graphene signal mixer for sensing applications

Published: June 02, 2011

r 2011 American Chemical Society 12128 dx.doi.org/10.1021/jp202790b | J. Phys. Chem. C 2011, 115, 12128–12134

ARTICLE

pubs.acs.org/JPCC

Graphene Signal Mixer for Sensing ApplicationsNorma L. Rangel,†,‡ Alejandro Gimenez,† Alexander Sinitskii,|| and Jorge M. Seminario*,†,‡,§

†Department of Chemical Engineering, ‡Materials Science and Engineering, and §Department of Electrical and Computer Engineering,Texas A&M University, College Station, Texas 77843, United States

)Department of Chemistry, Rice University, Houston, Texas 77005, United States

’ INTRODUCTION

Recent progress developing ideas andmethodologies to study,analyze, and propose nanodevices using novel and traditionalscenarios for molecular-electronics1�9 includes a variety of appli-cations such as molecular gates,10 single-electron transistors,11

ultrasmall memories,12 carbon-based devices,13,14 solar cells,15,16

nanocatalysis,17,18 nanoclusters,19�22 sensing chemical23 andbiological agents,24 medicine,25 semiconducting polymers,26 andphotoelectronics.27 Among them, those that are intrinsically withinelectronics are serious candidates to develop devices beyond thecomplementary metal�oxide�semiconductor (CMOS)28 era.Practical applications for the post-CMOS era are not only limitedto computational applications but also to other applicationsbeyond the traditional ones that are expected to develop simul-taneously. In particular, a mixer device takes two signals ofdifferent frequencies as inputs and yields one or more outputsignals with frequencies that are combinations of the input fre-quencies. This device is useful for the manipulation of signals toencode and transport information.29,30 When channels of com-munication are available at frequencies very different from thosecontaining the information, mixers can be used to modulatesignals to the channel frequencies and to demodulate signalsfrom the channel frequencies. In sensing science, a mixer is animportant electronic device because it can be used for the preciseand controlled detection of single molecules as has been shownfor displacement sensing31,32 and mass detectors.33

Devices whose output is not of the same frequency of the inputare nonlinear devices. Applications of nonlinear electronics includeradio frequency (RF) signal mixing32 and detection of very weak

forces and displacements.34,35 For example, carbon nanotubeshave been used as electromechanical oscillators able to act astransducers of small forces35 and as sensors of their ownmotion.36 It has been proposed that nanotube-based transistorsoperate at frequencies in the terahertz region30,37 as generators,frequency multipliers, and detectors. Carbon nanotube transis-tors are good candidates for RF and opto-electronics;38 however,fabrication of nanotube arrays with controllable chirality anddiameters is still a challenge, especially for large-scale fabrication.On the other hand, experimentally, graphene has been demon-strated as a channel for a transistor using high-k dielectrics.39

The cross section of graphene, just one atom wide, and itselectrical properties40,41 allow us to detect and amplify signalsencoded at the molecular level as vibrations or potentials (vibro-nics or molecular electrostatic potential scenarios, respectively)as well as to amplify signals for present electronic technologies.Graphene mechanical properties,42,43 such as stiffness, allow theimplementation of electromechanical resonators that integratedwith a graphene-based transducer device can be used as displace-ment sensors and detectors of very weak forces.33,44,45 Otherexamples of nonlinear devices are the graphene frequency multi-pliers,46,47 whereby frequency doubling is achieved by biasing thegate of a single-layer graphene transistor, and the signal fre-quency mixer,48 which has been shown using a single graphenetransistor acting as a RF mixer device.

Received: March 25, 2011Revised: May 8, 2011

ABSTRACT: A multilayer graphene device performing as achemistry-based signal mixer is shown by a theoretical�experi-mental approach. We find current fluctuations across a three-layer graphene cluster using a combination of density functionaland Green’s function theories. We suggest that these currentfluctuations are due to the effect of the external bias on plasmonscreated from electron delocalization in graphene plates. The biaspotentials affect the intrinsic behavior of the electron densitycorresponding to the frontier orbitals and perhaps other en-ergetically near orbitals. The theoretical finding suggests that if the sheets of graphene show a plasmon behavior they may be used tomix signals of different frequencies. We corroborate this suggestion performing a proof-of-concept experiment on a sample of few-layer graphene by introducing two signals of different frequencies. We find experimentally that the recovered output contains theinput frequencies, their sum and differences, as well as their second- and third-order harmonics, among others. Thus, plasmonsbetween graphene layers and their high sensitivity surface make the graphene layers a mixer device able to detect the frequencydifferences of the input signals. Eventually these input signals could come from vibrational modes of molecules, and such a mixerwould be of strong importance for sensing science and engineering at terahertz frequencies.

