Conductance Fluctuations in Chains of Particles Arising fromConformational Changes of Stabilizer MoleculesL. V. Govor and J. Parisi

Institute of Physics, Carl von Ossietzky University of Oldenburg, D-26111 Oldenburg, Germany

Reprint requests to L. V. G.; E-mail: leonid.govor@uni-oldenburg.de

Z. Naturforsch. 68a, 157 – 164 (2013) / DOI: 10.5560/ZNA.2012-0076Received July 31, 2012 / published online February 15, 2013

Dedicated to Alfred Klemm on the occasion of his 100th birthday 15 February 2013

We have bridged a pair of gold electrodes with various arrangements of gold nanoparticles stabi-lized with citrate molecules. The resulting devices exhibited current fluctuations at a constant biasvoltage and fluctuations of the differential conductance as a function of the bias voltage. These fluc-tuations were attributed to the interplay of molecular conformation, charge switching, and breakingof the links at the interface molecules–electrode. We found that, for all investigated samples, thecontact resistance at the interface molecules–electrode was by about one order of magnitude largerthan that between nanoparticles coupled by citrate molecules. We conclude that the mechanism ofcharge transport can be viewed as a series of discrete steps involving initial hopping (injection) ofthe charge from the left-hand-side gold electrode to the molecules, tunnelling of the charge throughthe molecules–nanoparticle–molecules (MNM) unit, hopping to the next MNM unit, etc., and finallyhopping (extraction) of the charge to the right-hand-side gold electrode.

Key words: Nanoparticle; Citrate Molecules; Charge Transport; Conductance Fluctuations.

1. Introduction

Charge transport through nanoparticle (NP) assem-blies represents a fundamental process that controlstheir physical properties, which are determined by thecoupling and arrangement of individual NPs and de-pend on their size, shape, and composition. Theory andexperiments unveil that, at sufficiently low temperaturebelow a threshold voltage Vt, no current flows throughthe particle array, while above Vt the current increases,according to the power law I ∼ (V −Vt)ζ with ζ = 1in a one-dimensional and ranging between 5/3 and 2in a two-dimensional array [1 – 3]. I denotes the cur-rent, V the voltage. Electronic coupling between indi-vidual particles is influenced by inter-NP spacing andby stabilizer molecules capping the NPs. The inherentpossibility of a switching between different molecu-lar conformations represents one peculiarity of thesemolecules which can strongly influence charge trans-port. Citrate represents a common electrostatically sta-bilizing agent for gold NPs, because the particles aretypically synthesized through a citric acid reductionreaction [4]. Switching of the molecular conductanceof citrate was demonstrated by Wang et al. [5], where

they used mechanical stretching of two conformers ofcitrate capped on and linked between the gold NPs.

The influence of stabilizer molecules on chargetransport through NP arrays has been reported re-cently [6 – 8], where we have examined charge trans-port between two gold electrodes bridged by a sin-gle gold NP or by one- and two-dimensional chainsof those (about 8 – 10 particles within the chain). Sucha configuration exhibits linear current–voltage (I–V )characteristics and current fluctuations in the range3 – 100 mHz at constant bias voltage. Moreover, we ob-served fluctuations of the differential conductance asa function of the bias voltage. We assume that thesefluctuations arose from equally probable conforma-tional changes of all citrate molecules along the chainof NPs induced by charge transfer through those, in-dependently of their location along the chain of NPsor at the electrode interface. In following, we presenta comparative analysis of I–V characteristics for chainsof NPs having variable size (both length and width).We demonstrate that the resistance between gold elec-trodes and gold NPs coated with citrate moleculesis significantly higher as compared to the resistancebetween two such citrate-coated NPs. The conduc-

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158 L. V. Govor and J. Parisi · Conductance Fluctuations in Chains of Particles

tance fluctuations can be attributed to interplay be-tween the molecular conformation, charge switching,and breaking of the bonds, taking place at the interfacemolecule–electrode. We found that the main contribu-tion to the charge transport in chains of NPs resultedfrom hopping.

