Apparent diameter of carbon nanotubes in scanning tunnelling microscopy measurements

Abstract

Geometric effects influencing scanning tunnelling microscopy (STM) image formation ofsingle wall carbon nanotubes (SWCNTs) were studied within the framework of a simplemodel potential. We focused on the geometrical effects which may influence the tunnellingprobabilities and lead to discrepancies between the apparent height of the nanotubesmeasured by STM and their real geometrical diameter. We found that there are two mainfactors responsible for the underestimation of nanotubes diameter by measuring theirheight in STM images: (1) the curvature of the nanotube affects the cross sectional shapeof the tunnelling channel; (2) the decay rate of tunnelling probabilities inside the tunnelgap increases with increasing curvature of the electrodes. For a nanotube with 1 nmdiameter an apparent flattening of about 10%, due to these geometry-relatedeffects, is predicted. Furthermore these effects are found to be dependent on thediameter of the tubes and tip–sample distances: an increasing flattening of the tubesis predicted for decreasing tube diameter and increasing tip–sample distance.