Impact of Surface States in Graphene/p-Si Schottky Diodes

Graphene-silicon Schottky diodes are intriguing devices that straddle the border between classical models and two-dimensional ones. Many papers have been published in recent years studying their operation based on the classical model developed for metal-silicon Schottky diodes. However, the results obtained for diode parameters vary widely in some cases showing very large deviations with respect to the expected range. This indicates that our understanding of their operation remains incomplete. When modeling these devices, certain aspects strictly connected with the quantum mechanical features of both graphene and the interface with silicon play a crucial role and must be considered. In particular, the dependence of the graphene Fermi level on carrier density, the relation of the latter with the density of surface states in silicon and the coupling between in-plane and out-of-plane dynamics in graphene are key aspects for the interpretation of their behavior. Within the thermionic regime, we estimate the zero-bias Schottky barrier height and the density of silicon surface states in graphene/type-p silicon diodes by adapting a kown model and extracting ideality index values close to unity. The ohmic regime, beyond the flat band potential, is modeled with an empirical law, and the current density appears to be roughly proportional to the electric field at the silicon interface; moreover, the graphene-to-silicon electron tunneling efficiency drops significantly in the transition from the thermionic to ohmic regime. We attribute these facts to (donor) silicon surface states, which tend to be empty in the ohmic regime.