Exploring the potential of simultaneous resonance in multi-frequency atomic force microscopy

We exploit simultaneous resonance phenomenon to improve performance of multifrequency atomic force microscopy. Simultaneous resonances, activated due to the nonlinear nature of the tip oscillations and intermodal couplings for a certain family of multi-frequency excitations, may be used to gather more information about the sample. To make simultaneous resonance occur, excitation frequencies are tuned in a way that two resonances take place simultaneously. We consider a non-contact atomic force microscope and model the three-dimensional probe-tip structure as an Euler-Bernoulli beam. Equation governing motion of the probe tip are obtained employing the Hamilton extended principle. Direct harmonic balance method is then used to solve this equation. It is found out, through extensive numerical simulations, that the present excitation scheme, which activates simultaneous resonance, improves both the resolution and the compositional contrast of images. Numerical investigations demonstrate that a small change in the Hamaker constant and the initial tip-sample distance leads to a significant change in the amplitude and/or phase shift of the simultaneous resonance. High sensitivity of the amplitude to the initial tip-sample distance can be utilized to increase the vertical resolution in environments with high and low quality factors. Also, simultaneous resonance phase shift sensitivity to the Hamaker constant is noticeably increased compared to that of the conventional multi-frequency atomic force microscopy. As a result, the compositional contrast is considerably enhanced.