Calibration of the lateral spring constant for a custom T-shaped atomic force microscopy probe

Atomic force microscopy (AFM) is a versatile tool for investigating nanotribology, where the probe's lateral spring constant is a critical parameter. This work introduced a method to calibrate the lateral spring constant of a T-shaped probe integrated into a custom AFM system. An expression for the lateral spring constant of the probe was derived by correlating the probe's lateral bending and torsional resonance frequencies with its reduced masses and moments of inertia. In the experiment, electrochemical etching was utilized to gradually reduce the mass of the probe tip. The probe's resonance was excited using three piezoelectric techniques, allowing the measurement of resonance frequencies across different vibration modes. Finite element analysis was performed to predict the lateral spring constants of probes with varying dimensions, confirming the reliability of the proposed method.