Optimization design of V-shaped microcantilevers for frequency ratio regulation and higher harmonic enhancement - Bangzhi Zhang; Changyun Yang; Xilong Zhou (AIP Advances)
V-shaped microcantilevers have advantages in dynamic atomic force microscopy (AFM) imaging, such as increased stability or decreased sample damage. However, for higher harmonic or multi-frequency imaging, the regulation of the frequency ratio between higher-mode resonance frequency and fundamental frequency is impeded for lacking a quantitative relationship between the frequency ratio and geometric parameters. In this work, a function model relating the frequency ratio to the dimensionless geometric parameters of V-shaped microcantilevers is obtained based on dimensional analysis. The finite difference method is employed to solve the vibrational equation, demonstrating that the frequency ratio is primarily governed by the normalized free-end width and leg width, but thickness and length ratios have negligible influence. A set of data incorporating frequency ratios under various geometric parameters is created and fitted into a two-variable function model. By adjusting the frequency ratio to specific integer multiples, optimized designs have been demonstrated to enhance higher harmonic amplitudes by up to 103.3%. This work provides a framework for optimizing V-shaped microcantilevers, enabling high-sensitivity, multi-frequency AFM imaging.