Single-particle tunneling in doped graphene-insulator-graphene junctions

Abstract

The characteristics of tunnel junctions formed between n-and p-doped graphene are investigated theoretically. The single-particle tunnel current that flows between the twodimensional electronic states of the graphene (2D-2D tunneling) is evaluated. At a voltage bias such that the Dirac points of the two electrodes are aligned, a large resonant current peak is produced. The magnitude and width of this peak are computed, and its use for devices is discussed. The influences of both rotational alignment of the graphene electrodes and structural perfection of the graphene are also discussed.

Magnitude of the current in 2D interlayer tunneling devices

“…electrodes in momentum space 6 (also, an additional voltage shift occurs because of the larger graphene-graphene capacitance at the higher voltage). The influence of device electrostatics is illustrated in Fig.…”

“…3,4,5 Large negative differential resistance (NDR) is observed, with potential applications in oscillators and other types of circuits. This characteristic is an example of 2D-2D tunneling, 6 a phenomenon that has been studied for more than 25 years in a different 2D system, quantum wells in epitaxial layers of three-dimensional semiconducting systems such as GaAs/AlxGa1-xAs. 7,8,9,10 A variant on the G/h-BN/G device has been proposed in which semiconducting 2D materials such as a transitional metal dichalcogenide (TMD) or phosphorene are used for the source and drain, rather than graphene.…”

Layered Two-Dimensional Heterostructures and Their Tunneling Characteristics

“…In this section we review the case of tunneling between two graphene sheets as rst worked out by Feenstra et al [110]. This review provides a good illustration of the Bardeen tunneling method described in Section 6.1, and it also forms the basis for later work presented in Chapters 7 and 8 of the thesis.…”

“…On the other hand, for any other bias voltage the bands will be energetically o set from one another (Fig. 6.5(c)), and although there are many states with matching energy in the opposing electrode, there will in general only be a few states with matching wavevector, and normally evaluated over all space in the lateral dimensions, is restricted to a nite region of wavefunction coherence [110] as discussed in detail in Chapter 7.…”

“…(6.8), we have introduced two new quantities, ∆E L and ∆E R , which represent position of the Fermi level in each electrode relative to the charge neutrality point of the graphene band structure (as discussed in Section 1.1.1). In the work of Feenstra et al [110], these terms were combined into one value, ∆E, which was equal in magnitude and opposite in sign between the two graphene layers due to the symmetry of the electrostatics model described therein. In a subsequent work, Zhao et al [111] calculated the tunneling current between two graphene sheets sandwiched between top and bottom gates, with a symmetric geometry and antisymmetric gate biases in order to enable an analytic form for the tunneling current.…”