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Charge Noise in Graphene Transistors pubs.acs.org/NanoLett Charge Noise in Graphene Transistors Iddo Heller,†,§ Sohail Chatoor,† Jaan Ma¨nnik,† Marcel A. G. Zevenbergen,† Jeroen B. Oostinga,†,‡ Alberto F. Morpurgo,†,‡ Cees Dekker,† and Serge G. Lemay*,†,| † Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands, and ‡ DPMC and GAP, University of Geneva, quai Ernest-Ansermet 24, CH-1211 Geneva 4, Switzerland ABSTRACT We report an experimental study of 1/f noise in liquid-gated graphene transistors. We show that the gate dependence of the noise is well described by a charge-noise model, whereas Hooge’s empirical relation fails to describe the data. At low carrier density, the noise can be attributed to fluctuating charges in close proximity to the graphene, while at high carrier density it is consistent with noise due to scattering in the channel. The charge noise power scales inversely with the device area, and bilayer devices exhibit lower noise than single-layer devices. In air, the observed noise is also consistent with the charge-noise model. KEYWORDS Graphene, liquid gate, transistor, 1/f noise, Hooge, charge noise nherent noise limits the performance of electronic de- voltage, the device dimensions, and the number of graphene vices in circuits and sensors. Here we focus on graphene, layers. We find that the dependence of the noise on the gate- which has been shown to function as a promising sensor induced carrier density qualitatively disagrees with the I 1 2 material in both the gas phase and the liquid phase. The Hooge relation. Instead, our experimental observations are sensing mechanism of these devices relies on local perturba- consistent with an augmented charge-noise model,11-13 tions of the graphene sheet that modulate its global transport which distinguishes between two separate contributions to 1,3 properties in a manner analogous to the field effect induced the noise. At low carrier density, the noise is dominated by 4 by a gate electrode. An exceptionally high sensitivity to ad- charge noise associated with random charge fluctuations in sorbed gas species was demonstrated, even down to single- the environment that couple to the device through a field 1 molecule sensitivity. When employed in liquid, carbon field- effect. This charge noise scales inversely with the device area effect devices based on carbon nanotubes, graphene, and and is lower for BLG than for SLG devices. At high carrier chemically modified graphene can be used as sensors for density, a gate-independent noise source becomes apparent 3,5-7 dissolved species such as charged biomolecules. Because that can be associated with scattering in the channel. These of the high sensitivity to local perturbations, it is expected findings are consistent with the augmented charge-noise that uncontrolled charge fluctuations in the vicinity of the model and previous observations of charge noise in liquid- device - as commonly associated with charge traps in the gated carbon nanotube devices.12,13 silicon oxide substrate8 - can result in considerable low- Two-terminal graphene devices were prepared from frequency noise, which is detrimental to device perfor- mechanically exfoliated graphite on oxidized silicon wafers mance. To date, few studies have addressed the noise (285 nm SiO ).4 The graphene flakes were identified by their properties of graphene. In the low-frequency limit, where 2 optical contrast14 and electrically contacted with Cr/Au sensing experiments are typically performed, graphene 8,9 electrodes patterned using e-beam lithography. Measure- exhibits a 1/f-type noise spectrum. A recent report on 1/f 13 8 ments were performed in a home-built flow cell filled with noise of graphene nanoribbons in vacuum suggests that single-layer graphene (SLG) obeys the empirical Hooge rela- an aqueous electrolyte buffered at pH 7.2 using 10 mM tion,10 whereas bilayer graphene (BLG) exhibits a suppres- phosphate buffer. A liquid-gate potential, Vlg, was applied to 15 sion of the noise. No report has so far addressed the noise an Ag/AgCl (3 M NaCl) reference electrode inserted in the properties of liquid-gated graphene, the configuration most flow cell. In such an electrolyte-gated configuration, the relevant for liquid-phase sensing. device is gated by a field effect from mobile ions that form 16-20 In this letter, we present an experimental study of 1/f an electrical double-layer in solution. noise in liquid-gated SLG and BLG devices. In particular, we Figure 1a depicts graphene in a liquid-gated transistor address the scaling of the noise properties with the gate layout. We measured the source-drain current, Isd, while applying a small dc bias voltage Vsd (e5 mV). All electrical * To