Spring constant calibration by frequency sweep

The spring constant of the cantilever and deflection sensitivity of the system are important parameters to perform quantitative force spectroscopy. In Software Version 3.7.3 we introduced a new calibration option determining the cantilever spring constant k from the frequency sweep window with visual feedback on fitting quality. Comparison of the sweep method with thermal noise data shows only minor differences in k found by the two methods.

Conventionally, the spring constant is determined from a thermal tune spectrum fitted with a simple harmonic oscillator model to obtain the resonance frequency and quality or Q factor. The spring constant is calculated with the method developed by John Sader and colleagues using the topview cantilever dimensions from a database in the AFM software.

For cantilevers in air the simple harmonic oscillator fit can also be applied on a frequency sweep to get the resonance frequency and quality factor of the cantilever oscillation. The Sader method only needs these two parameters from the resonance curve, in contrast to the equipartion theorem, which needs to know the calibrated area under the curve.

Consequently, the Sader method can be used with the data from a frequency sweep to calculate the spring constant. The difference between the two spring constant determinations is only 2%, thus within the absolute accuracy of the method.

This spring constant calibration method is part of the advanced spectroscopy option for NaioAFM, and Easyscan 2 or SPM S product lines if dynamic mode is available, making force spectroscopy more quantitative on these instruments. For CoreAFM and C3000 systems this option is part of the cantilever calibration option and allows the user to use both thermal tune and frequency sweeps to determine the spring constant.

If you want to know whether this option is available for your system or if you want to discuss your application with one of our experts, please contact us.

View or download the application note as PDF.

For the determination of the deflection sensitivity, the other calibration parameter required to convert the deflection into a force, the deflection needs to be measured on a hard surface. In the standard force spectroscopy mode kit a piece of silicon is included for this purpose.

Nanosurf application note TN01092

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