Quantum size effect in Pb(100) films: the role of symmetry and implication for film growth

TL;DR

This study uses density-functional calculations to reveal quantum size effects in Pb(100) films, showing bilayer periodicity in energies and work functions due to symmetry differences, with implications for film growth.

Contribution

It demonstrates the origin of quantum size effects in Pb(100) films from symmetry considerations and predicts the stability of even-layer films on substrates.

Findings

Pb(100) films show bilayer periodicity in energy and work function.

Quantum well states are classified into $\sigma$-bonded and $\pi$-bonded states.

Bilayer periodicity persists on semiconductor substrates.

Abstract

We show from density-functional calculations that Pb(100) thin films exhibit quantum size effect with a bilayer periodicity in film energies, film relaxations, and work functions, which originate from different symmetry of the stacking geometry of odd and even layer films. The bilayer periodicity of the film energy is argued to survive on a semiconductor substrate, which should allow the growth of ``magically'' thick even-layer Pb(100) films. Furthermore, it is found that the quantum well states in a simple metal film can be classified into $\sigma$-bonded and $\pi$-bonded states, which quantize independently.