General Theory of Microscopic Dynamical Response in Surface Probe Microscopy: From Imaging to Dissipation

We present a general theory of atomistic dynamical response in surface probe microscopy when two solid surfaces move with respect to each other in close proximity, when atomic instabilities are likely to occur. These instabilities result in a bistable potential energy surface, leading to temperature dependent atomic scale topography and damping (dissipation) images. The theory is illustrated on noncontact atomic force microscopy and enables us to calculate, on the same footing, both the frequency shift and the excitation signal amplitude for tip oscillations. We show, using atomistic simulations, how dissipation occurs through reversible jumps of a surface atom between the minima when a tip is close to the surface, resulting in dissipated energies of 1.6 eV. We also demonstrate that atomic instabilities lead to jumps in the frequency shift that are smoothed out with increasing temperature.

Figure 1

Potential energy surfaces for the tip-surface system. Each curve corresponds to a certain tip height $z$ and is plotted as a function of the vertical displacement from the lattice site $q$ of a Mg atom at the step edge. Note that the lateral position of the Mg atom is different at each value of $q$.

Figure 2

Probability $P_A(t)$ of the system to be in state $A$ (a) and the total force on the tip $F_s(t)$ (b) as functions of the tip height $z$ at time $t$ at two temperatures of 100 and 300 K.

Figure 3

Frequency shift $\Delta f$ (a) and the dissipated energy per oscillation cycle (b) as functions of tip closest approach $z_0-A$ at 100 K (dashed line) and 300 K (solid line). The frequency shift calculated by following the global minimum (only conservative interactions) is also shown (dotted line).