Numerical analysis of vibration modes of a qPlus sensor with a long tip

• Kebei Chen,
• Zhenghui Liu,
• Yuchen Xie,
• Chunyu Zhang,
• Gengzhao Xu,
• Wentao Song and
• Ke Xu

Beilstein J. Nanotechnol. 2021, 12, 82–92, doi:10.3762/bjnano.12.7

• horizontally and vertically. The vibration characteristics of qPlus sensors with different tip sizes were studied. An optimized tip size was derived from obtained values of tip amplitude, ratio between vertical and lateral amplitude components, output current, and quality factor. For high spatial resolution

• temperature range [1]. In addition, quartz tuning forks have a high elastic constant, a high quality factor (Q factor), and are self-sensing due to the piezoelectric effect [1]. Therefore, a quartz tuning fork can be used as a force sensor. The central part of the “qPlus sensor” is a quartz tuning fork of

Bulk chemical composition contrast from attractive forces in AFM force spectroscopy

• Dorothee Silbernagl,
• Media Ghasem Zadeh Khorasani,
• Natalia Cano Murillo,
• Anna Maria Elert and
• Heinz Sturm

Beilstein J. Nanotechnol. 2021, 12, 58–71, doi:10.3762/bjnano.12.5

• /m, and a quality factor Q = 421. The AFM-IR data were obtained using a NanoIR2s (Bruker/Anasys Instruments) coupled with a multichip quantum cascade laser (QCL) source (MIRcat, Daylight Solutions; with a tunable repetition rate in the range of 0–500 kHz and a spectral resolution of 0.1 cm−1

Nanomechanics of few-layer materials: do individual layers slide upon folding?

• Ronaldo J. C. Batista,
• Rafael F. Dias,
• Ana P. M. Barboza,
• Alan B. de Oliveira,
• Taise M. Manhabosco,
• Thiago R. Gomes-Silva,
• Matheus J. S. Matos,
• Andreij C. Gadelha,
• Cassiano Rabelo,
• Luiz G. L. Cançado,
• Ado Jorio,
• Hélio Chacham and
• Bernardo R. A. Neves

Beilstein J. Nanotechnol. 2020, 11, 1801–1808, doi:10.3762/bjnano.11.162

• small force or mass changes [16]. It is important to emphasize that the quality factor of the resonator depends on its maximum resonant frequency, which is intrinsically related to the flexural properties of the employed 2D material. As an example of an application based on the folds of a 2D material

Design of V-shaped cantilevers for enhanced multifrequency AFM measurements

• Mehrnoosh Damircheli and
• Babak Eslami

Beilstein J. Nanotechnol. 2020, 11, 1525–1541, doi:10.3762/bjnano.11.135

• spring constant, quality factor, and resonant frequencies. Research has been conducted to improve AFM cantilevers in terms of manipulation, approximating material property, and images contrast. V-shaped and triangular cantilevers are widely employed in AFM imaging techniques due to their stability

• . Bushan stated that the cantilever stylus used in the AFM should have properties such as low normal spring constant, high resonance frequency, high quality factor, high lateral spring constant, and short cantilever length [12]. V-shaped cantilevers have a unique set of properties, that is, low normal

•  16, the modal damping factors can be written as: In Equation 17, subscript i represents the corresponding eigenmode. By finding γi, the corresponding eigenmode quality factor can be found since: Qi = 1/2γi. The quality factors of each eigenmode in addition to their corresponding resonant frequencies

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

• 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

A review of demodulation techniques for multifrequency atomic force microscopy

• David M. Harcombe,
• Michael G. Ruppert and
• Andrew J. Fleming

Beilstein J. Nanotechnol. 2020, 11, 76–91, doi:10.3762/bjnano.11.8

• particularly suited to intermittent-contact AFM [9] when tip–sample contact is gentle. Environmental damping has a large effect on the quality factor (Q) of the cantilever. Values can range from as low as Q ≈ 1 in liquid [10], up to Q ≈ 10,000 in ultra-high vacuum [11]. This affects the mechanical bandwidth of

• the cantilever according to the expression f−3dB = f0/2Q, where f0 is the fundamental resonance frequency. Assuming all other components in the z-axis feedback loop are also working at high speed [3], a low quality factor can demand a fast demodulator [12]. Multifrequency AFM (MF-AFM) is a major field

