Thickness of elemental and binary single atomic monolayers

Abstract

The thickness of monolayers is a fundamental property of two-dimensional (2D) materials that has not found the necessary attention. It plays a crucial role in their mechanical behavior, the determination of related physical properties such as heat transfer, and especially the properties of multilayer systems. Measurements of the thickness of free-standing monolayers are widely lacking and notoriously too large. Consistent thicknesses have been reported for single layers of graphene, boronitrene, and SiC derived from interlayer spacing measured by X-ray diffraction in multilayer systems, first-principles calculations of the interlayer spacing, and tabulated van der Waals (vdW) diameters. Furthermore, the electron density-based volume model agrees with the geometric slab model for graphene and boronitrene. For other single-atom monolayers DFT calculations and molecular dynamics (MD) simulations deliver interlayer distances that are often much smaller than the vdW diameter, owing to further electrostatic and (weak) covalent interlayer interaction. Monolayers strongly bonded to a surface also show this effect. If only weak vdW forces exist, the vdW diameter delivers a reasonable thickness not only for free-standing monolayers but also for few-layer systems and adsorbed monolayers. Adding the usually known corrugation effect of buckled or puckered monolayers to the vdW diameter delivers an upper limit of the monolayer thickness. The study presents a reference database of thickness values for elemental and binary group-IV and group-V monolayers, as well as binary III–V and IV–VI compounds.