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552 DOI: 10.1021/la902026e Langmuir 2010, 26(1), 552–559 Published on Web 11/19/2009 pubs.acs.org/Langmuir © 2009 American Chemical Society Dielectrophoretic Growth of Metallic Nanowires and Microwires: Theory and Experiments Nitesh Ranjan,* Michael Mertig, Gianarelio Cuniberti, and Wolfgang Pompe Institute for Materials Science and Max Bergmann Center of Biomaterials, Dresden University of Technology, 01062 Dresden, Germany Received June 5, 2009. Revised Manuscript Received September 9, 2009 Dielectrophoresis-assisted growth of metallic nanowires from an aqueous salt solution has been previously reported, but so far there has been no clear understanding of the process leading to such a bottom-up assembly. The present work, based on a series of experiments to grow metallic nano- and microwires by dielectrophoresis, provides a general theoretical description of the growth of such wires from an aqueous salt solution. Palladium nanowires and silver microwires have been grown between gold electrodes from their aqueous salt solution via dielectrophoresis. Silver microwire growth has been observed in situ using light microscopy. From these experiments, a basic model of dielectrophoresis-driven wire growth is developed. This model explains the dependence of the growth on the frequency and the local field enhancement at the electrode asperities. Such a process proves instrumental in the growth of metallic nanowires with controlled morphology and site specificity between the electrodes. Introduction The continuous miniaturization trend of electronic circuits has guided the roadmap of the semiconductor industry for the last 50 years, and it is expected to enter the truly nanoelectronic regime by the next decade. Carbon nanotubes 1 (CNTs) and nanowires 2 are two of the most important bottom-up materials for nanocir- cuits. Of the many hurdles leading to the bottom-up integration of nanostructures, the most difficult one is the possibility to deposit nanowires and nanotubes precisely at a desired position. Dielec- trophoresis (DEP) has emerged as an effective process to handle such a deposition step. 3,4 Dielectrophoresis also provides a method to separate metallic CNTs from semiconducting ones 5 in the solution phase. DEP is also applied in biotechnology for cell sorting 6 and localization 7 as well as for controlled cell movement and positioning. 8,9 The dielectrophoretic-assisted growth of microwires between microelectrodes has been reported by several groups. Almost all of these reported processes use suspended particles that were assembled as wires. 10-12 Consequently, these wires cannot be made thinner than the constituting suspended particles. The growth of metallic nanowires from its aqueous salt solution has been recently reported. 13,14 Major advantages of this dielectro- phoretic-assisted growth method are site-specific growth and control over the thickness and morphology of the nanowires (being built from ions). It has been shown that nanowires as thin as 5-10 nm could be made from the aqueous metal salt solution. 14 Thus far, there has been no clear understanding of the growth process of metallic nanowires from its aqueous salt solution. In this article, we present experimental results on the growth of palladium (Pd) nanowires from aqueous palladium acetate solu- tion and propose a theoretical model for the entire process. Because it was not possible to observe the growth of palladium nanowires in situ, silver microwires (grown via the same principles from aqueous silver acetate solution) were used as an additional model system. During a typical experiment, aqueous solution was placed between the microelectrodes and an ac potential was applied between the electrodes. The nanowires (Pd) or microwires (Ag) grew between the electrodes (depending on the applied conditions), and the connection could be confirmed by a sudden increase in the current. In this article, we propose a model for the dielectrophoretically led growth of nano- and microwires. Silver microwires were used to observe the growth phenomena, and the model thus derived could also be applied to nanowires. Through our experiments and theoretical work, we show that the variation of growth para- meters such as frequency and voltage produce wires of different thickness and morphology. Our calculations show that the potential drop across the double layer and the field enhancement at the electrode asperities play pivotal roles in the growth. Simulations using the finite element method (FEM) show that *Corresponding author. Tel: þ49-(0)351-46331462. Fax: þ49-(0)-351- 46331422. E-mail: [email protected]. (1) (a) Iijima, S. Nature 1991, 354, 5658. (b) Dekker, C. Phys. Today 1999, 52, 2228. (2) Appell, D. Nature 2002, 419, 553555. (3) (a) Dong, L.; Bush, J.; Chirayos, V.; Solanki, R.; Ono, J. J.; Conley, J. F.; Ulrich, B. D. Nano Lett. 2005, 5, 21122115. (b) Kim, T. H.; Lee, S. Y.; Cho, N. K.; Seong, H. K.; Choi, H. J.; Jung, S. W.; Lee, S. K. Nanotechnology 2006, 17, 33943399. (c) Lee, S. W.; Bashir, R. Appl. Phys. Lett. 2003, 83, 38333835. (4) (a) Krupke, R.; Hennrich, F.; Weber, H. B.; Kappes, M. M.; Lohneysen, H. v. Nano Lett. 2003, 3, 10191023. (b) Monica, A. H.; Papadakis, S. J.; Osiander, R.; Paranjape, M. Nanotechnology 2008, 19, 085303. (5) Krupke, R.; Hennrich, F.; Lohneysen, H. v.; Kappes, M. M. Science 2003, 301, 344347. (6) Hu, X.; Bessette, P. H.; Qian, J.; Meinhart, C. D.; Daugherty, P. S.; Soh, H. T. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 1575715761. (7) Albrecht, D. R.; Underhill, G. H.; Wassermann, T. B.; Sah, R. L.; Bhatia, S. N. Nat. Methods 2006, 3, 369375. (8) (a) Muller, T.; Gerardino, A.; Schnelle, T.; Shirley, S. G.; Bordoni, V.; Gasperis, G. D.; Leoni, R.; Fuhr, G. J. Phys. D: Appl. Phys 1996, 29, 340349. (b) Tuukkanen, S.; Kuzyk, A.; Toppari, J. J.; Hakkinen, H.; Hytonen, V. P.; Niskanen, E.; Rinkio, M.; Torma, P. Nanotechnology 2007, 18, 295204. (9) (a) Bakewell, D. J. G.; Hughes, M. P.; Milner, J. J.; Morgan, H. Proceedings of the 20th Annual International Conference of the IEEE Engineering in Medicine and Biology Society 1998, 20, 10791082. (b) Morgan, H.; Hughes, M. P.; Green, N. G. Biophys. J. 1999, 77, 516525. (10) Bhatt, K. H.; Velev, O. D. Langmuir 2004, 20, 467476. (11) Lumsdon, S. O.; Scott, D. M. Langmuir 2005, 21, 48744880. (12) Hermanson, K. D.; Lumsdon, S. O.; Williams, J. P.; Kaler, E. W.; Velev, O. D. Science 2001, 294, 10821086. (13) (a) Cheng, C.; Gonela, R. K.; Gu, Q.; Haynie, D. T. Nano Lett. 2005, 5, 175178. (b) Cheng, C.; Haynie, D. T. Appl. Phys. Lett. 2005, 87, 263112. (14) Ranjan, N.; Vinzelberg, V.; Mertig, M. Small 2006, 2, 14901496.
Transcript
Page 1: Dielectrophoretic Growth of Metallic Nanowires and ......potential dropacrossthe double layerand thefield enhancement at the electrode asperities play pivotal roles in the growth.