The effect of heat treatment on the morphology and mobility of Au nanoparticles

• Sven Oras,
• Sergei Vlassov,
• Simon Vigonski,
• Boris Polyakov,
• Mikk Antsov,
• Vahur Zadin,
• Rünno Lõhmus and
• Karine Mougin

Beilstein J. Nanotechnol. 2020, 11, 61–67, doi:10.3762/bjnano.11.6

• calculated with the following equation [20]: where k is the cantilever spring constant, f0 is the resonance frequency of the cantilever, Aset is the setpoint amplitude, Apiezo is the drive amplitude, θ is the phase signal and Q is the quality factor of the AFM cantilever. The dissipated power was used as a

Integration of sharp silicon nitride tips into high-speed SU8 cantilevers in a batch fabrication process

• Nahid Hosseini,
• Matthias Neuenschwander,
• Oliver Peric,
• Santiago H. Andany,
• Jonathan D. Adams and
• Georg E. Fantner

Beilstein J. Nanotechnol. 2019, 10, 2357–2363, doi:10.3762/bjnano.10.226

• amplitude modulation AFM (HS-AM-AFM) enhanced by up to one order of magnitude due to their low mechanical quality factor (Q-factor) and hence their high mechanical bandwidth [23]. A tip made of SU8 or other structural polymers can be integrated into a polymer cantilever by moulding. Such tips have been

Nanoscale spatial mapping of mechanical properties through dynamic atomic force microscopy

• Zahra Abooalizadeh,
• Leszek Josef Sudak and
• Philip Egberts

Beilstein J. Nanotechnol. 2019, 10, 1332–1347, doi:10.3762/bjnano.10.132

• contaminants on the surface when measuring the mechanical properties of atomic-sized defects [15][16][17]. Furthermore, the high quality factor of the AFM cantilever that is achieved under UHV conditions can be very beneficial in dynamic AFM modes, as the Q-factor is inversely proportional to the force

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

• nanoparticle diameter) resulting in a positive phase shift: with A being the effective capacitive area, z the lift height, d the nanoparticle diameter, VCPD the contact potential difference between tip and substrate, Q the quality factor, k the spring constant of the cantilever, and ε0 the dielectric constant

• magnetized sphere [20][22][23]: where Q is the quality factor of the cantilever, k is the spring constant, µ0 is the vacuum permeability, mp is the magnetic moment of the nanoparticle, mtip is the magnetic moment of the tip, and a is the distance between the two dipoles and is shown schematically in Figure 5

Direct growth of few-layer graphene on AlN-based resonators for high-sensitivity gravimetric biosensors

• Jimena Olivares,
• Teona Mirea,
• Lorena Gordillo-Dagallier,
• Bruno Marco,
• José Miguel Escolano,
• Marta Clement and
• Enrique Iborra

Beilstein J. Nanotechnol. 2019, 10, 975–984, doi:10.3762/bjnano.10.98

• and quality factor of the resonators remain almost constant, with typical values of, respectively, 3% and 150 [20]. It is worth noting that the modulus of the impedance displays a minimum at around 3000 MHz due to the LC resonance that arises from the static capacitance of the resonator and the series

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

• ≈ 165 kHz, quality factor Qf1 ≈ 30000) with compensated contact potential difference. Kelvin probe force microscopy was performed in frequency-modulation mode using a voltage modulation applied together with the dc compensation voltage to the sample (Vac = 800 mV and fac = 1 kHz or 250 Hz). (a

Commercial polycarbonate track-etched membranes as substrates for low-cost optical sensors

• Paula Martínez-Pérez and
• Jaime García-Rupérez

Beilstein J. Nanotechnol. 2019, 10, 677–683, doi:10.3762/bjnano.10.67

• become smaller, which should make the spectrum return to its initial position. Regarding the spectrum, the best region to monitor how the position of its maxima changes when exposed to ethanol is between 2200 nm and 2500 nm. In this region, the peaks have a better quality factor and their amplitude is

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

• ). This is due to the large quality factor enhancement present on resonance, which would lead to a significant contribution to the total mechanical energy from even a small voltage (and thus field) applied near resonance, invalidating the perturbation approach to derive Equation 8. Validation measurement

• on a conducting sample with known voltage pulses. One foreseeable challenge will be in performing measurements under vacuum conditions, which is typically beneficial due to the large increase in quality factor that leads to a greater force sensitivity. However, for intermodulation spectroscopy

