Open-boundary reflection of quantum well states at Pb(111)

Abstract

Using a scanning tunneling microscope, confined electron states are studied that exist above subsurface nanometer-sized voids at Pb(111), where potential barriers at the parallel vacuum-Pb(111) and Pb(111)-void interfaces establish a principal series of quantum well states that are further confined laterally by strong reflection at the open boundaries at the edges of the void. The influence of the size, depth and shape of the voids on the effectiveness of the lateral confinement is discussed. Standing wave patterns observed in differential conductance maps unravel the dispersion of the relevant underlying Pb electron states.

Bringing ultimate depth to scanning tunnelling microscopy: deep subsurface vision of buried nano-objects in metals

“…† The generalization of our approach could also be enlarged considering other combinations of materials such as Cd, Cu, Pb, Ag or Al where near-surface QW observations have been reported. [16][17][18][19][20][21][22][23][24][29][30][31][32][33][34][35][36] Many other materials have yet to be tested.…”

“…Previously, several STM experiments reported the use of LDOS oscillations in a metallic layer for the subsurface detection and thus confirm the validity of this approach. For example, the steps at Si substrate covered with a flat Pb layer were imaged by analysing LDOS variation on the flat surface of lead [16][17][18][19][20][21][22][23] whereas the same effect was also observed with thin films of Cd [24]. A similar concept has been used by Weissman et al [25] and Kotzott et al [26].…”

“…Previously, several STM experiments reported the use of LDOS oscillations in a metallic layer for subsurface detection and thus confirmed the validity of this approach. For example, the steps at a Si substrate covered with a flat Pb layer were imaged by analysing the LDOS variation on a flat surface of lead [16][17][18][19][20][21][22][23] whereas the same effect was also observed with thin films of Cd. 24 A similar concept has been used by Weissman et al 25 and Kotzott et al 26 By observing LDOS interference rings on the copper surface, they were able to detect subsurface Co impurities and succeeded to indicate the depth of these impurities within several atomic layers by treating the diameter of the rings.…”

Quantum confinement of electrons at metal surfaces

“…3ac) are shown to vertically and laterally confine conduction electrons of the substrate. [142,143] The vertical confinement is conventionally achieved by potential steps at the Pb(111)-vacuum and Pb bulk-void interfaces, leading to a series of QWS as reported for Al (111). [144] The lateral confinement of these QWS is due to reflection at the open boundary where the thin Pb film atop the buried cavity restores its bulk thickness, that is, lateral confinement results from the removal of vertical confinement.…”

“…The boxlike line shape applies to low-energy QWS, which exhibit a quasifree-electron dispersion near the Brillouin zone center and flatten their bands for wave vectors close to the zone boundary due to hybridization with other QWS bands. [142,143,[145][146][147][148][149] For unoccupied QWS with elevated energies the effective mass at the zone center increases, which results in a flat band dispersion and a Lorentzian line shape in spectra. [150][151][152] To further shed light on the observations (Fig.…”