Vertical electron transport in van der Waals heterostructures with graphene layers

Abstract

We propose and analyze an analytical model for the self-consistent description of the vertical electron transport in van der Waals graphene-layer (GL) heterostructures with the GLs separated by the barriers layers. The top and bottom GLs serve as the structure emitter and collector. The vertical electron transport in such structures is associated with the propagation of the electrons thermionically emitted from GLs above the inter-GL barriers. The model under consideration describes the processes of the electron thermionic emission from and the electron capture to GLs. It accounts for the nonuniformity of the self-consistent electric field governed by the Poisson equation which accounts for the variation of the electron population in GLs. The model takes also under consideration the cooling of electrons in the emitter layer due to the Peltier effect. We find the spatial distributions of the electric field and potential with the high-electric-field domain near the emitter GL in the GL heterostructures with different numbers of GLs. Using the obtained spatial distributions of the electric field, we calculate the current-voltage characteristics. We demonstrate that the Peltier cooling of the two-dimensional electron gas in the emitter GL can strongly affect the current-voltage characteristics resulting in their saturation. The obtained results can be important for the optimization of the hot-electron bolometric terahertz detectors and different devices based on GL heterostructures.