Dynamic behavior of tuning fork shear-force structures in a SNOM system

• Nonlinear vibration equation is established for a deformable tuning fork probe assembly.
• Probe–sample interactions induced by Van der Waals force and viscous resistance are investigated.
• The viscous resistance between the probe and the water film is estimated using testing results.

Piezoelectric tuning fork shear-force structures are widely used as a distance control unit in a scanning near-field optical microscopy. However, the complex dynamic behavior among the micro-tuning forks (TFs), optical fiber probes, and the probe–surface interactions is still a crucial issue to achieve high-resolution imaging or near-field interaction inspections. Based on nonlinear beam tension-bending vibration theory, vibration equations in both longitudinal and lateral directions have been established when the TF structure and the optical fiber are treated as deformable structures. The relationship of the probe–surface interaction induced by Van der Waals force has been analyzed and the corresponding numerical results used to describe the vibrational behavior of the probe approaching the sample surface are obtained. Meanwhile, the viscous resistance of the liquid film on the sample surface has also been investigated using linear beam-bending vibration theory. Experiments testing the interaction between the probe and the water film on a single crystal silicon wafer have been carried out and the viscous resistance of the water film was estimated using the established equations. Finally, to use the TF-probe structure as a force sensor, the relation between the dynamic response of the TF-probe system and an external force on the probe tip was obtained.