Growing One-Dimensional Metallic Nanowires by Dielectrophoresis

Metallic nanowires

DOI: 10.1002/smll.200600350

Growing One-Dimensional Metallic Nanowires byDielectrophoresisNitesh Ranjan, Hartmut Vinzelberg, and Michael Mertig*

We report an electrical-field-controlled growth process for the directedbottom-up assembly of one-dimensional palladium nanowires betweenmicrofabricated electrodes. The wires, grown from an aqueous palladiumsalt solution by dielectrophoresis, have a thickness of only 5–10 nm and alength of up to several micrometers. The growth process depends largelyon both the strength of the applied ac field and the concentration of themetal salt solution. The conditions for optimum growth are evaluated.Room-temperature current–voltage measurements show ohmic behaviorand indicate electromigration effects at higher voltages. Low-temperaturetransport measurements reveal localization effects with a characteristic re-sistance minimum at 20 K. The temperature dependence below theminimum shows the wires to be one dimensional in their electron-transport properties. The investigated growth method is capable ofbuilding complex circuit patterns for future nanoelectronics.

Keywords:· conductivity· electrophoresis· nanowires· palladium· self-assembly

1. Introduction

Electronic circuits assembled from nanotubes and nano-wires are one way in which the miniaturization trend formu-lated by the well-known Moore�s law could be continuedover the next few decades.[1] Therefore, both nanotubes andnanowires are attracting increasing attention as they areconsidered to be the main building blocks of nanocircuits,which are intended to be formed by applying novel bottom-up fabrication routes based on self-assembly. Moreover, thefabrication and characterization of metallic structures of a

few nanometers in diameter and with high aspect ratios arenecessary to understand the effects of size and dimensionali-ty on their electronic properties. Experimental and theoreti-cal work on carbon nanotubes (CNTs) has contributed a lotin the proper understanding of the one-dimensional elec-tronic properties of tubes.[2] Nonetheless, the developmentof strategies for their directed assembly has only just beencommenced.[3, 4] Firstly, CNTs show metallic or semiconduct-ing properties depending on their chirality. But fabrication,sorting, and manipulation of tubes with a defined chiralityare difficult to attain so far. Secondly, there exist limitedmethods to incorporate CNTs into microelectronic contactstructures. Either electrodes are lithographically written ontop of predeposited CNTs[5] or CNTs are deposited ontopatterned contact structures.[4, 6] Whilst the former method isnot capable of parallel fabrication, the latter is always asso-ciated with high contact resistances. Unlike that of CNTs,the chemistry of semiconducting and metallic nanowires,which determines their electronic properties, is easier tocontrol. Recently, single-crystal semiconductor nanowireshave been synthesized by nanocluster-catalyzed vapor–liquid–solid growth[7] and assembled into functional electri-cal networks.[8] Moreover, several methods for growing met-

[*] N. Ranjan, Dr. M. MertigBioNanotechnology and Structure Formation GroupMax Bergmann Centre of BiomaterialsDresden University of Technology, 01062 Dresden (Germany)Fax: (+49)351-463-39401E-mail: [email protected]

Dr. H. VinzelbergIFW Dresden, P.O. Box 270116, 01171 Dresden (Germany)

Supporting information for this article (additional atomic forcemicroscopy (AFM) and scanning electron microscopy (SEM)images of grown nanowires and of the used gold contact pads)is available on the WWW under http://www.small-journal.com orfrom the author.

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full papers M. Mertig et al.

allic nanowires by template synthesis have been reported,with the most important being metal deposition into cylin-drical nanopores,[9] deposition at step edges on single-crystalsurfaces,[10] and template-directed metal growth at double-stranded DNA,[11] artificial DNA tubes,[12] and tubular pro-tein structures.[13] Cutting-edge atomic-sized nanowires havebeen obtained and studied by applying the break-junctiontechnique.[14] Here we report the first electrical-field-con-trolled self-assembly of one-dimensional palladium nano-wires, along with their low-temperature electrical characteri-zation. The wires, with a typical thickness below 10 nm anda length of several micrometers, are grown between micro-fabricated electrodes by dielectrophoresis (DEP).[15] Our re-sults demonstrate that DEP allows the growth of extremelythin metallic wires, their positioning, and their electricalconnection to the electrodes to be combined in only onefabrication step.

