Shin-Ming Lu

Determining the Thickness of Pb Film Similar to Bulk with Energy Dispersion Derived from Quantum Well States

It is known that the energy spacing between adjacent empty quantum well (QW) states in Pb islands on Cu(111) would reveal the shrinking characteristic originating from the effect of the image potential. Using the phase accumulation model, including a phase factor contributed from the image potential, the shrinking energy spacing can be quantitatively explained with the assumption of the parabolic energy versus wave vector (E–k) dispersion. However, an experimental dispersion acquired from analyzing the energies of the QW state reveals a linear E–k relationship corresponding to the Pb bulk band structure, implying the assumed parabolic dispersion is not appropriate. By combining the linear dispersion with the image potential effect in the calculation, it is found that the calculated values of energy spacing of island thickness below eight atomic layers are not in agreement with the experimental measurements. This implies that the electronic structure of Pb islands would be similar to that of the bulk when their thicknesses reach eight-atomic layers. # 2013 The Japan Society of Applied Physics

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.

Manifestation of the quantum size effect in transmission resonance

The transmission probability of the free electron scattered by the quantum well in metal film may reveal the phenomenon of resonance. This transmission resonance, appearing above the vacuum level, can be probed by scanning tunnelling spectroscopy (STS). In this paper, STS is used to observe the transmission resonance on Ag films grown on Si(111)7 × 7 surfaces. The transmission resonance appears at different bias voltages in the spectra depending on the film thickness; its energy level moves toward the vacuum level with increasing film thickness. When the film is thick enough, transmission resonance can occur twice in the biasing voltage range, and the energy separation between the resonances decreases with increasing film thickness. The existence of transmission resonance affects the contemporary standing wave states (SWS) and, in general, pushes the following SWS to higher energies.

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

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.

Energy spacing between electronic resonances: A physical quantity correlating to diverse phases of the dense Pb overlayers on Si(111)

The unoccupied states of Pb dense overlayers on Si(111) reveal an oscillatory character with two electronic resonance peaks that can be observed by scanning tunneling spectroscopy. By measuring the energy spacing between resonance peaks, it is found that the energy spacing is reduced with increasing the coverage of dense overlayer. The change of energy spacing originates from that the movement of the high-energy resonance peak is more pronounced than that of the low-energy peak with varying coverage. The authors demonstrate that this phase-dependent energy spacing is a useful quantity to identify that the room-temperature 1 × 1 and the low-temperature 7 × 3 phases have an identical coverage of 1.2 ML.

Disappearance of Lowest-Order Transmission Resonance in Ag Film of Critical Thickness

The quantum phenomenon of the transmission resonance can be observed in Ag films grown on a Si(111)7?7 surface using scanning tunneling spectroscopy. It is found that the energy of the transmission resonance moves toward lower energy with increasing film thickness. The formula used is derived from quantum mechanics to demonstrate that this lowering in the transmission resonance energy is proportional to (w+1)2/w2, where w is the number of atomic layers of film thickness. This relation is justified by experimental results, but only holds for thinner films. The formula also predicts that the lowest-order transmission resonance should disappear when the Ag film reaches its critical thickness. This disappearance of the transmission resonance has also been experimentally confirmed in the dI/dV spectrum.