whom correspondence should be addressed. E-mail: [email protected]. measurements were performed as described in ref 12. § Present address: Department of Physics and Astronomy, VU University, De Figure 1b shows typical source-drain conductance G(Vlg) Boelelaan 1081, 1081 HV Amsterdam, The Netherlands. curves measured for liquid-gated SLG and BLG devices. The | Present address: MESA+ Institute and Faculty of Science and Technology, curves exhibit a minimum in G(Vlg) at the Dirac point, and a University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. Received for review: 11/3/2009 monotonically increasing G(Vlg) on both sides away from the 21,22 Published on Web: 04/07/2010 Dirac point. We measured current-noise power spectra, © 2010 American Chemical Society 1563 DOI: 10.1021/nl903665g | Nano Lett. 2010, 10, 1563–1567 FIGURE 1. (a) Device schematic of a liquid-gated graphene transistor. (b) Source-drain conductance, G, vs liquid-gate voltage, Vlg, for a SLG (solid line) and a BLG (dashed line) device. (c,d) Normalized con- 2 - ductance-noise power spectra SG/G (f) for the SLG and BLG devices FIGURE 2. (a) Conductance, G, vs gate voltage, Vlg V0, for two SLG of (a) respectively. The spectra were obtained at values of Vlg as devices. V0 is the liquid-gate voltage where G is mimimal and indicated by the dots labeled I, II, and III in (b). Dashed lines indicate corresponds to the Dirac point. (b) Conductance noise power at 1 1/f slopes. Hz, SG(1 Hz), vs gate voltage. The curves represent the augmented charge-noise model separately fitted to the data for Vlg < V0 and > S (f) as function of V . Figure 1c,d plots the normalized Vlg V0. For plotting purposes the fits have been smoothed; see I lg Supporting Information, Figure S1 for unsmoothed fits. (c) Normal- 2 ) 2 2 conductance-noise power spectra, SG(f)/G SI(f)/Isd , for the ized noise amplitude SG(1 Hz)/G vs gate voltage. The curves repre- SLG and BLG devices of Figure 1b, respectively. Power sent best fits to the Hooge model. (d-f) Same as (a-c) but for two spectra are shown for three different gate voltages, as BLG devices. indicated in Figure 1b (grayscale dots labeled I-III). Strik- ingly, for both the SLG and the BLG device, the noise power Hooge model, Figure 2c,f shows the normalized noise 2 does not increase monotonically with increasing |Vlg|. In- amplitude at 1 Hz, SG(1 Hz)/G , for the devices of Figure 2b,e, stead the noise power exhibits a maximum at intermediate respectively. Similar to SG(1 Hz), the experimental data for 2 carrier density (II) where dIsd/dVlg is largest. This gate de- SG(1 Hz)/G exhibit a minimum at V0 and passes through a pendence of the noise power is indicative of charge noise, local maximum negative of V0. Comparing the Hooge pre- 11,12 2 as discussed below. diction SG(1 Hz)/G ) /G to the data in Figure 2c,f (solid To study in detail the dependence of the 1/f noise on the lines), where is treated as an adjustable parameter, it is number of gate-induced charge carriers, we characterized clear that the gate dependence of the noise in liquid-gated the noise as a function of Vlg for thirteen SLG and seven BLG graphene devices cannot be described by Hooge’s relation. devices. Figure 2 presents typical transport and noise data Whereas Hooge’s model predicts a maximum in SG(1 Hz)/ for two SLG devices (Figure 2a-c), and two BLG devices G2 at the Dirac point, where the carrier density is minimum, 2 (Figure 2d-f). In Figure 2a,d, the conductance G for each we instead observe a pronounced minimum in SG(1 Hz)/G device is plotted as function of the gate voltage. To facilitate for both SLG and BLG devices. comparison between different devices, the Vlg axes have Alternatively, we compare the data to an augmented charge- 11 been centered at V0, defined as the gate voltage at which G noise model proposed by Tersoff, which we recently used to is minimum. We recorded the noise power spectrum at each successfully describe 1/f noise in liquid-gated carbon nanotube gate voltage and, as a representative measure for the transistors.12,13 The augmented charge-noise model predicts 2 2 2 2 magnitude of the low-frequency noise, we extracted the that SI(1 Hz) )Vsd SG(1 Hz) ) Sinput(dIsd/dVlg) + AS(RS/Rtot) Isd . conductance noise power spectral density at 1 Hz, SG(1 Hz) Here the first (charge-noise) term represents current noise 2 ) SI(1 Hz)/Vsd , by fitting SI(f) ) SI(1 Hz)/f to each spectrum. associated with random charge fluctuations with power Sq Typically, the fitted noise exponent was 0.8 e e 1.2. in the vicinity of the device. These charge fluctuations Figure 2b,e shows SG(1 Hz) for the devices of Figure 2a,d, couple to the transistor with an effective gate capacitance respectively.
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