Coupling in piezoelectric tube scanners used in scanning probe microscopes

A new model for tube scanners used in scanning probe microscopes (SPM), and particularly in atomic force microscopes (AFM), is presented. The model captures the coupling between motion in different axes as well as a bending motion due to a supposedly pure extension of the tube. In addition, the effect of coupling on the AFM cantilever dynamics is presented in a revised version of our model in El Rifai, and Youcef-Toumi, (2000). It is shown that due to coupling, the bending mode becomes observable from the AFM cantilever deflection sensor output. This is contrary to the ideal uncoupled case. Consequently, to avoid exciting the first bending mode, a large reduction in feedback bandwidth is required (a factor of 35 for the commercial AFM under consideration). As a result, ringing might occur during scanning at relatively low scan speeds, few Hertz, which will introduce artifacts in the image. Furthermore, in scanning a 4 μm step, an estimated change of 12% will result in the steady state probe-sample force between the top and bottom of the step. This adversely affects the scanner calibration for large heights, adding to the nonlinear sensitivity of the piezoelectric material. The results presented within are supported by experimental data