DEP has been previously used as a tool to arrange col-loidal particles into complex assemblies.[16] Interconnectshave also been fabricated by dielectrophoretic deposition ofcolloidal particles,[17] nanorods,[18] and CNTs.[19] Colloid-par-ticle wires have been assembled up to lengths of several mil-limeters with diameters typically in the micrometer range.[17]

By using rods or tubes, smaller diameters have been ach-ieved.[18,19] In these cases, the diameters of the fabricatedwires were similar to those of the deposited rods and tubes.However, all these previously reported methods rely on theformation of nanometer-sized particles or rods prior to de-ACHTUNGTRENNUNGposition. Thus, the geometrical properties of the wires arenot controlled by the DEP process. DEP is solely used tomanipulate and align the particles in the electric field. Thisis different in the approach chosen by Cheng et al.,[20] whohave recently demonstrated that metallic nanowires with adiameter of approximately 100 nm can be directly grownfrom an aqueous solution by DEP. Here we show that theconditions for the direct growth of wires from an aqueouspalladium salt solution can be controlled by the electricalfield to obtain considerably thinner wires which exhibit one-dimensional electrical behavior. The method allows thegrowth of wires simultaneously at different locations whenmultiple contact arrays are used.

Dielectrophoresis can be considered as an electrical ana-logue to optical tweezers.[21] The application of an ac electricfield to a dielectric particle suspended in a liquid produces atime-varying dipole in the particle, caused by the redistribu-tion of free and bound charges in and on it, respectively.For a spherical particle with radius r, the induced dipole ex-periences a dielectrophoretic net force, FDEP, given byFDEP=2pr3emRe[K(w)]5 ACHTUNGTRENNUNG(Erms

2), where em is the permittivityof the suspending fluid medium and Erms and w are theroot-mean-squared value and the angular frequency of theapplied electrical field, respectively. Re[K(w)] is the realpart of the Clausius–Mossotti factor, given by K(w)=[e*p(w)�e*m(w)]/ ACHTUNGTRENNUNG[e*p(w)+2e*m(w)], where e*p and e*m arethe complex permittivities of the particle and the medium,respectively. The direction of the force acting on the dipoledepends on the sign of Re[K(w)], which may alter with fre-quency. If Re[K(w)] is positive, the particle is attracted intothe region of highest field strength. The magnitude of the

force acting on the particle depends on the gradient of theapplied field and on the volume of the particle. Consequent-ly, if the size of the particle is reduced from the micrometerto nanometer range and further to the molecular or atomicscale, its volume decreases by many orders of magnitudeand so does the force. Hence, large gradients of the appliedelectrical field are necessary to assemble low-dimensionalwires from aqueous solution.

2. Results and Discussion

2.1. Wire Morphology

We have fabricated Pd wires between microfabricatedgold electrodes by DEP by applying an electrical field at aconstant frequency of 300 kHz. We found that the thicknessof the assembled wires mainly depends on the strength ofthe applied electrical field and on the concentration of themetal salt solution used. With an 18-times-diluted solution(see the Experimental Section) and a maximum appliedpeak-to-peak voltage (Vp–p) of 10 V, the wires typically grewto a thickness of 200–300 nm (Figure 1), which is in agree-ment with the results reported by Cheng et al.[20] Considera-bly thinner wires were obtained when the used metal salt

Figure 1. a) Atomic force microscopy (AFM) image of a palladium wiregrown between gold electrodes 2 mm apart at an applied ac Vp–pvalue of 10 V. b) Height profile measured along the green line in (a).The wire is about 300 nm thick. c) The current–voltage (I–V) charac-teristics show perfectly ohmic behavior with a resistance of 794 W.