552 DOI: 10.1021/la902026e Langmuir 2010, 26(1), 552–559Published on Web 11/19/2009

pubs.acs.org/Langmuir

© 2009 American Chemical Society

Dielectrophoretic Growth of Metallic Nanowires and Microwires:

Theory and Experiments

Nitesh Ranjan,* Michael Mertig, Gianarelio Cuniberti, and Wolfgang Pompe

Institute for Materials Science and Max Bergmann Center of Biomaterials,Dresden University of Technology, 01062 Dresden, Germany

Received June 5, 2009. Revised Manuscript Received September 9, 2009

Dielectrophoresis-assisted growth of metallic nanowires from an aqueous salt solution has been previously reported,but so far there has been no clear understanding of the process leading to such a bottom-up assembly. The present work,based on a series of experiments to grow metallic nano- and microwires by dielectrophoresis, provides a generaltheoretical description of the growth of such wires from an aqueous salt solution. Palladium nanowires and silvermicrowires have been grown between gold electrodes from their aqueous salt solution via dielectrophoresis. Silvermicrowire growth has been observed in situ using light microscopy. From these experiments, a basic model ofdielectrophoresis-driven wire growth is developed. This model explains the dependence of the growth on the frequencyand the local field enhancement at the electrode asperities. Such a process proves instrumental in the growth of metallicnanowires with controlled morphology and site specificity between the electrodes.

Introduction

The continuous miniaturization trend of electronic circuits hasguided the roadmap of the semiconductor industry for the last50 years, and it is expected to enter the truly nanoelectronic regimeby the next decade. Carbon nanotubes1 (CNTs) and nanowires2

are two of the most important bottom-up materials for nanocir-cuits.Of themanyhurdles leading to the bottom-up integrationofnanostructures, the most difficult one is the possibility to depositnanowires and nanotubes precisely at a desired position. Dielec-trophoresis (DEP) has emerged as an effective process to handlesuch a deposition step.3,4 Dielectrophoresis also provides amethod to separate metallic CNTs from semiconducting ones5

in the solution phase.DEP is also applied in biotechnology for cellsorting6 and localization7 as well as for controlled cell movementand positioning.8,9

The dielectrophoretic-assisted growth of microwires betweenmicroelectrodes has been reported by several groups. Almost allof these reported processes use suspended particles that were

assembled as wires.10-12 Consequently, these wires cannot bemade thinner than the constituting suspended particles. Thegrowth of metallic nanowires from its aqueous salt solution hasbeen recently reported.13,14 Major advantages of this dielectro-phoretic-assisted growth method are site-specific growth andcontrol over the thickness and morphology of the nanowires(being built from ions). It has been shown that nanowires as thinas 5-10nmcould bemade from the aqueousmetal salt solution.14

Thus far, there has been no clear understanding of the growthprocess of metallic nanowires from its aqueous salt solution. Inthis article, we present experimental results on the growth ofpalladium (Pd) nanowires from aqueous palladium acetate solu-tion and propose a theoretical model for the entire process.Because it was not possible to observe the growth of palladiumnanowires in situ, silvermicrowires (grown via the sameprinciplesfrom aqueous silver acetate solution) were used as an additionalmodel system.During a typical experiment, aqueous solutionwasplaced between the microelectrodes and an ac potential wasapplied between the electrodes. The nanowires (Pd) ormicrowires(Ag) grew between the electrodes (depending on the appliedconditions), and the connection could be confirmed by a suddenincrease in the current.

In this article, we propose a model for the dielectrophoreticallyled growth of nano- and microwires. Silver microwires were usedto observe the growth phenomena, and the model thus derivedcould also be applied to nanowires. Through our experiments andtheoretical work, we show that the variation of growth para-meters such as frequency and voltage produce wires of differentthickness and morphology. Our calculations show that thepotential drop across the double layer and the field enhancementat the electrode asperities play pivotal roles in the growth.Simulations using the finite element method (FEM) show that

*Corresponding author. Tel: þ49-(0)351-46331462. Fax: þ49-(0)-351-46331422. E-mail: [email protected].(1) (a) Iijima, S. Nature 1991, 354, 56–58. (b) Dekker, C. Phys. Today 1999, 52,

22–28.(2) Appell, D. Nature 2002, 419, 553–555.(3) (a) Dong, L.; Bush, J.; Chirayos, V.; Solanki, R.; Ono, J. J.; Conley, J. F.;

Ulrich, B. D. Nano Lett. 2005, 5, 2112–2115. (b) Kim, T. H.; Lee, S. Y.; Cho, N. K.;Seong, H. K.; Choi, H. J.; Jung, S.W.; Lee, S. K.Nanotechnology 2006, 17, 3394–3399.(c) Lee, S. W.; Bashir, R. Appl. Phys. Lett. 2003, 83, 3833–3835.(4) (a) Krupke, R.; Hennrich, F.; Weber, H. B.; Kappes, M. M.; L€ohneysen, H.

v. Nano Lett. 2003, 3, 1019–1023. (b) Monica, A. H.; Papadakis, S. J.; Osiander, R.;Paranjape, M. Nanotechnology 2008, 19, 085303.(5) Krupke, R.; Hennrich, F.; L€ohneysen, H. v.; Kappes, M. M. Science 2003,

301, 344–347.(6) Hu, X.; Bessette, P. H.; Qian, J.; Meinhart, C. D.; Daugherty, P. S.; Soh, H.

T. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 15757–15761.(7) Albrecht, D. R.; Underhill, G. H.; Wassermann, T. B.; Sah, R. L.; Bhatia, S.

N. Nat. Methods 2006, 3, 369–375.(8) (a) M€uller, T.; Gerardino, A.; Schnelle, T.; Shirley, S. G.; Bordoni, V.;

Gasperis, G. D.; Leoni, R.; Fuhr, G. J. Phys. D: Appl. Phys 1996, 29, 340–349.(b) Tuukkanen, S.; Kuzyk, A.; Toppari, J. J.; H€akkinen, H.; Hyt€onen, V. P.; Niskanen, E.;Rinki€o, M.; T€orm€a, P. Nanotechnology 2007, 18, 295204.(9) (a) Bakewell, D. J. G.; Hughes, M. P.; Milner, J. J.; Morgan, H. Proceedings

of the 20th Annual International Conference of the IEEE Engineering in Medicineand Biology Society 1998, 20, 1079–1082. (b) Morgan, H.; Hughes, M. P.; Green, N. G.Biophys. J. 1999, 77, 516–525.

(10) Bhatt, K. H.; Velev, O. D. Langmuir 2004, 20, 467–476.(11) Lumsdon, S. O.; Scott, D. M. Langmuir 2005, 21, 4874–4880.(12) Hermanson, K. D.; Lumsdon, S. O.;Williams, J. P.; Kaler, E.W.; Velev, O.

D. Science 2001, 294, 1082–1086.(13) (a) Cheng, C.; Gonela, R. K.; Gu, Q.; Haynie, D. T. Nano Lett. 2005, 5,

175–178. (b) Cheng, C.; Haynie, D. T. Appl. Phys. Lett. 2005, 87, 263112.(14) Ranjan, N.; Vinzelberg, V.; Mertig, M. Small 2006, 2, 1490–1496.

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DOI: 10.1021/la902026e 553Langmuir 2010, 26(1), 552–559

Ranjan et al. Article

only processes occurring in the vicinity of the electrode surfacedetermine the wire formation; the bulk solution condition has noeffect on the assembly. This process of ac dielectrophoresis is quitedifferent from the electrolytic deposition occurring during thedirect current (dc) case. We also discovered that there exists anoptimum frequency window within which the wires are formed.When the applied frequency lies outside of this optimumwindow,wire assembly does not occur. The applied potential also has toexceed a minimum threshold for assembly to occur.11

Materials and Methods

Palladium acetate (Pd(CH3COO)2, Pd(Ace)) stock solutionwas prepared as reported before.14 Silver acetate (Ag(CH3-COO), Ag(Ace)) stock solution was prepared by dissolving5 mg of Ag(Ace) in 1 mL of doubly distilled water. The resultingsolution was then placed in an ultrasonic bath for 5 min. After-wards, the solution was centrifuged for 5 min at 2000g and thesupernatant was taken. The collected stock solution of Ag(Ace)was diluted to 1:10 for each experiment. The reason for growingAg microwire is the large diameter and the bright color of theelemental silver, which could be observed via an optical micro-scope (Carl Zeiss Axiovert 200 and Carl Zeiss Axiovert 200M).During an experiment, 15 μL of diluted Ag(Ace) solution wasplaced between the electrodes over a transparent glass substrateand an ac potential was applied. The experimental setup is shownin Figure 2 of Supporting Information. The entire process wasmonitored using a light microscope. Gold (Au) electrodes withdifferent configurations were used over a glass substrate.15 Thedistance between the electrodes depended on the configurationused and varied from 2 to 10 μm (Figure 1, Supporting In-formation).

To grow palladium nanowires, gold electrodes over siliconsubstrate were used. Nanowires were characterized by atomicforce microscopy (AFM) using a NanoScope IIIa (Digital In-struments) operated in tapping mode. A low-voltage scanningelectron microscope (Zeiss Gemini 982 equipped with a LaB6

cathode) was used for the characterization of the nano- andmicrowires.

Results and Discussion

Nanowire Deposition. To grow palladium nanowires, Pd-(Ace) stock solution was diluted by 1:40 and 15 μL of the dilutedsolution was placed between gold microelectrodes that wereseparated by 5 μm and a peak-to-peak voltage of 2.0 V wasapplied. The frequency of the applied ac potential was 30 kHz.The current in the circuit was observed with an oscilloscope, andthe connection between the electrodes was detected by a suddenincrease in the current, which was used as a trigger to switch offthe applied voltage. Figure 1a shows the morphology of theformed wires. The wires are about 20 nm in height, extremelystraight, and dendritic in shape.We observed that a change in themorphology of the wires could be achieved by changing thefrequency of the applied ac potential. The same dilution andvoltage conditions with a frequency of 300 kHz give extremelythin, branched wires that are about 5 nm thick14 (Figure 1b).Hence,we can conclude that the depositionprocess is governedbythe frequency of the applied electric field. Both nanowires shownin Figure 1 were grown on silicon substrates. Detailed workdescribing the change in the morphology of the nanowires withthe frequency of an ac field will be published elsewhere.16