2. Experiment

Figure 1a schematically illustrates the configura-tion investigated. The initial Au/Cr contact pads lo-cated on a SiO2/Si substrate were formed by pho-tolithography, where gold and chromium thin filmshave been electron beam deposited. The layer sequence(and thickness) from top to bottom is Au (20 nm)/Cr(5 nm)/SiO2 (230 nm)/Si (0.7 mm). A 100 nm or200 nm wide, 32 nm deep, and 4 µm long nanogapbetween electrodes has been formed by focused ionbeam (FIB) patterning [9]. Hereto, we have used a dualbeam system (FEI Helios Nanolab 600), combininga 30 keV (1 pA) gallium ion beam with a scanningelectron microscope (SEM). After FIB patterning, wemeasured a resistance of the non-connected gold elec-trodes of each sample being larger than 1014 Ω (Keith-

Fig. 1. (a) Schematic illustration of the NP chain located inbetween two gold electrodes. (b) SEM image of the smallchain of particles (Sample 1) connecting the gold electrodes.(c) and (d): SEM images of the wide chain of particles (Sam-ple 2) connecting the gold electrodes before and after FIBpatterning, respectively. The dashed lines indicate a gap be-tween the gold electrodes.

ley 6430). The samples and the corresponding two-pin holder were placed into a double-shielding box formeasurement.

Deposition of NPs in between the gold electrodeswas achieved via pinning the droplet edge of the so-lution with a concentration of 1.2 · 1011 particles/mLat the appropriate position between the gold elec-trodes [9, 10]. As a result, a concentric ring-like arrayof NPs forms along the droplet edge. The size of thearray strongly depends on pinning time and substratetemperature. After having positioned the NPs in be-tween the gold electrodes, the place surrounding a de-sired particle chain was additionally patterned withFIB. With this procedure, unwanted connections be-tween the electrodes were removed. As examples, tworepresentative samples are shown in Figure 1b – 1d,where the gold electrodes are bridged by a differentnumber of gold particles.

3. Experimental Results

The I–V characteristics of the samples investigatedwere recorded by two-contact-mode measurements at300 K. A maximal bias voltage V applied to each sam-ple was taken in correspondence to the resistance ofthe sample. As a criterion in the entire regime of theapplied voltage, we have chosen the current so thatits maximal value amounted to about 1 pA for smallsamples and 10 pA for wide samples. It is essentialto limit the charge transport, because larger values ofthe current typically cause degradation of the junc-tion, probably due to excessive heat dissipation ordue to local displacement of particles within a chain.We have observed current fluctuations at constant biasvoltage. To examine the nature of such peculiarity,we have recorded the current over time at intervalsof 625 ms. All five samples investigated show simi-lar and reproducible results. The typical temporal be-haviour of the current I(t) at V = 4 mV for Sample 1and at V = 200 mV for Sample 2 is displayed in Fig-ure 2a and 2b, where the current randomly fluctuatesaround a mean value. Figure 2c and 2d illustrate thecorresponding distributions of I(t) for Samples 1 and2, respectively. For a description of the I–V character-istics, we determined a mean value of this distribution,I0, and its standard deviation, Is, which we interpretedas fluctuation amplitude. The designation of I0 and Isis illustrated schematically in Figure 2. For compari-son, we investigated the I(t) behaviour of a resistor

L. V. Govor and J. Parisi · Conductance Fluctuations in Chains of Particles 159

Fig. 2. (a) and (b): Typical time depen-dence of the current I(t) for Samples 1and 2 recorded at bias voltage 4 mVand 200 mV, respectively. I0 and Is arethe mean current and its standard de-viation (fluctuation amplitude), respec-tively. The lower curve in (a) displaysthe dependence I(t) for a resistor. Note,the I axis span amounts 0.2 pA in (a)and 2 pA in (b). (c) and (d): Correspond-ing distributions for Samples 1 and 2,respectively.

