General interpretation and theory of apparent height in dynamic atomic force microscopy

We provide a general theory and interpretation behind the ubiquitous loss of apparent height of nanostructures in dynamic atomic force microscopy that occurs in the attractive regime irrespective of stiffness. We show analytically and numerically that while the true height of a nanostructure could be smaller than measured, lack of symmetry biases measurements towards height loss. In particular, the finite size of the tip always contributes to height loss while the nature of attractive forces might contribute to height gain or loss. The theory further predicts otherwise counterintuitive phenomena such as the possibility to gain height by increasing the interaction.