Calibration of higher eigenmodes of cantilevers

TL;DR

This paper introduces a calibration method for higher eigenmodes of atomic force microscopy cantilevers that simplifies the process by using a power-law relationship and ratio measurements, verified through multiple approaches.

Contribution

It presents a novel calibration routine that determines higher-mode stiffnesses using a power-law relationship and ratio measurements, reducing calibration effort for similar cantilevers.

Findings

Power-law relationships for higher-mode stiffnesses are established.

The method is validated with interferometric, AC approach-curve, and finite element analysis.

Calibration of mode amplitudes is achieved via thermal spectrum analysis.

Abstract

A method is presented for calibrating the higher eigenmodes (resonance modes) of atomic force microscopy cantilevers that can be performed prior to any tip-sample interaction. The method leverages recent efforts in accurately calibrating the first eigenmode by providing the higher-mode stiffness as a ratio to the first mode stiffness. A one-time calibration routine must be performed for every cantilever type to determine the power-law relationship between stiffness and frequency, which is then stored for future use on similar cantilevers. Then, future calibrations only require a measurement of the ratio of resonance frequencies and the stiffness of the first mode. This method is verified through stiffness measurements using three independent approaches: interferometric measurement, AC approach-curve calibration, and finite element analysis simulation. Power-law values for calibrating higher-mode stiffnesses are reported for three popular multifrequency cantilevers. Once the higher-mode stiffnesses are known, the amplitude of each mode can also be calibrated from the thermal spectrum by application of the equipartition theorem.