Nonlinear Dynamic Models of Piezoelectric Nano-Stages

High resolution imaging in scanning probe microscopes is conducted by rastering a sharp probe over a sample surface. The rastering is done using piezoelectric elements, converting applied voltage into mechanical motion. For example, imaging of a rectangular field of view is done by applying triangular waveforms with different frequencies to X and Y piezoelectric stage, respectively. A disadvantage of piezoelectric stages is their non-linear response to applied voltage. In addition to that, they show creep, i.e. moving even though the applied voltage is constant. This results in distortions of the acquired image. Furthermore, it can result in not precisely imaging the requested area. A common solution is to add position sensors to the piezoelectric stages and measure actual movements. By using a feedback it would be almost guaranteed that the piezoelectric stage moves as requested. The disadvantage of this approach is that it reduces the bandwidth and increases the noise. The aim of this paper is to study advanced piezoelectric stage models to better control the actual stage movement in an open-loop scan.