Simulation and Impedance Characterization of Piezoelectric Microcantilevers

Simulations of the resonant behaviour in the electrical impedance of piezoelectric cantilevers, and its experimental validation, have been performed. The results of characterization of resonance frequencies in commercial AFM tips are shown. A computational model has been developed to solve piezoelectric dynamic equations and obtain the natural frequencies of the device and their associated mode shapes. Stress and polarization charges in the structure, in the presence of harmonic voltage excitation, have been determined. On the other hand, an experimental characterization using impedance measurements has been carried out for frequencies up to 1 MHz. When the calculated and measured impedance resonances are compared, a good agreement is found for all the mode frequencies. However, certain modes that are computed as natural resonances do not show the corresponding resonant impedance change. In this paper, we give detailed arguments that justify this discrepancy in terms of the symmetry of the generated stress and piezoelectric charge under harmonic voltage excitation present in the impedance measurements. We show how computer simulations of piezoelectric microresonators can be used to understand the frequency response of the impedance and its relation with the symmetry in mode shape.