Implications of the Contact Radius to Line Step (CRLS) Ratio in AFM for Nanotribology Measurements

Investigating the mechanisms of defect generation and growth at surfaces on the nanometer scale typically requires high-resolution tools such as the atomic force microscope (AFM). To accurately assess the kinetics and activation parameters of defect production over a wide range of loads (F(z)), the AFM data should be properly conditioned. Generally, AFM wear trials are performed over an area defined by the length of the slow (L(sscan)) and fast scan axes. The ratio of L(sscan) to image resolution (res, lines per image) becomes an important experimental parameter in AFM wear trials because it defines the magnitude of the line step (LS = L(sscan)/res), the distance the AFM tip steps along the slow scan axis. Comparing the contact radius (a) to the line step (LS) indicates that the overlap of successive scans will result unless the contact radius-line step ratio (CRLS) is < or =(1)/(2). If this relationship is not considered, then the scan history (e.g., contact frequency) associated with a single scan is not equivalent at different loads owing to the scaling of contact radius with load (a proportional variant F(z)(1/3)). Here, we present a model in conjunction with empirical wear tests on muscovite mica to evaluate the effects of scan overlap on surface wear. Using the Hertz contact mechanics definition of a, the CRLS model shows that scan overlap pervades AFM wear trials even under low loads. Such findings indicate that simply counting the number of scans (N(scans)) in an experiment underestimates the full history conveyed to the surface by the tip and translates into an error in the actual extent to which a region on the surface is contacted. Utilizing the CRLS method described here provides an approach to account for image scan history accurately and to predict the extent of surface wear. This general model also has implications for any AFM measurement where one wishes to correlate scan-dependent history to image properties as well as feature resolution in scanned probe lithographies.