From low-bias mobility to high-bias current saturation: fundamental trade-offs in graphene based transistors

We describe the fundamental trade-offs in engineering the mobility, current saturation and ON- OFF ratios in graphene transistors. Surprisingly, the trade-offs arise solely from an asymptotic constraint on the high energy bandstructure and independent of scattering processes. This places graphite derivatives (bulk monolayer graphene, uniaxially strained graphene nanoribbons, carbon nanotubes and bilayer graphene) on the same 3-parameter mobility-bandgap-scattering length ({\mu} - Egap -{\lambda}) plot, proximal to other semiconductors. In addition to this low-bias trade-off, the high bias current bears signatures of the underlying saturation mechanism, arising through phonon scattering or {\Gamma}-point suppressed density of states opening bandgap.