Sensitivity analysis of a caliper formed atomic force microscope cantilever based on a modified couple stress theory

A relationship based on the modified couple stress theory is developed to investigate the flexural sensitivity of an atomic force microscope (AFM) with assembled cantilever probe (ACP). This ACP comprises a horizontal cantilever, two vertical extensions and two tips located at the free ends of the extensions which form a caliper. An approximate solution to the flexural vibration problem is obtained using the Rayleigh–Ritz method. The results show that the sensitivities of AFM ACP obtained by the modified couple stress theory are smaller than those evaluated by the classical beam theory at the lower contact stiffness. The results also indicate that the flexural sensitivities of the proposed ACP are strong size dependant when the thickness of the cantilever is close to the material length scale, especially at lower contact stiffness. Furthermore, the greatest flexural modal sensitivity occurs at a small contact stiffness of the system, in which the ratio of the cantilever thickness to the material length scale and the distance between the vertical extensions are also small. In this situation, the distance between the vertical extensions and the clamped end of the cantilever and also the vertical extensions lengths are large. The results reveal that the sensitivity of the right sidewall tip is higher than that of the left one.