Sensitivity of V-shaped atomic force microscope cantilevers based on a modified couple stress theory

A relationship based on a modified couple stress theory is developed to investigate the flexural sensitivity of a V-shaped cantilever of an atomic force microscope (AFM) taking into account the normal interaction force between the cantilever tip and the sample surface. An approximate solution to the flexural vibration problem is obtained using the Rayleigh–Ritz method. The results show that the sensitivity of the V-shaped AFM cantilever using the modified couple stress theory is smaller than that using the classical beam theory for the lower contact stiffness. However, when the contact stiffness becomes higher, the situation is reversed. Furthermore, as the ratio of cantilever thickness to internal material length scale parameter decreases, the sensitivity of the cantilever decreases.

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