Unsaturated drift velocity of monolayer graphene

Despite terahertz (THz) high electric field E$_{\mathrm{THz}}$ \textgreater 70 kV/cm, at which optical phonons can be emitted by hot electrons, graphene heating by energetic carriers can be controlled by adjusting the electrostatic doping concentration or E$_{\mathrm{F}}$. For E$_{\mathrm{F}}$ \textgreater \textgreater k$_{\mathrm{BT}}$, where k$_{\mathrm{B}}$ is the Boltzmann constant and T is the temperature, the electron--phonon scattering is enhanced because of large available phase space, resulting in a significant increase in the optical phonon temperature. However, for E$_{\mathrm{F}}$ \textless \textless k$_{\mathrm{BT}}$, electron--phonon scattering is suppressed because of the diminishing density of states at the Dirac point. Therefore, the carriers are kept accelerating by E$_{\mathrm{THz}}$ without losing their energy. This contributes to the drift velocity of the carriers at the concentration n $=$ 7.3 × 10$^{\mathrm{11}}$ cm$^{\mathrm{-2}}$ comparable to the Fermi velocity without heating the graphene lattice on Si substrate at 300 K.