Quantitative atom-resolved force gradient imaging using noncontact atomic force microscopy

Quantitative force gradient images are obtained using a sub-angström amplitude, off-resonance lever oscillation method during scanning tunneling microscopy imaging. We report the direct observation of short-range bonds, and the measured short-range force interaction agrees well in magnitude and length scale with theoretical predictions for single bonds. Atomic resolution is shown to be associated with the presence of a prominent short-range contribution to the total force interaction. It is shown that the background longer-range interaction, whose relative magnitude depends on the tip structure, has a significant effect on the contrast observed at the atomic scale.