Mechanical detection and mode shape imaging of vibrational modes of micro and nanomechanical resonators by dynamic force microscopy

Abstract

We describe a method based on the use of higher order bending modes of the cantilever of a dynamic force microscope to characterize vibrations of micro and nanomechanical resonators at arbitrarily large resonance frequencies. Our method consists on using a particular cantilever eigenmode for standard feedback control in amplitude modulation operation while another mode is used for detecting and imaging the resonator vibration. In addition, the resonating sample device is driven at or near its resonance frequency with a signal modulated in amplitude at a frequency that matches the resonance of the cantilever eigenmode used for vibration detection. In consequence, this cantilever mode is excited with an amplitude proportional to the resonator vibration, which 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 around 1.6 GHz are imaged. In the second example, bending modes of carbon nanotube resonators up to 3.1 GHz are characterized. In both cases, the method provides subnanometer-scale sensitivity and the capability of providing otherwise inaccessible information about mechanical resonance frequencies, vibration amplitude values and mode shapes.