Behaviour of forbidden modes in the impedance characterization and modeling of piezoelectric microcantilevers

A systematic impedance analysis of the resonance response obtained from commercial piezoelectric scanning force microscopy (SFM) cantilevers, comprising both experimental and simulation work, has been carried out. A finite element model (FEM) has been developed and fitted using experimental data, from which valuable conclusions have been reached. Although non-fundamental modes are less used in sensing applications, they have been emphasized in this work. Two main arguments justify a deeper study of these higher order modes. First, an SFM cantilever acting as a gravimetric sensor and driven at a non-fundamental resonance frequency shows a real potential to enhance its mass detection sensitivity when compared with its performance in the usual driving scheme at the fundamental frequency. Secondly, the characterization of some non-fundamental modes, torsionally shaped, reveals an unexpected behaviour that should be known and understood previously to any gravimetric sensor design using torsional modes. Results show that modes of torsional nature cannot be detected electrically because they are not even excited by the applied ac field. Moreover, torsional modes, successfully excited by an external harmonic mechanical stimulus, cannot be detected electrically either. An explanation to this phenomenon, based on the redistribution and cancellation of surface reaction charges, is given in detail and supported by simulation results.