Free Electron Theory for Thin Metal Films

TL;DR

This paper analyzes different free-electron models for thin metal films, comparing their realism and effectiveness in predicting electronic properties, with a focus on soft-wall boundary conditions validated against experimental data.

Contribution

It introduces and compares three free-electron models for thin films, highlighting the soft-wall model's improved realism and experimental validation.

Findings

Soft-wall model closely matches experimental data.

Hard-wall and periodic models are less realistic.

Soft-wall boundary conditions provide better electronic property predictions.

Abstract

Quantum free electrons, i.e. plane waves, with wavevector k, and occupancy constrained by the Pauli exclusion principle, are explained in all solid state physics texts. Although overly simplified, free-electron theory works surprisingly well for many properties of simple metals. For bulk materials, it is assumed that the sample is effectively infinite and that surfaces are irrelevant. Over the past 30 years, experiments that visualize surfaces and enable the study of 2-d materials have revolutionized solid state physics, stimulating new experiment, theory, and applications. Modified free electron models, adapted to films, have enabled modeling of electronic properties of films. This paper analyzes three such models: periodic boundary conditions, hard-wall boundary conditions, and soft-wall (SW) boundary conditions, in order of increasing realism. The SW case is illustrated for an aluminum film consisting of six atomic layers, comparing SW free-electron theory with a scanning tunneling spectroscopy experiment.