Fig. 3. (a) and (b): I0–V characteristicsmeasured one after another for Sam-ples 1 and 2. R1, R2, and etc. indicatethe corresponding values of the sam-ple resistance. (c) and (d): Differen-tial conductance dI0/dV for Sample 1(Curve 3) and for Sample 2 (Curve 2)shown in parts (a) and (b), respectively.(e) and (f): Log–log plot of the I0–Vcurves for Samples 1 and 2 shown inparts (a) and (b) with the best-fit ofexponent ζ .

160 L. V. Govor and J. Parisi · Conductance Fluctuations in Chains of Particles

with 1.3·1010 Ω (thermal noise) and did not observeany similarly pronounced fluctuations (lower curve inFig. 2a). This clearly demonstrates that the fluctua-tions solely result from the presence of NP junctions.We found that, independent of the configuration of theparticle chain, by increasing the current through an in-crease of the bias voltage, the relative fluctuation am-plitude Is/I0 amounts to about 0.05, roughly indepen-dent of the applied voltage. A Fourier analysis of theI(t) fluctuations measured at different bias voltage in-dicates that the frequency of the dominant fluctuationslies in the range 3 – 100 mHz [6, 7].

Typical I0–V characteristics for two samples witha different number of particles in the chain are il-lustrated in Figure 3a and 3b, respectively. There aretwo important observations: (i) Two sequentially mea-sured I0–V curves can exhibit increased conductanceof the chain (Fig. 3a). (ii) Subsequently measured I0–Vcurves may also have a lower conductance (Fig. 3b).These peculiarities of the individual I0–V curves canbe clearly seen in Figure 3c and 3d, where the de-pendence of the differential conductance (dI0/dV ) onvoltage is presented. A further important observationis the following: The amplitude of the random fluctua-tions of the differential conductance increases with thevoltage applied. These experimental findings indicatethat not only the value of the applied voltage, but alsothe state of the conducting path in the particle chain,which may depend on the history of the sample, canaffect its conductance. Figure 3e and 3f demonstratethat all I0–V curves shown in Figure 3a and 3b followthe same power-law scaling I0 ∼V ζ with an exponentζ ≈ 1. Such value of the exponent ζ indicates a linearbehaviour for charge transport in the chain of particles,i.e., a linear conduction path. Again, comparison of theI0–V curves for a small chain of particles and for a widechain demonstrates the similarity in behaviour.

4. Discussion

The theoretical approach I ∼ (V −Vt)ζ for the sin-gle electron charging effect in arrays of particles de-veloped by Middleton and Wingreen [1] considersonly the zero-temperature limit, where the local en-ergy levels are delineated and barriers between neigh-bouring sites are well defined. That means that, fora bias voltage lower than Vt, charge transport shouldnot occur. The latter differs from the results of our ex-periment, where due to thermal energy a finite conduc-

tance g0 = dI0/dV even at V = 0 and T = 300 K takesplace. Figure 3c and 3d illustrate that the conductanceg0 amounts to about 5 ·10−10 A/V and 2 ·10−11 A/Vfor Samples 1 and 2, respectively. The linear suppres-sion of the threshold voltage Vt(T ) with temperaturewas considered by Bezryadin et al. [11] and Eltetoet al. [12] in studies of one-dimensional nanoparti-cle chains, where the dependence Vt(T ) ≈ Vt(0) −NpkBT/e was established, where Np is the number ofparticles in the chain. That means that, with increas-ing temperature, the nonlinear I–V characteristics, de-scribed by the power law I ∼ (V −Vt)ζ , monotonouslyshifts to the left until a constant conductance g0 atV = 0 is reached. In other words, if energy levels forthe transport of electrons from one site to another aredistributed within bkBT , thermally excited electronscan be transferred to neighbouring sites. The param-eter b describes the extent of thermal broadening anddepends on details of the electronic level distribution(b = 2.4, [12]).

