Contact mechanics and tip shape in AFM-based nanomechanical measurements.

Stiffness-load curves obtained in quantitative atomic force acoustic microscopy (AFAM) measurements depend on both the elastic properties of the sample and the geometry of the atomic force microscope (AFM) tip. The geometry of silicon AFM tips changes when used in contact mode, affecting measurement accuracy. To study the influence of tip geometry, we subjected ten AFM tips to the same series of AFAM measurements. Changes in tip shape were observed in the scanning electron microscope (SEM) between individual AFAM tests. Because all of the AFAM measurements were performed on the same sample, variations in AFAM stiffness-load curves were attributed to differences in tip geometry. Contact-mechanics models that assumed simple tip geometries were used to analyze the AFAM data, but the calculated values for tip dimensions did not agree with those provided by SEM images. Therefore, we used a power-law approach that allows for a nonspherical tip geometry. We found that after several AFAM measurements, the geometry of the tips at the very end is intermediate between those of a flat punch and a hemisphere. These results indicate that the nanoscale tip-sample contact cannot easily be described in terms of simple, ideal geometries.