Exciting cantilever into resonance

A fixed-free cantilever beam M-Test structure fabricated in Polyl of the PolyMUMPS process can also be used as a resonator by exciting it into resonance with an AC drive signal applied to a PolyO counter-electrode defined below the end of the beam. To estimate the resonant frequency we use the spring constant for a fixed-free beam that is 20 pm wide and 150 pm long subjected to a point load at its free end ... 

The cantilever is excited into resonance by electrically exciting the piezoelectric cantilever mount. The frequency of the excitation wave is scanned in a given frequency range, and the frequency of maximum cantilever amplitude is taken as the resonance frequency. The frequency spectrum of the cantilever response shows the fundamental frequency as well as the harmonics of cantilever vibration. The cantilevers, however, also resonate in response to ambient conditions such as room temperature or acoustic noise without requiring any external power. 

Better control of the cantilever oscillation in liquid environment can be achieved when the cantilever is oscillated directly by an external force. This idea was implemented by the so-called Magnetic-Alternative-Current Mode (MAC Mode) [194]. A magnetic cantilever is driven by an external magnetic field which is generated by a solenoid placed beneath the sample. The direct excitation of the cantilever avoids unwanted resonance s from the cantilever holder, the fluid body, and the sample itself. Furthermore, the improved signal-to-noise ratio allows smaller oscillation amplitudes and set point ratios Asp/Af closer to 1. Both factors result in a significant reduction in the energy deposited into the sample,... 

The prime differences among the different AFM modes, such as CM (discussed above) and intermittent CM, as elucidated in the following section, are the feedback parameters and the choice of the cantilever. For intermittent contact (tapping) mode AFM, a stiff cantilever (k typically 10—50 N/m) with a resonance frequency of 100—400 kHz is chosen. The cantilever, which is inserted in an identical manner as for CM into the cantilever holder, is excited to vibrate by an integrated piezo actuator. Instead of deflection (contact force), the amplitude of the forced oscillating lever is detected, analyzed, and utilized in the feedback loop (Fig. 2.20). 

As mentioned above rectangular AFM cantilever beams can also be forced to torsional vibrations. In this case the experimental set-up is such that an ultrasonic transducer emits shear waves into the sample causing in-plane surface vibrations. The shear wave transducer is oriented so that the surface vibrations are polarized perpendicular to the long axis of the cantilever. If low excitation amplitudes (0.1 nm) are applied and if the excitation frequency is set close to a contact resonance frequency, the amplitude and the phase of the cantilever vibration contain now information about the local lateral tip-sample stiffness. Used as imaging quantity, they yield images of shear stiffness. By increasing the lateral excitation amplitude much above... 

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