Spring constant calibration of atomic force microscope cantilevers of arbitrary shape

Area of Science:

• Physics
• Materials Science
• Nanotechnology

Background:

• Accurate spring constant determination is crucial for quantitative atomic force microscopy (AFM) measurements.
• Existing calibration methods, like Sader et al.'s, are primarily for rectangular cantilevers.
• Hydrodynamic functions are essential for relating cantilever properties to measurements in fluid.

Purpose of the Study:

• To develop and present hydrodynamic functions for a range of irregular and non-rectangular AFM cantilevers.
• To enable accurate spring constant calibration for commonly used, non-ideal cantilever geometries.
• To provide a method applicable to micro- and nanomechanical systems.

Main Methods:

• Calculation of hydrodynamic functions for various non-rectangular AFM cantilever geometries (arrow, V-shape, irregular rectangular, etc.).
• Development of an approximate formulation for arbitrary microcantilever geometries.
• Analysis of implementation, uncertainties, and conversion factors for static and dynamic spring constants.

Main Results:

• Hydrodynamic functions are provided for multiple irregular AFM cantilever shapes.
• An approximate formulation for arbitrary geometries is proposed.
• The method allows for accurate and routine determination of spring constants for diverse cantilevers.

Conclusions:

• The presented hydrodynamic functions extend accurate AFM cantilever calibration to non-rectangular and irregular shapes.
• This work facilitates precise measurements and enhances the design and application of micro- and nanomechanical systems.
• The findings offer practical solutions for researchers using diverse AFM cantilever geometries.