Generalized Phase Diagrams for Graphene CVD growth on Cu(111)

Understanding the competition between first-layer lateral expansion and second-layer nucleation is essential for layer-controlled graphene growth via chemical vapor deposition (CVD). Here, we develop a generalized phase-diagram framework that incorporates two key effects often neglected in existing growth models: substrate strain induced by thermal expansion and chemical desorption arising from reverse dehydrogenation. Combining first-principles calculations with rate-equation theory, we map the complex multi-step CVD process onto an effective quasi-physical vapor deposition description and establish generalized growth phase diagrams. The resulting diagrams reveal that tensile strain expands the bilayer graphene (BLG) growth window for critical nucleus sizes i^* > 1, whereas chemical desorption suppresses BLG formation under low deposition fluxes. By directly connecting experimentally controllable variables, including temperature, hydrogen pressure, and substrate strain, to graphene layer selectivity, this framework provides a predictive guide for rational synthesis of high-quality uniform single- or bilayer graphene and offers practical parameter-tuning strategies for graphene-based nanomaterials.