12129 dx.doi.org/10.1021/jp202790b |J. Phys. Chem. C 2011, 115, 12128–12134

The Journal of Physical Chemistry C ARTICLE

We have previously proposed two sensing scenarios usinggraphene ribbons. One is based on the generation of character-istic terahertz signals from vibrations between an absorbedmolecule on a single layer of graphene; the generated signalsare characteristic for each molecule, which can be detected by thegraphene surface. The second scenario is based on the electricaltransport through graphene electrodes; when the agent moleculeis absorbed between graphene layers, different conductancestates are reached due to the interaction of the absorbedmoleculewith the delocalized electron density of graphene. The highsensitivity of graphene ribbons49 is due to their full delocalizationof frontier molecular orbitals (plasmonics), which improve thedetection of very small species from the effect on large substratesrather than detecting the actual small molecules.

The appearance of terahertz (THz) modes in the graphenespectrum occurs when molecules or extra layers are adsorbed onthe graphene surface, yielding characteristic peaks that can beused as THz fingerprints. This is because a pattern of peaks ischaracteristic for every single molecule, and along with thechanges in the conductivity, these peaks allow the implementa-tion of graphene molecules as highly selective and sensitivesensors/generators of terahertz signals. In this work, triggeredby a computational analysis of proposed sensors, we develop achemical signal mixer using few graphene layers to modulate anddemodulate signals produced from standard signal generators.In the future, perhaps with the development of a carbonlithography and when the fabrication of graphene devices issolved, the signals might come from the vibrational modes ofagent molecules.

’METHODOLOGY

The proposed research methodology is a combination ofmolecular calculations and proof of concept experiments;although theory and experiment belong to very different sizescales, they complement each other in the field of nanotechnol-ogy. Theory allows us to predict atomistic behavior very pre-cisely, which can be extrapolated to microscopic sizes, triggeringscalable experiments.Theoretical Approach. Geometry optimizations and second

derivatives are calculated, searching for local minima, i.e., for non-negative eigenvalues in the Hessian matrices. Second derivativesof the energy (Hessian matrix) at local minima are needed toobtain vibrational spectra. Calculations are performed with theprogram Gaussian-09.50 The M05-2X metafunctional is used forthe geometry optimization of systems with nonbonded interac-tions and π�π stacking;51 it also yields acceptable bindingenergies from geometry optimizations of molecules noncova-lently bonded. The basis set used is 6-31G(d)52 for carbon,sulfur, and hydrogen atoms and the Los Alamos National Lab(LANL2DZ) basis set and effective core potentials53,54 forheavier atoms such as gold.19

In our theoretical procedure, a “target”molecule is approachedor addressed by gold nanotips ending in single gold atoms,followed by sulfur. The sulfur atoms bond chemically to thetarget molecule, which in our case is a graphene trimer, a three-layer graphene (Figure 1). The target molecule is fully optimizedwithout any constraints, and the sulfur and the interfacial goldatoms are attached to the external graphene layers to performsingle point calculations of the complex. The geometry of aC�S�Au group is also optimized using the same level of theoryused for the target.

Calculations to obtain the Hamiltonian and overlap matriceswhen a dipole field is applied to the extended molecule areperformed. The partial density of states (DOS) of the goldnanoelectrodes is calculated using the programCrystal-06.55 TheHamiltonian (H) and overlap matrices (S) as well as the DOS ofthe contacts are entered into our in situ developed program,

Figure 1. Optimized three graphene layers (“target” molecule) withsulfur clips and gold interface atoms to bond chemically the grapheneribbon to gold nanoelectrodes. The extended molecule is composed ofthe target molecule, sulfur clips, and the interface gold atom. The threegraphene layers are separated by distances A and B that vary from theoptimized values to investigate their displacements.

