A non-contact, thermal noise based method for the calibration of lateral deflection sensitivity in atomic force microscopy

Calibration of lateral forces and displacements has been a long standing problem in lateral force microscopies. Recently, it was shown by Wagner et al. that the thermal noise spectrum of the first torsional mode may be used to calibrate the deflection sensitivity of the detector. This method is quick, non-destructive and may be performed in situ in air or liquid. Here we make a full quantitative comparison of the lateral inverse optical lever sensitivity obtained by the lateral thermal noise method and the shape independent method developed by Anderson et al. We find that the thermal method provides accurate results for a wide variety of rectangular cantilevers, provided that the geometry of the cantilever is suitable for torsional stiffness calibration by the torsional Sader method, in-plane bending of the cantilever may be eliminated or accounted for and that any scaling of the lateral deflection signal between the measurement of the lateral thermal noise and the measurement of the lateral deflection is eliminated or corrected for. We also demonstrate that the thermal method may be used to characterize the linearity of the detector signal as a function of position, and find a deviation of less than 8% for the instrument used.