Cantilever resonant frequency

Pulsed-force mode AFM (PFM-AFM) is a method introduced for fast mapping of local stiffness and adliesion with lower required data storage than recording force-distance curves at each point on the x-y plane [115]. A sinusoidal or triangular modulation is applied between the tip and sample (either via lever or sample piezo) at a lower frequency than that of either the piezo or cantilever resonance frequency. Tip and sample then come... 

Fig. 13.20. Optical heterodyne force microscopy (OHFM) and its application to a copper strip of width 500 nm, thickness 350 nm, on a silicon substrate, with subsequent chemical vapour deposition (CVD) of a silicon oxide layer followed by polishing and evaporation of a chromium layer of uniform thickness 100 nm and flatness better than 10 nm (a) amplitude (b) phase 2.5 [im x 2.5 m. Ultrasonic vibration at fi = 4.190 MHz was applied to the cantilever light of wavelength 830 nm was chopped at fo = 4.193 MHz and focused through the tip to a spot of diameter 2 im with incident mean power 0.5 mW the cantilever resonant frequency was 38 kHz. The non-linear tip-sample interaction generates vibrations of the cantilever at the difference frequency f2 — f = 3 kHz (Tomoda et al. 2003).

FIGURE 4.3.11 (a) EFM measurement with the tip biased at the surface potential (F = Fj) the cantilever resonant frequency is (b) EFM measurement above the sample surface with Vgp Vg, the cantilever frequency shift A/, j is due to the tip-substrate capacitive force gradients, (c) Additional capacitive frequency shift A/g when the EFM tip passes over a conducting domain of dielectric constant e (A/g = 0 if = F ). (d) Additional frequency shift A/g when an amount of charge Q is located inside the domain. (From Melin, T. et al., Phys. Rev. B 69, 35321, 2004. With kind permission.)... 

Depending on the dimensions and constmction of the composite cantilever, resonance frequencies were observed in the range of 0.7 to 1.2 MHz. The resonance spectra (Fig. IB) in vacuum ( 50 mTorr, 23.6 °C), in air (23.6 °C) and in phosphate buffered saline (lOmM, PBS 30 °C) are shown for the dominant high-order mode at 941.5 kHz in air (Q = 41). The parameter Q is a measure of peak sharpness and is equal to the ratio of resonance frequency to half-height peak width. When mounted in a specially constructed sample flow cell and PBS is flowed in at 0.4 to 1.0 mL/min, the resonant frequency decreased ( 50 kHz) due to added mass effect and the peak height decreased by 20 to 60%. At 1 mL/min, Q-value remained sufficiently high ( 23), that the resonant frequency can be measured with an accuracy of 20-40 Hz. Resonant frequency in... 

These two electronic transitions depend on the nuclear state and therefore have different resonance frequencies. Let coeo and coei be the two electronic resonances, corresponding to the nuclear states 0> and 1>, respectively. If a r-pulse is applied to the electron spin in the frequency a>eo, the spin will rotate only if the nucleus is in the state 0). Now, if the cantilever resonance frequency is a>c, applying tt-pulses at frequency nuclear state can be detected. 

The sample-tip-cantilever system can be modeled as a mechanical system with springs and dash-pots 11,12). Solving the motion equations of this model at low frequency (i.e. below the cantilever resonance frequency) and neglecting the damping constants (i.e. neglecting viscoelastic effects in polymers) leads to the following relation for the ratio between the sample modulation amplitude, z, and the tip response amplitude, also called the dynamic elastic response ... 

Figure 18.1b shows the amplitude and phase versus frequency curves plotted around the cantilever resonance frequency (/o). 

Topography The surface topography of the films was analysed by (a) atomic force microscopy (AFM Nanoscope IIIA Multimode SPM, Veeco Instmments) in tapping mode under ambient conditions (cantilever resonant frequencies were in the range 330-350 kHz and the force constant was 42 N/m) and (b) high-resolution scanning electron microscopy (HRSEM FEI, NovaNano SEM 230). 

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