Figure 2. Scanning electron micrograph image of the chip fabricated byelectron-beam lithography. Four platinum electrodes of approximately20 nm thick; the narrow gap is 100 nm long, and the top and bottomelectrodes are separated 2 μm from the gap.

Table 1. Total and Relative Energies for the Three-LayerGraphene Alone (Target Molecule) When Freely Optimized(Opt) and When A and B Are Frozen (Opt modR)

calculation type A (Å) B (Å) total energy (Ha)

relative energy

(kcal/mol)

Opt 3.42 3.44 �2765.562715 0.00

Opt modR 3.42 3.42 �2765.562699 0.01

Opt modR 3.32 3.52 �2765.562231 0.30

Opt modR 3.32 3.32 �2765.561983 0.45

Opt modR 3.52 3.52 �2765.561875 0.52



GENIP,14,56�58 to calculate the electron transport characteristicsof the junction. The formalism in GENIP is a combination ofdensity functional and Green’s function theories. Thus, thecombined formalism considers the discrete states of themolecule mixed with the continuous electronic states of thenanocontacts. Subsequently, calculations varying the interlayerdistances A and B (Figure 1) at constant values of 3.32, 3.42, and3.52 Å are performed to obtain the effect of displacementsbetween layers on the conductivity. The selected displacementsare related to the intergraphene modes, and they are in the rangeof THz.Experimental Approach. The chip structure consists of four

metal electrodes on top of an insulator substrate silicon waferwith a 200 nm thick thermal silicon oxide (Figure 2). The left andright electrodes are separated by a 100 nm gap; bottom and topelectrodes are positioned at 2 μm from the narrow gap. The chipsare fabricated using a conventional electron-beam litho-graphy technique.59 An amount of 20 nm of platinum is depositedon a silicon wafer substrate via electron-beam evaporation.The graphene sample is placed and adsorbed physically on top

of the electrode gaps. The “scotch tape” pealing, a technique thatis based on mechanical exfoliation,60 is used to obtain graphenesamples of a few layers.61 This technique has been widely used byresearchers because it is simple, cheap, and effective, although thefilms are usually uneven, e.g., several sizes, shapes, and number oflayers are obtained.The fabricated device is characterized morphologically using

the scanning electron microscope (SEM) JSM-6400, JEOL.62

The electronic characterization of the devices is performed insidea probe station (Lakeshore Cryogenic probe station),63 in a highvacuum (about 10�7 Torr) chamber to exclude environmental

effects.Measurements are performedusing aHP4145 semiconductorparameter analyzer and function generators (AFG 3252)64 andoscilloscope (TDS 5104).65 The maximum operating frequencyis limited by the instrument and coaxial cable capabilities. Thetemperature during the measurements is kept constant at 300 K.The number of layers in each graphene sample is roughly esti-mated through a closer view of the graphene sample edges usingthe SEM; the samples used in this work have an estimatedthickness of six graphene layers.

’RESULTS AND DISCUSSION

A geometry optimization of the three-layer graphene mol-ecules (target molecule) yields an optimized average distance

Table 2. Distances A and B, Total, Relative, HOMO, LUMO, and HLG Energies and Au�Au Distances of Single PointCalculations for the Three-Layer Graphene Molecules Attached to Sulfur Clips and Gold Interface Atoms (Extended MoleculeShown in Figure 1)

A (Å) B (Å) total energy (Ha) relative energy (kcal/mol) HOMO (eV) LUMO (eV) HLG (eV) Au�Au distance (Å)

- - �3832.190621 0.00 �3.65 �2.76 0.88 12.82

3.42 3.42 �3832.189789 0.52 �3.65 �2.76 0.89 12.76

3.32 3.52 �3832.188905 1.06 �3.64 �2.76 0.89 12.76

3.32 3.32 �3832.187500 1.93 �3.64 �2.72 0.92 12.51

3.52 3.52 �3832.189885 0.46 �3.65 �2.79 0.86 13.00

Figure 3. Current�voltage characteristics using Genip. (a) Current�voltage characteristics at the optimized distances A = 3.42 Å and B = 3.44 Å. (b)Current�voltage characteristics when the distance between layers is atA= B= 3.32 Å (green),A=B = 3.52 Å (purple), andA= 3.32 Å andB = 3.52 Å (blue).

