N. Zimron-Politi, R.C. Tung
University of Nevada, Reno,
Keywords: atomic force microscopy, contact resonance, data analysis, mechanical properties, fitting technique
Summary:In this work, we improve data analysis techniques for contact resonance atomic force microscopy. Using our proposed scheme, we find a significant increase in the prediction accuracy of the sample's stiffness compared to previously used techniques. In Contact Resonance (CR) atomic force microscopy (AFM), the microsensor is brought into firm contact with the sample of interest and the coupled sensor-sample system resonance frequency is measured. By processing the measured resonance frequency with a theoretical model, we are able to estimate the sample's mechanical properties. The theoretical model is developed using the Euler-Bernoulli (E-B) beam theory, relating the eigenvalues of the system to the system parameters through the boundary conditions of the beam. In common practice for CR data analysis, two eigenfrequencies from two experimentally measured eigenmodes taken at the same applied force are used to solve the CR model for two unknown system parameters, this is referred to as the “mode-crossing” approach. Recently, Friedrich and Cappella suggested a new data analysis approach in which the relationship between the applied force and the corresponding resonance frequency is fit with a combination of a simplified version of a CR model containing a single spring located near the beam end, and the Hertz contact mechanics model for a spherical indenter. In their work, they used the first eigenmode and showed good results on polymer samples. In this work, we expand the data analysis fitting technique suggested in Friedrich and Cappella’s work, to a generalized form that can be used in other CR models without any simplification to the characteristic equation. By expanding this data analysis method to other CR models, we allow for the use of higher-order models, which include multiple system parameters. Historically, these higher-order models were developed to include effects from: tip location, tip length, sensor's tilt angle, normal and lateral sample's stiffness and more. The large amount of system parameters introduced due to the inclusion of multiple effects resulted in large complex models which were impractical without quantitative knowledge for some of the system parameters. Following the derivation of the data analysis technique, we perform a numerical experiment using data from high-fidelity Finite Element (FE) modal analysis. We compare traditional mode-crossing results with the proposed technique, and show how CR accuracy can be improved using the proposed method, along with high order models.