H ₂ -dependent attachment kinetics and shape evolution in chemical vapor deposition graphene growth

Abstract Experiments on graphene growth through chemical vapor deposition (CVD) involving methane (CH ₄ ) and hydrogen (H ₂ ) gases reveal a complex shape evolution and a non-monotonic dependence on the partial pressure of H ₂ ( {p}_{{H}₂} ). To explain these intriguing observations, we develop a microkinetic model for the stepwise decomposition of CH ₄ into mobile radicals and consider two possible mechanisms of attachment to graphene crystals: CH radicals to hydrogen-decorated edges of the crystals and C radicals to bare crystal edges. We derive an effective mass flux and an effective kinetic coefficient, both of which depend on {p}_{{H}₂} , and incorporate these into a phase field model. The model reproduces both the non-monotonic dependence on {p}_{{H}₂} and the characteristic shapes of graphene crystals observed in experiments. At small {p}_{{H}₂} , growth is limited by the kinetics of attachment while at large {p}_{{H}₂} growth is limited because the effective mass flux is small. We also derive a simple analytical model that captures the non-monotone behavior, enables the two mechanisms of attachment to be distinguished and provides guidelines for CVD growth of defect-free 2D crystals.