• measurements, this will lead to a smaller frequency window in which quality factor enhancement will be available to boost the relative amplitudes of the IMPs. This is illustrated in Figure 10 where panel (a) shows synthetic data for a standard cantilever in ambient (Q = 200) with several IMPs clearly visible

Electromagnetic analysis of the lasing thresholds of hybrid plasmon modes of a silver tube nanolaser with active core and active shell

• Denys M. Natarov,
• Trevor M. Benson and
• Alexander I. Nosich

Beilstein J. Nanotechnol. 2019, 10, 294–304, doi:10.3762/bjnano.10.28

• ). Thus, Note that if γN << 1, then Equation 13 can also be cast to the form given in Equation 15; this is equivalent to Equation 14 but presented in terms of the dielectric permittivity of the gain material in the active region, Thus the lowest-threshold mode is not the one with the highest quality

• factor, QN(0), of the pump-off cavity, but the mode with the largest product of and QN(0). The expression obtained, in either form, communicates the fundamental engineering rule for the design of low-threshold laser: take the highest-Q mode of the cavity and equip it with the active region matching its

Magnetic-field sensor with self-reference characteristic based on a magnetic fluid and independent plasmonic dual resonances

• Kun Ren,
• Xiaobin Ren,
• Yumeng He and
• Qun Han

Beilstein J. Nanotechnol. 2019, 10, 247–255, doi:10.3762/bjnano.10.23

• MDM waveguide, the energy stored in the stubs will be reduced and the quality factor of the stubs will decrease. As a result, broad transmission dips are formed. The disk resonator has narrower transmission dip than the stubs. This is because the disk is side-coupled to the waveguide. Besides, the

• disk resonator can support whispering gallery modes. These can greatly reduce the propagation loss in the disk resonator. Therefore its quality factor is higher and the corresponding transmission dip is narrower. The spectral shape of the transmission for a single resonator agrees well with the

Femtosecond laser-assisted fabrication of chalcopyrite micro-concentrator photovoltaics

• Franziska Ringleb,
• Stefan Andree,
• Berit Heidmann,
• Jörn Bonse,
• Katharina Eylers,
• Owen Ernst,
• Torsten Boeck,
• Martina Schmid and
• Jörg Krüger

Beilstein J. Nanotechnol. 2018, 9, 3025–3038, doi:10.3762/bjnano.9.281

• , n the diode quality factor and T the temperature. By solving for VOC = V(I = 0) and performing the substition of ISC = IL with ISC·C, where C is the concentration factor and ISC the short-circuit current we obtain: This is inserted into the expression for the efficiency: With the incident power

Effective sensor properties and sensitivity considerations of a dynamic co-resonantly coupled cantilever sensor

• Julia Körner

Beilstein J. Nanotechnol. 2018, 9, 2546–2560, doi:10.3762/bjnano.9.237

• and the degree of frequency matching. Consequently, while an individual cantilever is characterized by its eigenfrequency, spring constant, effective mass and quality factor, the resonance peaks of the co-resonantly coupled system can be described by effective properties which are a mixture of both

• -resonant system’s effective properties. While the effective spring constant and effective mass mainly define the sensitivity of the coupled cantilever sensor, the effective quality factor primarily influences the detectability. Hence, a balance has to be found in optimizing both parameters in sensor design

• response of an individual cantilever to an external interaction depends on the cantilever’s properties, i.e., its resonance frequency f, spring constant k, effective mass meff and also quality factor Q (with regard to detectability [19]). While a single cantilever only exhibits one resonance peak for each

Metal–dielectric hybrid nanoantennas for efficient frequency conversion at the anapole mode

• Valerio F. Gili,
• Lavinia Ghirardini,
• Davide Rocco,
• Giuseppe Marino,
• Ivan Favero,
• Iännis Roland,
• Giovanni Pellegrini,
• Lamberto Duò,
• Marco Finazzi,
• Luca Carletti,
• Andrea Locatelli,
• Aristide Lemaître,
• Dragomir Neshev,
• Costantino De Angelis,
• Giuseppe Leo and
• Michele Celebrano

Beilstein J. Nanotechnol. 2018, 9, 2306–2314, doi:10.3762/bjnano.9.215

• condition and reduces the quality factor because of increased radiation losses. As a result, while the F value in the hybrid antenna is enhanced by more than two orders of magnitude, the SHG yield is only increased by one order of magnitude (see Figure 5d,f). Furthermore, in the hybrid configuration, SHG

