A Universal Description of Workfunction

TL;DR

This paper extends the Lang-Kohn model to accurately describe the workfunction across various materials by linking charge spill-out to the bulk workfunction, unifying understanding of surface dipoles in metals, semiconductors, and insulators.

Contribution

It introduces a generalized approach that incorporates the bulk workfunction into the Lang-Kohn model, broadening its applicability beyond simple metals.

Findings

The degree of charge spill-out is controlled by the bulk workfunction.

The extended model successfully explains workfunctions of metals, semiconductors, and insulators.

The approach unifies surface dipole understanding across different material classes.

Abstract

At the surfaces of materials, the bulk symmetry of the charge density is broken and electron spill-out into the vacuum region creates a surface dipole. Such spill-out has been historically calculated by Lang and Kohn [Phys. Rev. B \textbf{3}, 1215 (1971)] using average electron density to sucessfully explain the workfunction in metals. However, despite its initial success, in the fifty years since it has not been extended beyond simple metals. Here we show that the degree of charge spill-out is largely controlled by the innate bulk workfunction $\phi_I$, which is the Fermi level position of $\it bulk$ relative to the ideal vacuum. By incorporating the contribution of $\phi_I$ to the surface dipole we show that Lang-Kohn's $\it jellium$ based approach can be broadly expanded to understand the workfunction over a wide range of metals, semiconductors, and insulators.