Calibration of higher eigenmode spring constants of atomic force microscope cantilevers

Area of Science:

• Physics
• Materials Science
• Nanotechnology

Background:

• Dynamic atomic force microscopy (dAFM) relies on precisely calibrated cantilever spring constants.
• Accurate calibration is crucial for quantitative measurements in dAFM.
• Higher eigenmodes of cantilevers are increasingly utilized for advanced dAFM applications.

Purpose of the Study:

• To compare the suitability of standard spring constant calibration methods for higher eigenmodes in dAFM.
• To identify the most reliable calibration method for higher eigenmodes.
• To provide experimental validation for theoretical findings.

Main Methods:

• Theoretical analysis of Sader's spring constant calibration method.
• Theoretical analysis of the thermal noise method for spring constant calibration.
• Experimental measurement of thermal vibrations for representative dAFM cantilevers in air.

Main Results:

• Sader's method is ill-suited for higher eigenmode calibration due to its reliance on a priori eigenmode shape knowledge.
• The thermal noise method is valid for higher eigenmodes as it does not require prior knowledge of the eigenmode shape.
• Experimental data supports the theoretical conclusion that the thermal noise method is more robust for higher eigenmodes.

Conclusions:

• The thermal noise method is the recommended approach for calibrating higher eigenmodes of dAFM cantilevers.
• Standard calibration methods may fail when applied to higher-order modes, necessitating alternative approaches.
• This study clarifies the applicability of different calibration techniques in advanced dAFM.