Calibration of T-shaped atomic force microscope cantilevers using the thermal noise method

The tip-sample interaction force measurements in atomic force microscopy (AFM) provide information about materials' properties with nanoscale resolution. The T-shaped cantilevers used in Torsional-Harmonic AFM allow measuring the rapidly changing tip-sample interaction forces using the torsional (twisting) deflections of the cantilever due to the off-axis placement of the sharp tip. However, it has been difficult to calibrate these cantilevers using the commonly used thermal noise-based calibration method as the mechanical coupling between flexural and torsional deflections makes it challenging to determine the deflection sensitivities from force-distance curves. Here, we present thermal noise-based calibration of these T-shaped AFM cantilevers by simultaneously analyzing flexural and torsional thermal noise spectra, along with deflection signals during a force-distance curve measurement. The calibration steps remain identical to the conventional thermal noise method, but a computer performs additional calculations to account for mode coupling. We demonstrate the robustness of the calibration method by determining the sensitivity of calibration results to the laser spot position on the cantilever, to the orientation of the cantilever in the cantilever holder, and by repeated measurements. We validated the quantitative force measurements against the known unfolding force of a protein, the I91 domain of titin, which resulted in consistent unfolding force values among six independently calibrated cantilevers.