Calibration and characterization of piezoelectric elements as used in scanning tunneling microscopy

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Abstract
We investigated the behavior of piezoelectric elements used in an STM for fine positioning of the tip. Special attention was paid to the influence of hysteresis. We found that the expansion coefficient of the elements depends on the magnitude of the displacements they produce. If the range is limited to several nanometers, the sensitivity can be taken constant and hysteresis can be neglected. However,if displacements of about a micron are involved, the sensitivity is about 40% higher and the hysteresis will significantly disturb the image. We also compared different calibration methods. An inductive displacement transducer yields results which correspond to those obtained with the known height of steps on a flat gold surface. A Michelson interferometer yields results which are valid for large displacements which cannot be used if small‐scale structures are imaged.