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We report on the influence of a silicon nitride gate dielectric in graphene-based field-effect transistors (FETs). The silicon nitride is formed by a plasma-enhanced chemical vapor deposition method. The process is based on a low-density plasma at a high pressure (1 torr), which results in a low degradation of the graphene lattice during the top-gate formation process. Microwave measurements of the graphene FET show a cutoff frequency of 8.8 GHz for a gate length of 1.3 μm. A carrier mobility of 3800 cm2/V·s at room temperature was extracted from the dc characteristic.