Generalized Phase Diagrams for Graphene CVD growth on Copper

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 $\mathrm{\Gamma }$, 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 $\alpha$, $\mathrm{\Gamma }$, and a newly introduced desorption parameter $Z$. Our results show that tensile strain expands the bilayer graphene (BLG) growth window for critical nucleus sizes $i^{\ast }>1$. In contrast, chemical desorption suppresses BLG formation in the high-$\mathrm{\Gamma }$ 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.