Force feedback in dynamic atomic force microscopy

The feedback perspective of dynamic AFM provides a powerful tool to investigate the non-linear system dynamics from a system theoretic point of view. Including the higher order dynamics of the extended cantilever beam in the model the contact resonances can be reproduced faithfully without the need to solve the partial differential equation of motion directly. The investigation of the non-linear dynamics provides valuable insight into the generation of higher harmonics in dynamic AFM. However, the light]ever detection scheme is widely used in dynamic AFM. This means that - strictly speaking - the tip-deflection is not a measurable quantity: the local deflection angle is measured but not the deflection itself. Additionally, time-delays may be introduced into the system influencing the dynamic behavior. Apart from system inherent time delays, a delayed force feedback is often used in order manipulate the system's resonance characteristics (quality factor). Such an active control of the oscillatory behavior of the cantilever used in atomic force microscopy (AFM) allows one to tune the quality factor to purpose. For experiments requiring a high force sensitivity an enhancement of the quality factor is desirable whereas in time critical experiments additional damping may be needed. In order to control the quality factor a feedback signal is used that approximates the time derivative of the system state within the bandwidth of interest.