Modeling the hysteresis of a scanning probe microscope

Most scanning probe microscopes use piezoelectric actuators in open loop co nfigurations. Therefore a major problem related to these instruments is the image distortion due to the hysteresis effect of the piezo. In order to el iminate the distortions, cost effective software control based on a model f or hysteresis can be applied to the scanner. We describe a new rate-indepen dent model for the hysteresis of a piezo scanner. Two reference standards w ere used to determine the accuracy of the model; a one-dimensional grating with a period of 3.0 mu m 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 ra nge was covered. A least-squares fit of the experiments to the hysteresis m odel provided standard deviations per scan range of around 0.2%. This repre sents an uncertainty of 1 pixel. Since our model is based on a differential equation, it is flexible even to simulate arbitrary experimental condition s such as a sudden change in the offset. (C) 2000 American Vacuum Society. [S0734-211X(00)08902-2].