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Field-Effect Tunneling Transistor Based on Vertical Graphene Heterostructures

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Science  24 Feb 2012:
Vol. 335, Issue 6071, pp. 947-950
DOI: 10.1126/science.1218461

Abstract

An obstacle to the use of graphene as an alternative to silicon electronics has been the absence of an energy gap between its conduction and valence bands, which makes it difficult to achieve low power dissipation in the OFF state. We report a bipolar field-effect transistor that exploits the low density of states in graphene and its one-atomic-layer thickness. Our prototype devices are graphene heterostructures with atomically thin boron nitride or molybdenum disulfide acting as a vertical transport barrier. They exhibit room-temperature switching ratios of ≈50 and ≈10,000, respectively. Such devices have potential for high-frequency operation and large-scale integration.

The performance of graphene-based field effect transistors (FETs) has been hampered by graphene’s metallic conductivity at the neutrality point (NP) and the unimpeded electron transport through potential barriers caused by Klein tunneling, which limit the achievable ON-OFF switching ratios to ~103 and those achieved so far at room temperature to <10 (17). These low ratios are sufficient for individual high-frequency transistors and analog electronics (47), but they present a fundamental problem for any realistic prospect of graphene-based integrated circuits (17). A possible solution is to open a band gap in graphene—for example, by using bilayer graphene (8, 9), nanoribbons (10, 11), quantum dots (11), or chemical derivatives (12)—but it has proven difficult to achieve high ON-OFF ratios without degrading graphene’s electronic quality.

We report an alternative graphene transistor architecture—namely, a field-effect transistor based on quantum tunneling (1317) from a graphene electrode through a thin insulating barrier [in our case, hexagonal boron nitride (hBN) or molybdenum disulfide of ~1 nm thickness]. The operation of the device relies on the voltage tunability of the tunneling density of states (DOS) in graphene and of the effective height Δ of the tunnel barrier adjacent to the graphene electrode. To illustrate the proposed concept, we concentrate on graphene-hBN-graphene devices [an alternative barrier material (MoS2) is discussed in (18)].

The structure and operational principle of our FET are shown in Fig. 1. For convenience of characterization, both source and drain electrodes were made from graphene layers in the multiterminal Hall bar geometry (18). This device configuration allowed us to not only measure the tunnel current-voltage curves (I-V) but also characterize the response of the graphene electrodes, thus providing additional information about the transistor operation. The core graphene-hBN-graphene structure was encapsulated in hBN so as to allow higher quality of the graphene electrodes (19, 20). To fabricate the device shown in Fig. 1A, we first used the standard cleavage technique (21) to prepare relatively thick hBN crystals on top of an oxidized Si wafer (300 nm of SiO2), which acted as a gate electrode (Fig. 1 and fig. S1). The crystals served as a high-quality atomically flat substrate and a bottom encapsulation layer (19). Monolayer graphene (GrB) was then transferred onto a selected hBN crystal (20 to 50 nm thick) using a dry transfer procedure (19, 22). After deposition of metal contacts (5 nm Ti/50 nm Au) and etching to form a multiterminal Hall bar mesa, the structure was annealed at 350°C in forming gas. A few-atom-thick hBN crystal was identified (23) and transferred on top of GrB by using the same procedures. This hBN layer served as the tunnel barrier. The whole process of positioning, annealing, and defining a Hall bar was repeated to make the second (top) graphene electrode (GrT). Last, a thick hBN crystal encapsulated the entire multilayer structure (Fig. 1A and fig. S1). Further details of our multistep fabrication procedures can be found in (18, 22). We tested devices with tunnel barriers having thickness d from 1 to 30 hBN layers (18). To illustrate the basic principle of the tunneling FETs, we focus on the data obtained from four devices with a tunnel barrier made of 4 to 7 layers and discuss the changes observed for other d.

Fig. 1

Graphene field-effect tunneling transistor. (A) Schematic structure of our experimental devices. In the most basic version of the FET, only one graphene electrode (GrB) is essential, and the outside electrode can be made from a metal. (B) The corresponding band structure with no gate voltage applied. (C) The same band structure for a finite gate voltage Vg and zero bias Vb. (D) Both Vg and Vb are finite. The cones illustrate graphene’s Dirac-like spectrum and, for simplicity, we consider the tunnel barrier for electrons.

When a gate voltage Vg was applied between the Si substrate and the bottom graphene layer (GrB), the carrier concentrations nB and nT in both bottom and top electrodes increased because of the weak screening by monolayer graphene (24), as shown schematically in Fig. 1C. The increase of the Fermi energy EF in the graphene layers could lead to a reduction in Δ for electrons tunneling predominantly at this energy (18). In addition, the effective height also decreased relative to the NP because the electric field penetrating through GrB altered the shape of the barrier (25, 26). Furthermore, the increase in the tunneling DoS as EF moved away from the NP (24) led to an increase in the tunnel current I. Depending on parameters, any of the above three contributions could dominate changes in I with varying Vg. We emphasize that the use of graphene in this device architecture is critical because this exploits graphene’s low DOS, which for a given change in Vg led to a much greater increase in EF as compared with a conventional two-dimensional gas with parabolic dispersion (1317). This difference translated into much greater changes of both Δ and tunneling DOS.