Microwire Deposition. As stated before, silver microwireswere grown to gain insight into the process. For the experiment,15 μL of the diluted stock solution was placed in between the gold

microelectrodes over a glass substrate.Anacpotential of 10Vanda frequency of 30 kHz were applied between the neighboringelectrodes (Figure 1b, Supporting Information), which wereabout 7 μm apart. The entire microwire growth process wasobserved via light microscopy. We observed that the wire assem-bly can be divided into two different stages, viz., the nucleationand the growth phase. During nucleation, the wire begins to growstochastically from one of the electrode surfaces, and during thegrowth phase, it propagates from one electrode to the other. Itshould be noted that nucleation does not occur everywhere overthe electrode surface but only at few selected points. Experimen-tally, such selective nucleation regions at the electrode surface canbe observed in Figure 2 (shown by an arrow at time t = 0 and

Figure 1. Palladium nanowires formed via dielectrophoresis withdifferent applied ac field frequencies. (a) AFM image of dendriticpalladium nanowires deposited at 30 kHz. (b) Thin branchedpalladium nanowires deposited at 300 kHz, and (d) they are about5-10 nm thick. (c) The structure in (a) is characterized by perfectlystraight segments and has a constant height of around 20 nm.

(15) Refer to the Supporting Information.(16) Ranjan, N.; , Mertig, M.; , Pompe, W., in preparation.

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554 DOI: 10.1021/la902026e Langmuir 2010, 26(1), 552–559

Article Ranjan et al.

0.4 s). We emphasize that the kinetics is nucleation-dominatedbecause the growth phase is quite fast. Once the nucleation at aparticular location over the electrode surface has occurred, wiresgrow extremely fast and are connected to the next adjacentelectrode. Figure 2a shows the time sequence of the growing Agmicrowire, and from it the average velocity of the moving front iscalculated to be about 1 μm/s (movie clip 1, Supporting In-formation). We stress that the observation of the growing silvermicrowire via lightmicroscopy gave us qualitative information onthe growth process of palladiumnanowires occurring between theelectrodes under similar conditions.Dielectrophoresis Model. According to the Debye-H€uckel

theory,17 in nonideal solutions the formation of an ion-counterion complex is energetically favored. This complex be-haves as a single neutral entity. As shown in Figure 3, the ion-counterion complex can be visualized as a central ion surroundedby the oppositely charged counterions. In an equilibrium situa-tion, the positive charge center overlaps with the surroundingoppositely charged center.18 When an electric field is applied tothe solution, the positive charge centers move in the direction ofthe field and the negative charge center shifts in the oppositedirection. This leads to the formation of an electric dipole. Thisinduced dipolemaynow feel a dielectrophoretic force andmove inthe solution. Throughout the article, we call these ion-counterioncomplexes as ‘particles’ undergoing dielectrophoresis in the aqu-eous solution. When the direction of the field is reversed, theinduced polarization is also reversed. The effect is similar tothe polarization of neutral colloidal particles in a solution. Thestrength with which the counterion cloud is bound to the centralionic core and its flexibility to become distorted with the externalapplied field determine the strength of the dipole moment and its

relaxation time constant. The response of the induced dipole tothe frequency of the external applied field refers to the dielectricdispersion of the system. A similar mechanism has been pre-viously discussed to explain the ionic polarization of macromo-lecules in polyelectrolytes19 and the dielectrophoretic response ofcharged biomolecules such as DNA.20

When placed in an ac electric field, these dipoles experience thedielectrophoretic force.21Approximating these dipoles as spheres,the dielectrophoretic force is given by22

FDEP ¼ 4πRe½KðωÞ�a3r εmERMS2

2

!¼ ΓVrðFEÞ ð1Þ

Here, εm is the permittivity of the medium, a is the radius of thesphere, Erms is the root mean square of the local ac electric field,and K(ω) is the Clausius-Mossotti factor. Γ is a constant(= 3Re[K(ω)]) for a particular frequency, V = (4πa3/3) is thevolume of the dipole, and FE (= εmERMS

2/2) is the electric energydensity. Equation 1 states that the dielectrophoretic force isproportional to the volume of the particle (FDEP � V). Whenthe particle diameter is reduced, for instance, from the micro- tothe nanometer scale, the volume decreases by 9 orders of magni-tudeand sodoes the force.Thus, to overcome thermal fluctuationsand friction, very high electric field magnitudes and inhomogene-ities are needed in order to assemble nanodimensional particles.According to eq 1, the dielectrophoretic force is also proportionalto the gradient of the electric energy density (FDEP � r(FE)). Aspatial plot of (r(FE)) at any instant in the growth process givesthe distribution of the dielectrophoretic force. This fact has beenused in the analysis shown in Figures 4 and 5.

We discuss now the energetics involved in the dielectrophoreticdeposition process. All of the calculations presented are for theexperimental condition and the electrode configuration shown inFigure 2. An ion dissolved in water has a thermal energy given by1.5kBT, which corresponds to approximately 38 meV at roomtemperature and is responsible for random Brownian motion.Assuming a regime of positive dielectrophoresis (Re[K(ω)] ≈ 1),the energy associated with the dielectrophoretic force (given byeq 1) could be simplified asFDEP=-rUDEP=r(2πa3εmErms

2).This leads to UDEP = -2πa3εmErms

2. The dielectrophoretic

Figure 2. (a)Optical images showing nucleation andgrowthof thesilver microwires with the corresponding time scale. Arrows showregions of the electrode that serve as nucleation points. (b) Silvermicrowire nucleating at one electrode and growing toward theother (t=24.4 s). (c) SEM image of a palladium nanowire grownbetween two gold electrodes. (b, c) Arrows mark the curved routetaken by the wire following the electric field lines, showing that thesame process occurs on both the micro- and nanoscale. (d)Magni-fied SEM image of the palladium nanowires depicted in image c.For these experiments, diagonally arranged electrodes were used(Figure 1b, Supporting Information).

