Mode space approach for tight-binding transport simulations in graphene nanoribbon field-effect transistors including phonon scattering

In this paper, we present a mode space method for atomistic non-equilibrium Greens function simulations of armchair graphene nanoribbon field effect transistors (FETs) that includes electron-phonon scattering. With reference to both conventional and tunnel FET structures, we show that, in the ideal case of a smooth electrostatic potential, the modes can be decoupled in different groups without any loss of accuracy. Thus, inter-subband scattering due to electron-phonon interactions is properly accounted for, while the overall simulation time considerably improves with respect to real-space, with a speed-up factor of 40 for a 1.5-nm-wide device. Such factor increases with the square of the device width. We also discuss the accuracy of two commonly used approximations of the scattering self-energies: the neglect of the off-diagonal entries in the mode-space expressions and the neglect of the Hermitian part of the retarded self-energy. While the latter is an acceptable approximation in most bias conditions, the former is somewhat inaccurate when the device is in the off-state and optical phonon scattering is essential in determining the current via band-to-band tunneling. Finally, we show that, in the presence of a disordered potential, a coupled mode space approach is necessary, but the results are still accurate compared to the real-space solution.