Single molecule detection using graphene electrodes

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2010 J. Phys. B: At. Mol. Opt. Phys. 43 115101

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IOP PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS

J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 115101 (5pp) doi:10.1088/0953-4075/43/11/115101

Single molecule detection using grapheneelectrodesNorma L Rangel1,2 and Jorge M Seminario1,2,3,4

1 Department of Chemical Engineering, Texas A&M University, College Station, TX, USA2 Materials Science and Engineering, Texas A&M University, College Station, TX, USA3 Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX,USA

Received 13 December 2009, in final form 9 April 2010Published 19 May 2010Online at stacks.iop.org/JPhysB/43/115101

AbstractIt is shown using density functional theory that the trapping of molecules between grapheneelectrode plates can be used to sense molecules through their vibrational fluctuations. Thishypothesis is tested using water trapped in two graphene molecules connected to a potentialdifference. The electric current fluctuations generated through the junction correspond to thefluctuations of the vibrational modes. Since this system yield currents in a range workable bypresent electronic devices, there is no need for further ‘molecular amplification’. Fluctuationsof the three modes of water yield similar changes of potentials in the neighbourhood accessibleto other molecules; therefore, vibrations from a single water molecule, as an example, orvibrations from any other molecule can be transduced into electrical currents of magnitudecompatible with present silicon technology. In the particular case of the water molecule, arectified potential signal is obtained from the fluctuations of the antisymmetric stretchingmode and a simple transduction is obtained from the symmetric stretching and bending modes.It is argued that the high sensitivity is due to the strong delocalization of the frontier molecularorbitals or molecular plasmons on graphene electrodes, which guarantees the detection basedon molecular potentials or molecular vibrations; these plasmon-like molecules are of majorimportance for the development of molecular and nano electronics.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Novel scenarios based on vibronics [1–9] and molecularelectrostatic potentials (MEPs) [8, 10, 11] have been developedand proposed to encode and process information at themolecular level [1, 4, 12]. When a signal is injected to a linearmolecule, the signal is transmitted through vibrations, which inturn modifies the molecular potentials in their neighbourhood[7, 12]. Changes in the neighbourhood of a molecule canbe amplified into current–voltage characteristics [13]. Ananalogue transmission may also take place on very delocalizedmolecules through electron density waves or plasmons[14, 15].

Within the margins of what is allowed by quantummechanical rules, the ability to read small perturbationsof molecules, such as vibrations or molecular potentials,is a key point to implement the use of molecules as

4 Author to whom any correspondence should be addressed.

sophisticated molecular/electronic devices. Vibronics and thecapability of molecular potentials to encode information arethe two key scenarios for a new era of electronics [4, 16].However, amplifiers and transducers of signals for thesetwo scenarios are required to detect, transport, and encodeinformation at the molecular level, and to reach the deliveryof this technology. We are proposing graphene moleculesused as terahertz generators [17] as the base molecules toelaborate the reading/writing of information at the molecularlevel thanks to its atomic thickness. Graphene systemsare considered the perfect materials to serve as interfacesbetween molecular/nano electronics and current siliconelectronics.

2. Methodology

Graphene molecules [17] are used as plasmonic platesconnected to a power supply through gold electrodes and

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J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 115101 N L Rangel and J M Seminario

(b)(a)

(d)(c)

Figure 1. (a) Molecular potential contours of the optimized water molecule in vacuum. Red lines are negative and blue lines are positivepotential contours of values ranging from −2.7 to 2.7 V. All potential fluctuations of the water molecule are due to its vibrational modes andare calculated at the point × located at 1.8 A from the oxygen atom. (b) Bending mode and (c) symmetric stretching: The MEP is linear forbending and symmetric stretching displacements; therefore, the potential (MEP) corresponds to the variations in geometry at the point ×(transduction). This correspondence is highly linear for the angle fluctuations and quadratic for the bond lengths. (d) antisymetric stretchingmode: positive or negative displacements in either of the O–H bond lengths with respect to the equilibrium geometry yield the same value ofthe molecular potential, resembling the behaviour of a full rectifier.

sulfur clips. Water molecules (as a typical example of amolecule) with several geometries following vibrational modedisplacements are placed between fixed graphene plates tocalculate their effect in the current–voltage characteristics of agraphene–water–graphene junction and we correlate the MEPsfound for the isolated vibrating water molecule with theircurrent.

The level of theory used is the Becke three-parameterhybrid exchange functional with the Perdew–Wang correlationfunctional (B3PW91) [18]. The 6-31G(d) [19] basis set is usedfor the H, C, S and O atoms, and the LANL2DZ basis setsand effective core potentials [20, 21] are used for Au atoms.Specifically, we run full optimizations with no constrains withinitial geometries based on a previous reported experience[22] and find that graphene sheets do not stay parallel as wewould need to perform suitable comparisons among the severalvibrational modes. However, partially optimized or optimizedseparately calculations are done of the graphene moleculesattached to the sulfur clips and with the water molecule inbetween, in order to compare current responses at the samedistance.

Second derivatives are calculated and none of theoptimized structures show negative eigenvalues in theirHessian matrices, indicating that all structures correspond tolocal minima. The analytical second derivatives of the energyyielding the Hessian are also needed to obtain molecularvibrations. Then, molecular potentials are calculated fromthe nuclei and electron density contributions. The electrondensity ρ(r) is obtained by adding the density of each occupied

molecular orbital [23–26]. The complex and single moleculesare calculated using the program Gaussian 03 [27] and thecurrent–voltage characteristics using the program GENIP[28–32]. For details about methods and basis set used, see[13] and references therein.