Figure 4a schematically illustrates a single par-ticle Aun with chemisorbed citrate molecules con-necting a gold electrode Aue (on the right). A vari-ety of interactions between citrate molecule and goldelectrode is possible, ranging from a physisorptionto a chemisorption. The physisorbed citrate moleculeinteracts only weakly with gold atoms and, corre-spondingly, charge transfer is more difficult (weakcoupling). Chemisorption is characterized by cova-

Fig. 4. (a) Schematic illustration of a single gold particle Aunstabilized with citrate molecules (denoted as MNM, box)connecting a gold electrode Aue (on the right). (b) Schematicillustration of the one-dimensional chain of particles andhopping transport through that. The rectangular boxes rep-resent MNM units (local hopping site) shown in part (a). Thearrows represent thermally activated charge hopping over thebarriers between local sites.

L. V. Govor and J. Parisi · Conductance Fluctuations in Chains of Particles 161

lent bonds which makes charge transfer between goldatoms and citrate molecule easier (strong coupling). Inbetween weak and strong coupling, other types of in-teraction are possible, based on interface effects likeinteger charge transfer through tunnelling (physisorp-tion), rearrangement of electron densities and attrac-tion through image forces (physisorption), and par-tial charge transfer (weak chemisorption) [13 – 15]. Asa result of metal–molecule coupling, the electron or-bitals of citrate molecules can hybridize with states ofthe gold atoms. Consequently, the original molecularlevels broaden and shift compared to a free molecule invacuum. For example, in the case of covalently linkedmolecules (chemisorption), the broadening can be sev-eral hundred meV [16], i.e., much larger than the ther-mal energy at room temperature (26 meV).

It was already demonstrated that the maximum sat-uration coverage of a gold particle by citrate moleculesamounts to about 2.7 molecules/nm2 [17, 18]. Fora particle with a diameter of 20 nm, we assume thaton average at each Aue–Aun junction about 10 cit-rate molecules oriented in parallel can link the NPto the electrode, and about 20 molecules can trans-fer a charge across a Aun–Aun junction (10 moleculesfrom each particle). Considering the preparation proce-dure of the devices investigated, we conclude that thecitrate molecules are chemisorbed on the gold nanopar-ticle (bond Aun–O) and physisorbed on the gold elec-trode (bond Aue–O). In other words, in devices wherea chain of particles bridges the gold electrodes, thephysical links of Aue–O at the two electrode interfacesdetermine the properties of the device. That means thatthe experimentally observed I–V curves are to a largeextent determined by the physical bonds Aue–O, ratherthan by intrinsic molecular properties or the chemicalbonds Aun–O. The resistance of the devices investi-gated lies in the range (109 – 1011) Ω, and we concludethat the high device resistance is due to the contact re-sistance between electrode and molecules. This can beconfirmed by comparing the resistance of Sample 1to that of Sample 2. For geometrical reasons, it wasexpected that the resistance of Sample 2 will be sig-nificantly smaller compared to Sample 1, but it is thewrong way.

For understanding the current fluctuations at thefixed voltage, we take into account (Fig. 2) a molecu-lar switching mechanism that includes conformationalchanges, electrostatic charge trapping at defects, andmetal–molecule contact breaking. The conformational

