  The calculated electron mobility for a graphene nanoribbon as a function of
applied electric field has been found to have a large threshold field for
entering a nonlinear transport regime. This field depends on the lattice
temperature, electron density, impurity scattering strength, nanoribbon width
and correlation length for the line-edge roughness. An enhanced electron
mobility beyond this threshold has been observed, which is related to the
initially-heated electrons in high energy states with a larger group velocity.
However, this mobility enhancement quickly reaches a maximum due to the Fermi
velocity in graphene and the dramatically increased phonon scattering.
Super-linear and sub-linear temperature dependence of mobility seen in the
linear and nonlinear transport regimes. By analyzing the calculated
non-equilibrium electron distribution function, this difference is attributed
separately to the results of sweeping electrons from the right Fermi edge to
the left one through the elastic scattering and moving electrons from
low-energy states to high-energy ones through field-induced electron heating.
The threshold field is pushed up by a decreased correlation length in the high
field regime, and is further accompanied by a reduced magnitude in the mobility
enhancement. This implies an anomalous high-field increase of the line-edge
roughness scattering with decreasing correlation length due to the occupation
of high-energy states by field-induced electron heating.