The MEP, V (�r), is calculated from the nuclei and electrondensity contributions [26]:

V (�r) =∑

i

Zie

| �Ri − �r|−∫

ρ(�r ′)|�r − �r ′| dτ ′ (1)

where Zi is atomic number of atom i located at �Ri . The MEPcan be calculated using wavefunction methods [26, 33–35] orusing density functional theory [36–38].

3. Results and discussion

Molecular vibrations of the water molecule yield oscillationsof the molecular potentials, which are calculated at 1.8 Aabove the oxygen atom (figure 1(a)). This is a reachabledistance to observe the MEPs because most of the importantinter-molecular interactions take place around that distance[23, 24]. Usually, vibrations of the agent (water in this case)are far beyond those of the detector and therefore are not ableto follow the vibrations of the agent; however, the concertedmotion of delocalized electrons in the detector may allow usto follow those vibrations.

Classically, a transducer is a device able to convertenergy of one type into energy of other type; for instance,a microphone converts pressure vibrations in air into an

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J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 115101 N L Rangel and J M Seminario

Figure 2. Current response when a bias of 0.5 V is applied through two graphene ribbons acting as electrode plates and a water molecule(with several geometries associated with their vibrational modes) is placed in between the plates. From left to right the optimized geometryis shown (HOH angle 104◦ and OH bond lengths of 0.96 A) followed by variations of this geometry due to the normal vibrational modes.For each geometry, the bond length and angle fluctuations affect the molecular potentials (squares and right vertical axis) and are detectedthrough their effects on the current (diamonds and left vertical axis) across the junction.

(a) (b)

(c) (d)

Figure 3. Current–voltage characteristics (a) and their fluctuations (b), of two (c) and three (d) graphene molecules. The effect of theexternal voltage on the current (a) and (b) through the graphene plates when nothing (c) and when another graphene molecule (d) issandwiched in between the plates.

electrical current. In this case, we extend the use of the termtransducer to include changes in molecular potentials due tothe vibrational movement of the atoms. When comparing themolecular potentials versus the movement of atoms due to thebending mode (figure 1(b)), we find a linear relationship—a transduction process—which is also observed, at least forsmall displacements, with the antisymmetric stretching mode(figure 1(c)). A full rectification, although nonlinear, can beobserved from the symmetric stretching mode (figure 1(d)). Afull rectifier yields the same polarity when the input is eitherpositive or negative.

Therefore, changes in molecular potentials due tomolecular vibrations can be transduced and amplified intocurrent–voltage characteristics on the delocalized electronicsurface of graphene molecules [5]. A current response fromeach vibrational mode is obtained when a constant voltageof 0.5 V is applied through a couple of graphene plates asshown in figure 2. These changes in the molecular geometry

due to vibrational modes produce current fluctuations in thetwo-layer graphene junction.

The presence of a molecule between the graphene plates(sensor) produces changes in the current response, dueto perturbations of the fully delocalized electronic density(plasmons) of graphene molecules. The plasmons are sensitivenot only to the trapped molecule (probe) but also to thechanges in the MEPs due to the movement of the atoms.The contribution of the electrons can be either constructiveor destructive to the conductivity, producing changes in thecurrent response for each change in the MEPs.

If instead of the water molecule, another graphenemolecule is placed in between the junction, i.e. having nowa junction of three graphene molecules, the current–voltagecharacteristics can be compared to the empty two-graphenejunction characteristics (figure 3). The optimized triple layergraphene distances of 3.26 and 3.44 A are found and westart the optimization with the layers at the same distance of3.47 A, which is slightly longer (0.02 A) than the optimized

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J. Phys. B: At. Mol. Opt. Phys. 43 (2010) 115101 N L Rangel and J M Seminario

bilayer [5] and no imaginary frequencies are found indicatingthat the three-layer graphene is a local minimum. On the otherhand, we do not expect any major changes under the voltagedue to the uncharged nature of each layer of graphene andthe very small dipole moment (0.001 Debye) of the layers.Figure 2 shows how vibrational modes can be detectedusing graphene plates, and figure 3 shows the effect of theexternal voltage on the current (figures 3(a) and (b)) throughthe graphene plates when nothing (figure 3(c)) and whenanother graphene molecule (figure 3(d)) is placed in betweenthe graphene plates.

The three-layer graphene molecule yields a slightly largercurrent than the two-layer graphene molecule (figure 3); thisis against the expectation that longer systems would yieldsmaller currents thus there is an additive effect when thethird graphene molecule is added. The two-graphene junctionshows oscillations due to the vibrational modes between thegraphene plates; the three-graphene junction current–voltagecharacteristic oscillations are also shown. We clearly observetwo similar and additive oscillations in both curves. The lowfrequency one corresponds to 1.2 cycles V−1 and the highfrequency to 5 cycles V−1 and their corresponding amplitudesare 0.4 and 0.5 mA, respectively.

There are fluctuations in the current through the detectorwhen an external bias is applied. These fluctuations come fromtwo contributions: one from the nuclei vibrations (vibronics)and the other from electron oscillations (plasmonics). Theformer are the usual intrinsic frequencies affecting theinstantaneous potential in their neighbourhood (figure 2).However, in the latter, electrons are fully delocalized on thegraphene molecules, allowing fluctuations and oscillations ofthe electron density corresponding to the HOMO and othernear molecular orbitals. Thus, the two types of fluctuationsyield changes in the current–voltage characteristics.

Plasmons on the graphene surface enhance transductionof molecular characteristics into signals readable by standardelectronics. Thus, changes in both MEPs and vibrations ofan arbitrary molecule can be transduced and amplified intocurrent–voltage characteristics.

Acknowledgments

We acknowledge financial support from the US ArmyResearch Office, Project nos W911NF-06-1-0231 andW91NF-07-1-0199, and from the US Defense ThreatReduction Agency DTRA.

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