Figure 3. Cation with the negatively charged surrounding coun-terion cloud in an aqueous solution. In the absence of an electricfield, both charge centers match each other. An external electricfield displaces the charge centers, giving rise to an electric dipolemoment.Δþ is the net excess positive charge developed in the spaceas a result of the migration of the charge centers (Δþ=Δ-), and Ris the polarizability of the system.

(17) Compton; R. G.; Sanders, H. W. Electrode Potentials, Oxford UniversityPress Inc.: New York, 1996; Chapter 2-3.(18) Robison, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworth

Publications limited: London, 1965.

(19) Chester, B.; O’Konski, T. J. Phys. Chem. 1960, 64, 605–619.(20) Asbury, C. L.; Diercks, A. H.; van den Engh, G. Electrophoresis 2002, 23,

2658–2666.(21) Pohl, H. A.Dielectrophoresis, Cambridge University Press: Cambridge, 1978.(22) Hughes, M. P. Nanotechnology 2001, 11, 124–132.

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DOI: 10.1021/la902026e 555Langmuir 2010, 26(1), 552–559

Ranjan et al. Article

energy gain, causing ordered assembly, must exceed the randomi-zing effect of the thermal energy. A peak ac voltage of Vapplied =10 V is applied between electrodes that are L= 7 μm apart. Thisgives an average field strength (Erms = Vapplied/(2)

1/2Lκw) ofabout 1.27� 104 V/m, where κw is the dielectric constant of water

(κw = εw/ε0). The average ordering dielectrophoretic energy fora hydrated silver ion with a radius23 of about 341 pm is about

Figure 4. (a)Distributionof the scaled electric field and (b) the gradient of the electric energy density at a particular instant of growthover theentire substrate. The electric field is enhanced at the growing tip and at the electrode asperities; it decays gradually bymoving away from theselocations. The gradient of the energy density is negligible over the entire substrate but intensifies to extremely high values (>6000) at the tipand the electrode asperities, as shown by arrows (b). This favors the process of nucleation and growth. The field distributions have beencalculated by solving the Poisson equation using an FEM algorithm.

Figure 5. Shown above are (a) the electrostatic field and (b) the gradient of the electric energy density distribution around a split tip at aparticular instant of wire growth. For the dc field, the electric field causing the deposition has sufficiently high values behind and in betweenthe growing tips (shown by the arrows in image a). This leads to a random distribution over the entire electrode surface, as shownexperimentally in image c. For the ac field, the dielectrophoretic force has extremely high values in an extremely localized space around eachtip but drops to very low values in regions immediately behind and in between the tips (shown by the arrows in image b). This leads to apatterned deposition, as shown experimentally in image d. The electrode distance is∼10 μm.

(23) Schreiber, L.; Elshatshat, S.; Koch, K.; Lin, J.; Santrucek, J. Planta 2006,223, 283–290.

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556 DOI: 10.1021/la902026e Langmuir 2010, 26(1), 552–559

Article Ranjan et al.

1.7� 10-7 meV for the bulk solution, which is around 8 orders ofmagnitude smaller than the randomizing thermal energy. Hence,it seems that energetically such subnanometer-sized particles willprimarily undergo random motion in the solution because thedielectrophoretic energy existing in the bulk solution is too smallto facilitate the ordered deposition required for the growth of thewires. Therefore, a simple explanation by energy considerationsdoes not explain the wire assembly, and other effects should alsobe taken into account. We found that the additional effect of apotential drop across the double layer and local electric fieldenhancements at electrode asperities play important roles in thewire assembly, as is discussed below.Wire Growth Controlled by Field Enhancement.When an

electrode is dipped into an electrolyte, a double layer (DL) isassumed to form according to the Gouy-Chapman model24 atthe electrode/electrolyte interface. Shown in Figure 3 of theSupporting Information is the equivalent circuit for the currentflow between the two electrodes dipped into a solution. The DLformed at each electrode acts as a capacitor, and the solutionbehaves as a resistor in series. The thickness of the DL or theDebye length (Δx) is given by the expression25

Δx ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiεwkBT

2n0z2e2

s≈ 0:3ffiffiffiffiffiffi

C�p nm ð2Þ

where εw is the permittivity of water, kB is the Boltzmannconstant, T is the temperature, n0 is the ion number density, z isthe charge on the ion in units of electronic charge e, and C* is theconcentration of the ions in mol/L. Using this expression andC*= 1.6 mM (concentration of the silver ions15), we get a Debyelength or diffusion layer thickness of 7.5 nm. The voltage dropacross the double layer can be estimated to be

VDL ¼ Vappliedffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4 þ jZsol=ZCj2

qwhere ZC and Zsol are the impedances of the capacitor and theresistor, respectively. At an electrode distance of L =7 μmand a frequency of 30 kHz, the impedances can be estimatedto beZC= 5.76� 10-5Ωm2/A andZsol = 4.18� 10-4Ωm2/A,where A is the representative cross-sectional area of the array.15

Thus, about 13% of the applied voltage drops at each of thecapacitors. Thismakes the voltage drop across each of theDLs tobe 1.3 V for an applied peak voltage of 10 V. The correspondingaverage electric field within the DL can be estimated to beERMS=VDL/(2)

1/2κwΔx≈ 1.61� 106V/m. The dielectrophoretic

energy resulting from this value of the electric field corresponds toan energy of about 2.8� 10-3 meV. This is 4 orders ofmagnitudehigher than the value calculated for the bulk solution but still lessthan the randomizing thermal energy. Therefore, there should bea secondmechanism causing an additional field enhancement.Weassume that the electrode asperities at the tips of the growing wirelead to an increase in the local electric field by many orders ofmagnitude. Depending on the radius of curvature of the tips, theelectric field and the gradient of the electric field energy in thevicinity of the tips are many orders of magnitude higher thanthe far-field values. Therefore, the dielectrophoretic energy in thenear field can be expected to exceed the random thermal energy

and so lead to ordered assembly. To understand the effect ofelectrode asperities and tip radius on the electric field and electricenergy density distribution, we performed a finite elementmethod(FEM) calculation at a particular instant of growth over asubstrate as shown in Figure 4.

