Generalized Phase Diagrams for Graphene CVD growth on Copper

TL;DR

This paper develops an advanced phase diagram model for graphene CVD growth on copper, incorporating substrate strain and chemical desorption effects to better predict bilayer graphene formation.

Contribution

It introduces a generalized phase diagram framework that includes substrate strain and chemical desorption, enhancing predictive control over graphene layer growth.

Findings

Tensile strain expands the bilayer graphene growth window.

Chemical desorption suppresses bilayer graphene in high-growth regimes.

The model links microscopic mechanisms to macroscopic growth parameters.

Abstract

Understanding the competition between first-layer lateral expansion and second-layer nucleation is essential for layer-controlled graphene growth via chemical vapor deposition (CVD). Building on our previous phase diagram framework based on the dimensionless parameters $\alpha$ and $\Gamma$, we develop an enhanced model incorporating two previously neglected effects: thermal-expansion-induced substrate strain and chemical desorption of carbon monomers via reverse dehydrogenation. First-principles calculations are employed to determine the strain-dependent diffusion and attachment barriers on both exposed and graphene-covered Cu(111) surfaces. By mapping the multi-step CVD process into an effective quasi-physical vapor deposition, we construct a generalized phase diagram characterized by the coupled effects of $\alpha$, $\Gamma$, and a newly introduced desorption parameter $Z$. Our results show that tensile strain expands the bilayer graphene (BLG) growth window for critical nucleus sizes $i^*>1$. In contrast, chemical desorption suppresses BLG formation in the high-$\Gamma$ regime via $Z$-dependent monomer depletion. This unified framework provides a predictive guide for the rational synthesis of high-quality bilayer graphene by linking macroscopic growth parameters to microscopic layer-selection mechanisms.