pubs.acs.org/NanoLett
Tunable Nanoscale Graphene Magnetometers Simone Pisana, Patrick M. Braganca, Ernesto E. Marinero, and Bruce A. Gurney* San Jose Research Center, Hitachi Global Storage Technologies, 3403 Yerba Buena Road, San Jose, California 95135 ABSTRACT The detection of magnetic fields with nanoscale resolution is a fundamental challenge for scanning probe magnetometry, biosensing, and magnetic storage. Current technologies based on giant magnetoresistance and tunneling magnetoresistance are limited at small sizes by thermal magnetic noise and spin-torque instability. These limitations do not affect Hall sensors consisting of high mobility semiconductors or metal thin films, but the loss of magnetic flux throughout the sensor’s thickness greatly limits spatial resolution and sensitivity. Here we demonstrate graphene extraordinary magnetoresistance devices that combine the Hall effect and enhanced geometric magnetoresistance, yielding sensitivities rivaling that of state of the art sensors but do so with subnanometer sense layer thickness at the sensor surface. Back-gating provides the ability to control sensor characteristics, which can mitigate both inherent variations in material properties and fabrication-induced device-to-device variability that is unavoidable at the nanoscale. KEYWORDS Graphene, transport properties, sensors, magnetoresistance
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rapid decay of magnetic field within the layer itself would result in a significant reduction in sensitivity. In contrast, graphene can provide a unique path to the detection of magnetic fields within an atom-thick sensing layer which can be located at or near the sensor surface. Graphene’s high mobility is expected to give high signal in Hall, geometric magnetoresistance,21 and extraordinary magnetoresistance (EMR) devices,22,30 where the geometric magnetoresistance is enhanced by the addition of metal inclusions. Furthermore, the response of the graphene EMR devices to back gate potentials can provide a facile route to tailoring the sensitivity and resistance of the device after fabrication and/ or to compensate for variations in the transport properties of graphene. For scanning probe applications, graphene sensors provide an advantage over magnetic force microcopy (MFM)14,15 or spin-polarized scanning tunneling microscopy (sp-STMs)16,17 because they have no ferromagnetic components, which can exert an additional force component or alter the magnetization being detected.12 Though superconducting quantum interference devices (SQUIDs)31,32 and scanning micro SQUIDs33 can be noninvasive and provide micrometer spatial resolution and high magnetic field sensitivity, they are limited to cryogenic operation. In the EMR effect,30 as the magnetic field is increased the current flowing through the device is partially excluded from a metallic shunt and is redistributed in the semiconductor, increasing the nonlocal resistance (Figure 1a). Our EMR devices use a particular arrangement of current injection (I) and voltage detection (V) electrodes in which the sensitivity is further improved by the additional contribution of a Halllike signal.27,34 The resulting structure is a conformal equivalent to a shunted circular van der Pauw disk geometry,20 with the additional benefit of having the sensitivity localized in a small area.35 EMR devices with 200 nm lead spacing and 150 nm lead to shunt separation were fabricated on n-doped c-Si substrates covered by 300 nm of thermally grown SiO2, which serves as a back gate. The graphene was
n recent years, graphene has been the focus of significant work, stimulated by the material’s rich physics, electronic characteristics, and structural properties.1–7 The combination of high mobility, long spin relaxation times, and atomic thickness has attracted interest for several applications, including high-frequency transistors, single molecule gas sensing, and spintronics.8–11 For the detection of nanoscale magnetic domains, an essential goal in scanning probe magnetometry,12–17 biosensing,18,19 and magnetic storage,20–22 it is important to have a sensor whose thickness and distance from the nanomagnet is as small as possible in order to maintain high spatial resolution and maximum excitation. This prerequisite imposes very stringent constraints on magnetic spacing d, where for magnetic storage applications with information densities above 1 Tbit/ in.2 the bit size b will be below 25 nm. At such high density, the magnetic field will fall exponentially as e-πd/b, according to the Wallace spacing loss relationship,23 resulting in 63% loss in as little as 8 nm from the surface of the media. Giant magnetoresistance (GMR)24 and tunneling magnetoresistance (TMR)25 have been successfully exploited in the magnetic storage industry for more than 10 years but are expected to be limited at small sizes by thermal magnetic noise22,26,27 and spin-torque instability.28,29 Devices built from high mobility semiconducting heterostructures with channels forming a two-dimensional electron gas (2DEG) are promising to detect magnetic fields at submicrometer scales and have been studied for applications in scanning probe microscopy12,13 and biosensing.18,19 Typically, the 2DEG sensing channel is located beneath capping and insulating layers to form the well, placing the channel 20 nm or more beneath the sensor’s surface. Additionally, such structures have 2DEG layer thickness ranging from 4 to 20 nm, so the
* Corresponding author,
[email protected]. Received for review: 11/4/2009 Published on Web: 12/23/2009 © 2010 American Chemical Society
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FIGURE 2. Device response maps as function of back gate voltage (Vg) and magnetic field (B) for (a) the nonlocal voltage signal (Vdiff) and (b) the magnetoresistance (MR). The measurements were made at a constant bias current of 150 µA, which corresponds to a crosssectional current density at the source and drain electrodes of ∼108 A/cm2. The resolution of the sweeps was of 0.8 V for Vg and of 0.1 T for B.
