Sharpness-induced energy shifts of quantum well states in Pb islands on Cu(111)

Abstract

We elucidate that the tip sharpness in scanning tunneling microscopy (STM) can be characterized through the number of field-emission (FE) resonances. A higher number of FE resonances indicates higher sharpness. We observe empty quantum well (QW) states in Pb islands on Cu(111) under different tip sharpness levels. We found that QW states observed by sharper tips always had lower energies, revealing negative energy shifts. This sharpness-induced energy shift originates from an inhomogeneous electric field in the STM gap. An increase in sharpness increases the electric field inhomogeneity, that is, enhances the electric field near the tip apex, but weakens the electric field near the sample. As a result, higher sharpness can increase the electronic phase in vacuum, causing the lowering of QW state energies. Moreover, the behaviors of negative energy shift as a function of state energy are entirely different for Pb islands with a thickness of two and nine atomic layers. This thickness-dependent behavior results from the electrostatic force in the STM gap decreasing with increasing tip sharpness. The variation of the phase contributed from the expansion deformation induced by the electrostatic force in a nine-layer Pb island is significantly greater, sufficient to effectively negate the increase of electronic phase in vacuum.

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

“…Thus, we know that the effective sharpness is 121.1°for the six resonances in figure 3(a) and 84.6°for the nine resonances in figure 3(b). Evidently, a larger number of FERs corresponds to higher effective sharpness, which is consistent with the results of our previous study [19].…”

“…On the other hand, from the slope of the FEP in figure 2(b), it can be known that the electric field strength of the FERs is 0.29 V/Å. Consequently, the electric field of the field emission is stronger than that of FERs, which can be attributed to the sharpness of the STM tip that enhances the electric field near the tip but weakens that near the sample [19]. This situation is unable to be explained by the model in the inset in figure 2(a) where the STM tip is a plane.…”

“…Since Binning et al and Becker et al observed FER using STM [2,3], FER has been a powerful technique widely exploited to investigate the surface reconstructions [4,5] and properties [6], the atomic structure of the insulator surface [7], local work functions [8][9][10][11][12], the resistance at the nanometer scale [13], as well as the dynamics [14,15] and lateral quantization [16,17] of surface electrons above the vacuum level. Our recent studies have demonstrated that the field enhancement factor and sharpness of an STM tip can be qualitatively identified by counting the number of FERs [18,19]. Higher sharpness is manifested by a larger number of FERs.…”

Observing quantum trapping on MoS2 through the lifetimes of resonant electrons: revealing the Pauli exclusion principle

“…Recent studies have explained that under the same current, more FERs result from a sharper STM tip. [22][23][24] Fig. 1(b) also shows that the higher-order peaks in the spectra with three and ve FERs are all much narrower than those in the spectra with four and six FERs.…”

“…21 The zero valley intensities appearing around the FER may indicate that the observed material has a band gap above the vacuum level. 21 The number of FERs can manifest the sharpness [22][23][24] and eld enhancement factor 25 of the STM tip. Previous studies have demonstrated that FER can be used to investigate the atomic structure of an insulator, 26 plasmon-assisted electron tunneling, 27 and the dynamics 28,29 and lateral quantization [30][31][32] of surface electrons above the vacuum level.…”