Analytical model for the remote epitaxial potential

TL;DR

This paper introduces an analytical model for the remote epitaxial potential through graphene, accounting for covalent, van der Waals interactions, and screening effects, providing insights into tunability and experimental measurement of remote bonding.

Contribution

The model uniquely incorporates screening effects and covalent interactions, offering a physically interpretable framework for understanding remote epitaxy potentials.

Findings

Remote potential magnitude is comparable to van der Waals potential.

Screening by graphene carriers can tune the remote potential.

Multiple graphene layers significantly diminish the remote potential.

Abstract

We propose an analytical model for the remote bonding potential of the substrate that permeates through graphene during remote epitaxy. Our model, based on a Morse interatomic potential, includes the attenuation due to the increased film-substrate separation and due to graphene free carrier screening. Compared with previous slab density functional theory calculations, which use the electrostatic potential as a proxy for bonding, our analytical model includes covalent and van der Waals bonding interactions, includes screening (which is often ignored), and is based on simple, physically interpretable, and well benchmarked parameters that build understanding. We show that for typical graphene free carrier concentrations of order $10^{12}$ cm$^{-2}$, the magnitude of $|\phi_{remote}|$ for most semiconductor and oxide substrates is few to tens of meV, similar to the van der Waals potential of graphene. This suggests interference between the graphene and remote substrate potentials must be considered when interpreting experiments on remote epitaxy. Furthermore, we show that (1) the strength of the remote potential is tunable by screening (graphene carrier density), (2) the remote potential is vanishingly weak through two or more graphene layers, (3) the spatial extent of the potential, rather than degree of ionicity, controls the strength of the permeated bonding potential. Our model provides a simple framework for benchmarking direct measurements of the remote epitaxial potential, and we propose several experimental paths to measure this quantity. De-convolving the effects of the native remote potential, graphene defects, and tunable growth kinetics is key to understanding and tuning the mechanisms of remote epitaxy.