Contribution to the understanding of quantitative measurements of piezoelectric coefficients of thin films using AFM piezoresponse mode

In order to better understand the behaviour of piezoelectric films when probed with an Atomic Force Microscope, we have modeled the system cantilever/probe/piezoelectric thin film/silicon substrate with a home-made finite elements method. The results of the simulation in terms of amplitude of vibration are compared with real piezoelectric measurements performed with a commercial AFM instrument on a PZT thin film formed by rf-magnetron sputtering. The possibility of operating quantitative and very local measurements of the piezoelectric coefficients is discussed using this operating mode.