change is consistent with a voltage-induced chemi-cal structure variation involving changes in molecu-lar conformation with charge redistribution along themolecule [19 – 21]. The charge switching can appearwhen the lifetime of the tunnelling electron on themolecule is sufficiently long by a mechanism that sta-bilizes the extra charge on the molecule [22 – 24].The metal–molecule contact breaking is caused bychanges in the bond between the molecules and thegold electrode [20]. We assume the following scenariofor switching events that may occur at the molecule–electrode interface. By injecting electrons into the cit-rate molecule, a conformational/orientational changein the molecule is initiated, where the O–C–O groupphysically connecting to the gold electrode can be ro-tated around the C–C axis of the citrate molecule [25].Note, depending on the bias voltage applied to thesamples, the thermal energy kBT ≈ 26 meV can playan important or even dominant role in the rotation ofthe O–C–O group. Due to the rotation of the O–C–Ogroup, the length of the distance between electrodeand molecule increases. The larger distance reducesthe tunnelling coupling between molecule and elec-trode, and the corresponding ionic reorganization onthe surface of the gold electrode due to an added elec-tron on the molecule can even stabilize this chargestate. The bare Aue–O bond energy has been estimatedto 90 meV for –COOH adsorption on the gold sur-face [26, 27], which is too large for allowing the break-ing of the bonds at room temperature by an appliedbias voltage of few mV only. Thus, the comparativelysmall activation energy for the breaking of the bondsin the case of our experiments seems to be a conse-quence of the weakened Aue–O bonds due to con-formational changes of the citrate molecule [20]. Inthis case, the transmission probability Te is exponen-tially sensitive to changes in the distance of the Aue–Obond, de: Te ≈ exp(−2kde), where k is the decay con-stant. A similar processes can arise at the molecule–molecule interface, where the length of the O–O bondbetween two molecules connecting neighbouring par-ticles in the junction Aun–Aun may be modified duringthe charge transfer.

Figure 3e and 3f demonstrate that I0–V curves in-dicate a linear behaviour for charge transport throughthe small and the wide chains of particles. Severalmechanisms of charge transport through the junctionsmetal–molecule–metal give rise to the linear I–V char-acteristics at low bias voltage, which are coherent tun-

162 L. V. Govor and J. Parisi · Conductance Fluctuations in Chains of Particles

nelling, incoherent tunnelling, and hopping. Coher-ent tunnelling is characterized by the probability ofan electron transfer through a barrier of some thick-ness and height, where the phase of the electron doesnot change. The transmission rate of the coherent tun-nelling decreases exponentially with barrier thicknessand is small over distances larger than 2.5 nm, wherecharge transport can usually be described by an inco-herent tunnelling or hopping [28]. In the case of in-coherent tunnelling, the electron tunnels along a se-ries of sites separated by potential wells, where theresidence time of the electron is large enough to dis-turb its phase, and the process is formulated as a seriesof discrete steps. Both, coherent and incoherent tun-nelling exhibit two main features: (i) exponential de-pendence on barrier thickness L and (ii) weak depen-dence on temperature. These properties are expressedas [29]

R = R0 exp(βL) , (1)

where R0 gives the effective contact resistance and β =2(2mφ)1/2/h a structure-dependent tunnelling attenu-ation factor. φ means the effective tunnelling barrierheight, m the electron effective mass, and h Planck’sconstant.

Hopping is a thermally activated process, where thetransmission rate of the electrons follows a classicalArrhenius relation. Hereto, the electron can traverseone or more sites, like in incoherent tunnelling, butfor the case of hopping, the involvement of a nuclearmotion (bond rotation, bond stretching) becomes nec-essary. That means, electron transfer over the barriercannot occur until the thermal motion of nuclei resultsin a favourable molecular geometry, i.e., the moleculemust rearrange for electron transfer. Hopping transportexhibits two main characteristics: (i) the transmissionrate varies with barrier thickness as 1/L, because hop-ping involves a series of transitions between sites, and(ii) strong dependence on temperature. These proper-ties can be expressed in terms of a resistance as [29]

R = R0 +αL = R0 +α∞Lexp

(Ea

kBT

), (2)

where α = α∞ exp(Ea/kBT ) is a molecular specific pa-rameter with units of resistance per unit length and Ea

the activation energy associated with hopping (bondrotation, bond stretching).

For simplicity, we denoted a unit ‘molecules–nanoparticle–molecules’ as MNM unit (box in Fig 4a).

