Modeling the hysteresis of a scanning probe microscope

Most scanning probe microscopes use piezoelectric actuators in open loop configurations. Therefore a major problem related to these instruments is the image distortion due to the hysteresis effect of the piezo. In order to eliminate the distortions, cost effective software control based on a model for hysteresis can be applied to the scanner. We describe a new rate-independent model for the hysteresis of a piezo scanner. Two reference standards were used to determine the accuracy of the model; a one-dimensional grating with a period of 3.0 μm and a two-dimensional grating with 200 nm pitch. The structures were scanned for different scan ranges varying from 5 V peak to peak to 440 V peak to peak, so that 99% of the scanners’ full motion range was covered. A least-squares fit of the experiments to the hysteresis model provided standard deviations per scan range of around 0.2%. This represents an uncertainty of 1 pixel. Since our model is based on a differential equation, it is flexible even to simulate arbitrary experimental conditions such as a sudden change in the offset.