Figure 1. Graphene-BN resonant tunnelling transistor.

(a) Schematic diagram of the devices. (b) Measured current-voltage characteristics of one of our devices (device A) at 6 K. The hBN barrier is four atomic layers thick, as determined by atomic force microscopy and optical contrast13; the active area for the flow of tunnel current is 0.3 μm². The V_g values range, in 5 V steps, from +15 V (top red curve), through −20 V (black symmetric curve) to −55 V (bottom blue curve). The inset shows schematically the relative positions of the Fermi energies (chemical potentials) of the doped Si substrate gate electrode (represented by hatched lines) and of the two graphene layers at the peak of the I(V_b) curve in forward bias with V_g=+15 V. (c) Theoretical simulation of device A obtained by using the Bardeen model and including the effect of doping in both graphene electrodes. Parameters: q_c⁻¹=12 nm; bottom layer is n-doped at 4.4 × 10¹¹ cm⁻² and the top graphene p-doped at 1.0 × 10¹² cm⁻². As our top graphene layers are exposed to the environment, we expect them to have stronger residual (~10¹² cm⁻²) doping than the bottom layers, as often observed in partially encapsulated double-layer graphene devices5. The top inset (i) shows the chemical potentials μ_T and μ_B in the top (T) and bottom (B) electrodes, respectively, for V_b=0 and V_g=−20 V, which corresponds to the symmetric I(V_b) shown in black; for inset (ii) V_g=+15 V and V_b=0.3 V, which corresponds to the peak of the I(V_b) curve. The lower inset shows the V_g dependence of the PVR=I_p/I_v obtained from our simulations, where I_p,v are the currents at the peak and the valley (minimum) beyond.