Phase Contribution of Image Potential on Empty Quantum Well States in Pb Islands on the Cu(111) Surface

Abstract

We use scanning tunneling spectroscopy to explore the quantum well states in the Pb islands grown on a Cu(111) surface. Our observation demonstrates that the empty quantum well states, whose energy levels lie beyond 1.2 eV above the Fermi level, are significantly affected by the image potential. As the quantum number increases, the energy separation between adjacent states is shrinking rather than widening, contrary to the prediction for a square potential well. By simply introducing a phase factor to reckon the effect of the image potential, the shrinking behavior of the energy separation can be reasonably explained with the phase accumulation model. The model also reveals that there exists a quantum regime above the Pb surface in which the image potential is vanished. Moreover, the quasi-image-potential state in the tunneling gap is quenched because of the existence of the quantum well states.

Theoretical study of constant current scanning tunneling spectroscopy in Pb overlayers

“…Note that the field E = 0.05 eV/a 0 corresponds to a tip-surface distance as large as 4 nm for a bias of 4 eV. The actual electric fields obtained with the WPP for the conditions of constant current STS experiments (see below) of Yang et al 21 are also shown in Fig. 4.…”

“…Note that in Ref. 21 the labels n exp differ from the present definition of n as n exp = n − 1. However, n exp were not directly obtained but were deduced from the modeling of the data with the phase accumulation model.…”

“…Results are shown within the energy range of 1 < E < 5 eV with respect to the Fermi level, i.e., the one encompassed in the constant current STS experiments. 21,22 The principal quantum number n of the states, as indicated in the figure, corresponds to the nodal structure of the wave function. 50 At zero field, the QWSs mix with image potential states (ISs) forming Rydberg-like series converging toward the vacuum level.…”

“…The bulk electronic structure of the film material evolves then into a set of subbands characterized by the quantized electron motion perpendicular to the film, and bulklike dispersion in the film plane. [20][21][22][23] The QWSs can thus be readily understood in terms of the discrete level structure of a 1D potential well. In particular, the phase accumulation model [24][25][26] appears extremely efficient in describing the energies of the QWSs at¯ point.…”

“…We address theoretically recent STM and STS experiments on confined states in large Pb(111) islands deposited on Cu(111) and Ag(111) surfaces. 21,22 These STS studies were performed at constant current regime, so that high-energy QWSs could be sampled as compared to previous works. When the lateral extension of the Pb island is large enough, the quantization in the plane parallel to the surface resulting from the reflection by the island boundaries can be neglected because of the lifetime broadening.…”