Correspondingly, the single current path in the chainof particles schematically outlined in Figure 4b con-sists of several such MNM units connected in series,where the orientation of the xz-plane of the individualunits can be different. We conclude that the main con-tribution to the charge transport in chains of particles isprovided by hopping. This mechanism can be regardedas a series of discrete steps initially involving the hop-ping (injection) of a charge from the left-hand-sideelectrode to the MNM unit, tunnelling of the chargethrough the MNM unit, hopping to the next MNM unit,etc., and finally hopping (extraction) of the charge tothe right-hand-side electrode. An evaluation of the con-tact resistance and that of the MNM unit was deducedfrom the I0–V curves in Figure 3a (Curve 3) and Fig-ure 3b (Curve 2) with (2), where Ea, Rm = α∞L, andR0 were treated as variable parameters. It is found thata good agreement between the experimental data andthe model for Sample 1 is obtained with Ea = 24 meV,R0 = 2.7·109 Ω, and Rm = 3.5·107 Ω. For Sample 2,we had to take Ea = 25 meV, R0 = 4.4·1010 Ω, andRm = 1.2·109 Ω. We, furthermore, deduced that thecontact resistance R0 is larger than Rm by about oneorder of magnitude for all samples investigated. Theresistance Rm means the sum of resistance contribu-tions described with (1) and (2) excluding R0. It is notpossible to separate these two contributions to chargetransport on the basis of I–V characteristics. Moreover,the influence of the interface molecule–molecule (mostlikely via an O–O link) cannot clearly be identified.Hereto, measurements of the I–V curves at differenttemperatures would be necessary.

Figure 3c and 3d show that the fluctuations ofdI0/dV (V ) are not exactly periodic. The mean pe-riod ∆V of these fluctuations can be roughly evalu-ated to about 0.5 – 1 mV for Sample 1 and 5 – 7 mVfor Sample 2. The ratio of the values of ∆V for dif-ferent samples correlates with the ratio of the valuesof the contact resistance R0. Consequently, we believethat the fluctuations of the differential conductancedI0/dV (V ) most likely originate from the Aue–O in-terface, as a result of the interplay between molecularconformation, charge switching, and breaking of thelinks. The quasi-periodicity of the dI0/dV (V ) fluctu-ations can be understood as a consequence of the ro-tation of the O–C–O group around the C–C axis ofthe citrate molecule (at the Aue–O interface). Whenmany citrate molecules connected in parallel partici-pate at the charge transport, only the ‘mean frequen-

L. V. Govor and J. Parisi · Conductance Fluctuations in Chains of Particles 163

cies’ of dI0/dV (V ) oscillations can be observed ex-perimentally (Fig. 3).

We have demonstrated that, for all samples inves-tigated, the conductance of a sample, deduced fromtwo sequentially measured I–V curves, decreases forthe third and all following measurements. The lattercan be caused due to the displacement of the parti-cles within a chain, caused by the acting electric fieldor due to the heating of the sample at the interfaceelectrode–molecule as a consequence of the high con-tact resistance.

5. Conclusion

We have bridged a pair of gold electrodes throughsmall and wide chains of gold nanoparticles, whichwere stabilized by a coating of citrate molecules. Weperformed a comparative analysis of current–voltagecharacteristics for chains of nanoparticles having vari-able size. Besides stochastic current fluctuations ata constant bias voltage and quasi-periodic fluctuationsof the differential conductance arising from conforma-tional changes of citrate molecules, we also observed

that the arrangement and distribution of nanoparticlescan be changed by the electric field applied, contribut-ing to conductance fluctuations and leading to irre-versible changes and finally rupture of the conduct-ing bridge. Although in all cases gold is bridged bythe same citrate molecules, a significantly higher re-sistance between gold electrodes and the citrate coatedgold nanoparticles was found as compared to the resis-tance between identical nanoparticles. Such differenceis attributed to the fact that citrate molecules are chem-ically attached to the nanoparticles, but are only phys-ically interacting with the electrodes. Thus, the resis-tance of the bridge is not only a function of the numberof molecular contacts, but also depends on the strengthof the individual interactions between metal conductorand molecules.

Acknowledgement

The authors acknowledge G. Reiter and G.H. Bauerfor discussion of the experimental results. This workwas financially supported by the Deutsche Forschungs-gemeinschaft (DFG) under the grant number PA378/10-2 and funding by EWE AG Oldenburg.

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