From images to interactions: high-resolution phase imaging in tapping-mode atomic force microscopy.

In tapping-mode atomic force microscopy, the phase shift between excitation and response of the cantilever is used as a material-dependent signal complementary to topography. The localization of information in the phase signal is demonstrated with 1.4-nm lateral resolution on purple membrane of Halobacterium salinarum in buffer solution. In a first-order approximation, the phase signal is found to correlate with modulations of the tip oscillation amplitude, induced by topography. Extending the analysis to contributions of the tip-sample interaction area as a second-order approximation, a method is proposed to extract information about the interaction from the phase signal for surfaces with a roughness in the order of the tip radius.