Analytical modeling and experimental verification for vibration of piezoelectric U-shaped AFM incorporating thermal loading and surface effect

ABSTRACT

In this work, an experimental model and a simplified analytical model of U-shaped atomic force microscopy (AFM) probe are described. The effects of surface elasticity, surface piezoelectricity and thermal loading on U-shaped probe are considered for the first time. The obtained experimental results are for commercial U-shaped probe AN2-300 when it is mounted on the afm+ system. The results indicate that modeled beams on the basis of the couple stress theory have higher stiffness than the modeled ones based on the classical continuum theory. It is shown that both the surface elasticity and surface residual stress influence the natural frequencies. Also, it can be observed that the piezoelectric field shows both decreasing and increasing effects depending on the sign of the voltage. In order to check the accuracy of the presented theory for the U-shaped AFM probe, the analytical results achieved by the modified couple stress theory are compared with experimental results, and it is found that they are in a very good agreement. This work will improve understanding the vibrational behavior of U-shaped probes and may be of special interest in design and application of nanoscale structures.

KEYWORDS:

• U-shaped probe
• AFM
• modified couple stress theory
• piezoelectric
• thermal loading