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 nanotubes1 (CNTs) and nanowires2 are two of the most important bottom-up materials for nanocircuits. 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. Dielectrophoresis (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 ones5 in the solution phase. DEP is also applied in biotechnology for cell sorting6 and localization7 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 *Corresponding author. Tel: þ49-(0)351-46331462. Fax: þ49-(0)-35146331422. 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 Medicine and Biology Society 1998, 20, 1079–1082. (b) Morgan, H.; Hughes, M. P.; Green, N. G. Biophys. J. 1999, 77, 516–525.
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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 dielectrophoretic-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 solution 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 parameters 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 (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.
Published on Web 11/19/2009
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only processes occurring in the vicinity of the electrode surface determine the wire formation; the bulk solution condition has no effect on the assembly. This process of ac dielectrophoresis is quite different from the electrolytic deposition occurring during the direct current (dc) case. We also discovered that there exists an optimum frequency window within which the wires are formed. When the applied frequency lies outside of this optimum window, wire assembly does not occur. The applied potential also has to exceed a minimum threshold for assembly to occur.11
Materials and Methods Palladium acetate (Pd(CH3COO)2, Pd(Ace)) stock solution was prepared as reported before.14 Silver acetate (Ag(CH3COO), Ag(Ace)) stock solution was prepared by dissolving 5 mg of Ag(Ace) in 1 mL of doubly distilled water. The resulting solution was then placed in an ultrasonic bath for 5 min. Afterwards, the solution was centrifuged for 5 min at 2000g and the supernatant was taken. The collected stock solution of Ag(Ace) was diluted to 1:10 for each experiment. The reason for growing Ag microwire is the large diameter and the bright color of the elemental silver, which could be observed via an optical microscope (Carl Zeiss Axiovert 200 and Carl Zeiss Axiovert 200M). During an experiment, 15 μL of diluted Ag(Ace) solution was placed between the electrodes over a transparent glass substrate and an ac potential was applied. The experimental setup is shown in Figure 2 of Supporting Information. The entire process was monitored using a light microscope. Gold (Au) electrodes with different configurations were used over a glass substrate.15 The distance between the electrodes depended on the configuration used and varied from 2 to 10 μm (Figure 1, Supporting Information). To grow palladium nanowires, gold electrodes over silicon substrate were used. Nanowires were characterized by atomic force microscopy (AFM) using a NanoScope IIIa (Digital Instruments) operated in tapping mode. A low-voltage scanning electron microscope (Zeiss Gemini 982 equipped with a LaB6 cathode) was used for the characterization of the nano- and microwires.
Results and Discussion Nanowire Deposition. To grow palladium nanowires, Pd(Ace) stock solution was diluted by 1:40 and 15 μL of the diluted solution was placed between gold microelectrodes that were separated by 5 μm and a peak-to-peak voltage of 2.0 V was applied. The frequency of the applied ac potential was 30 kHz. The current in the circuit was observed with an oscilloscope, and the connection between the electrodes was detected by a sudden increase in the current, which was used as a trigger to switch off the applied voltage. Figure 1a shows the morphology of the formed wires. The wires are about 20 nm in height, extremely straight, and dendritic in shape. We observed that a change in the morphology of the wires could be achieved by changing the frequency of the applied ac potential. The same dilution and voltage conditions with a frequency of 300 kHz give extremely thin, branched wires that are about 5 nm thick14 (Figure 1b). Hence, we can conclude that the deposition process is governed by the frequency of the applied electric field. Both nanowires shown in Figure 1 were grown on silicon substrates. Detailed work describing the change in the morphology of the nanowires with the frequency of an ac field will be published elsewhere.16 Microwire Deposition. As stated before, silver microwires were grown to gain insight into the process. For the experiment, 15 μL of the diluted stock solution was placed in between the gold (15) Refer to the Supporting Information. (16) Ranjan, N.; , Mertig, M.; , Pompe, W., in preparation.
