noise measurement of a cantilever with a high Q-factor, the spectrum analyser measures the total displacement noise spectral density (f) for the nth cantilever

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

• find an excellent agreement between the calculated and measured values for dΔf. Furthermore, we demonstrate that thermal noise in dΔf, defining the ultimate limit in NC-AFM signal detection, can be kept low by a proper choice of the cantilever whereby its Q-factor should be given most attention. A

• systems based on other force sensors and detection schemes. Under ultrahigh-vacuum (UHV) conditions, the thermal noise of the cantilever is usually small compared to the noise of the detection system due to the high Q-factor of the cantilever in vacuum [6]. The instrumental noise sources in an optical

• 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

Drive-amplitude-modulation atomic force microscopy: From vacuum to liquids

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

Beilstein J. Nanotechnol. 2012, 3, 336–344, doi:10.3762/bjnano.3.38

• dynamics of the cantilevers are similar to what is typically observed in UHV chambers at room temperature (the values of the Q factor in UHV operation are commonly between 8000 and 25000). All the experiments were carried out at room temperature. Figure 3a–d portrays four topography images of a calibration

Models of the interaction of metal tips with insulating surfaces

• Thomas Trevethan,
• Matthew Watkins and
• Alexander L. Shluger

Beilstein J. Nanotechnol. 2012, 3, 329–335, doi:10.3762/bjnano.3.37

• Elastic constant: 148.7 N/m; natural frequency: 189000.0 Hz; setpoint amplitude: 5 nm; Q-factor: 10000.0. Macroscopic van der Waals: Hamaker constant: 0.999 eV; Tip radius: 18.0 nm (a) Side-on view of the structure of the Cr and W cluster tip models. (b) The structure of the periodic Cr tip model. (a

Wavelet cross-correlation and phase analysis of a free cantilever subjected to band excitation

• Francesco Banfi and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2012, 3, 294–300, doi:10.3762/bjnano.3.33

• the liquid environment is principally of interest. In liquids the typical cantilever Q-factor ranges from 5 [18] up to 40, for this reason we will focus our attention on the simulation of low-Q oscillators. Wavelet cross-correlation The wavelet transform has shown great potential in various scientific

• evolution of the oscillator response, when the impulsive driver action has died down. We consider the same excitation as in Figure 3, but with an oscillator that has a much higher Q-factor, Q = 40. The time evolution is shown in Figure 5. We note that the initial displacement is not amplified in proportion

• to the Q-factor, as one would have anticipated on the basis of standard resonance amplification, as can be seen from the comparison with Figure 3. The higher Q-factor manifests as a response of the oscillator that now extends over a longer time span, well beyond the driver pulse. The wavelet cross

Current-induced dynamics in carbon atomic contacts

• Jing-Tao Lü,
• Tue Gunst,
• Per Hedegård and
• Mads Brandbyge

Beilstein J. Nanotechnol. 2011, 2, 814–823, doi:10.3762/bjnano.2.90

• window by changing the gate potential. In the following, we look at the bias and gate dependence of the inverse Q-factor (1/Q) and effective phonon number N. The inverse Q-factor for mode i (note we use index i for full modes including the current-induced forces) is defined as where ωi are the

• correlation function, We show the bias and gate potential dependence of the inverse Q-factor and phonon number in Figure 4 and Figure 5. The coupling of these two modes due to the bias (gate) dependent NC and BP force changes their lifetime. The two modes always have opposite dependence. The vibrational

• indicated by an increasing radius with time. The motion is a phase-shifted linear combination of the two modes in (a). We can see the elliptical motion of the carbon atoms from the plot. The enclosed area indicates that work can be done by the current-induced NC force. (a) Inverse Q-factor (1/Q) as a