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One-Dimensional Palladium Nanowires

solution was further diluted and the applied field was re-duced. Figure 2 shows an example for the wire assemblyunder the optimized conditions, from a Pd acetate solutiondiluted by a factor of 40. The applied Vp–p value was 2 V.The grown wires have a thickness of 5–10 nm. The DEPdeposition process was found to be very reproducible (seethe Supporting Information, Figure A). Although branching

is a general feature of wires assembled from colloidal[17] oraqueous metal salt solutions,[20] it seems to be more pro-nounced for the thin wires than for the thicker ones. Theformed nanowires are extremely stable. They withstand highsurface tension while drying, multiple thermal cycling be-tween room and helium temperature, and even normal me-chanical stresses applied by slightly bending the substrate.They remain functional under normal conditions formonths.

2.2. Mechanism of Wire Growth

The mechanism underlying the growth of metal wiresfrom aqueous solutions by DEP has not been investigatedin detail yet.[20] In particular, there is no sound physical un-derstanding of how dissolved metal ions can be manipulatedin space by an alternating electrical field, a process that inprinciple requires that dipole moments can be induced atthe ion sites by the applied external field. Since the Pd ionsare dissolved in a polar liquid, they possess—like any othercharged particle—a counterion cloud around them. Weassume that this counterion cloud can cause the formationof a dipole at the Pd-ion site when the applied external fieldleads to displacement of the cloud relative to the chargedPd ion. A similar mechanism has been discussed before toexplain the ionic polarization of macromolecules in poly-electrolytes[22] and the dielectrophoretic response of chargedbiomolecules like DNA.[23] Due to the high dielectrophoret-ic force near to the electrodes, the Cpolarized Pd ions� willbe attracted towards the electrodes, will eventually get re-duced there, and thus will be deposited onto the rims of theelectrodes.

Figure 3 shows that the deposition of Pd onto the elec-trodes does not take place homogeneously along the rim.Wires start to grow only from a few distinct sites, presuma-bly those which experience the highest electric-field gradi-ents due to small inhomogeneities in the electrode geome-try. This observation shows evidence that high-field magni-tudes and gradients are necessary to assemble low-dimen-sional wires from aqueous solution. It also indicates that the

Figure 2. a) AFM image of a palladium wire grown between gold elec-trodes 5 mm apart. The applied ac Vp–p value was 2 V. The insetshows a close-up view of the wire. b) Height profile measured alongthe green line in (a). The thickness of the wire is 5–10 nm. c) The I–Vcharacteristics shows ohmic behavior at low bias. The measuredresistance was �25 kW. d) At higher bias, nonlinearities areobserved, which hint at the occurrence of electromigration effects inthese wires.

Figure 3. Scanning electron microscopy (SEM) image showing the ini-tiation of the growth process at the tip of the electrode. The wiregrowth starts from a few distinct regions of the electrode. Theseregions experience a high electric-field gradient due to the geometri-cal inhomogeneity of the electrode.

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initial wire growth might even be better controlled locallyby using electrodes with smaller dimensions or specific geo-metries. Once wire growth has been nucleated at the rim ofthe electrodes, the growing nanowire creates local fields ofhigher intensity and gradient at its tip. As a consequence,wire growth is self-regulated. Now, Pd is exclusively deposit-ed at the tip of the growing wire and the wire grows towardsthe opposite electrode. The growth of wires can simultane-ously take place from both electrodes as the nucleation ofwires entirely depends on the existence of inhomogeneitiesin the electrode geometries. The wires growing from oppo-site electrodes may not be perfectly aligned to each other.However, as they move toward each other, the electric fieldbetween the growing tips gets stronger. This can cause thewires to change their growth direction and finally join witheach other. Sometimes it may also happen that nucleationstarts only from one of the electrodes but the growth is fastenough to reach the second electrode before any nucleationcan start on it.

