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Chemical vapour deposition (CVD) is a cost-effective technique for growing high-quality graphene on catalytic metal subtrates such as Cu, Ni and noble metals. The technical challenge is to nondestructively transfer the ultrathin graphene film from the grown substrates to target substrates. An alternative pathway is to directly synthesize graphene on insulating substrates, which enable the transfer-free fabrication of graphene-based electronic and optoelectronic devices. We focus our recent efforts on the CVD growth of high-quality graphene on various insulators. We have successfully synthesized monolayer graphene on high-k SrTiO3 and the on-site field effect transistors showed excellent electronic performances. Particular focus was laid on the controlled growth on hexagonal boron nitride (h-BN), a perfect dielectric substrate demonstrating the extremely high carrier mobility of graphene.