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Figure 1. Palladium nanowires formed via dielectrophoresis with different applied ac field frequencies. (a) AFM image of dendritic palladium nanowires deposited at 30 kHz. (b) Thin branched palladium nanowires deposited at 300 kHz, and (d) they are about 5-10 nm thick. (c) The structure in (a) is characterized by perfectly straight segments and has a constant height of around 20 nm.
microelectrodes over a glass substrate. An ac potential of 10 V and a frequency of 30 kHz were applied between the neighboring electrodes (Figure 1b, Supporting Information), which were about 7 μm apart. The entire microwire growth process was observed via light microscopy. We observed that the wire assembly can be divided into two different stages, viz., the nucleation and the growth phase. During nucleation, the wire begins to grow stochastically from one of the electrode surfaces, and during the growth phase, it propagates from one electrode to the other. It should be noted that nucleation does not occur everywhere over the electrode surface but only at few selected points. Experimentally, such selective nucleation regions at the electrode surface can be observed in Figure 2 (shown by an arrow at time t = 0 and DOI: 10.1021/la902026e
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Figure 3. Cation with the negatively charged surrounding counterion cloud in an aqueous solution. In the absence of an electric field, both charge centers match each other. An external electric field displaces the charge centers, giving rise to an electric dipole moment. Δþ is the net excess positive charge developed in the space as a result of the migration of the charge centers (Δþ = Δ-), and R is the polarizability of the system. Figure 2. (a) Optical images showing nucleation and growth of the silver microwires with the corresponding time scale. Arrows show regions of the electrode that serve as nucleation points. (b) Silver microwire nucleating at one electrode and growing toward the other (t = 24.4 s). (c) SEM image of a palladium nanowire grown between two gold electrodes. (b, c) Arrows mark the curved route taken by the wire following the electric field lines, showing that the same process occurs on both the micro- and nanoscale. (d) Magnified SEM image of the palladium nanowires depicted in image c. For these experiments, diagonally arranged electrodes were used (Figure 1b, Supporting Information).
0.4 s). We emphasize that the kinetics is nucleation-dominated because the growth phase is quite fast. Once the nucleation at a particular location over the electrode surface has occurred, wires grow extremely fast and are connected to the next adjacent electrode. Figure 2a shows the time sequence of the growing Ag microwire, and from it the average velocity of the moving front is calculated to be about 1 μm/s (movie clip 1, Supporting Information). We stress that the observation of the growing silver microwire via light microscopy gave us qualitative information on the growth process of palladium nanowires occurring between the electrodes under similar conditions. Dielectrophoresis Model. According to the Debye-H€uckel theory,17 in nonideal solutions the formation of an ioncounterion complex is energetically favored. This complex behaves as a single neutral entity. As shown in Figure 3, the ioncounterion complex can be visualized as a central ion surrounded by the oppositely charged counterions. In an equilibrium situation, the positive charge center overlaps with the surrounding oppositely charged center.18 When an electric field is applied to the solution, the positive charge centers move in the direction of the field and the negative charge center shifts in the opposite direction. This leads to the formation of an electric dipole. This induced dipole may now feel a dielectrophoretic force and move in the solution. Throughout the article, we call these ion-counterion complexes as ‘particles’ undergoing dielectrophoresis in the aqueous solution. When the direction of the field is reversed, the induced polarization is also reversed. The effect is similar to the polarization of neutral colloidal particles in a solution. The strength with which the counterion cloud is bound to the central ionic core and its flexibility to become distorted with the external applied field determine the strength of the dipole moment and its (17) Compton; R. G.; Sanders, H. W. Electrode Potentials, Oxford University Press Inc.: New York, 1996; Chapter 2-3. (18) Robison, R. A.; Stokes, R. H. Electrolyte Solutions, 2nd ed.; Butterworth Publications limited: London, 1965.
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relaxation time constant. The response of the induced dipole to the frequency of the external applied field refers to the dielectric dispersion of the system. A similar mechanism has been previously discussed to explain the ionic polarization of macromolecules in polyelectrolytes19 and the dielectrophoretic response of charged biomolecules such as DNA.20 When placed in an ac electric field, these dipoles experience the dielectrophoretic force.21 Approximating these dipoles as spheres, the dielectrophoretic force is given by22
FDEP
εm ERMS 2 ¼ 4πRe½KðωÞa r 2 3
! ¼ ΓVrðFE Þ
ð1Þ
Here, εm is the permittivity of the medium, a is the radius of the sphere, 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 the volume of the dipole, and FE (= εmERMS2/2) is the electric energy density. Equation 1 states that the dielectrophoretic force is proportional to the volume of the particle (FDEP V). When the particle diameter is reduced, for instance, from the micro- to the nanometer scale, the volume decreases by 9 orders of magnitude and so does the force. Thus, to overcome thermal fluctuations and friction, very high electric field magnitudes and inhomogeneities are needed in order to assemble nanodimensional particles. According to eq 1, the dielectrophoretic force is also proportional to the gradient of the electric energy density (FDEP r(FE)). A spatial plot of (r(FE)) at any instant in the growth process gives the distribution of the dielectrophoretic force. This fact has been used in the analysis shown in Figures 4 and 5. We discuss now the energetics involved in the dielectrophoretic deposition process. All of the calculations presented are for the experimental condition and the electrode configuration shown in Figure 2. An ion dissolved in water has a thermal energy given by 1.5kBT, which corresponds to approximately 38 meV at room temperature 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 by eq 1) could be simplified as FDEP = -rUDEP = r(2πa3εmErms2). This leads to UDEP = -2πa3εmErms2. The dielectrophoretic (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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Figure 4. (a) Distribution of the scaled electric field and (b) the gradient of the electric energy density at a particular instant of growth over the entire substrate. The electric field is enhanced at the growing tip and at the electrode asperities; it decays gradually by moving away from these locations. The gradient of the energy density is negligible over the entire substrate but intensifies to extremely high values (>6000) at the tip and the electrode asperities, as shown by arrows (b). This favors the process of nucleation and growth. The field distributions have been calculated 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 a particular instant of wire growth. For the dc field, the electric field causing the deposition has sufficiently high values behind and in between the growing tips (shown by the arrows in image a). This leads to a random distribution over the entire electrode surface, as shown experimentally in image c. For the ac field, the dielectrophoretic force has extremely high values in an extremely localized space around each tip 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 a patterned deposition, as shown experimentally in image d. The electrode distance is ∼10 μm.
