Models for quantitative charge imaging by atomic force microscopy

Two models are presented for quantitative charge imaging with an atomic-force microscope. The first is appropriate for noncontact mode and the second for intermittent contact (tapping) mode imaging. Different forms for the contact force are used to demonstrate that quantitative charge imaging is possible without precise knowledge of the contact interaction. From the models, estimates of the best charge sensitivity of an unbiased standard atomic-force microscope cantilever are found to be on the order of a few electrons.