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

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 MoS and conductor, semiconductor, and insulator substrates. For substrate work function (Φ) values below 4.5 eV we find that Fermi level pinning occurs, involving electron transfer to native MoS gap states below the conduction band. For Φ above 4.5 eV, vacuum level alignment prevails but the charge injection barriers do not strictly follow the changes of Φ 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 MoS by dielectric screening, which depends on the dielectric constant (ε) of the substrate. Based on these observations, we introduce an expanded Schottky-Mott rule that accounts for band gap renormalization by ε -dependent screening and show that it can accurately predict charge injection barriers for monolayer MoS. 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.