Graphene or carbon nanotube devices with localized bottom gates and gate dielectric

Transistor devices having nanoscale material-based channels (e.g., carbon nanotube or graphene channels) and techniques for the fabrication thereof are provided. In one aspect, a transistor device is provided. The transistor device includes a substrate; an insulator on the substrate; a local bottom gate embedded in the insulator, wherein a top surface of the gate is substantially coplanar with a surface of the insulator; a local gate dielectric on the bottom gate; a carbon-based nanostructure material over at least a portion of the local gate dielectric, wherein a portion of the carbon-based nanostructure material serves as a channel of the device; and conductive source and drain contacts to one or more portions of the carbon-based nanostructure material on opposing sides of the channel that serve as source and drain regions of the device.