Simple and efficient modeling of the E–k relationship and low-field mobility in Graphene Nano-Ribbons

This paper proposes a simple analytical formulation for the dispersion relationship of extended electronic states in Graphene Nano-Ribbons (GNRs). The model has been validated by comparison with Tight-Binding calculation of GNRs in the presence of edge disorder. The model is suited for inclusion in semiclassical models for GNRs featuring widths down to approximately 2 nm. Monte-Carlo simulations accounting for phonons and edge roughness scattering are then used to understand the ribbon width of the low-field mobility. The mechanisms responsible for the low mobility values measured in narrow ribbons compared to graphene sheets are the increased phonon scattering rate and mobility effective mass due to the strong band structure modification induced by the reduced lateral dimensions and the increased scattering with the edges. However, scattering with phonons and with edges is not sufficient to reproduce the experimental mobility on insulating substrates, suggesting that the effect of remote polar phonons originating in the substrate can be significant in graphene based devices.