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 angleresolved 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 (Phi(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 Phi(sub) above 4.5 eV, vacuum level alignment prevails but the charge injection barriers do not strictly follow the changes of Phi(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 (epsilon(r)) of the substrate. Based on these observations, we introduce an expanded Schottky-Mott rule that accounts for band gap renormalization by epsilon(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 materialspecific experimental benchmark data are available.