In this simulation, a potential of 2 V was applied to one of theelectrodes, the other being grounded. The Poisson equation wassolved over the entire area (Fcharge_density = 0, κm = 1). Becausethe distance between the electrodes in the simulation does notcorrespond to actual distances between the electrodes in theexperiments, the electric field values obtained are normalized tothe external electric field. The normalizing electric field (E0)shown in Figures 4 and 5 is the one that takes into account thescaling of the dimensions of themodeled geometry with respect tothe dimensions of the experimental substrate. The simulation thusprovides a qualitative description of the distribution of |E| and|r(FE)| over the substrate. We choose the spatial plots of |E| and|r(FE)| because they represent two different driving forces for themovement of particles in the solution. In the dc field, the electricfield distribution |E| governs themovement of ions in the solutionand hence the deposition pattern is governed by the field dis-tribution (|E|). In the ac field, dielectrophoresis governs themovement of neutral particles (ion-counterion complex in ourcase) in the solution and hence the deposition pattern is governedby the distribution of the gradient of the electric field density(|r(FE)|). Hence, the plots depict the qualitative difference for thedeposition taking place in the solution during the dc and ac fields.We stress that the simulations just show the spatial distributionsof |E| and |r(FE)| at a particular instant of deposition, dependentonly on the instantaneous geometry of the electrodes and wires.The additional effects of the double layer and frequency depen-dence are taken into account by breaking the continuous mediainto three different parts, viz., the two double layers at theelectrodes (acting as a capacitor) and the aqueous mediumbetween the electrodes (modeled as a resistor) as discussed before.The Poisson equation has been applied as an approximation to aquasi-stationary solution of the time-dependent electric field,assuming that the characteristic wavelengths of the field varia-tions are small in comparison to 2πc/ωRe[n(ω)]≈ 2πc(2ε0/ω 3σ)

1/2,where c is the light velocity, ω = 2πf is the frequency of thedielectrophoretic excitation, n(ω) is the complex diffraction coeffi-cient, ε0 = 8.854 � 10-12 A s/V m is the dielectric vacuumpermittivity, and σ is the solvent conductivity. For f = 30 kHzand σ=1.6� 10-2Ω-1m-1, we get 2πc/ωRe[n(ω)]≈ 145m. Thatmeans that the quasi-stationary approximation can be applied forthe experimentally interesting frequency range. (For more details,see Supporting Information.)

Figure 4 depicts both processes of nucleation (asperities at thesurface of the right electrode) and growth (wire tip at the leftelectrode). A close observation of Figure 4a,b shows thatalthough both the electric field |E| and the gradient of the electricfield energy density |r(FE)| intensify at the electrode asperitiesand at the tip, |r(FE)| is extremely high for these geometries andimmediately falls to extremely low values even as we slightlymoveaway from these regions (Figure 4b). Because the dielectrophore-tic force is proportional to |r(FE)| (eq 1), an extremely highdielectrophoretic force exists in these regions, bringing aboutnucleation and growth. No dielectrophoretic deposition occurs inany other region even in the vicinity of the substrate because theforce values are extremely low. Hence, the deposition process isperfectly self-aligned. The enhanced electric field |E|, on thecontrary, has a much broader distribution (i.e., the field dropsgradually from the tip to the bulk values) (Figure 4a). Hence in adc case even if the field enhancement occurs at these locations,

(24) Fisher, A. C. Electrode Dynamics, Oxford University Press Inc.: New York,1996; Chapter 4.(25) Bard, A. J.; Faulkner, L. Electrochemical Methods: Fundamentals and

Applications, 2nd ed.; Wiley: New York, 2001.

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Ranjan et al. Article

various other locations in the vicinity of these geometries are alsoprone to deposition; consequently, we get a structureless deposi-tion over the entire electrode.

On the basis of our calculations, we propose a model forthe particle movement and deposition taking place in an ac field.In bulk solution, the thermal energy is much higher than thedielectrophoretic energy and hence it keeps the concentrationhomogeneous throughout the solution. This is equivalent tosaying that there is an absence of any dielectrophoretic-force-assisted drift of particles in the bulk solution; the force being tooweak, the particles undergo randomBrownianmotion. However,field enhancement occurs at the electrodes, which leads to self-assembly. There exist two major mechanisms for field enhance-ment, viz., that due to double-layer formation and the tip radius.Within the double layer, the field gradients are about 2 to 3 ordersof magnitude higher than the bulk solution, and the resultingdielectrophoretic energy will be about 4 to 6 orders of magnitudehigher in this region. However, this value is less than that requiredto bring about the ordered deposition because the thermal energyis still higher. However, additional field enhancement occurs atthe tip of the growing wire and at the electrode asperities, whichmay lead to a manifold increase in the dielectrophoretic force inthese regions. The high dielectrophoretic force would increase theflux of particles from the bulk solution to the DL.Within the DL,the ions dielectrophoretically drift toward the electrodes and areable to approach the electrode at a distance limitedby its solvationshell. It is assumed thatwithin the outerHelmholtz plane (OHP)24

only a monolayer of solvation exists between the ion and theelectrode. The metal ions may then be reduced via electrontransfer from the electrode to the cation and are deposited thereas part of the growing tip. Electrochemical reduction happensinstantaneously at each electrode when they act as a cathode.Charge transfer (reduction/oxidation) occurs only at the electrodesurface, not throughout the solution (movie clip 1, SupportingInformation). The field enhancement due to double-layer forma-tion is dependent on the frequency of the applied ac field. Thepercentage of the voltage drop across the diffusion layer decreaseswith increasing frequency, and at 1 MHz, only 0.4% of theapplied voltage drop at each DL.15,26 This corresponds to adielectrophoretic energy gain of about 2.66 � 10-6 meV in theDL, which is about 3 orders of magnitude lower than whenthe frequency is 30 kHz.Hence by varying the frequency, onemaybe able to change the concentration of particles locally at the tip,which may lead to a different morphology of the assembledstructure (Figure 1).Patterning.Wire growth initiated by a randomdistribution of

