Equivalent Electromechanical Model for Quartz Tuning Fork Used in Atomic Force Microscopy.

Quartz tuning forks (QTFs) are self-sensing and possess a high quality factor, allowing them to be used as probes for atomic force microscopes (AFMs) for which they offer nano-scale resolution of sample images. Since recent work has revealed that utilizing higher-order modes of QTFs can offer better resolution of AFM images and more information on samples, it is necessary to understand the relationship between the vibration characteristics of the first two symmetric eigenmodes of quartz-based probes. In this paper, a model that combines the mechanical and electrical characteristics of the first two symmetric eigenmodes of a QTF is presented. Firstly, the relationships between the resonant frequency, amplitude, and quality factor between the first two symmetric eigenmodes are theoretically derived. Then, a finite element analysis is conducted to estimate the dynamic behaviors of the analyzed QTF. Finally, experimental tests are executed to verify the validity of the proposed model. The results indicate that the proposed model can accurately describe the dynamic properties of a QTF in the first two symmetric eigenmodes either under electrical or mechanical excitation, which will provide a reference for the description of the relationship between the electrical and mechanical responses of the QTF probe in the first two symmetric eigenmodes as well as the optimization of higher modal responses of the QTF sensor.