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Quantum Hall Effect in a Gate-Controlled p-n Junction of Graphene

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Science  03 Aug 2007:
Vol. 317, Issue 5838, pp. 638-641
DOI: 10.1126/science.1144657

Abstract

The unique band structure of graphene allows reconfigurable electric-field control of carrier type and density, making graphene an ideal candidate for bipolar nanoelectronics. We report the realization of a single-layer graphene p-n junction in which carrier type and density in two adjacent regions are locally controlled by electrostatic gating. Transport measurements in the quantum Hall regime reveal new plateaus of two-terminal conductance across the junction at 1 and Embedded Image times the quantum of conductance, e2/h, consistent with recent theory. Beyond enabling investigations in condensed-matter physics, the demonstrated local-gating technique sets the foundation for a future graphene-based bipolar technology.

Graphene, a single-layer hexagonal lattice of carbon atoms, has recently emerged as a fascinating system for fundamental studies in condensed-matter physics (1), as well as a candidate for novel sensors (2, 3) and postsilicon electronics (410). The unusual band structure of single-layer graphene makes it a zero-gap semiconductor with a linear (photonlike) energy-momentum relation near the points where valence and conduction bands meet. Carrier type—electron-like or holelike—and density can be controlled by using the electric-field effect (10), obviating conventional semiconductor doping, for instance via ion implantation. This feature, doping via local gates, would allow graphene-based bipolar technology devices comprising junctions between holelike and electron-like regions, or p-n junctions, to be reconfigurable using only gate voltages to distinguish p (holelike) and n (electron-like) regions within a single sheet. Although global control of carrier type and density in graphene using a single back gate has been investigated by several groups (1113), local control (8, 9) of single-layer graphene has remained an important technological milestone. In addition, p-n junctions are of great interest for low-dimensional condensed-matter physics. For instance, recent theory predicts that a local step in potential would allow solid-state realizations of relativistic (Klein) tunneling (14, 15) and a surprising scattering effect known as Veselago lensing (16), comparable to scattering of electromagnetic waves in negative-index materials (17).

We report the realization of local top gating in a single-layer graphene device that, combined with global back gating, allows individual control of carrier type and density in adjacent regions of a single atomic layer. Transport measurements at zero perpendicular magnetic field B and in the quantum Hall (QH) regime demonstrate that the functionalized aluminum oxide (Al2O3) separating the graphene from the top gate does not significantly dope the layer nor affect its low-frequency transport properties. We studied the QH signature of the graphene p-n junction and found new conductance plateaus at 1 and Embedded Image, consistent with recent theory addressing equilibration of edge states at the p-n interface (18).

Graphene sheets were prepared via mechanical exfoliation using a method (19) similar to that used in (10). Graphite flakes were deposited on 300 nm of SiO2 on a degenerately doped Si substrate. Inspection with an optical microscope allowed potential single-layer regions of graphene to be identified by a characteristic coloration that arises from thin-film interference (Fig. 1A). These micrometer-scale regions were contacted with thermally evaporated Ti/Au (5/40 nm) that was patterned using electron-beam lithography. Next, a ∼30-nm layer of oxide was deposited atop the entire substrate. As illustrated (Fig. 1B), the oxide consisted of two parts, a nonconvalent functionalization layer (NCFL) and Al2O3. This deposition technique (19) was based on a recipe successfully applied to carbon nanotubes (20). The NCFL serves two purposes. One is to create a noninteracting layer between the graphene and the Al2O3, and the other is to obtain a layer that is catalytically suitable for the formation of Al2O3 by atomic layer deposition (ALD). The NCFL was synthesized by 50 pulsed cycles of NO2 and trimethylaluminum (TMA) at room temperature inside an ALD reactor. Next, five cycles of H2O-TMA were applied at room temperature to prevent desorption of the NCFL. Lastly, Al2O3 was grown at 225°C with 300 H2O-TMA ALD cycles. To complete the device, a second step of electron-beam lithography defined a local top gate (5/40 nm Ti/Au) covering a region of the device that includes one of the metallic contacts.

Fig. 1.

(A) Optical micrograph of a device similar to the one measured. Metallic contacts and top gate appear in orange and yellow, respectively. Darker regions below the contacts are thicker graphite from which the contacted single layer of graphene extends. (B) Illustration of the oxide deposition process. A noncovalent functionalization layer is first deposited with NO2 and TMA (50 cycles), and Al2O3 is then grown by ALD using H2O-TMA (305 cycles yielding ∼30-nm thickness). (C) Schematic of the device measured in this experiment.