asperities at the electrode surfaces is characterized in the laterstages by typical pattern development. The most striking featuresare the so-called tip splitting12 and shadowing, which can also beobserved during nanowire growth (Figure 1). Figure 5a,b showsthe FEM simulation of a split tip and the relative stability of thedaughter branches. The region close to the electrodes with a small

radius of curvature R will cause a high dielectrophoretic (DEP)force, which scales as (FDEP � E2/R), whereas the electrostaticforce scales with the local electric field (FE � E). When an acpotential is applied, the DEP force drives the deposition. It hashigh values at the tip but drops to extremely low values in regionsaround and in between the tip (shown by the arrows inFigure 5b).Such a configuration favors the self-alignment of the depositingparticles and leads to the stable growth of both branches. Noparticle deposition will occur in the vicinity of or in between thetips. When a dc potential is applied, the electrostatic force drivesthe deposition. As shown by the arrows in Figure 5a, the fieldintensity |E|/E0 at the newly formed tips has high values. Besidesthis, the regions around and in between the tips also haverelatively high values. Hence, particles will be deposited homo-genously not only at the tip but also in its vicinity as shown by thearrows. This will lead to a deposition over the entire area.Experimental results are shown in Figure 5c,d. Figure 5c showsgrowth in the presence of a dc voltage of 0.5 V between theelectrodes immersed in a Ag(Ace) solution. A dense, structurelessfilm covering the entire electrodes can be observed. It growswithout any characteristic pattern. In Figure 5d, much highervoltages (10V) have been applied between the electrodes under anac driving frequency of 30 kHz.We see in the Figure the growth oftypical dendritically shaped Ag microwires. Between thelarger dendrites, there are shadowed regions of diminished Agdeposits.Optimal ProcessWindow.We found that very high frequen-

cies prevent wires from growing, and at low frequencies (theextreme case being the dc setup) random, structureless depositionwas observed over the entire electrodes. In the frequency windowwithin 30-500 kHz, patterned wires could be formed. The wirestructure and morphology change drastically within this fre-quency window (Figures 1 and 6).

Figure 6. Agmicrostructures grown at different frequencies and aconstant peak voltage of 10 V. Each window (a-f) shows theelectrode structure after the application of a fixed frequency for afixed period of time. (See the legends.) (a-c) Electrode structureafter applying frequencies of 1 MHz, 500 kHz, and 300 kHz for1 min each. (d) Electrode structure 1 s after the application of afrequency of 100 kHz. (e) Structure after the application of afrequency of 100 kHz for 1 min. (f) Structure after the applicationof a frequency of 30 kHz for 0.5 s. The electrode distance is∼4 μm.

(26) The complex impedance of a capacitor is ZC ¼ 1jωC, and it depends on the

frequency (ω) of the applied AC electric potential; the Ohmic resistance of thesolution is Zsol (constant with respect to ω); f

VC ¼ Vapplied1

j2 þ Zsol=ZC jVC ¼ Vappliedffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

4 þ ðϖCZsolÞ2q

limωf¥

VC ¼ 0; limωf0

VC ¼ Vapplied

2

Thus at low frequencies, the applied voltage (Vapplied) drops equally at the twocapacitors and no voltage drops along the solution (Zsol). At very high frequencyno voltage drops along the capacitors and the complete voltage drops across theresistance Zsol in the solution.

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558 DOI: 10.1021/la902026e Langmuir 2010, 26(1), 552–559

Article Ranjan et al.

For this experiment, a parallel set of electrodes (Figure 1c,Supporting Information) on a glass substrate was used with anelectrode distance of 4 μm. An ac signal of 10 V was appliedbetween the electrodes corresponding to the electric field value ofErms = 2.26� 104 V/m. Different frequencies (1 MHz, 500 kHz,300 kHz, 100 kHz, and 30 kHz) were applied chronologically for1 min each, as shown in Figure 6. Each of the panels inFigure 6a-f shows the electrode structure after the applicationof the particular frequency for the indicated period of time.As shown in Figures 6a,b, no wire formation happened at thehigher frequencies of 1MHz and 500 kHz, respectively, even after1 min. An extremely small assembly could be observed at afrequency of 300 kHz (Figure 6c). The growth kinetics is faster at100 kHz, and we could see the metal assembling immediatelybetween the electrodes (Figure 6d), which grewwith time to give adenser structure after 1 min (Figure 6e). The growth kinetics wasextremely fast at a frequency of 30 kHz, and a dense structure wasformed between the electrodes immediately within a fraction of asecond (Figure 6f). This shows that the process builds up as wemove from high frequencies to low frequencies. Because of theparallel structure of the electrodes, the wires are confined withinthem so they grow laterally and join with the neighboringbranches, giving a dense structure as shown in Figure 6e,f.