The grown wires usually appear branched. Their mor-phology resembles a pattern whose formation is dominatedby diffusion-limited aggregation (DLA) of the depositedmaterial, for example, as previously observed for metallicstructures that were electrochemically deposited at low ap-plied voltages and solute concentrations.[24] Since in our casethe growth conditions are similar, we suppose that the ob-served branching of wires during their growth can be de-scribed by the DLA model.[25] It accounts for surface effectsessential during growth processes, which are described interms of the sticking coefficient, a parameter stating theprobability that a Pd ion coming into contact with the grow-ing tip will stick there. The larger the sticking coefficient,the larger the probability that the ion dielectrophoreticallydriven to the tip surface will irreversibly stick there andlead to the formation of branched structures. Therefore, weexpect the sticking coefficient to be unity for the chosendeposition conditions. Since tip instability and consequenttip splitting occurs more easily at thinner tips, we observethat the thinner wires are more branched than the thickerones. The faster growing branch may electrically shield theother branches, which consequently will prevent their fur-ther growth. We assume that this is the reason why we typi-cally observe the continual growth of only a few mainbranches.

Previous investigations on wire assembly from colloi-dal[17] and aqueous metal salt solutions[20] have revealed aminimum threshold value for the dielectrophoretic force (orelectric field) necessary to facilitate material deposition.This value is also an important parameter that defines thethickness of the growing wire. When the applied electricalfield is too high, the conditions for Pd-ion deposition arenot only fulfilled at the end of the growing tip, but also forsome distance Cbehind� the tip of the wire, depending on thefield strength. This will allow deposition of Pd ions also atthe Cside� of the growing wire and will thus lead to an in-crease in wire thickness. How fast the wire will grow inthickness in this case depends also on the concentration ofPd ions near to the wire. Therefore, the growth of very thinwires requires conditions where material deposition is only

facilitated at the very end of the wire tip. A further thicken-ing of the wire will be prevented when the dielectrophoreticforces behind the tip are smaller than the threshold value.In our experiments, conditions where the dielectrophoreticforce exceeds the threshold value only at the growing tip ofthe wire are found at an applied ac Vp–p of 2 V. Thus, thethickness of the wire can be controlled by reducing thenumber of particles required for the deposition and forcingthe deposition to occur only at one distinct site, namely, thevery tip of the growing wire.

2.3. Electrical Characterization of the Wires

At room temperature and low bias, both types of wiresexhibit ohmic behavior (Figure 1 c and Figure 2c). The re-sistance of the thick wires was typically below 1 kW, whichshows that their contact resistance to the Au contact pads islow. By assuming the contact resistances to be zero, we canestimate the specific resistivity of the thick wires to be�600–3000 mWcm. This is much larger than the specific re-sistivity of pure bulk palladium at room temperatureACHTUNGTRENNUNG(�10 mWcm), a result indicating that the polycrystallinewires exhibit a coarse grain structure. For the thin wires,typical resistances in the range of 8–30 kW were measured.Under the same assumption as above, this reveals a specificresistivity of 70–100 mWcm. This is only a factor of 7–10more than that of pure bulk palladium, thereby again show-ing that the contact resistances between the wires and theAu contacts are indeed low. As mentioned before, high con-tact resistance is the most widely encountered problemwhile depositing nanostructures and nanotubes betweenelectrodes. Interestingly, the estimated specific resistivity ofthe thinner wires is much lower than that of the thick onesand approaches nearly the value of bulk palladium. In ac-cordance with the results obtained for colloidal particles,[18]

we suppose that this counterintuitive effect can be explainedby differences in the growth rates for the two types of wire.The thick wires grow fast. Consequently, their grain struc-ture is coarse, which limits the number of electrical contactsbetween individual grains. The thinner wires are grown atslower rate, which leads to a higher packing density of thedeposited material[17] and consequently to more grain–graincontacts within the wire. As a result, the specific resistivitydecreases when the growth rate is lowered.