A completed device, similar in design to that shown in the optical image in Fig. 1A, was cooled in a 3He3 refrigerator and characterized at temperatures T of 250 mK and 4.2 K. Differential resistance, R = dV/dI, where I is the current and V the source-drain voltage, was measured by standard lock-in techniques with a current bias of 1 nArms at 95 Hz for T = 250 m K and 10 nArms for T = 4.2 K. The voltage across two contacts on the device, one outside the top-gate region and one underneath the top gate, was measured in a four-wire configuration, eliminating series resistance of the cryostat lines but not contact resistance. Contact resistance was evidently low (∼1 kohm), and no background was subtracted from the data. A schematic of the device is shown in Fig. 1C.

The differential resistance, R, as a function of back-gate voltage, VBG, and top-gate voltage, VTG, at B = 0 (Fig. 2A) demonstrates independent control of carrier type and density in the two regions. This two-dimensional (2D) plot reveals a skewed, crosslike pattern that separates the space of top-gate and back-gate voltages into four quadrants of well-defined carrier type in the two regions of the sample. The horizontal and diagonal ridges correspond to charge neutrality, i.e., the Dirac point, in regions 1 and 2, respectively. The slope of the charge-neutral line in region 2, along with the known distances to the top gate and back gate gives a dielectric constant κ ∼ 6 for the functionalized Al2O3. The center of the cross at (VTG, VBG) ∼ (–0.2 V, –2.5 V) corresponds to charge neutrality across the entire graphene sample. Its proximity to the origin of gate voltages demonstrates that the functionalized oxide does not chemically dope the graphene substantially.

Fig. 2.

(A) Two-terminal differential resistance R as a function of VTG and VBG at B = 0 and T = 4.2 K, demonstrating independent control of carrier type and density in regions 1 and 2. Labels in each of the four quadrants indicate the carrier type (first letter indicates carrier type in region 1). (B and C) Horizontal slices at VBG and vertical slices at VTG; settings corresponding to the colored lines superimposed on Fig. 2A. (D) I-V curves at the gate voltage settings corresponding to the solid circles in Fig. 2A are representative of the linear characteristics observed everywhere in the plane of gate voltages.

Slices through the 2D conductance plot at fixed VTG are shown in Fig. 2C. The slice at VTG = 0 shows a single peak commonly observed in devices with only a global back gate (1013). By using a Drude model away from the charge-neutrality region, we estimated mobility at ∼7000 cm2/Vs (10). The peak width, height, and back-gate position are consistent with single-layer graphene (1113) and provide evidence that the electronic structure and degree of disorder of the graphene are not strongly affected by the oxide. Slices at finite |VTG| reveal a doubly peaked structure. The weaker peak, which remains near VBG ∼ –2.5 Vat all VTG, corresponds to the Dirac point of region 1. The stronger peak, which moves linearly with VTG, is the Dirac point for region 2. The difference in peak heights is a consequence of the different aspect ratios of regions 1 and 2. Horizontal slices at fixed VBG corresponding to the horizontal lines in Fig. 2A are shown in Fig. 2B. These slices show a single peak, corresponding to the Dirac point of region 2. This peak becomes asymmetric away from the charge-neutrality point in region 1. We note that the VBG dependence of the asymmetry is opposite to that observed in (9), where the asymmetry is studied in greater detail. The changing background resistance results from the different density in region 1 at each VBG setting. Current-voltage (I-V) characteristics, measured throughout the (VTG, VBG) plane, show no sign of rectification in any of the four quadrants or at either of the charge-neutral boundaries between quadrants (Fig. 2D), as expected for reflectionless (Klein) tunneling at the p-n interface (14, 15).

In the QH regime at large B, the Dirac-like energy spectrum of graphene gives rise to a characteristic series of QH plateaus in conductance, reflecting the presence of a zero-energy Landau level that includes only odd multiples of 2e2/h (that is, 2, 6, 10,... × e2/h) for uniform carrier density in the sheet (2123). These plateaus can be understood in terms of an odd number of QH edge states (including a zero-energy edge state) at the edge of the sheet, circulating in a direction determined by the direction of B and the carrier type. The situation is somewhat more complicated when varying local density and carrier type across the sample.

