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Vibrations of free and surface-coupled atomic force microscope cantilevers. Theory and experiment

: Rabe, U.; Arnold, W.; Janser, K.


Review of scientific instruments 67 (1996), Nr.9, S.3281-3293
ISSN: 0034-6748
ISSN: 1089-7623
Fraunhofer IZFP ()
atomic force microscopy; Balkenschwingung; elastic beam; elastic constant; elastische Konstante; Kraftmikroskopie; micro-nondestructive testing; mikro-zerstörungsfreie Prüfung

With an optical interferometer, the free vibration spectra and the local vibration amplitude of four rectangular atomic force microscope cantilevers made of silicon have been examined experimentally in a spectral range of 100 kHz to 10 MHz. A good agreement with the flexural wave theory of elasti beams was found. Coupling to torsional vibrations was also ovserved. When the sensor tip of the cantilever is in contact with a sample surface the resonances are shifted in frequency and the vibration amplitudes along the cantilever change. A method is presented to calculate this frequency shift using a linear approximation for the tip-sample interaction forces, and the results are compared with the frequency shift calculated from the point-mass model. The measured resonance frequencies of a surface-coupled cantilever do not correspond as well to the theoretical ones as in the free case even if the elastic-beam model is used. The reason for the disagreement is found to be the geometry of the c ommerical cantilevers and the nonlinearity of the tip-sample interaction force.