Optical modulation effects on nonlinear electron transport in graphene in terahertz frequency range

We describe very fast electron dynamics for a graphene nanoribbon driven by a control electromagnetic field in the terahertz frequency regime. The mobility as a function of bias field has been found to possess a large threshold value when entering a nonlinear transport regime. This value 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 governed by the Fermi velocity in graphene and the dramatically increased phonon scattering. Super-linear and sub-linear temperature dependences of the mobility are seen in the linear and nonlinear transport regimes, which is attributed separately to the results of sweeping electrons from the right Fermi edge to the left one through 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. Additionally, a self-consistent device modeling has been proposed for graphene transistors under an optical modulation on its gate, which employs Boltzmann moment equations up to the third-order for describing fast carrier dynamics and full wave electromagnetics coupled to the Boltzmann equation for describing spatial-temporal dependence of the total field. Finally, a detailed comparison of the derived Maxwell-Boltzmann moment equations in this paper with the well known Vlasov-Maxwell equations is also included.