A 2D color plot of differential conductance g = 1/R as a function of VBG and VTG at B = 4 T is shown in Fig. 3A. A vertical slice at VTG = 0 through the p-p and n-n quadrants (Fig. 3B) reveals conductance plateaus at 2, 6, and 10e2/h in both quadrants, demonstrating that the sample is single layer and that the oxide does not significantly distort the Dirac spectrum.

Fig. 3.

(A) Differential conductance g as a function of VTG and VBG at B = 4 T and T = 250 mK. (B) Vertical slice at VTG = 0, traversing p-p and n-n quadrants. Plateaus are observed at 2e2/h and 6e2/h, the QH signature of single-layer graphene. (C) Horizontal slice at ν1 = 6 showing conductance plateaus at 6, 2, and Embedded Image. (D) Horizontal slice at ν2 showing QH plateaus at 2, 1, and Embedded Image. (E) Table of conductance plateau values as a function of filling factors calculated with Eqs. 1 and 2. Black, purple, and red lines correspond to slices in (B), (C), and (D), respectively. (F) Schematic of countercirculating edge states at filling factors ν1 = –ν2 = 2.

QH features are investigated for differing filling factors ν1 and ν2 in regions 1 and 2 of the graphene sheet. A horizontal slice through Fig. 3A at filling factor ν1 = 6 is shown in Fig. 3C. Starting from the n-n quadrant, plateaus are observed at 6e2/h and 2e2/h at top-gate voltages, corresponding to filling factors ν2 = 6 and ν2 = 2, respectively. Crossing over to the n-p quadrant by further decreasing VTG, a new plateau at Embedded Image appears for ν2 = –2. In the ν2 = –6 region, no clear QH plateau is observed. Another horizontal slice at ν1 = 2 shows 2e2/h plateaus at both ν2 = 6 and ν2 = 2 (Fig. 3D). Crossing into the n-p quadrant, the conductance exhibits QH plateaus at 1e2/h for ν2 = –2 and near Embedded Image for ν2 = –6.

For ν1 and ν2 of the same sign (n-n or p-p), the observed conductance plateaus follow Embedded Image(1) This relation suggests that the edge states common to both regions propagate from source to drain, whereas the remaining |ν1–ν2| edge states in the region of highest absolute filling factor circulate internally within that region and do not contribute to the conductance. This picture is consistent with known results on conventional 2D electron gas systems with inhomogeneous electron density (2426).

Recent theory (18) addresses QH transport for filling factors with opposite sign in regions 1 and 2(n-p and p-n). In this case, countercirculating edge states in the two regions travel in the same direction along the p-n interface (Fig. 3F), which presumably facilitates mode mixing between parallel-traveling edge states. For the case of complete mode mixing, that is, when current entering the junction region becomes uniformly distributed among the |ν1|+|ν2| parallel-traveling modes, quantized plateaus are expected (18) at values Embedded Image(2) A table of the conductance plateau values given by Eqs. 1 and 2 is shown in Fig. 3E. Plateau values at 1e2/h for ν1 = –ν2 = 2 and at Embedded Image for ν1 = 6 and ν2 = –2 are observed in the experiment. Notably, the Embedded Image plateau suggests uniform mixing among four edge stages (three from region 1 and one from region 2). All observed conductance plateaus are also seen at T = 4 K and for B in the range from 4 to 8 T [Supporting Online Material (SOM) text].

We do find some departures between the experimental data and Eqs. 1 and 2, as represented in the grid of Fig. 3E. For instance, the plateau near Embedded Image in Fig. 3D is seen at a value of ∼1.4e2/h, and no clear plateau at 3e2/h is observed for ν1 = –ν2 = 6. We speculate that the conductance in these regions being lower than their expected values is an indication of incomplete mode mixing. We also observe an unexpected peak in conductance at a region in gate voltage between the two 1e2/h plateaus at ν1 = ±ν2 = 2. This rise in conductance is clearly seen for |VTG| values between ∼1 and 2 V and VBG values between ∼ –5 and –2V. This may result from the possible existence of puddles of electrons and holes near the charge-neutrality points of regions 1 and 2, as previously suggested (27).

Supporting Online Material

www.sciencemag.org/cgi/content/full/1144657/DC1

Materials and Methods

SOM Text

Fig. S1

References and Notes

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