A method for in situ characterization of tip shape in ac-mode atomic force microscopy using electrostatic interaction

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Abstract
We present a method for in situ characterization of the tip shape in atomic force microscopes that can operate in noncontact ac mode. By sweeping the voltage between tip and sample while recording the sample position as it is regulated to give a constant force gradient, we obtain curves giving information about the tip geometry. The measurements were performed in ultrahigh vacuum using electrochemically etched tungsten tips against a surface of doped silicon. Our results show that the sphere model gives a good description of the interaction, and that the radii we obtain are consistent with data from scanning electron microscopy. The method can also be used to estimate the value of the Hamaker constant and the contact potential between tip and sample.