The behavior of in-plane resistivity ρ for the GrB and GrT layers as a function of Vg is shown in Fig. 2A. The curves indicate little residual doping for encapsulated graphene (≈0 and <1011 cm−2 for GrB and GrT, respectively). In both layers, ρ strongly depended on Vg, showing that GrB did not screen out the electric field induced by the Si-gate electrode. The screening efficiency was quantified by Hall effect measurements (Fig. 2, B to D), which showed that the gate induced approximately the same amount of charge in both layers at low concentrations—that is, there was little screening if nB was small. As the concentration in GrB increased, the nB(Vg) and nT(Vg) dependences became super- and sublinear, respectively (Fig. 2, B and C), because of the increase in nB, which led to an increasingly greater fraction of the gate-induced electric field being screened out by GrB (18). Hence, more electrons accumulated in the bottom graphene electrode, and fewer reached the top electrode. The total charge accumulated in both layers varied linearly in Vg (Fig. 2D), as expected. We could describe the observed redistribution of the charge between the two graphene layers in terms of the corresponding sequential circuit including the quantum capacitance (13, 27) of the graphene layers (fig. S2). For a parabolic band, the ratio between nB and nt would be independent on Vg, and therefore, the electric field penetrating into the tunnel barrier would be substantially reduced even in the limit of zero nB (13).

Fig. 2

Graphene as a tunneling electrode. (A) Resistivities of the source and drain graphene layers as a function of Vg. (B to D) Carrier concentrations in the two layers induced by gate voltage, which were calculated from the measured Hall resistivities ρxy by using the standard expression n = B/eρxy, where B is the magnetic field and e is the electron charge. Close to the NP, the spikes appear (shown by dotted curves) because the above expression is not valid in the inhomogeneous regime of electron-hole puddles. The shown device has a 4-layer hBN barrier.

A bias voltage Vb applied between GrB and GrT gave rise to a tunnel current through the thin hBN barrier that scaled with device area. I-V characteristics for one of our devices at various Vg are shown in Fig. 3A. First, we consider the case of zero Vg. At low Vb, I was linear in bias, yielding a tunnel resistivity ρT = Vb/I ≈100 gigohms μm2 for this hBN thickness. At higher voltages (Vb above ~0.1 V), I grew more rapidly. The I-V curves could be described (Fig. 3A, inset, and fig. S3) by the standard quantum-tunneling formulae (25, 26), assuming energy conservation but no momentum conservation at the mismatched graphene-hBN interface (28).

Fig. 3

Tunneling characteristics for a graphene-hBN device with 6 ± 1 layers of hBN as the tunnel barrier. (A) I-Vs for different Vg (in 10-V steps). Because of finite doping, the minimum tunneling conductivity is achieved at Vg ≈ 3V. The inset compares the experimental I-V at Vg = 5 V (red curve) with theory (dark), which takes into account the linear DOS in the two graphene layers and assumes no momentum conservation. Further examples of experimental curves and their fitting can be found in (18). (B) Zero-bias conductivity as a function of Vg. The symbols are experimental data, and the solid curve is our modeling. The curve is slightly shifted with respect to zero Vg because of remnant chemical doping. In all the calculations, we assumed the hole tunneling with m = 0.5 m0 and Δ ≈ 1.5 eV (29, 30) and used d as measured by atomic force microscopy. Both I and σ are normalized per tunnel area, which was typically 10 to 100 μm2 for the studied devices. Temperature, 240 K.

As shown below, we could distinguish experimentally between electron and hole tunneling and found that the tunneling was due to holes. This result is in agreement with a recent theory for the graphene-hBN interface (29), which reports a separation between the Dirac point in graphene and the top of the hBN valance band of ≈1.5 eV, whereas the conduction band is >4 eV away from the Dirac point. The fit to our data with Δ = 1.5 eV yielded a tunneling mass m ≈ 0.5 m0 (m0 is the free electron mass), which is in agreement with the effective mass for holes in hBN (30). Furthermore, our analysis indicated that I varied mainly with the change in the tunneling DOS, whereas the change in tunneling probability with applied bias was a secondary (albeit important) effect (18). For our atomically thin hBN barriers with relatively low ρT, we were not in a regime of exponential sensitivity to changes in Δ[EF(Vb)].

We demonstrate transistor operation in Fig. 3A, which plots the influence of gate voltage on I. Vg substantially enhanced the tunnel current, and the changes were strongest at low bias. The field effect was rather gradual for all gate voltages up to ±50 V, a limit set by the electrical breakdown of our SiO2 gate dielectric (typically ≈60 V). This response is quantified in Fig. 3B, which plots the low-bias tunneling conductivity σT = I/Vb as a function of Vg. The influence of Vg was highly asymmetric: σT changed by a factor of ≈20 for negative Vg (holes) and by a factor of 6 for positive Vg (electrons). We observed changes up to ≈50 for hole tunneling in other devices and always the same asymmetry (fig. S4) (18). Also, the ON-OFF ratios showed little change between room and liquid-helium temperatures, as expected for Δ >> thermal energy.

