Theory of amplitude modulation atomic force microscopy with and without Q-Control

The present text reviews the fundamentals of amplitude-modulation atomic force microscopy (AM-AFM), which is frequently also referred to as dynamic force microscopy, non-contact atomic force microscopy, or “tapping mode” AFM. It is intended to address two different kinds of readerships. First, due to a thorough coverage of the theory necessary to explain the basic features observed in AM-AFM, it serves theoreticians that would like to gain overview on how nanoscale cantilevers interacting with the surrounding environment can be used to characterize nanoscale features and properties of suitable sample surfaces. On the other hand, it is designed to introduce experimentalists to the physics underlying AM-AFM measurements to a degree that is not too specialized, but sufficient to allow them measuring the quantities they need with optimized imaging parameters.More specifically, this article first covers the basics of the various driving mechanisms that are used in AFM imaging modes relying on oscillating cantilevers. From this starting point, an analytical theory of AM-AFM is developed, which also includes the effects of external resonance enhancement (“Q-Control”). This theory is then applied in conjunction with numerical simulations to various situations occurring while imaging in air or liquids. In particular, benefits and drawbacks of driving exactly at resonance frequency are examined as opposed to detuned driving. Finally, a new method for the continuous measurement of the tip–sample interaction force is discussed.