Imaging of flexural and torsional resonance modes of atomic force microscopy cantilevers using optical interferometry

Commercial rectangular atomic force microscope cantilever beams made of silicon were set into vibration, using a piezoelectric ultrasonic transducer coupled to the chip of a cantilever. The transducer was excited with continuous rf in the frequency range of 100 kHz to 3 MHz. The vibrations were monitored using an optical Michelson heterodyne-interferometer allowing the surface of the cantilever under examination to be scanned with a lateral resolution of several μm. A number of free torsional and flexural vibration modes of the beams were imaged quantitatively. Comparison of the experimental resonance frequencies and the amplitude and phase distribution of the modes to theoretical models showed that asymmetries in the beam strongly influence the vibrational behavior of the beam. The consequences for quantitative local stiffness measurements are discussed.