Calibration of higher eigenmodes of cantilevers

Area of Science:

• Nanotechnology
• Materials Science
• Physics

Background:

• Atomic Force Microscopy (AFM) relies on cantilever dynamics for imaging.
• Accurate calibration of higher eigenmodes (resonant modes) is crucial for advanced AFM applications.
• Existing methods for higher eigenmode calibration can be complex and time-consuming.

Purpose of the Study:

• To present a novel, pre-interaction calibration method for higher eigenmodes of AFM cantilevers.
• To establish a reliable relationship between higher-mode stiffness and first-mode stiffness.
• To enable accurate amplitude calibration of each mode using the equipartition theorem.

Main Methods:

• Developed a method to determine higher-mode stiffness as a ratio to the first mode stiffness.
• Established a one-time calibration routine to find a power-law relationship between stiffness and frequency for each cantilever type.
• Verified the method using interferometric measurement, AC approach-curve calibration, and finite element analysis simulations.

Main Results:

• Reported power-law values for higher-mode stiffness calibration across several cantilever models.
• Demonstrated that future calibrations require only resonant frequency ratios and first-mode stiffness.
• Showed that higher-mode stiffness calibration allows for subsequent amplitude calibration from thermal spectra.

Conclusions:

• The presented method offers a simplified and accurate approach to calibrating higher eigenmodes in AFM cantilevers.
• This technique reduces calibration time and complexity, making advanced AFM analyses more accessible.
• The established power-law relationship and ratio-based calibration are robust and validated by multiple independent methods.