Characterization of external potential for field emission resonances and its applications on nanometer-scale measurements

The form of the external potential (FEP) for generating field emission resonance (FER) in a scanning tunneling microscopy (STM) junction is usually assumed to be triangular. We demonstrate that this assumption can be examined using a plot that can characterize FEP. The plot is FER energies versus the corresponding distances between the tip and sample. Through this energy-distance relationship, we discover that the FEP is nearly triangular for a blunt STM tip. However, the assumption of a triangular potential form is invalid for a sharp tip. The disparity becomes more severe as the tip is sharper. We demonstrate that the energy-distance plot can be exploited to determine the barrier width in field emission and estimate the effective sharpness of an STM tip. Because FERs were observed on Pb islands grown on the Cu(111) surface in this study, determination of the tip sharpness enabled the derivation of the subtle expansion deformation of Pb islands due to electrostatic force in the STM junction.