A piezoelectric controller plays a crucial role in the operation of atomic force microscope (AFM) cantilevers. The primary functions of this controller are as follows:

1. Precise Movement Control: The piezoelectric controller is responsible for the precise movement of the cantilever. It enables the fine positioning of the cantilever tip over the sample surface with nanometer accuracy. This precision is essential for obtaining high-resolution images and measurements at the atomic scale.

2. Vibration and Oscillation: In dynamic AFM modes, such as tapping mode or non-contact mode, the piezoelectric controller drives the oscillation of the cantilever. It controls the frequency and amplitude of the cantilever's vibrations, which are critical parameters for maintaining stable interactions between the tip and the sample.

3. Feedback Mechanism: The controller is part of the feedback loop that maintains a constant force or distance between the cantilever tip and the sample. By adjusting the voltage applied to the piezoelectric elements, the controller can modulate the cantilever's position in response to changes in the sample's topography or other properties.

4. Surface Scanning: The piezoelectric controller facilitates the scanning of the sample surface by moving the cantilever in a raster pattern. This scanning capability is essential for constructing detailed images of the sample's surface features.

Overall, the piezoelectric controller is integral to the AFM's ability to perform precise measurements and imaging, enabling researchers to study materials at the nanoscale with high accuracy and reliability.