Modeling noncontact atomic force microscopy resolution on corrugated surfaces

• Kristen M. Burson,
• Mahito Yamamoto and
• William G. Cullen

Beilstein J. Nanotechnol. 2012, 3, 230–237, doi:10.3762/bjnano.3.26

• in terms of contours of constant frequency shift. We discuss the first results of this model, specifically showing attenuation of the substrate corrugation in imaging. We also report a deviation from the generally assumed Hamaker force law for the interaction of a sphere with a flat surface (F ~ AHR

• model itself is more generally applicable to other corrugated surfaces. Model of the corrugated-surface resolution Here we briefly outline the analytic development of the model. Ultimately we wish to find the dependencies of the potential, force, frequency shift, etc., for the case of a spherical tip

• shifts Once the tip–surface interaction potential Wt–s is obtained, the interaction force Ft–s is found straightforwardly by differentiation with respect to z. We then compute the frequency shift using the following expression [28], which is exact to 1st order in classical perturbation theory: with

An NC-AFM and KPFM study of the adsorption of a triphenylene derivative on KBr(001)

• Antoine Hinaut,
• Adeline Pujol,
• Florian Chaumeton,
• David Martrou,
• André Gourdon and
• Sébastien Gauthier

Beilstein J. Nanotechnol. 2012, 3, 221–229, doi:10.3762/bjnano.3.25

• different signal channels available in NC-AFM. Constant Δf images were recorded simultaneously with maps of the Kelvin voltage, the frequency shift, the amplitude and the excitation voltage. For all the images presented in this paper, the excitation voltage map was uniform, at a value close to its value in

• scheme and (b) structure of HCPTP optimized in vacuum. Constant-frequency-shift image of the KBr surface after the deposition of a small amount of molecules at room temperature. Imaging conditions: Δf = −5 Hz, oscillation amplitude A = 2 nm. Upper image: topography and lower image: Kelvin map of a KBr

A measurement of the hysteresis loop in force-spectroscopy curves using a tuning-fork atomic force microscope

• Manfred Lange,
• Dennis van Vörden and
• Rolf Möller

Beilstein J. Nanotechnol. 2012, 3, 207–212, doi:10.3762/bjnano.3.23

• Manfred Lange Dennis van Vorden Rolf Moller Faculty of Physics, University of Duisburg-Essen, Lotharstr.1-21 47048 Duisburg, Germany 10.3762/bjnano.3.23 Abstract Measurements of the frequency shift versus distance in noncontact atomic force microscopy (NC-AFM) allow measurements of the force

• ) [1] has made it possible to achieve true atomic resolution [2] with a NC-AFM. In this mode the distance between the sample and the tip is adjusted by maintaining the frequency shift of the cantilever at a constant value while scanning the sample. During operation the oscillation amplitude is kept

• single- or double-layer islands. The PTCDA islands can be clearly distinguished from the Ag/Si(111) √3 × √3 surface by the simultaneously recorded frequency-shift (AFM) image (Figure 1b). The frequency shifts on the PTCDA islands and Ag/Si(111) √3 × √3 surface are about −1 Hz and −2 Hz, respectively

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

• method enables the simultaneous recording of several material properties and, at the same time, it also increases the sensitivity of the microscope. Here we apply fractional calculus to express the frequency shift of the second eigenmode in terms of the fractional derivative of the interaction force. We

• Lennard-Jones and Derjaguin–Muller–Toporov forces. Keywords: AFM; atomic force microscopy; bimodal AFM; frequency shift; integral calculus applications; Introduction Since the invention of the atomic force microscope (AFM) [1], numerous AFM studies have been pursued in order to extract information from

• between observables and forces is difficult to deduce. Since the observable quantities in dynamic modes are averaged over many cycles of oscillation (amplitude and phase shift for amplitude modulation AFM (AM-AFM) [20][21], and frequency shift and dissipation for FM-AFM [22][23]), it is not

Molecular-resolution imaging of pentacene on KCl(001)