a pair of adjacent leads, to minimize the effect of current spreading to the nearby shunt.38 For this purpose, the contact overlap between metal lead and graphene flake, as determined by scanning electron microscopy, was used as the channel width, while the length was 200 nm. The response of the EMR devices was taken at either a constant bias voltage or constant bias current, with similar results, and with cross-sectional current densities of up to 1.7 × 108 A/cm2, assuming a graphene layer thickness of 0.34 nm. As the back gate voltage (Vg) and the magnetic field (B) were varied, the biasing voltage (Vb) and current (Ib) at the I+ lead were measured, as well as the potentials at the V+ and V- sensing leads, whereas the I- lead was kept at ground potential (Figure 1a). From the measurements one can extract the nonlocal voltage signal, Vdiff ) V+ - V-, and the nonlocal magnetoresistance (Figure 2)
FIGURE 1. (a) Schematic illustration of the current flow (arrows) through a graphene EMR device for hole conduction at zero magnetic field (black) and large out of plane fields as indicated by the symbols to the left (green and red). The colors in the schematic represent the SiO2 surface (purple), the graphene sheet (gray), and the metal electrodes (yellow). The blue rectangle highlights the region where the sensitivity is localized. (b) SEM picture of a completed EMR device with 200 nm lead width. The graphene flake consists of regions with different number of layers, with darker gray representing thicker regions. The device is fabricated on monolayer graphene, as determined by its Raman spectrum (inset). The scale bar is 1 µm.
deposited by cleaving highly oriented pyrolytic graphite, and one- and two-layer flakes were identified by Raman spectroscopy.36 The leads were fabricated by defining patterns in poly(methyl methacrylate) by e-beam lithography, deposition of Ta/Au (2.5 nm/20 nm), and lift-off. The devices were measured at 300 K in a probe station equipped with a superconducting magnet at pressures of 10-7 Torr. Prior to the measurements in magnetic field, the devices were treated in high currents in order to remove some of the residues left by the fabrication process.37 The contact resistance and mobility of each device were estimated from the back gate dependence of a low bias current (∼1 µA) through © 2010 American Chemical Society
MR )
Rnl(B) - Rnl(B ) 0) Rii(B ) 0)
(1)
where Rnl ) Vdiff/Ib is the nonlocal resistance and Rii ) Vb/Ib is the two terminal resistance measured through the current 342
DOI: 10.1021/nl903690y | Nano Lett. 2010, 10, 341-346
leads. Note that this conservative definition of magnetoresistance is closely connected to the SNR, a necessary consideration in defining a successful detection system. Alternative definitions that are sometimes used give artificially large values as a result of dividing by the nonlocal resistance at zero field (which can be negligible when the potentials at the voltage sensing leads are similar in magnitude) and which are not connected to the noise sources relevant to electrical SNR. The magnetic field sensitivity can be obtained by the slope of Vdiff with respect to B and normalized by the current at B ) 0. The response of the voltage signal Vdiff with respect of the back gate voltage is readily understood in terms of variation of the graphene sheet’s resistivity with carrier concentration,1 with a maximum near the charge neutral Dirac point (VD) and decreasing resistivity for increasingly higher concentrations of electrons (Vg > VD) and holes (Vg < VD). As the magnetic field is varied, two different regimes can be identified, as shown in Figure 3a. At high carrier concentrations (|Vg| . VD) the response is linear, which we associate with a Hall signal dominated regime: Vdiff ∝ GIbB/qn, where G is a geometric factor that depends on width and length, n is the carrier concentration, and q is the carrier charge. In this regime the sign of the slope depends on the carrier type (electrons or holes). Near VD, an additional component proportional to B2 can be identified and the linear response is suppressed. The quadratic dependence can be more clearly identified in the modulation of Rii (Figure 3b), which is not influenced by the Hall voltage (see Supplementary Text and Figure 1 in Supporting Information). This second-order response can be due to two mechanisms: (i) the simultaneous presence of electron and holes through a