Within this picture, it is also possible to understand theelectrical behavior of the wires at higher bias. The coarsethick wires break immediately when the voltage is raisedover a certain threshold (Figure 1c), whereas the thinnerwires with a more elaborate grain structure show nonlineari-ties at higher voltage that can be related to electromigrationeffects in the wire. With electromigration effects, we implythat domains of the wire with high local resistance mayCmelt� locally at a certain current density and reassemble soas to lower the resistance. The I–V characteristic depicted inFigure 2d shows an example of this. Above 2 V the currentstarts to increase nonlinearly. Then, a dip in the current isobserved slightly below 3 V. The initial nonlinearity in thecurrent could be due to electromigration, after which the



local melt might resolidify into a rearranged structure,thereby leading to the dip in the current. However, the pos-sibility of the burning of any sub-branches cannot be ruledout. At about 9 V the current again increases nonlinearly,but here the structure is not able to reassemble and the wirebreaks.

The resistance of the wire decreases when the samplesare cooled down to lower temperatures (Figure 4). The ini-

tial decrease is nearly linear in temperature and can be at-tributed to the decreasing electron–phonon interaction. Theresistance versus temperature curve shows a minimum atabout 20 K. Below that, the resistance increases again. At4.2 K, the wires exhibit a very weak nonlinearity in the I–Vcharacteristics (data not shown) measured in the current-biased regime.

The observed decrease in conductance with decreasingtemperature below 20 K is a signature of electron-localiza-tion effects. Scaling theory explains the localization of elec-trons by formulating the conductance as a function of theconductor size at zero temperature.[26] If the inelastic scat-tering time, tin, is greater than the elastic scattering time, tel,the electron will diffuse a distance, L, between the dephas-ing inelastic collisions, given by L= (Dtin)

1/2, where D is theelectron-diffusion constant. Quantum interferences of elec-trons, necessary for the occurrence of localization, are cutoff beyond the phase coherence length L. In this regime,the conductance, s, is inversely proportional to L. By de-scribing the functional dependence of L on temperature, the

localization effects in conductance can also be described atnonzero temperatures. Since tin increases with decreasingtemperature, L also increases when the temperature is low-ered, and thus s decreases with a decrease in the tempera-ture. The effective dimensionality of a conductor is thenumber of dimensions for which the conductor size is great-er than L. Hence, the conductance of structures with differ-ent dimensions (1D–3D) has different temperature depend-ences.[26] In the low-temperature localization regime, thetemperature dependences of s for 3D, 2D, and 1D struc-tures are given by s(T)3D�T1/2, s(T)2D� ln(T), and s(T)1D�T�1/2, respectively. In the inset of Figure 4, the conductanceis plotted versus T�1/2. Below 20 K a linear dependence isobtained, clearly showing that the conduction through thefabricated nanowires wires obeys one-dimensional behavior.We are working to investigate the behavior of these wires inthe millikelvin range and in the presence of magnetic fields,which, we hope, will reveal many of interesting electronicproperties.

3. Conclusions

We have demonstrated the self-assembly of one-dimen-sional metallic nanowires between adjacent electrodes.From an aqueous metal salt solution, wires with diametersbelow 10 nm have been fabricated by DEP. The length ofthe fabricated wires was in the micrometer range and wasdetermined by the distance between the electrodes. Howev-er, from the observed growth behavior, we anticipate thatthere is no physical limitation to growing even longer wireswith similar properties. By a proper setup of the physicaland chemical deposition conditions, we were able to pro-duce wires which showed one-dimensional electron-trans-port properties. Low-temperature resistance measurementsclearly revealed localization effects with s(T)�T�1/2, as pre-dicted for one-dimensional wires by the scaling theory of lo-calization. The specific resistivity of the nanowires wasfound to be less than a factor of 10 higher than that of purebulk palladium, a result indicating that a fine and densegrain structure of the polycrystalline wires was obtainedunder the optimized growth conditions. We want to assertthat this method of electric-field-directed growth of thinwires has immense potential for utilization in the field ofnanotechnology. By parallel or alternate application of acfields between different electrodes, it will be possible tomake intricate nanocircuits with one-dimensional nanowiresconnecting different sets of electrodes in a complex fashion.Furthermore, the applied method exhibits the intrinsic po-tential to contact nanoparticles which are deposited be-tween the electrodes in a controlled fashion, a processwhich could be used to contact preformed nanoelectronicdevices electrically and thus to assemble complex nanoelec-tronic circuits in a desired way. The low contact resistanceachieved by this method is of large importance for thebuild-up of interconnects in nanocircuits. The simplicity andcontrol over the growth parameters offered by this methodwill make it a suitable candidate for the future assembly ofnanoelectronic circuits.

