Oblique angle scanning electron micrographs of (a) arrays of 205 nm thick single crystal silicon suspended cantilever devices. Scale bar corresponds to . Released structures with dimensions of (b) , and (c) , . Scale bar corresponds to .
Illustration of the experimental apparatus emphasizing the weakly coupled, noncontact, and scanning modes of operation. The red dashed line initiating from the free end of the cantilever structure indicates the length of the AFM scan during tapping mode imaging of the interactions.
Oblique angle scanning electron micrograph of (a) , single crystal silicon device. (Scale bar corresponds to .) The AFM tapping mode probe is scanned along the dashed line with the slow scan axis in a disabled state. Without excitation , 25 representative line scans for (b) height and (c) phase show stable output signals.
Tapping mode AFM scans across the piezodriven cantilever between 3.5 and 6.5 MHz. (a) The height image displacement is due to the resonant coupling of the interacting system. (b) Phase contrast and (c) amplitude images show the spectral characteristics of the nanomechanical oscillator. Dashed blue line is a fit to a Lorentzian function.
Measured frequency spectra of the NEMS cantilever in (a)air and (b)vacuum using optical interferometry and excitation. Lorentzian fitting functions are represented by the solid curves.
Measured extension-retraction cycle of the probe amplitude vs the -piezo scanner position. This dynamic force curve was obtained with the cantilever driven well below the first eigenfrequency. Two regions, free vibration and contact, along with direction of the extension (black arrow) and retraction (blue arrow) cycles are identified. The vibrational amplitude was highest in the noncontact (free vibration) regime. The insets schematically represent (not to scale) the probe-cantilever interactions at several points along the dynamic force curve.
Measured vibrational amplitude (open circles) of the probe, near the vicinity of the point of contact, vs drive frequency of the cantilever structure with dimensions and . The two figure insets show zoomed-in amplitude vs piezo position for various points in the spectral curve. The arrows indicate the respective measured spectral data point. The solid blue line is a least square fit using a Lorentzian function. From the Lorentzian fit, the resonant frequency and mechanical quality factor were 2.3 MHz and 4.1, respectively.
Measured vibrational amplitude (open circles) of the probe, in the free vibration regime (hovering mode), as a function of the drive frequency of the cantilever with dimensions and . The solid line represents a least square fit using a Lorentzian function. The measured resonant frequency and mechanical quality factor were 2.3 MHz and 5.15, respectively.
Schematic representation highlighting relevant geometric parameters of a vibrating cantilever structure interacting with an AFM probing tip at a separation distance . Typical dimensions in the lateral direction range from to with .
Simulated resonant curves of the NEMS cantilever for (1) , (2) , (3) , and (4) amplitudes of excitation.
Displacement time history of the AFM probe interacting with the cantilever for the case of resonant excitation . Time history for different initial separation distances (a) (hovering mode) and (c) (contact mode). (b) and (d) represent zoomed in portions of (a) and (c), respectively. The resonant amplitude of the NEMS cantilever was 78 nm. Thick solid lines in (b) and (d) represent the AFM probe motion, while directly below, the thinner line represents higher frequency NEMS oscillations.
Displacement time history of the AFM probe driven at resonance and interacting with NEMS cantilever driven at for initial separation distance (a) and (b) , (c) and (d) , and (e) and (f) . The former of the matched pairs shows only the probe deflection, while the latter illustrates the motion of both oscillators. Resonant amplitudes of the AFM probe and of the NEMS cantilever were 15 and 78 nm, respectively. Thick solid lines in (b), (d), and (f) represent the AFM probe motion and the thinner line represents the NEMS oscillations.
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