Apparent diameter of carbon nanotubes in scanning tunnelling microscopy measurements

Geometric effects influencing scanning tunnelling microscopy (STM) image formation of single wall carbon nanotubes (SWCNTs) were studied within the framework of a simple model potential. We focused on the geometrical effects which may influence the tunnelling probabilities and lead to discrepancies between the apparent height of the nanotubes measured by STM and their real geometrical diameter. We found that there are two main factors responsible for the underestimation of nanotubes diameter by measuring their height in STM images: (1) the curvature of the nanotube affects the cross sectional shape of the tunnelling channel; (2) the decay rate of tunnelling probabilities inside the tunnel gap increases with increasing curvature of the electrodes. For a nanotube with 1 nm diameter an apparent flattening of about 10%, due to these geometry-related effects, is predicted. Furthermore these effects are found to be dependent on the diameter of the tubes and tip-sample distances: an increasing flattening of the tubes is predicted for decreasing tube diameter and increasing tip-sample distance.