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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. 

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. 

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. 

In this work, we present a new theoretical model for use in contact resonance atomic force microscopy. This model incorporates the effects of a long, massive sensing tip and is especially useful to interpret operation in the so-called trolling mode. The model is based on traditional Euler–Bernoulli beam theory, whereby the effect of the tip as well as of the sample in contact, modeled as an elastic substrate, are captured by appropriate boundary conditions. A novel interpretation of the flexural and torsional modes of vibration of the cantilever, when not in contact with the sample, is used to estimate the inertia properties of the long, massive tip. Using this information, sample elastic properties are then estimated from the in-contact resonance frequencies of the system. The predictive capability of the proposed model is verified via finite element analysis. Different combinations of cantilever geometry, tip geometry, and sample stiffness are investigated. The model’s accurate predictive ranges are discussed and shown to outperform those of other popular models currently used in contact resonance atomic force microscopy.