energy gain, causing ordered assembly, must exceed the randomizing effect of the thermal energy. A peak ac voltage of Vapplied = 10 V is applied between electrodes that are L = 7 μm apart. This gives an average field strength (Erms = Vapplied/(2)1/2Lκw) of about 1.27 104 V/m, where κw is the dielectric constant of water Langmuir 2010, 26(1), 552–559
(κw = εw/ε0). The average ordering dielectrophoretic energy for a hydrated silver ion with a radius23 of about 341 pm is about (23) Schreiber, L.; Elshatshat, S.; Koch, K.; Lin, J.; Santrucek, J. Planta 2006, 223, 283–290.
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1.7 10-7 meV for the bulk solution, which is around 8 orders of magnitude smaller than the randomizing thermal energy. Hence, it seems that energetically such subnanometer-sized particles will primarily undergo random motion in the solution because the dielectrophoretic energy existing in the bulk solution is too small to facilitate the ordered deposition required for the growth of the wires. Therefore, a simple explanation by energy considerations does not explain the wire assembly, and other effects should also be taken into account. We found that the additional effect of a potential drop across the double layer and local electric field enhancements at electrode asperities play important roles in the wire assembly, as is discussed below. Wire Growth Controlled by Field Enhancement. When an electrode is dipped into an electrolyte, a double layer (DL) is assumed to form according to the Gouy-Chapman model24 at the electrode/electrolyte interface. Shown in Figure 3 of the Supporting Information is the equivalent circuit for the current flow between the two electrodes dipped into a solution. The DL formed at each electrode acts as a capacitor, and the solution behaves as a resistor in series. The thickness of the DL or the Debye length (Δx) is given by the expression25 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi εw kB T 0:3 Δx ¼ ≈ pffiffiffiffiffiffi nm 2n0 z2 e2 C
ð2Þ
where εw is the permittivity of water, kB is the Boltzmann constant, T is the temperature, n0 is the ion number density, z is the charge on the ion in units of electronic charge e, and C* is the concentration of the ions in mol/L. Using this expression and C* = 1.6 mM (concentration of the silver ions15), we get a Debye length or diffusion layer thickness of 7.5 nm. The voltage drop across the double layer can be estimated to be Vapplied VDL ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 þ jZsol =ZC j2 where ZC and Zsol are the impedances of the capacitor and the resistor, respectively. At an electrode distance of L = 7 μm and a frequency of 30 kHz, the impedances can be estimated to be ZC = 5.76 10-5 Ω m2/A and Zsol = 4.18 10-4 Ω m2/A, where A is the representative cross-sectional area of the array.15 Thus, about 13% of the applied voltage drops at each of the capacitors. This makes the voltage drop across each of the DLs to be 1.3 V for an applied peak voltage of 10 V. The corresponding average electric field within the DL can be estimated to be ERMS = VDL/(2)1/2κwΔx ≈ 1.61 106 V/m. The dielectrophoretic energy resulting from this value of the electric field corresponds to an energy of about 2.8 10-3 meV. This is 4 orders of magnitude higher than the value calculated for the bulk solution but still less than the randomizing thermal energy. Therefore, there should be a second mechanism causing an additional field enhancement. We assume that the electrode asperities at the tips of the growing wire lead to an increase in the local electric field by many orders of magnitude. Depending on the radius of curvature of the tips, the electric field and the gradient of the electric field energy in the vicinity of the tips are many orders of magnitude higher than the far-field values. Therefore, the dielectrophoretic energy in the near field can be expected to exceed the random thermal energy (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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and so lead to ordered assembly. To understand the effect of electrode asperities and tip radius on the electric field and electric energy density distribution, we performed a finite element method (FEM) calculation at a particular instant of growth over a substrate as shown in Figure 4. In this simulation, a potential of 2 V was applied to one of the electrodes, the other being grounded. The Poisson equation was solved over the entire area (Fcharge_density = 0, κm = 1). Because the distance between the electrodes in the simulation does not correspond to actual distances between the electrodes in the experiments, the electric field values obtained are normalized to the external electric field. The normalizing electric field (E0) shown in Figures 4 and 5 is the one that takes into account the