Field enhancement factors and self-focus functions manifesting in field emission resonances in scanning tunneling microscopy

Field emission (FE) resonance (or Gundlach oscillation) in scanning tunneling microscopy (STM) is a phenomenon in which the FE electrons emitted from the microscope tip couple into the quantized standing-wave states within the STM tunneling gap. Although the occurrence of FE resonance peaks can be semi-quantitatively described using the triangular potential well model, it cannot explain the experimental observation that the number of resonance peaks may change under the same emission current. This study demonstrates that the aforementioned variation can be adequately explained by introducing a field enhancement factor that is related to the local electric field at the tip apex. The peak number of FE resonances increases with the field enhancement factor. The peak intensity of the FE resonance on the reconstructed Au(111) surface varies in the face-center cubic, hexagonal-close-packed, and ridge regions, thus providing the contrast in the mapping through FE resonances. The mapping contrast is demonstrated to be nearly independent of the tip-sample distance, implying that the FE electron beam is not divergent because of a self-focus function intrinsically involved in the STM configuration.