# Structure and energetics of embedded Si patterns in graphene

## TL;DR

This study investigates the geometry and stability of embedded silicon patterns in graphene, combining empirical potentials and density functional theory to understand how Si structures can be integrated into the graphene lattice.

## Contribution

It introduces a combined empirical and DFT approach to analyze the geometry and stability of various Si patterns in graphene, addressing size and distortion limitations.

## Key findings

- Classical geometries effectively model large Si structures in graphene.
- Discrepancies between empirical and DFT results highlight limitations of classical potentials.
- Embedded Si patterns' stability depends on their shape and size.

## Abstract

Recent experiments have revealed the possibility of precise electron beam manipulation of silicon impurities in graphene. Motivated by these findings and studies on metal surface quantum corrals, the question arises what kind of embedded Si structures are possible within the hexagonal lattice, and how these are limited by the distortion caused by the preference of Si for $sp^{3}$ hybridization. In this work, we study the geometry and stability of elementary Si patterns in graphene, including lines, hexagons, triangles, circles and squares. Due to the size of the required unit cells, to obtain the relaxed geometries we use an empirical bond-order potential as a starting point for density functional theory. Despite some interesting discrepancies, the classical geometries provide an effective route for the simulation of large structures.