Dynamic operation modes of AFM: Non-linear behavior and theoretical analysis of the stability of the AFM oscillator

The first part of this paper gives a theoretical study of the mechanics of contact of an AFM tip on viscous materials. Analytical expressions are derived showing the non-linear behaviors specifically related to the use of dynamic operation modes of AFM on viscous materials. A detailed analysis of the dissipated energy as a function of the tip indentation is presented. The second part is dedicated to a theoretical analysis investigating the domain of stability of the oscillator and the influence of the machine. The theoretical approach includes the electronic feedback loop used with the frequency modulation mode. Because the interaction between the tip and the sample produces a dynamical non-linear behavior, an unstable branch occurs that can change the stability of the oscillator. In particular, a sudden jump of the oscillating tip can be produced. In spite of the complexity of the problem, the analytical approach ends with two simple equations. The two equations provide an unambiguous way of discriminating between the contributions from the machine and the tip sample interaction.