Schematics of the first four bending modes of a cantilever seen from the side. Due to the nodal points certain parts of the cantilever do not take part of the vibration, and the particle depicted approximately from the base of the cantilever is in theory not detectable in the second mode.
Schematic of the setup used in the experiments. The micro cantilever chip is clamped on a piezo actuator driven by a gain/phase analyzer. Both cantilever and piezoactuator are placed in a vacuum chamber. A laser is focused on the cantilever and the position of the reflected beam is detected by a photodiode, and the signal is feed into the gain/phase analyzer.
(a) SEM image showing part of the micro cantilever with a gold bead positioned close to the apex. The scale bar is . The inset shows a close-up of the gold particle (scale bar 500 nm). (b) Simulated structure used for calculation of the theoretical shift in resonance as a function of mass position. The simulated cantilever has the same dimensions as the cantilever used in the experiment, and the mesh generated for the calculations consists of bricks which are in the length direction of the cantilever.
Resonant peaks for the second bending mode as function of position and the average factor for the recorded bending modes. The positions are indicated in Fig. 1. Only part of the recorded second bending mode peaks are shown for clarity.
Measured shift in resonance as a function of position compared to the simulated values shown for the first four bending modes of vibration.
The resonant frequency measured and simulated for the first four bending modes of the cantilever together with the experimentally observed maximum change in frequency and relative sensitivity for the specific mode.
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