scaling of the dimensions of the modeled geometry with respect to the dimensions of the experimental substrate. The simulation thus provides 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 the movement of particles in the solution. In the dc field, the electric field distribution |E| governs the movement of ions in the solution and hence the deposition pattern is governed by the field distribution (|E|). In the ac field, dielectrophoresis governs the movement of neutral particles (ion-counterion complex in our case) in the solution and hence the deposition pattern is governed by the distribution of the gradient of the electric field density (|r(FE)|). Hence, the plots depict the qualitative difference for the deposition taking place in the solution during the dc and ac fields. We stress that the simulations just show the spatial distributions of |E| and |r(FE)| at a particular instant of deposition, dependent only on the instantaneous geometry of the electrodes and wires. The additional effects of the double layer and frequency dependence are taken into account by breaking the continuous media into three different parts, viz., the two double layers at the electrodes (acting as a capacitor) and the aqueous medium between the electrodes (modeled as a resistor) as discussed before. The Poisson equation has been applied as an approximation to a quasi-stationary solution of the time-dependent electric field, assuming that the characteristic wavelengths of the field variations are small in comparison to 2πc/ωRe[n(ω)] ≈ 2πc(2ε0/ω 3 σ)1/2, where c is the light velocity, ω = 2πf is the frequency of the dielectrophoretic excitation, n(ω) is the complex diffraction coefficient, ε0 = 8.854 10-12 A s/V m is the dielectric vacuum permittivity, and σ is the solvent conductivity. For f = 30 kHz and σ = 1.6 10-2 Ω-1 m-1, we get 2πc/ωRe[n(ω)] ≈ 145m. That means that the quasi-stationary approximation can be applied for the experimentally interesting frequency range. (For more details, see Supporting Information.) Figure 4 depicts both processes of nucleation (asperities at the surface of the right electrode) and growth (wire tip at the left electrode). A close observation of Figure 4a,b shows that although both the electric field |E| and the gradient of the electric field energy density |r(FE)| intensify at the electrode asperities and at the tip, |r(FE)| is extremely high for these geometries and immediately falls to extremely low values even as we slightly move away from these regions (Figure 4b). Because the dielectrophoretic force is proportional to |r(FE)| (eq 1), an extremely high dielectrophoretic force exists in these regions, bringing about nucleation and growth. No dielectrophoretic deposition occurs in any other region even in the vicinity of the substrate because the force values are extremely low. Hence, the deposition process is perfectly self-aligned. The enhanced electric field |E|, on the contrary, has a much broader distribution (i.e., the field drops gradually from the tip to the bulk values) (Figure 4a). Hence in a dc case even if the field enhancement occurs at these locations, Langmuir 2010, 26(1), 552–559
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various other locations in the vicinity of these geometries are also prone to deposition; consequently, we get a structureless deposition over the entire electrode. On the basis of our calculations, we propose a model for the particle movement and deposition taking place in an ac field. In bulk solution, the thermal energy is much higher than the dielectrophoretic energy and hence it keeps the concentration homogeneous throughout the solution. This is equivalent to saying that there is an absence of any dielectrophoretic-forceassisted drift of particles in the bulk solution; the force being too weak, the particles undergo random Brownian motion. However, field enhancement occurs at the electrodes, which leads to selfassembly. There exist two major mechanisms for field enhancement, viz., that due to double-layer formation and the tip radius. Within the double layer, the field gradients are about 2 to 3 orders of magnitude higher than the bulk solution, and the resulting dielectrophoretic energy will be about 4 to 6 orders of magnitude higher in this region. However, this value is less than that required to bring about the ordered deposition because the thermal energy is still higher. However, additional field enhancement occurs at the tip of the growing wire and at the electrode asperities, which may lead to a manifold increase in the dielectrophoretic force in these regions. The high dielectrophoretic force would increase the flux of particles from the bulk solution to the DL. Within the DL, the ions dielectrophoretically drift toward the electrodes and are able to approach the electrode at a distance limited