The frequency region can be divided into three domains withrespect to the dielectrophoretically led assembly, viz., the high-frequency domain, the optimum frequency region at whichpatterned wires are formed, and the extremely low frequencydomain. Both particles and media have their own characteristicdielectric relaxation times. At high frequencies, the time period ofthe external electric field is smaller than the relaxation time of thedielectric particle. At such frequencies, there exists a constantphase shift between the external electric field and the polarizationof the particle. This leads to negative dielectrophoresis, thusinhibiting the assembly. Within the optimal frequency window,the counterion cloud has enough time to react to the external fieldand hence dipoles are formed in phase with the external field.These dipoles then drift into the dielectrophoretic force field andhence assembly can occur.At very low frequencies, we fail to formwires but get random depositions. This could be explained by thefact that in an ac field the positive and negative charge centers ofthe ion-counterion complex can be assumed to vibrate about themean central position (thus bringing about the time-dependentdipole moment) and hence the net electrostatic drift of either ofthe charge centers can be assumed to be zero. This zero electro-static drift can be assumed to occur onlywhen the displacement ofthe ion (and also the surrounding counterion) in the half cycle(δxhc) is small enough that the electric field can be considered tobe homogeneous in that region [i.e., (E(x þ δxhc) ≈ E(x)]. Whenthe ionic displacement (δxhc) over the half cycle is larger than thedistance over which the field can be considered to be homoge-neous, the ion may not return to the original position in the nexthalf cycle. Thus when E(x þ δxhc) 6¼ E(x), there would be a netelectrostatic drift of ions even in the ac case. In the microelec-trode systems, high spatial field inhomogeneities exist. Hencethe electrostatic drift of the ions can commence at low fre-quency because the net ionic displacement in the half cycle isinversely proportional to the applied frequency (δxhc � 1/f).Once the movement of the ions is governed by the electrostaticdrift rather than the dielectrophoretic drift, metal depositioncan no longer occur in a patterned way on the basis of the self-alignment mechanism due to near-field enhancement at the tip,as discussed in Figure 5b. Consequently, the wire-formationprocess is disturbed, which requires self-aligned material de-position brought about only by the dielectrophoretic force.

This may account for the random particle deposition at lowfrequencies.

The deposition of the nano- and microwires was found todepend on the magnitude of the applied ac field, and we foundthat in each case a minimum threshold of electric field (and hencethe dielectrophoretic force) is necessary to initiate the process.11

We estimated the minimum threshold values of the electric fieldrequired for the dielectrophoretic deposition of patterned Agmicrowires. In this experiment, we applied a 30 kHz frequencyand varied the applied voltage between a parallel set of electrodeswith a 4 μmdistance.We applied in ascending order for 1min eachof the following voltages: 0.5, 1.5, 3.0, and 5.0 V. Nothingappreciable happened for the first three values, as shown in Figure7a. Thewires were immediately seen to be formedwhen the appliedvoltage was 5.0 V (Erms = 1.13 � 104 V/m). Figure 7b shows thatthe wires formed immediately within the first 1.5 s of the applica-tion of 5.0 V. The wires grew denser with time, and after 1 min, theentire space between the electrodes was covered by them.

This shows that there exists a threshold voltage/field belowwhich the kinetics is too small to detect anything noticeable. Theelectric field is calculated by assuming flat electrode surfacesplaced opposite to each other and gives a value for the bulksolution. A detailed calculation individually taking into accountthe potential drop across the double layer and the bulk solution isreported in the Supporting Information. Local geometrical in-homogeneities at the electrode surface and growing tips enhancethe field up to various extents, depending on their shape, andbring about localized nucleation and growth wherever the thresh-old is crossed. These two experiments prove that noticeableassembly occurs at some optimized values of frequency andvoltage.When any of these parameters lie outside their respectivedomains, no assembly is observed.

Conclusions

We have introduced a dielectrophoretic model for the growthof metallic nanowires from their aqueous salt solution. Most ofthe experiments were performed on the growth of silver micro-wires, observed in situ using a light microscope. Ions with thesurrounding counterion clouds behave as neutral particles res-ponding to the dielectrophoretic force field. The assembly couldbe divided into nucleation and growth phases. Kinetic parametersrelated to these processes have also been reported. Our calcula-tions show that the dielectrophoretic assembly is not feasible by asimple energy consideration,with the thermal energy being ordersof magnitude higher. An additional effect of the electric fieldenhancement is needed, which is brought about by two differentfactors. First a double layer formed at the foremost front of thegrowing electrode seems to enhance the field 2 to 3 orders ofmagnitude higher than that of the bulk. Second, the electrodeasperities and the growing tip enhance this field bymanyorders of

Figure 7. Ag microwires grown at a different potential at a con-stant frequency of 30 kHz for the stated period of time. (a) Theelectrode structure remains the same after the application of 0.5,1.5, and 3.0 V for 1 min each. (b) Image taken 1.5 s after theapplication of 5.0 V. The electrode distance is∼4 μm.

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Ranjan et al. Article

magnitude because of their extremely small radius of curvature.These two factors have a profound effect on the growth whereasthe conditions of the bulk solution have no effect on the assemblyprocess. The thermal energy is too high throughout the bulksolution and keeps the concentration homogeneous. We showedthat there exists an optimum window of frequency within whichthewires can assemble.There also exists a threshold voltage belowwhich the wires fail to form.

This process of nanowire formation has potential implica-tions on the future development of the bottom-up assembly ofnanomaterials. Beyond the formation of metallic nanostructures,there could bemany other options for the organized deposition ofnanostructures by dielectrophoresis. A proper understanding ofthe theory will help in exploiting the process over much widerareas of bionanotechnology.

Acknowledgment. We are grateful to Daniel Sickert andGerald Eckstein (Siemens AG), Munich, Germany, for thepreparation of the electrodes. We thank Anja Bl€uher for her

support with SEM imaging and Markus P€otschke for helpwith the FEM simulations. This work was supported byBMBF (contract 13N8512), DFG, and European ERANANOSCIENCE NET (project S5; ME 1256/11-1) grants toM.M.

Supporting Information Available: Electrode structure.Setup for dielectrophoretic deposition. Schematic view ofelectrodes dipped in a solution for a closed circuit and theequivalent circuit for the electric current between thetwo electrodes. Images of deposited Ag microstructures,depending on the applied dc voltage. Images of a silvermicrowire growing from the corner of one electrodes tothe other in the aqueous silver acetate solution. Movieshowing the deposition of silver micorwires from the aqu-eous silver acetate solution. Explanation of the Poissonequation approximation. Calculations for silver wires. Thismaterial is available free of charge via the Internet at http://pubs.acs.org.


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