In situ measurement of large piezoelectric displacements in resonant atomic force microscopy

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Abstract
In resonant atomic force microscopy (AFMR) the calibration of the tip–sample relative displacement remains a major problem. Commonly used PZT piezoceramics exhibit a nonlinear behavior response for large applied voltages. For low voltages applied to the piezoceramics (i.e., small corrugations), the calibration can be performed by measuring the height of known structures. For large displacements, the interferometric heterodyne detection used in the AFMR provides a relative tip–sample displacement up to 10 μm, without removing the piezo‐tube from the microscope. From these measurements, it was established that the piezosensitivity is not a constant parameter. Its averaged value during an excursion depends linearly on the applied voltage. With this system, routine controls are very easy and an example is given of the displacement corrections related to the nonlinearity of the piezo‐tube for the electrostatic interaction between the tip and a gold surface.