Figure 4. (a) Four-probe station chamber: each probe tip has a 3 μmdiameter. (b) Fabricated device: a graphene sample of approximately sixlayers covers the gaps. Two electrical signals are applied from the bottomof the graphene using a pair of electrodes, and the output is recoveredfrom the top of the graphene sample.



between layers of A = 3.42 Å and B = 3.44 Å (Figure 1). Tounderstand further the displacements between layers, subse-quent optimizations are carried out keeping the distance betweenlayers, A and B, constant at 3.32, 2.42, and 3.52 Å. A resemblanceto a “breathing” displacement between layers is performed,setting A and B for compression (A = B = 3.32 Å), stretching(A = B = 3.52 Å), and antisymmetric (A = 3.32 and B = 3.52 Å)displacements between layers. The largest barrier to keep thelayers at a constant distance is 0.52 kcal/mol (Table 1), corre-sponding to the relative energy of the layers separated by A = B =3.52 Å with respect to the freely optimized system.

Energies from single-point calculations for the target molecule(Figure 1) are shown in Table 1 and for the extended molecule inTable 2. The largest barrier is for the graphene layers at 3.32 Å,and the shortest barrier corresponds to the stretched complex.The gold�gold distance varies from 12.82 to 13.05 Å, and theeffect can be observed on the current�voltage curves, where thecompressed case is more conductive than the stretched one.(Figure 3).

Calculations of electron transport for the three-layer grapheneextended molecule show a small component of the current withoscillations or ripples (Figure 3a) at the equilibrium geometry. Inthis weakly nonlinear conductance behavior shown as ripples inthe output current, the response current is not directly propor-tional to its input voltage. This kind of noise in the conductivity isattributed to fluctuations in electron density of the graphenesurface plasmons due to the application of the bias voltagebetween layers. Additional calculations performed at distancesdifferent from the equilibrium one (Figure 3b) also yield ripplesbut slightly lower than those of the equilibrium geometry,indicating that the plasmon intensity is a maximum at geome-trical equilibrium. These control calculations are performed for adistance A of 3.32 Å shorter than B (3.52 Å); if these currents aresubtracted from the equilibrium current, we would be mimickingan antisymmetric displacement, and the I�V curve showsoscillations (Figure 3b, blue line) similar to the case where themolecule is at a local minimum (Figure 3a). Two more controlcalculations are performed: first a contraction case where the twographene layers are closer at a distance of 3.32 Å and theexpansion where the layers are separated at a distance of3.52 Å. The calculated current�voltage curves are shown inFigure 3b; the expansion (purple line) and contraction (greenline) follow the expected behavior. When contraction occurs, theAu�Au distance is shorter, and thus larger conductivity is shown;this is contrary to the expansion case, where the conductivityslightly changes down. The noise in the conductivity decreaseswhen the graphene layers are kept at the same distance suggest-ing that the amount of ripples in the conductivity might also

increase for antisymmetric staking and sliplike modes betweengraphene layers.

This weakly nonlinear current found theoretically suggeststhat multilayer graphenes may act as a signal mixer; thus, theoryprovides information on the atomistic nature that could be scale-up to micrometer sizes.

Pairs of electrodes from the chip are used as input 1 and input2 to introduce two signals of frequencies F1 and F2 at the bottomof the sample. The output is recovered directly from the top ofthe graphene sample using a 3 μm diameter probe as is shown inFigure 4b.

Second- and third-order frequency signals are recovered at theoutput; the results shown in this work are representative of all ofour measured devices. When we apply a large-frequency signal of2500 kHz (F1) and a low-frequency signal of 300 kHz (F2) to thegraphene sample, we recover at the output the two inputs andsecond-order modulated signals corresponding to the peaks at2200 kHz (|F2 � F1|), 2800 kHz (F1 þ F2), and otherharmonics (Figure 5a). In addition, when two signals close infrequency F1 = 2500 and F2 = 2800 kHz are set to the inputelectrodes, the graphene sample is able to demodulate the signalby subtracting the two inputs (|F2� F1|) and showing a peak at300 kHz as is shown in Figure 5b.

