Double injection, resonant-tunneling recombination, and current-voltage characteristics in double-graphene-layer structures

Abstract

We evaluate the effect of the recombination associated with interlayer transitions in ungated and gated double-graphene-layer (GL) structures on the injection of electrons and holes. Using the proposed model, we derive analytical expressions for the spatial distributions of the electron and hole Fermi energies and the energy gap between the Dirac points in GLs as well as their dependences on the bias and gate voltages. The current-voltage characteristics are calculated as well. The model is based on hydrodynamic equations for the electron and hole transport in GLs under the self-consistent electric field. It is shown that in undoped double-GL structures with weak scattering of electrons and holes on disorder, the Fermi energies and the energy gap are virtually constant across the main portions of GLs, although their values strongly depend on the voltages and recombination parameters. In contrast, the electron and hole scattering on disorder lead to substantial nonuniformities. The resonant inter-GL tunneling enables N-shaped currentvoltage characteristics provided that GLs are sufficiently short. The width of the current maxima is much larger than the broadening of the tunneling resonance. In the double-GL structures with relatively long GLs the N-shaped characteristics transform into the Z-shaped characteristics. The obtained results are in line with the experimental observations [1] and might be useful for design and optimization of different devices based on double-GL structures, including field-effect transistors and terahertz lasers.

Effect of the intra-layer potential distributions and spatial currents on the performance of graphene SymFETs

“…Moreover, in qualitative agreement with the discussion in Ref. 16, we also observe that when increasing coherence length, the resonance becomes more asymmetric, e.g. when comparing the I-V DS curve in Fig.…”

“…Therefore, it is observed that in practice distributed effects can have a major impact on the OFF-state rather than on the ON-state current, which is consistent with the observation by Ryzhii et al of spatial distributions on Fermi-level being more significant under low charge-densities. 16 If we increase the coherence length from 50 nm to 1200 nm with t t = 0.66 nm (∼ 2 atomic layers of BN), to increase the tunnel current, then the potential drops across the resistive elements again become non-negligible and the results from the 2-D model again deviate from those in the 1-D approximation. Shown in Fig.…”

“…14,15 In this context, using a hydrodynamic model, Ryzhii et al studied spatial-effects in SymFET structures by introducing scattering and recombination parameters. 16 It was found that under low two-dimensional-electron-gas/two-dimensional-hole-gas concentrations the scattering of electrons and holes on disorder results in spatial distributions of the Fermi energy. In this paper, we introduce a rigorous distributed circuit model to represent these 2-D electrostatic effects, which takes into consideration: (a) the intra-graphene-layer potential distributions, and (b) the internal current flows through the device, as suggested in the work of Zhao et al 7 as a future element to be considered in further work.…”

Magnitude of the current in 2D interlayer tunneling devices

“…a simple voltage drop across the 2D leads and/or metallic junctions that connect to a device, 17,22 or in a more intrinsic way, as a continuously varying voltage drop along the source and drain materials themselves (which can significantly perturb the tunneling). 22,23,41 The former effect has been shown to be quite significant in recent experimental results, 42 and the latter effect can in principle be well treated with full computational packages that include three-dimensional electrostatic modeling as well as scattering in the electrodes. 21,22,23 Separately, another issue that can occur in interlayer tunneling devices is the formation of moiré (interference) patterns that form between lattice-mismatched layers of 2D material.…”

Graphene active plasmonics for terahertz device applications

“…The DGL core shell works as a nano-capacitor [7], [8] exhibiting inter-GL resonant tunneling (RT) when the band offset between the two GLs is aligned [4]. The RT produces a strong nonlinearity with a negative differential conductance (NDC) in the DGL current-voltage characteristics [5], [9]. The excitation of the graphene plasmons in the GLs strongly modulates the inter-GL RT [10], [11], so that it could dramatically enhance the quantum efficiency of various device operations like detection [10], self-oscillation [10], frequency multiplication [10], intensity modulation [12], photomixing [13], as well as lasing [14] in the THz device implementations.…”