disordered network of charge puddles that cancels out the Hall field39 (leaving the graphene’s longitudinal magnetoresistance which is proportional to B2), and (ii) the increased current flow through the metallic shunt as the resistivity of the graphene increases40 (which enhances the EMR effect and also provides a component proportional to B2). The range in back gate voltage where a quadratic component is observed (>30 V) is bigger than the plateau width of the resistance maximum (∼5 V) within which the mixed region of electrons and holes is present,39 suggesting that electron/hole compensation near VD (i) is not solely responsible for the effect without invoking strong (>2 × 1012 cm-2) doping variations within the sample area. Finite element modeling (FEM) indicates that the current flowing through the shunt varies from 48% to 13% of the total current in the device when the graphene sheet resistance in the model is varied from the values estimated at Vg ) VD to Vg ) 40 V (see supplementary text and Figure 2 in Supporting Information). The variation in the current flowing through the shunt in the model reflects the variation in the strength of the quadratic component of Rii at different values of Vg, suggesting a significant contribution from the shunting mechanism (ii). Although FEM does not provide quantitative agreement with the experiment for the © 2010 American Chemical Society
FIGURE 3. (a) The nonlocal voltage signal Vdiff has a linear dependence on magnetic field B for |Vg| . VD due to the Hall effect, but it acquires a parabolic component near the Dirac point VD. (b) Secondorder derivative with respect to magnetic field of the resistance measured across the current electrodes. The second-order term is enhanced near the Dirac point, where the graphene’s resistivity is higher and more current flows though the shunt. The parabolic component is at its maximum within a ∼5 V back gate voltage range around VD (pink shaded area), where the simultaneous presence of electrons and holes induces an additional magnetoresistance effect. The inset shows the back gate voltage dependence of the resistance through the current electrodes at zero magnetic field, indicating that VD ∼ 0 V and that the high-resistance plateau width is ∼5 V. The curves were taken at a constant bias current of 150 µA.
strength of the parabolic EMR signal solely from the shunting mechanism, we note that the two effects (i and ii) are additive, and both are likely to be participating in the signal. Further investigations can help elucidate the relative strength of these mechanisms and lead to improved sensitivity. The sensitivity of the graphene devices studied in this work (Figure 4) is comparable to the best Hall devices of similar area that used structures with significantly thicker sense layers.21,41 As observed previously,27 the sensitivity is found to be linear with the bias current, so that high sensitivity is achievable using the high current densities that graphene is able to sustain.37 The device to device variation in sensitivity is determined by material-specific and fabrica343
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FIGURE 4. (a) Sensitivity (slope of Vdiff over (0.5 T, normalized by the current) as function of back gate voltage, demonstrating the widely tunable nature of the sensor. (b) Peak sensitivity over (0.5 T field as function of cross-sectional current density. The devices show an approximately constant response through a broad range of current densities, highlighting the robust nature of the graphene. The device to device variation in sensitivity is mainly attributed to the overlap between graphene and the metal contacts, which dominates the two terminal resistance. (c) Johnson-limited SNR for (50 mT signals at a bandwidth of 1 GHz as function of the two terminal resistance measured through the current leads (Rii). SNRs greater than 10 dB are obtained even for devices having lower sensitivities. Note that every factor of 10 decrease in bandwidth adds 10 dB to the SNR. Improved contacts and mobility will likely increase the SNR to above 25 dB. In (b) and (c), the symbol color distinguishes different samples, with the filled symbols representing single layer graphene and the empty symbols bilayer graphene. The circled symbol refers to the sample and bias condition of the data shown in (a) as well as Figures 2 and 3. The arrows in (b) and (c) indicate increasing current density.