• Julia L. Neff,
• Jan Götzen,
• Enhui Li,
• Michael Marz and
• Regina Hoffmann-Vogel

Beilstein J. Nanotechnol. 2012, 3, 186–191, doi:10.3762/bjnano.3.20

• same frequency shift, the images change repeatedly between these two patterns. Pattern I is characterized by a nearly square surface unit cell (Figure 2c). The molecular unit cell is roughly aligned with the [010] and [100] directions of the KCl substrate. The difference between the experimentally

qPlus magnetic force microscopy in frequency-modulation mode with millihertz resolution

• Maximilian Schneiderbauer,
• Daniel Wastl and
• Franz J. Giessibl

Beilstein J. Nanotechnol. 2012, 3, 174–178, doi:10.3762/bjnano.3.18

• (FM-AFM) the measured frequency shift Δf is proportional to an averaged force gradient with kts = −∂Fts/∂z; Fts is the force acting between tip and sample within one oscillation period; the z-direction is perpendicular to the sample surface. Within the gradient approximation, Δf is given by: To

• necessary in order to reduce the noise by reducing the bandwidth. In Figure 2b the flattened raw data of the frequency-shift channel gathered in lift-mode show an image contrast of ±5 mHz along the bit tracks. According to the resonance frequency f0 = 24097 Hz and spring constant k = 1250 Nm−1 of the sensor

• to be set to relatively slow values, allowing for a small bandwidth, but leading to sizeable drift, as seen in both sets of Figure 3. The frequency-shift data set in the second (MFM) path was flattened by applying a simple parabolic fit and shows an image contrast of ±10 mHz (Figure 3b). Along the

Effect of the tip state during qPlus noncontact atomic force microscopy of Si(100) at 5 K: Probing the probe

• Adam Sweetman,
• Sam Jarvis,
• Rosanna Danza and
• Philip Moriarty

Beilstein J. Nanotechnol. 2012, 3, 25–32, doi:10.3762/bjnano.3.3

• -induced imaging variation At 5 K we routinely observe the c(4 × 2) reconstruction and associated surface defects (Figure 1a). Note that in order to avoid perturbation of the surface during scanning we typically image at a setpoint corresponding to low tip–sample interaction (i.e., at a frequency shift

• confirmed by force spectroscopy experiments (see discussion below). It is instructive to note that direct comparison of the frequency shift setpoints for each image is not a good measure of the site specific (short-range) tip–sample interaction, as the magnitude of Δf is highly dependent on the macroscopic

• forces between different scans, as this occurs at a reasonably well-defined tip–sample interaction force. Force spectroscopy In order to further elucidate the differences in interaction between different apices, we performed experiments to measure the frequency shift versus z (i.e., Δf(z)) with a number

Distinguishing magnetic and electrostatic interactions by a Kelvin probe force microscopy–magnetic force microscopy combination

• Miriam Jaafar,
• Oscar Iglesias-Freire,
• Luis Serrano-Ramón,
• Manuel Ricardo Ibarra,
• Jose Maria de Teresa and
• Agustina Asenjo

Beilstein J. Nanotechnol. 2011, 2, 552–560, doi:10.3762/bjnano.2.59

• microscopy (KPFM) and MFM. The KPFM technique allows us to compensate in real time the electrostatic forces between the tip and the sample by minimizing the electrostatic contribution to the frequency shift signal. This is a great challenge in samples with low magnetic moment. In this work we studied an

• magnetic field during the MFM operation [14][15][16]; (ii) performing a combination of Kelvin probe force microscopy (KPFM) [17][18] and MFM to compensate the electrostatic contribution to the frequency shift signal. In the first method the evolution of the MFM signal with the magnetic field is a signature

• usual procedure in MFM, we record two images simultaneously, the topography, obtained at small tip–sample distance, and the frequency shift, which is obtained at a retrace distance of 30 nm. Figure 1a and Figure 1b shows the topography and the frequency shift images of the Co wires. Figure 1c

