Theory of graphene–insulator–graphene tunnel junctions

Abstract

Graphene-insulator-graphene vertical tunneling structures are discussed from a theoretical perspective. Momentum conservation in such devices leads to highly nonlinear current-voltage characteristics, which with gates on the tunnel junction form potentially useful transistor structures. Two prior theoretical treatments of such devices are discussed; the treatments are shown to be formally equivalent, although some differences in their implementations are identified. The limit of zero momentum conservation in the theory is explicitly considered, with a formula involving the density-of-states of the graphene electrodes recovered in this limit. Various predictions of the theory are compared to experiment.

Layered Two-Dimensional Heterostructures and Their Tunneling Characteristics

“…1 As discussed in prior work, the interlayer states are free-electron 1 The interlayer band that we are discussing here, occurring in the 0 8 eV range, is actually the lowest band of a pair of two bands. The upper band has energy of 14 22 eV, at least for the case of graphene.…”

“…This analysis can be taken a step further by noting that a linear dispersion directly results from a Dirac-like Hamiltonian in two dimensions, [19,20] H K = v F σ · k, (1.3a) H K = v F σ * · k, (1.3b) around the K and K points, where k is now relative to an origin placed at K or K , utilizing the Pauli matrices σ = (σ x , σ y ) and σ * = (σ x , −σ y ). The eigenenergies both 1 In this section, units are selected such that = 1. Atomic structure of monolayer hexagonal boron nitride (h-BN) viewed from the out-of-plane direction.…”

“…[136,137] An even more intriguing distinction with MLG is that, under the in uence of external elds, the band structure of bilayer graphene (BLG) near the charge neutrality point becomes quartic, changing from semi-metallic to semiconducting as a small band gap is induced. were originally proposed for conventional 2D quantum wells, [26] but the theory was recently treated for MLG, [1,31,110,111,115,116,135,144] and NDR was observed experimentally in high-quality devices shortly thereafter. [31 33] The theory discussed in the present work is particularly relevant to the recent observations of Fallahazad et al [33] 8…”

Magnitude of the current in 2D interlayer tunneling devices

“…35,36,37 Considering a two-band model for evanescent states, the maximal value of along a complex-k loop connecting the conduction and valence bands varies like the square root of the band gap. 26 This estimated effect of the band gap correction yields a significant reduction in the tunnel current. To quantify this effect, a GW computation of the wave functions and resulting tunnel currents would be best; such a computation is, however, quite challenging.…”

“…26 This value, which in retrospect is much too small, produced relatively large tunnel currents. Computed tunnel currents in Fig.…”