Figure 4. Temperature dependence of the wire resistance. A resist-ance minimum is observed at about 20 K. The inset shows a close-up view of the temperature region between 4.2 K and 50 K. At tem-peratures below 20 K, the conductance varies linearly with T�1/2. Theobserved difference in the measurements at 50 nA and 500 nA is aconsequence of the weak nonlinearity in the I–V curves in this tem-perature region (I–V curve not shown).



4. Experimental Section

To prepare the metal salt solution for the DEP experiments,palladium acetate (5 mg, Merck) was dissolved in 10 mm 2-[4-(2-hydroxyethyl)-1-piperazinyl]ethanesulfonic acid (HEPES) buffer(pH 6.5, 1 mL). The resulting solution was sonicated for 5 minand centrifuged for 5 min at 2000 g, then the supernatant wastaken as the saturated stock solution. In a typical DEP experi-ment, solution (about 15 mL), diluted from the stock solution todifferent extents, was placed onto the electrodes, and an exter-nal sinusoidal Vp–p value of up to 10 V was applied to the elec-trodes at a frequency of 300 kHz. Within 2–5 min, the wires grewbetween electrodes 5 mm apart, which is equivalent to a growthrate of >1 mmmin�1. During the deposition, the charge flow be-tween both electrodes was monitored. There is a clear and sharpjump in the current when the first wire is completely assembled.This signal was used to trigger switch-off of the bias voltage. Inthis way, the number of wires in contact with both electrodescan be limited to one. This regime was usually applied to allsamples used for the conductivity measurements. Hence, theelectrical measurements were always performed on single con-nections, even when several electrode pairs arranged in parallelin one frame were used (see the Supporting Information). Purelyto demonstrate parallel fabrication between several electrodes,we waited until other electrodes were also connected (see theSupporting Information, Figure C). To prevent the wire from beinginstantaneously burned, we used backup resistors in series withthe electrodes.

The planar gold electrodes with gap distances of either 2 mmor 5 mm were manufactured by standard optical lithography withthermally oxidized n-type silicon wafers (100) as the substrates(see the Supporting Information). The electrodes have a thick-ness of 25 nm. A 5-nm-thick Cr grafting layer was used to pro-mote adhesion of the Au film to the substrate. After assembly ofthe wires, excess solution was blotted with filter paper. There-after, the sample was rinsed and air dried. The morphology ofthe wires was characterized by AFM, by using a NanoScope IIIaapparatus (Digital Instruments) operated in tapping mode, andby low-voltage SEM, by using a XL30SFEG field-emission micro-scope (Philips). The electrical characterization of the sampleswas performed in the temperature range between 4.2–300 K, byutilizing a helium cryostat with a variable temperature inset. Thecurrent–voltage characteristics and the two-terminal resistivitywere measured by standard direct-current techniques. Since weused thermally oxidized silicon wafers with an oxide layer ap-proximately 150 nm thick beneath the gold electrodes, we donot expect the substrate to play any role in the conductivitymeasurements.

Acknowledgements

We are grateful to Daniel Sickert and Gerald Eckstein fromSiemens AG, Munich, for the preparation of the electrodes.We thank Sebastian Taeger for his help during the setup of

the experimental system and for useful comments on the ex-periments. This work was partially supported by the BMBF(grant no.: 13N8512).

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Received: July 14, 2006



Growing One-Dimensional Metallic Nanowires by Dielectrophoresis

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