Towards a scalable and accurate quantum approach for describing vibrations of molecule–metal interfaces

• David M. Benoit,
• Bruno Madebene,
• Inga Ulusoy,
• Luis Mancera,
• Yohann Scribano and
• Sergey Chulkov

Beilstein J. Nanotechnol. 2011, 2, 427–447, doi:10.3762/bjnano.2.48

• frequencies – as is commonly done in a number of studies – does not improve much the prediction of the frequency shift at the harmonic level. Indeed, if we use the experimental HF-stretch frequency to compute a scaling factor [ν(HF,exp)/ω(HF) = 1.050], we obtain only a very modest improvement of the shift

Manipulation of gold colloidal nanoparticles with atomic force microscopy in dynamic mode: influence of particle–substrate chemistry and morphology, and of operating conditions

• Samer Darwich,
• Karine Mougin,
• Akshata Rao,
• Enrico Gnecco,
• Shrisudersan Jayaraman and
• Hamidou Haidara

Beilstein J. Nanotechnol. 2011, 2, 85–98, doi:10.3762/bjnano.2.10

• Equation 1 [36]. UHV measurements The images in UHV were acquired with a custom built AFM available at the University of Basel [21]. The base pressure was below 10−9 mbar. Due to the high quality factor in UHV, the out-of-contact-resonance frequency shift was used as the imaging parameter instead of the

Oriented growth of porphyrin-based molecular wires on ionic crystals analysed by nc-AFM

• Thilo Glatzel,
• Lars Zimmerli,
• Shigeki Kawai,
• Ernst Meyer,
• Leslie-Anne Fendt and
• Francois Diederich

Beilstein J. Nanotechnol. 2011, 2, 34–39, doi:10.3762/bjnano.2.4

• binding energy of the molecules to the substrate: Already during the change of the set point, parts of the layer on the left lower side were removed while scanning from bottom to top. The first few lines of Figure 3c were scanned with an increased frequency shift of Δf1st = −11 Hz. After the removal of

Defects in oxide surfaces studied by atomic force and scanning tunneling microscopy

• Thomas König,
• Georg H. Simon,
• Lars Heinke,
• Leonid Lichtenstein and
• Markus Heyde

Beilstein J. Nanotechnol. 2011, 2, 1–14, doi:10.3762/bjnano.2.1

• -AFM or STM, the other channel can always be co-recorded. Great care was taken to ensure that both channels, NC-AFM and STM, were electrically separated from each other in order to prevent cross talk. The great advantage of this setup is the simultaneous data acquisition of the frequency shift and the

• . The simultaneously measured frequency shift Δf and tunneling current It give insight into the local surface potential as well as into the local electronic structure. The corresponding results of such an experiment are shown in Figure 7, where the tip scanned across an F0 defect. The three stacked

• graphs show the simultaneously recorded oscillation amplitude, the frequency shift and the tunneling current. The colored traces indicate constant height scans at different tip-sample separations. At all tip-sample distances the oscillation amplitude can be considered as constant, which is a prerequisite

Tip-sample interactions on graphite studied using the wavelet transform

• Giovanna Malegori and
• Gabriele Ferrini

Beilstein J. Nanotechnol. 2010, 1, 172–181, doi:10.3762/bjnano.1.21

• is repeated at various separations from the surface, up to the jump-to-contact distance. The force gradient of the interaction dFts/dz (where Fts is the tip-sample force and z the tip-sample distance, positive along the surface normal direction) is directly evaluated by the observed frequency shift

• the thermal regime since we are dealing with small oscillations (less than 0.2 nm) [9]. If the frequency shift is proportional to the interaction elastic constant [1]. From the same PSD, besides the force gradient, it is possible to measure the quality factor Q of the mode, that is determined by

• . As a rule of thumb, CWT should allow to follow more easily the single-thermal-excitation-event time decay in high-Q environments and measure its frequency linewidth in low-Q environments. The first flexural mode frequency shift near the surface (Figure 7b) provides a complete force distance curve