Quantifying the role of defects in monolayer graphene diffusion barriers

We quantify the mechanisms for diffusion in Mn/graphene/semiconductor heterostructures, as a function of the defects induced by graphene sample preparation. These heterostructures are important for applications in spintronics; however, challenges in synthesizing graphene directly on technologically important substrates such as GaAs necessitate layer transfer steps, which can introduce defects into the graphene. \textit{In-situ} photoemission spectroscopy measurements reveal that graphene grown directly on a Ge substrate reduces the diffusion coefficient by a factor of 1000 compared to samples without graphene ($D_{gr,direct} \sim 4\times10^{-18}$cm$^2$/s, $D_{no-gr} \sim 5 \times 10^{-15}$ cm$^2$/s at 500$^\circ$C). Transferred graphene on Ge suppresses diffusion by a factor of 10 compared to no graphene ($D_{gr,transfer} \sim 4\times 10^{-16}cm^2/s$). For both transferred and directly-grown graphene, the low activation energy ($E_a \sim 0.1-0.5$ eV) suggests that Mn diffusion through graphene occurs primarily at graphene defects and the diffusivity prefactor $D_0$ scales with the defect density.Similar diffusion barrier performance is found on GaAs substrates; however, it is not currently possible to grow graphene directly on GaAs. Our results highlight the importance of developing graphene growth directly on functional substrates, to avoid the damage induced by layer transfer.