Sensitivity of higher mode of rectangular atomic force microscope to surface stiffness in air environment

The sensitivity of the resonance frequencies and the amplitudes of the first four flexural vibration modes of atomic force microscopy with a rectangular cross-section cantilever in an air environment to variation of a sample´s stiffness have been analysed. The cantilever has been modelled using Timoshenko beam theory, and the vertical and tangential forces between the tip and the sample in this simulation have been considered. The effect of tip position and the angle of the tip relative to the sample in changes of these sensitivities have been studied. Results indicate that for soft materials, the first mode compared with other modes is more sensitive to changes in the sample´s elasticity, so the first mode is the best mode for supplying high-contrast images but by increasing the sample´s stiffness, the higher mode will be sensitive, respectively. In addition, by increasing the angle between the cantilever and the sample´s surface, the first mode is less sensitive and higher modes will be sensitive faster because of changes in material stiffness but in contrast, by increasing the distance between the tip´s position and the free end of the cantilever, the sensitivity of the first mode increases and the higher mode will be sensitive for more stiff material.