The mixing performance of a multilayer graphene is repro-ducible repeatedly; however, not all the samples show second-order harmonics as those shown in Figure 5. We perform severalcontrol experiments where we do exactly the same procedureover surfaces such as the silicon dioxide, copper, and polymersurfaces. The signal mixer behavior is only obtained using thegraphene sample. Some of the samples, especially those with toomany layers, are more feasible to show third-order harmonics asthose shown in Figure 6 and tabulated in Table 3. In controlexperiments, we have applied up to 5 MHz, which is the largestpossible frequency that the instrument allows us to introduce tothe sample due to the intrinsic characteristics of the instrumentand the coaxial cables. For every combination of frequency valueswe apply, the graphene samples show frequency mixing features.Even more, third-order harmonics are obtained for several com-binations of input frequencies (Table 3). Since graphene platesvibrate at frequencies in the range of a few THz as verified bysecond derivative ab initio calculations, we can safely expect thatsignals with frequencies of THz can be safely used. There is nothingin the theory or experiment that might indicate or suggest that themixer will not work at THz frequencies, which correspond to thelower part of the vibrational spectrum of sandwiched graphenes;thus, it should work up to the THz region at least.

For sensing applications, the input signals from the agent arecoupled by the adsorption of the agent molecule to the surface of

Figure 5. Graphene signal mixer. (a) Modulation of signals 300 and 2500 kHz. (b) Demodulation of 2500 and 2800 kHz.



graphene; these input signals are mixed with the intrinsicvibrations of the detector (few-layer graphene), which is ableto change the electronic characteristics of the detector. Improve-ment in sensitivity and selectivity is because the mixer outputs,among others, one signal whose frequency is the difference of thetwo input frequencies, assuming one of the inputs is a referencefrequency we want to detect and the other is of unknownfrequency. Once they are mixed, the frequency of the outputwill tell us directly how close the unknown signal frequency fromthe reference is. When the output frequency is zero of or close tozero, the output is simply aDC signal that can be easily measured.

’CONCLUSIONS

The ripples in the current transversally calculated for fewgraphene layers have a contribution from the plasmonic nature ofthe electron density as is shown from the I�V curves of thegraphene layers. In addition, compressed and stretched pairs ofgraphene plates create additional nonlinear ripple behavior thatallows the detection of signals with different vibrational frequen-cies. The theoretical analysis determines unambiguously theexistence of ripples in the current through graphene plates. Sincethe current is calculated at a fixed geometry, at the equilibriumgeometry, the source for the ripples is something intrinsic to theelectronic behavior. As these ripples have not been observed in

other calculations of molecules that are not fully delocalized, wecan suggest with a good degree of confidence that the effect issimilar to what empirically is known as a plasmonic surface. Sinceon a plasmonic surface the mixing of signals is possible, ourexperiment actually proved the mixing of signals of differentfrequencies yielding as a result the correct components at theoutput originated from the input signals. Samples of few gra-phene layers can be used as sensors where the input signal is avibrational mode, in the terahertz region, from agent moleculesadsorbed on the graphene surface. The inputted signals aremixed with the intrinsic vibrational modes of the graphenedetector and thus can be modulated and demodulated using thischemistry-based graphene mixer device for their detection.

’ACKNOWLEDGMENT

We acknowledge financial support from the U.S. DefenseThreat Reduction Agency DTRA through the U.S. Army Re-search Office, Project Nos. W91NF-06-1-0231, ARO/DURINTproject # W91NF-07-1-0199, and ARO/MURI project #W911NF-11-1-0024. We also acknowledge the Microscopyand Imaging Center facilities at Texas A&M University.

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Figure 6. Third-order harmonics obtained at the output for different input combinations.

Table 3. Five Different Combinations of the Input Signals F1and F2 and the Third-Order Signals Obtained in the Output

F1 F2 2F1 þ F2 2F1 � F2 2F2 þ F1 2F2 � F1

100 kHz 500 kHz 700 300 1100 900

500 kHz 650 kHz 1650 350 1800 800

8 kHz 35 kHz 51 19 78 62

1 MHz 1.2 MHz 3.2 0.8 3.4 1.4

1 MHz 5 MHz 7 3 11 9



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graphene signal mixer for sensing applications

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