An improved AFM model in z-direction with dynamics-coupling effect

This study considers two models in the z-direction displacement for an atomic force microscope (AFM), in which one was modeled without the coupling effect and another one was modeled being coupled with the x and y directions. The modeled AFM is a commercial type NT-MDT as the same one used in [1]. The piezoelectric tube scanner in the z-axis has the different dynamics behavior comparing with the piezoelectric actuators in the x or y axis. The measured frequency response for the z-axis model without the coupling effect shows the only one resonance located at 5kHz. However, the measured frequency response data in the AFM z-axis shows three resonances, if both the x-axis and y-axis scanners are supplied by the specified full-voltage source. These two resonances are located at 695Hz and 1.06kHz which are assumed to be generated by the coupling effect from the x and y directions. The coupled piezo-effect is verified in the paper and the model with the coupled effect fits quite well with the measured data.