Shot noise suppresion and hopping conduction in graphene nanoribbons

FIG. 1. (a) Schematics of an etched GNR. (b) False color scanning electron micrograph of sample A, highlighing the graphene and the GNR (in blue) and the leads (in yellow).

Its intrisic high mobility (above 200000 cm2/V.s) and its bidimensionality make graphene a promising material for the realisation of new nano-electronic components [1]. To compete with actual silicon-based transistors, field-effect graphene devices should own a large on-off ratio. This condition can typically be achieved by mean of an electrical transport gap. Even so intrisic graphene does not own any band-gap, this latter can be created in bilayer graphene with external doping [2,3]. An other way to open a gap is to reduce the transversal size of the graphene channel to form a graphene nanoribbon (GNR). The transport gap in GNR has first been calculated in Ref. 4 and should depend on the edges being either armchair or zigzag. However, experiments performed on GNRs [5] tend to prove that the origin of the gap may be more complex that the early theoretical studies suggested [4]. Indeed, doping inhomogeneities and rough edges complicate significantly the GNR transport.

FIG. 2. [(a) and (b)] Conductance G vs. Vgate at various temperatures for sample A and B, respectively. A transport gap (high impedance region) is seen and becomes more visible at the lowest temperatures. [(c) and (d)] Color map of dI / dV vs. Vbias and Vgate at T~5 K. Coulomb-diamonds-like structures suggest strong Coulomb interactions in the GNR.

We have investigated the conductance and shot-noise of two GNR samples. Both samples, labeled in the following A and B, show the same qualitative results. They were build-up by using standard electron-beam lithography and Ti/Au bilayer evaporation. The GNR constriction is patterned by etching away the unwanted graphene region with an Ar plasma and by protecting the ribbon area with a PMMA mask. The sample A of width 90 nm and length 600 nm is shown in Fig. 1. The zero-bias conductance of the GNRs depends strongly on the gate voltage, presenting a gap (large impedance region) of around 14 V and 18 V for samples A and B, respectively. The conductance drops from G~2e2/h at high charge density down to ~3\cdot10-3 and ~3\cdot10-5e2/h in the gap for samples A and B, respectively. At fixed gate voltage, the source-drain voltage dependence of the conductance shows a gate voltage-dependent gap. The modulation of the gap leads to Coulomb-diamond-like structures shown in the surface plot of the conductance vs. gate and source-drain voltages [Fig. 2]. The diverse size of the diamonds suggests the presence of several dots (localized charges) inside the GNR subjected to different Coulomb interactions. We found that the transport follows a variable range hopping law in agreement with the presence of localized states [Fig. 3]. The Fano factor, defined by the ratio between the shot-noise and the Poisonian noise, is measured around 0.1 within the gap [Fig. 4]. This strong reduction of the noise is understood by inelastic hopping conduction in the quasi-1D limit.

FIG. 3. I-V characteristics of sample A ((b), blue curve in (a)) and B ((c), red curve in (a)) at Vgate = 25.4 and 11 V at T=4.9 and 5.2 K for sample A and B, respectively. (a) The plot shows a linear behaviour in the log scale with 1/V_{bias}^{1/2} above the gap [flat part of (b) and (c)] and below a certain voltage V0, as expected for a variable range hopping transport through localized states.
FIG. 4. Spectral density of the current noise SI vs. the current I around Vgate = 25.4 V and T = 4.9 K for sample A (blue curve), and Vgate = 11 V and T = 5.2 K for sample B (red curve). The small value of the Fano factor (0.1) in the gap is understood by inelastic hopping conduction.

[1] A. H. Castro Neto \et al., Rev. Mod. Phys. 81, 109 (2009); N. M. Peres, ibid. 82,2673 (2010); S. Das Sarma et al., arXiv:1003.4731.

[2] T. Ohta et al, Science 313, 951 (2006).

[3] J. B. Oostinga et al, Nature Mater. 7, 151 (2008).

[4] K. Nakada et al., Phys. Rev. B 54, 17954 (1996).

[5] M.Y. Han et al., Phys. Rev. Lett. 98, 206805 (2007);

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Shot noise suppresion and hopping conduction in graphene nanoribbons

Phys. Rev. B 82, 161405(R) (2010).