Simple and accurate estimation of metal, semiconductor, and insulator work functions

Abstract

Work-function $\ensuremath{\phi}$ measures the work needed for an electron to escape a solid. For simple metals, it is almost exclusively the result of the surface dipole created by spill-out of electrons from bulk into the vacuum as shown in the seminal work by Lang and Kohn [Phys. Rev. B 3, 1215 (1971)] using a jellium model. Despite a half century of intense efforts, however, such understanding has not been extended past metals. Here we present a universal model for $\ensuremath{\phi}$ which contains a previously unrecognized bulk contribution ${\ensuremath{\phi}}_{I}$ [Phys. Rev. Lett. 121, 196802 (2018)]. By incorporating ${\ensuremath{\phi}}_{I}$ into the jellium model, we find that it dictates the dipole due to charge spill out and provides a description which applies to a wide range of materials, ranging from metals, semiconductors, to insulators.