Frequency shifts and analytical solutions of an AFM curved beam

The squeeze damping coefficient between the cantilever of a straight AFM probe and the surface of a biological sample in liquids is inversely proportional to their distance to the third power. Due to the small cantilever-sample distance, the quality factor of AFM in liquid is too small and results in a low signal-noise ratio. In this study, an AFM curved beam is proposed to solve this problem. Results show that the squeeze damping is significantly decreased and thus the quality factor of an AFM curved beam is greatly increased. An effective mass-spring-damper model is presented and its analytical solution is derived. Moreover, the formulas of the resonant quality factor and frequency shift are discovered. In addition to the requirement of the low squeeze damping, high frequency shifts or sensitivities is necessary for accurate measurement. Results indicate that the effects of the arc angle and several parameters on the quality factor and the frequency shifts are significant. The optimum parameters for high quality and frequency shift are also investigated.