The Jellium Edge and the Size Effect of the Chemical Potential and Surface Energy in Metal Slabs

TL;DR

This paper investigates the effects of electron confinement in thin metal slabs, demonstrating that the chemical potential and surface energy depend on thickness and electron quantization, with implications for free electron models in nanostructures.

Contribution

It rigorously shows that the geometric edge coincides with the potential edge in free electron models when quantization is considered, clarifying the size effects in metal slabs.

Findings

Chemical potential increases as slab thickness decreases.

Surface energy shows an increasing trend with decreasing thickness.

Thickness-dependent oscillations occur due to electron number discreteness.

Abstract

Although free electron models have been established in order to capture the essential physics of interfacial and bulk properties in metals, some issues still remain regarding the application of free electron models to thin metal films. One of the issues relates to whether the geometric edge coincides with the potential edge in order to satisfy the charge neutrality condition when the potential profile is modeled as a rectangular potential well. We show that they coincide by rigorously taking into account the quantization effect arising from electron confinement in a thin metal slab. As a result, the overall behaviors of the chemical potential and surface energy show an increasing trend by decreasing the thickness of the slab. The chemical potential and surface energy show an oscillatory thickness dependence by further taking into account the discreteness of the total number of free electrons.