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The use of bending eigenmodes of an AFM cantilever beyond the fundamental mode has been identified as a succesful way for improving the versatility and sensitivity of dynamic force microscopy methods for studying different sample properties. In this contribution, we present the use of higher cantilever eigenmodes to characterize vibrations of micro and nanomechanical resonators at arbitrarily large resonance frequencies. Our method consists on using a particular cantilever mode for standard feedback control in tapping mode while another mode is used for detecting and imaging the resonator vibration. The resonator is driven at or near its resonance frequency with a signal modulated in amplitude at a frequency that matches the resonance of the cantilever mode used for detecting the resonator vibration. In consequence, this cantilever mode is excited with an amplitude proportional to the resonator vibration, that is detected with an external lock-in amplifier. We show two different application examples of this method. In the first one, acoustic wave vibrations of a Film Bulk Acoustic Resonator (FBAR) around 1.6 GHz are characterized. Our method overcomes the limitations of conventional contact-mode acoustic imaging, allowing an up to five times faster tip scan speed, minimizing tip-surface interaction effects and preventing image artifacts from thermo-mechanical effects. In the second example, the application of the method for characterizing bending modes of carbon nanotube (CNT) resonators is presented. In this case, the low force constant of the CNT resonators, typically lower than usual cantilever force constants, makes the use of contact mode impractical. By our method, the resonance frequencies and mode shapes of the first three bending eigenmodes of multi-wall nanotube resonators are found to be close to what expected from elastic beam theory. In contrast, the results for single-wall devices are found to deviate significantly from theory, which is attributed to the effects of stress, slack or contamination. Our results demonstrate that AFM can provide essential information about the performance of micro and nanomechanical resonators and hence contribute to the development of their application in RF signal processing, ultrasensitive mass detection, etc. |