Cathodoluminescence as a probe of the optical properties of resonant apertures in a metallic film

• Kalpana Singh,
• Evgeniy Panchenko,
• Babak Nasr,
• Amelia Liu,
• Lukas Wesemann,
• Timothy J. Davis and
• Ann Roberts

Beilstein J. Nanotechnol. 2018, 9, 1491–1500, doi:10.3762/bjnano.9.140

• other optical methods. These modes are of intrinsic interest, however, and have also attracted attention due to their relatively high quality factor and long lifetimes that may underpin new optical sensors with a higher sensitivity and figure-of-merit than devices utilising “bright” dipole modes [35

Excitation of nonradiating magnetic anapole states with azimuthally polarized vector beams

• Aristeidis G. Lamprianidis and
• Andrey E. Miroshnichenko

Beilstein J. Nanotechnol. 2018, 9, 1478–1490, doi:10.3762/bjnano.9.139

• to eliminate, the norm of the vector B. If we define the quality factor of the anapole excitation as Q = (4Pinc/Psca) − 1, then, by expanding the output vector again on the basis of the left-singular vectors, finally we have: It becomes obvious now that the ability of a particle to host a

• quality factor of the supported anti-resonances is quite low as well. A plasmonic nanoparticle can only provide us with a very poor (anti-)resonant spectrum to work with. So, we resort to high-index silicon nanoparticles as a platform to excite a nonradiating anapole state of magnetic type. Silicon

Electrostatically actuated encased cantilevers

• Benoit X. E. Desbiolles,
• Gabriela Furlan,
• Adam M. Schwartzberg,
• Paul D. Ashby and
• Dominik Ziegler

Beilstein J. Nanotechnol. 2018, 9, 1381–1389, doi:10.3762/bjnano.9.130

• , and a quality factor of Q = 50.0. Using the Sader method [25] we find a spring constant of kdyn = 18 N·m−1. Figure 2d compares electrostatically excited resonance peaks for air and deionized water. For regular cantilevers without an encasement viscous losses to the surrounding medium are the dominate

• damping mechanism. The quality factor of the cantilever typically drops by a factor of 50 when immersed in water. By trapping air inside the hydrophobic encasement [26][27][28][29], the resonator maintains a high quality factor and resonance frequency. For the liquid air comparison a softer cantilever (L

• ≈ 90 μm) with a stiffness of k = 4 N·m−1 and a resonance frequency of f0 = 144.525 kHz and Qair = 36.5 is used. After immersion in water the quality factor remained high Qwater = 27.4, which enables high-resolution imaging with small interaction forces in liquids. Moreover, the clean electrostatic

Artifacts in time-resolved Kelvin probe force microscopy

• Sascha Sadewasser,
• Nicoleta Nicoara and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2018, 9, 1272–1281, doi:10.3762/bjnano.9.119

• quality factor. The first three (i = 1,2,3) eigenmodes of the cantilever are used. Only the electrostatic forces relevant for electrostatic and Kelvin probe force microscopy are considered according to [2]: Here, Vdc is the applied dc voltage, Vac the ac-detection voltage, fac the frequency of the ac

Electrostatic force spectroscopy revealing the degree of reduction of individual graphene oxide sheets

• Yue Shen,
• Ying Wang,
• Yuan Zhou,
• Chunxi Hai,
• Jun Hu and
• Yi Zhang

Beilstein J. Nanotechnol. 2018, 9, 1146–1155, doi:10.3762/bjnano.9.106

• of dergree of the samples' reduction as: sample 0 < sample 1 ≈ sample 2 < sample 4 < sample 3 < sample 5. The parabola of ∆φn − ∆φMica versus tip bias (Equation 8) is consistent with the previous results [31] that the small phase shifts ∆φ can be approximated by where Q is the quality factor of the

Imaging of viscoelastic soft matter with small indentation using higher eigenmodes in single-eigenmode amplitude-modulation atomic force microscopy

• Miead Nikfarjam,
• Enrique A. López-Guerra,
• Santiago D. Solares and
• Babak Eslami

Beilstein J. Nanotechnol. 2018, 9, 1116–1122, doi:10.3762/bjnano.9.103

• the first three flexural eigenmodes, using an individual equation of motion for each of them, all coupled through the tip–sample forces: Here zi, ki, Qi and refer to the i-th (with i = 1, 2, 3) eigenmode displacement, cantilever stiffness, cantilever quality factor, and resonance frequency