Energy transfer between eigenmodes in multimodal atomic force microscopy

Abstract

We present experimental and computational investigations of tetramodal and pentamodal atomic force microscopy (AFM), respectively, whereby the first four or five flexural eigenmodes of the cantilever are simultaneously excited externally. This leads to six to eight additional observables in the form of amplitude and phase signals, with respect to the monomodal amplitude modulation method. We convert these additional observables into three or four dissipation and virial expressions, and show that these quantities can provide enhanced contrast that would otherwise remain hidden in the original observables. We also show that the complexity of the multimodal impact leads to significant energy transfer between the active eigenmodes, such that the dissipated power for individual eigenmodes may be positive or negative, while the total dissipated power remains positive. These results suggest that the contrast of individual eigenmodes in multifrequency AFM should be not be considered in isolation and that it may be possible to use different eigenfrequencies to probe sample properties that respond to different relaxation times.

Periodicity in bimodal atomic force microscopy

“…Finally, the energy irreversibly lost to the tip-sample interaction E dis is the contribution of energy transfer from all modes, 7,37 i.e., in bimodal, the first two modes, as…”

“…[5][6][7][8] In standard monomodal AFM, the cantilever is externally excited at a single frequency. 9 When the tip interacts with the nonlinear tip-sample forces, exact multiples of the drive frequency, i.e., its higher harmonics, are excited.…”

“…Then, the amplitude, phase, and mean deflection of the cantilever at the frequency of the drive are the experimental observables. In the multifrequency approach, two 13 or more 7,14,15 external drives are employed to excite the cantilever at or near the natural frequencies or eigenmodes of the free cantilever. The simultaneous excitation of two frequencies (see a illustration of bimodal excitation in Fig.…”

“…18 Still, while attractive for the development of the field, the simultaneous excitation of multiple frequencies at or near the eigenmodes comes at the cost of additional instrumentation, 19 added complexity to cantilever dynamics 20,21 and the requirement of interpreting secondary contrast channels. 7,14,22,23 Furthermore, in order to exploit the potential of bimodal AFM, it is of great interest to understand whether the motion is, or can be forced to be, periodic. Periodic motion in this context implies that there is a fundamental frequency the integer multiples of which constitute the full set of higher frequencies present in the signal.…”

Optimization of phase contrast in bimodal amplitude modulation AFM

“…The power dissipated by the 2nd mode also shows a maximum with A 1 /A 01 near 0.2 ( Figure 4c). A discussion about the energy transfer among different modes is presented by Solares and co-workers [48]. The data plotted in Figure 3 and Figure 4 has been obtained by using the dForce simulator [49].…”