# Gate-dependent vacancy diffusion in graphene

## TL;DR

This study investigates how vacancy defects in graphene diffuse under different doping conditions, revealing that electron doping can effectively immobilize vacancies and highlighting the importance of lattice relaxation and quantum effects.

## Contribution

It provides a detailed first-principles analysis of vacancy diffusion mechanisms in graphene, including the effects of carrier doping and lattice relaxation, which were not previously comprehensively understood.

## Key findings

- Electron doping increases the activation barrier for vacancy diffusion.
- Lattice relaxation perpendicular to graphene significantly influences vacancy migration.
- Quantum corrections are important for accurate barrier predictions.

## Abstract

Kinetics of vacancy defect in graphene drives structural modifications leading to disorder, multi-vacancy complex and edge reconstruction. Within the first-principles calculations, we study the dynamic Jahn-Teller distortion and diffusion of a vacancy defect. Further, the intricate dependence of carrier doping is systematically investigated. The experimental observation of dynamic Jahn-Teller distortion is argued to be blocked by defect functionalization and charge doping. We demonstrate that lattice relaxation perpendicular to the graphene sheet along with the in-plane strain relaxation plays predominant roles in predicting the correct microscopic mechanism for vacancy diffusion. The importance of quantum correction to the classical barrier is discussed. The calculated activation barrier increases upon both electron and hole doping and the observed trends are explained by the differential charge density distribution and hardening of the responsible low-energy phonon modes. Electron doping essentially freezes the vacancy motion, and thus any degradation mediated by it. While tracking and analyzing the vacancy diffusion experimentally in graphene is a difficult task, the present results will motivate new experimental efforts and assist interpretation of the results.