Quantum size effects in Pb islands on Cu(111): Electronic-structure calculations

TL;DR

This study uses electronic structure calculations to understand the quantum size effects and 'magic' heights in Pb islands on Cu(111), revealing oscillatory energy patterns that match experimental observations.

Contribution

It introduces a self-consistent electronic structure model that accurately reproduces experimental eigenenergies and explains the stability of specific Pb island heights.

Findings

Total energy oscillates with overlayer thickness.

Energy minima align with experimentally observed 'magic' heights.

Proper substrate modeling is essential for accurate results.

Abstract

The appearance of "magic" heights of Pb islands grown on Cu(111) is studied by self-consistent electronic structure calculations. The Cu(111) substrate is modeled with a one-dimensional pseudopotential reproducing the essential features, i.e. the band gap and the work function, of the Cu band structure in the [111] direction. Pb islands are presented as stabilized jellium overlayers. The experimental eigenenergies of the quantum well states confined in the Pb overlayer are well reproduced. The total energy oscillates as a continuous function of the overlayer thickness reflecting the electronic shell structure. The energies for completed Pb monolayers show a modulated oscillatory pattern reminiscent of the super-shell structure of clusters and nanowires. The energy minima correlate remarkably well with the measured most probable heights of Pb islands. The proper modeling of the substrate is crucial to set the quantitative agreement.