To analyze the observed behavior of σT(Vg), we modeled the zero-bias conductivity by using the relation σT ∝ DOSB(Vg) × DOST(Vg) × T(Vg), where the indices refer to the two graphene layers and T(Vg) is the transmission coefficient through the hBN barrier (25, 26). The resulting curve shown in Fig. 3B accounts qualitatively for the main features in the measured data, using self-consistently the same tunneling parameters m and Δ given above. At Vg near zero, corresponding to tunneling from states near the NP, the tunneling DOS in both graphene layers was small and nonzero and was the result of residual doping, disorder, and temperature effects (18). The application of a gate voltage of either polarity led to a higher DOS and, therefore, higher σT. The gradual increase in σT(Vg) for both polarities in Fig. 3B was therefore caused by the increasing DOS. However, Vg also affected the transmission coefficient. Because of the shift of EF with changing Vg, the effective barrier height Δ decreased for one sign of charge carriers and increased for the other (Fig. 1B), which explains the asymmetry in both experimental and calculated σT(Vg) in Fig. 3B in terms of the change in T(Vg). For our devices, the effect of Vg on T(Vg) was relatively weak (nonexponential) and comparable with the effect caused by changes in the tunneling DOS. The sign of the asymmetry infers that the hBN barrier height was lower for holes than for electrons, which is in agreement with the graphene-hBN band structure calculations (29). The weaker dependence of I on Vg at high bias can also be understood in terms of the more gradual increase in the tunneling DOS and in EF at high doping (Vb = 0.5V correspond to nB ≈ 1013 cm−2).

Our results and analysis suggest that higher ON-OFF ratios could be achieved by using either higher Vg or making devices with larger d, so that the tunneling depends exponentially on bias and is controlled by the barrier height rather than the DOS. The former route is limited by the electrical breakdown of dielectrics at ~1 V/nm (Vg ≈ 300V for our SiO2 thickness). By extrapolating the analysis shown in Fig. 3B to such voltages, we found that ON-OFF ratios >104 would be possible for our 4-to-7-layer devices if SiO2 of highest quality were used. However, it would still require unrealistically large Vg to enter the regime where EF becomes comparable with Δ and changes in σT(Vg) are exponentially fast. Therefore, we explored the alternative option and investigated devices with both thinner and thicker hBN barriers. For 1- to 3-hBN layers, zero-bias σT increased exponentially with decreasing number of layers, which is consistent with quantum tunneling, and we observed a weaker influence of Vg on I, as expected for the more conductive regime. On the other hand, the thicker hBN barriers were prone to electrical breakdown. Nonetheless, for a few devices with d ≈ 6 to 9 nm, we were able to measure a tunnel current without breakdown. A current >10 pA appeared at biases of several volts and increased exponentially with Vb. The thicker devices’ I-V characteristics could be fitted by using the same hole-tunneling parameters used above, thus indicating quantum tunneling rather than an onset of electrical breakdown. Unfortunately, no substantial changes (exceeding 50%) in the tunnel current could be induced by Vg. This insensitivity to gate voltage remains to be understood but was probably caused by charge traps that screened the influence of the gate.

An alternative method to achieve an exponential dependence of the tunneling current on gate voltage would be to use a barrier dielectric with a smaller Δ, which would be comparable with typical EF realizable in graphene. One of such candidate materials is MoS2, which has a band gap of about 1.3 eV and can be obtained in a mono- or few-layers state similar to hBN and graphene (21). Our first graphene-MoS2–based devices demonstrate ON-OFF ratio close to 10.000 (fig. S5), which is sufficient for certain types of logic circuits.

We conclude that our tunneling devices offer a viable route for high-speed graphene-based analog electronics. The ON-OFF ratios already exceed those demonstrated for planar graphene FETs at room temperature by a factor of 10 (37). The transit time for the tunneling electrons through the nanometer-thick barriers is expected to be extremely fast (a few femtoseconds) (1317) and exceeds the electron transit time in submicrometer planar FETs. It should also be possible to decrease the lateral size of the tunneling FETs down to the 10 nm scale, a requirement for integrated circuits. Furthermore, there appears to be no fundamental limitation to further enhancement of the ON-OFF ratios by optimizing the architecture and by using higher-quality gate dielectrics and, in particular, lower tunnel barriers (Δ < maximum achievable EF).

Supporting Online Material

www.sciencemag.org/cgi/content/full/science.1218461/DC1

Materials and Methods

SOM Text

Figs. S1 to S5

References (31–35)

References and Notes

  1. Materials and methods are available as supporting material on Science Online.
  2. Acknowledgments: This work was supported by the European Research Council, European Commision FP7, Engineering and Physical Research Council (UK), the Royal Society, U.S. Office of Naval Research, U.S. Air Force Office of Scientific Research, and the Körber Foundation. A.M. acknowledges support from the Swiss National Science Foundation.
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