Experimental determination of mode correction factors for thermal method spring constant calibration of AFM cantilevers using laser Doppler vibrometry.

Mode correction factors (MCFs) represent a significant adjustment to the spring constant values measured using the thermal cantilever calibration method. Usually, the ideal factor of 0.971 for a tipless rectangular cantilever is used, which adjusts the value by 3% for the first flexural mode. An experimental method for determining MCFs has been developed that relies on measuring the areas under the first few resonance peaks for the flexural mode type. Using this method, it has been shown that MCFs for the first flexural mode of commercially available atomic force microscope cantilevers actually vary from 0.95 to 1.0, depending on the shape and end mass of the cantilever. Triangular shaped cantilevers tend to lower MCFs with tipless versions providing the lowest values. Added masses (including tips) tend to increase the first flexural mode's MCF to higher values with large colloid probes at the high extreme. Using this understanding and applying it to the recently developed laser Doppler vibrometry thermal calibration method it is now possible to achieve very accurate and precise cantilever spring constant calibrations (uncertainties close to ±1%) with commonly available commercial cantilevers such as tipped rectangular and triangular cantilevers, and colloid probes.