The Schottky–Mott Rule Expanded for Two-Dimensional Semiconductors: Influence of Substrate Dielectric Screening

Abstract

A comprehensive understanding of the energy level alignment mechanisms between two-dimensional (2D) semiconductors and electrodes is currently lacking, but it is a prerequisite for tailoring the interface electronic properties to the requirements of device applications. Here, we use angle-resolved direct and inverse photoelectron spectroscopy to unravel the key factors that determine the level alignment at interfaces between a monolayer of the prototypical 2D semiconductor MoS₂ and conductor, semiconductor, and insulator substrates. For substrate work function (Φ_sub) values below 4.5 eV we find that Fermi level pinning occurs, involving electron transfer to native MoS₂ gap states below the conduction band. For Φ_sub above 4.5 eV, vacuum level alignment prevails but the charge injection barriers do not strictly follow the changes of Φ_sub as expected from the Schottky-Mott rule. Notably, even the trends of the injection barriers for holes and electrons are different. This is caused by the band gap renormalization of monolayer MoS₂ by dielectric screening, which depends on the dielectric constant (ε_r) of the substrate. Based on these observations, we introduce an expanded Schottky-Mott rule that accounts for band gap renormalization by ε_r -dependent screening and show that it can accurately predict charge injection barriers for monolayer MoS₂. It is proposed that the formalism of the expanded Schottky-Mott rule should be universally applicable for 2D semiconductors, provided that material-specific experimental benchmark data are available.