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In this work, a new theoretical model for contact resonance atomic force microscopy, which incorporates the elastic dynamics of a long sensing tip is presented. The model is based on the Euler–Bernoulli beam theory and includes coupling effects from the two-beam structure, also known as an ‘L-shaped’ beam in the literature. Here, high-accuracy prediction of the sample stiffness, using several vibration modes with a relative error smaller than 10% for practical working ranges, is demonstrated. A discussion on the model’s capability to predict the dynamic phenomena of eigenmode veering and crossing, as the force applied to the sample increases, is presented. The L-shaped beam model presented here is also applicable for structural applications such as: micro-electro-mechanical systems, energy harvesting, and unmanned aerial vehicle landing gear.

 

Abstract In this work, we present an experimental validation of a new contact resonance atomic force microscopy model developed for sensors with long, massive tips. A derivation of a new technique and graphical method for the identification of the unknown system parameters is presented. The technique and contact resonance model are experimentally validated. The agreement between our contact resonance experimental measurements and values obtained from nanoindentation show a minimal error of 1.4%–4.5% and demonstrate the validity of the new contact resonance model and system parameter identification technique. 

Abstract In this article, we present a new contact resonance atomic force microscopy-based method utilizing a square, plate-like microsensor to accurately estimate viscoelastic sample properties. A theoretical derivation, based on Rayleigh–Ritz method and on an “unconventional” generalized eigenvalue problem, is presented and a numerical experiment is devised to verify the method. We present an updated sensitivity criterion that allows users, given a set of measured in-contact eigenfrequencies and modal damping ratios, to select the best eigenfrequency for accurate data estimation. The verification results are then presented and discussed. Results show that the proposed method performs extremely well in the identification of viscoelastic properties over broad ranges of nondimensional sample stiffness and damping values. 

Abstract Numerous nanometrology techniques concerned with probing a wide range of frequency-dependent properties would benefit from a cantilevered sensor with tunable natural frequencies. In this work, we propose a method to arbitrarily tune the stiffness and natural frequencies of a microplate sensor for atomic force microscope applications, thereby allowing resonance amplification at a broad range of frequencies. This method is predicated on the principle of curvature-based stiffening. A macroscale experiment is conducted to verify the feasibility of the method. Next, a microscale finite element analysis is conducted on a proof-of-concept device. We show that both the stiffness and various natural frequencies of the device can be controlled through applied transverse curvature. Dynamic phenomena encountered in the method, such as eigenvalue curve veering, are discussed and methods are presented to accommodate these phenomena. We believe that this study will facilitate the development of future curvature-based microscale sensors for atomic force microscopy applications. 

In this study, we propose a novel plate-like sensor which utilizes curvature-based stiffening effects for enhanced nanometrology. In the proposed concept, the stiffness and natural frequencies of the sensor can be arbitrarily adjusted by applying a transverse curvature via piezoelectric actuators, thereby enabling resonance amplification over a broad range of frequencies. The concept is validated using a macroscale experiment. Then, a microscale finite element analysis is used to study the effect of applied curvature on the microplate static stiffness and natural frequencies. We show that imposed transverse curvature is an effective way to tune the in-situ static stiffness and natural frequencies of the plate sensor system. These findings will form the basis of future curvature-based stiffening microscale studies for novel scenarios in atomic force microscopy.