A compact model of the backscattering coefficient and mobility of a graphene FET for SiO ₂ and h-BN substrates

A field-dependent compact model of the backscattering coefficient and quasi-ballistic mobility of charge carriers in graphene has been developed for two different substrates: silicon dioxide (SiO ₂) and hexagonal boron nitride (h-BN). The formulation of the backscattering coefficient is performed using the Landauer and McKelvey flux theory in a quasi-ballistic regime. In graphene, the acoustic phonon, surface optical phonon, and charged impurity scattering affect the transport of the charge carriers. This is carefully considered in our formulation of the backscattering coefficient (R) and quasi-ballistic mobility (μ_eff). We find that the graphene field effect transistor (GFET) with the h-BN substrate has lower backscattering and higher quasi-ballistic mobility. The modeled expressions for backscattering coefficient and quasi-ballistic mobility are substituted in the drain (I_DS) equation. The results are in good agreement with experimental results.