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In this work, graphene field effect transistors (FETs) were fabricated on a trench structure made by carbonized poly(methylmethacrylate) to modify the graphene surface. The trench-structured devices showed different characteristics depending on the channel orientation and the pitch size of the trenches as well as channel area in the FETs. Periodic corrugations and barriers of suspended graphene on the trench structure were measured by atomic force microscopy and electrostatic force microscopy. Regular barriers of 160 mV were observed for the trench structure with graphene. To confirm the transfer mechanism in the FETs depending on the channel orientation, the ratio of experimental mobility (3.6-3.74) was extracted from the current-voltage characteristics using equivalent circuit simulation. It is shown that the number of barriers increases as the pitch size decreases because the number of corrugations increases from different trench pitches. The noise for the 140 nm pitch trench is 1 order of magnitude higher than that for the 200 nm pitch trench.