tion-specific properties. The graphene’s resistivity at VD is affected by the number of layers in the graphene sample and extrinsic factors such as inhomogeneous doping. In our devices variations in two terminal resistance result from variations in graphene resistivity, contact resistivity, and differences in the penetration of the electrodes into the graphene sheet of 70-400 nm in our devices. A useful characteristic of graphene sensors is the possibility to easily tune their response by applying a back gate potential, as shown in Figure 4a. This feature is not accessible in GMR and TMR sensors and when implemented in 2DEG Hall sensors it can significantly increase the magnetic spacing (via top gating42), or it involves including a back gate in close proximity to the epitaxially grown 2DEG structure (a substantial technical challenge). The back gate potential can also be used to vary the graphene device resistance, allowing for the optimization of sensitivity and SNR to best suit the detection technique and bandwidth for a particular application (kilohertz range for scanning probe and biosensing, gigahertz range for magnetic storage). Furthermore, back gating can provide a facile route to offset yield losses © 2010 American Chemical Society
in manufacturing that are bound to arise from device-todevice variations as the sensor size is reduced to the nanoscale. At room temperature the dominating source of noise in graphene nanostructures is attributed to extrinsic fluctuators such as the trapping/detrapping of defect states near the graphene sheet, leading to a noise dependence which is inversely proportional to the frequency43 (1/f). Passivation of oxide defects and screening in multilayer devices can reduce the 1/f noise by more than an order of magnitude, so that detection would be limited by Johnson noise.10,43,44 Encapsulating the device with a suitable nanometer-thick layer can eliminate contamination of the graphene that can introduce additional electronically active traps while providing physical protection desirable in magnetic recording and scanning probe applications. In order to estimate the Johnson noise figure for our devices at operating temperature, we used a temperature rise of 3.3 K per kW cm-2 of electrical power dissipated from Joule heating over the device area.45 This peak temperature was then reduced by 50%, consistent with the cooling 344
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reported in the graphene sheet in close proximity to metal contacts.45 Interestingly, the calculated Johnson-limited SNR at the peak current densities tested is comparable among several devices regardless of the magnetic field sensitivity, due to the correlation of device resistance and sensitivity (Figure 4c). The use of multilayer graphene10 and optimized contact metals46 can reduce the device and contact resistance and hence limit the Johnson noise. As an example, our estimated contact resistivity of 3 × 10-6 Ω cm2 can be reduced to ∼10-7 Ω cm2 by using Pd as a contact metal.46,47 The much reduced contact resistance would result in a transition in device operation to a regime where the graphene sheet resistance dominates the total resistance. When combined with a mobility of 5000 cm2/(V s) a reduction of twoterminal resistance by a factor of 7-10 in our single layer graphene devices is possible, with an associated improvement in Johnson-limited SNR by a factor of 1.8-2.5 and an overall SNR of up to 26 dB for a 1 GHz bandwidth. There are additional factors that are expected to improve the sensitivity and lower the noise in future graphene-based EMR devices, which have not yet been optimized here. The carrier mobility in our devices is typically 1000-5000 cm2/ (V s), as estimated through adjacent pairs of contacts in the EMR device.38 A higher mobility, which can be achieved by reducing the dominant sources of scattering,48 can increase the signal in terms of its Hall and geometric magnetoresistance components.21,30 As the device size is reduced and is made smaller than the mean free path, boundary scattering from the edges of the graphene sheet and contact metals will dominate and the intrinsic mobility of graphene may not play a relevant role in the signal amplitude. It is not fully understood how the signal will be affected when the mean free path greatly exceeds the device size. However, recent experimental and theoretical work demonstrates that signals comparable to or exceeding those found in the purely diffusive limit can be obtained in structures with thick sense layers.27,49–51 Additionally, in the ballistic regime, shot noise in graphene is strongly suppressed as the width to length ratio is reduced and the carrier concentration increased, so Johnson noise will likely be the dominant contribution to noise.52,53 The four-terminal EMR structure presented here may not represent the optimum compromise between device performance and ease of fabrication. In fact, a three-terminal structure, where one of the two voltage sensing leads is eliminated, can be advantageous for the reduction of device size and spatial resolution without substantially reducing its sensitivity, as seen in the most sensitive devices by monitoring the potential at each of the voltage leads separately as the magnetic field is varied. Finally, the magnetic field response may be shifted to higher sensitivity (an improvement of almost a factor of 3) and more linear operating regions by the addition of an external magnetic biasing field (see Figure 3 in Supporting Information). © 2010 American Chemical Society
In conclusion, we have demonstrated a novel magnetometer implementation using graphene, having a sense layer thickness of atomic dimensions located at the device surface, which, combined with ability to tune the device’s sensitivity and noise, paves the way toward magnetic field sensors capable of nanoscale spatial resolution that are tolerant to fabrication variations. Acknowledgment. The authors thank M. Pelliccione for assistance in developing the fabrication process. Supporting Information Available. Additional detail regarding measurements under different probe configurations, finite element modeling, and magnetic field sensitivity at higher biasing magnetic fields. This material is available free of charge via the Internet at http://pubs.acs.org. REFERENCES AND NOTES (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28)
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