Variable frequency characterization of interaction at nanoscale in   linear dynamic AFM: an FFM primer
  Using electrostatic coupling between an AFM tip and a metallic surface as a test interaction, we here present the measurement of the force between the tip and the surface, together with the measurement of the interaction stiffness and the associated dissipation. These three quantities constitute a full characterization of the interaction at nanoscale. They are measured independently, simultaneously and quantitatively at the same place. This is made possible thanks to a force feedback method that ensures the DC immobility of the tip and to the simultaneous application of a sub-nanometer oscillation to the tip. In this established linear regime, stiffness and damping are directly obtained from amplitude and phase change measurements. The needed information for this linear transformation is solely the lever properties in the experimental context. Knowledge of k, its stiffness, its damping coefficient and Q0, its first resonance frequency is shown to be sufficient in the frequency range we are here exploring. Finally, we demonstrate that this method is not restricted to the lever resonance frequency. To the contrary, this interaction characterization whose resolution is limited by the Brownian motion, can be used at any frequencies with essentially the same performances. We believe that simultaneous and independent measurements of force, stiffness and damping, out of lever resonance, at nanoscale, and within the context of linear response define a new AFM paradigm that we call Force Feedback Microscopy (FFM). This article details the use of FFM using a well known and easy to implement electrostatic interaction between a regular AFM tip and a metallic surface in air. 
Simon Carpentier, Mario S.Rodrigues, Jo\"el Chevrier
cond-mat.mes-hall