by its solvation shell. It is assumed that within the outer Helmholtz plane (OHP)24 only a monolayer of solvation exists between the ion and the electrode. The metal ions may then be reduced via electron transfer from the electrode to the cation and are deposited there as part of the growing tip. Electrochemical reduction happens instantaneously at each electrode when they act as a cathode. Charge transfer (reduction/oxidation) occurs only at the electrode surface, not throughout the solution (movie clip 1, Supporting Information). The field enhancement due to double-layer formation is dependent on the frequency of the applied ac field. The percentage of the voltage drop across the diffusion layer decreases with increasing frequency, and at 1 MHz, only 0.4% of the applied voltage drop at each DL.15,26 This corresponds to a dielectrophoretic energy gain of about 2.66 10-6 meV in the DL, which is about 3 orders of magnitude lower than when the frequency is 30 kHz. Hence by varying the frequency, one may be able to change the concentration of particles locally at the tip, which may lead to a different morphology of the assembled structure (Figure 1). Patterning. Wire growth initiated by a random distribution of asperities at the electrode surfaces is characterized in the later stages by typical pattern development. The most striking features are the so-called tip splitting12 and shadowing, which can also be observed during nanowire growth (Figure 1). Figure 5a,b shows the FEM simulation of a split tip and the relative stability of the daughter branches. The region close to the electrodes with a small 1 (26) The complex impedance of a capacitor is ZC ¼ jωC , and it depends on the frequency (ω) of the applied AC electric potential; the Ohmic resistance of the solution is Zsol (constant with respect to ω); f 1 VC ¼ Vapplied j2 þ Zsol =ZC j Vapplied VC ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 þ ðϖCZsol Þ2 Vapplied lim VC ¼ 0; lim VC ¼ ωf¥ ωf0 2
Thus at low frequencies, the applied voltage (Vapplied) drops equally at the two capacitors and no voltage drops along the solution (Zsol). At very high frequency no voltage drops along the capacitors and the complete voltage drops across the resistance Zsol in the solution.
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Figure 6. Ag microstructures grown at different frequencies and a constant peak voltage of 10 V. Each window (a-f) shows the electrode structure after the application of a fixed frequency for a fixed period of time. (See the legends.) (a-c) Electrode structure after applying frequencies of 1 MHz, 500 kHz, and 300 kHz for 1 min each. (d) Electrode structure 1 s after the application of a frequency of 100 kHz. (e) Structure after the application of a frequency of 100 kHz for 1 min. (f) Structure after the application of a frequency of 30 kHz for 0.5 s. The electrode distance is ∼4 μm.
radius of curvature R will cause a high dielectrophoretic (DEP) force, which scales as (FDEP E2/R), whereas the electrostatic force scales with the local electric field (FE E). When an ac potential is applied, the DEP force drives the deposition. It has high values at the tip but drops to extremely low values in regions around and in between the tip (shown by the arrows in Figure 5b). Such a configuration favors the self-alignment of the depositing particles and leads to the stable growth of both branches. No particle deposition will occur in the vicinity of or in between the tips. When a dc potential is applied, the electrostatic force drives the deposition. As shown by the arrows in Figure 5a, the field intensity |E|/E0 at the newly formed tips has high values. Besides this, the regions around and in between the tips also have relatively high values. Hence, particles will be deposited homogenously not only at the tip but also in its vicinity as shown by the arrows. This will lead to a deposition over the entire area. Experimental results are shown in Figure 5c,d. Figure 5c shows growth in the presence of a dc voltage of 0.5 V between the electrodes immersed in a Ag(Ace) solution. A dense, structureless film covering the entire electrodes can be observed. It grows without any characteristic pattern. In Figure 5d, much higher voltages (10 V) have been applied between the electrodes under an ac driving frequency of 30 kHz. We see in the Figure the growth of typical dendritically shaped Ag microwires. Between the larger dendrites, there are shadowed regions of diminished Ag deposits. Optimal Process Window. We found that very high frequencies prevent wires from growing, and at low frequencies (the extreme case being the dc setup) random, structureless deposition was observed over the entire electrodes. In the frequency window within 30-500 kHz, patterned wires could be formed. The wire structure and morphology change drastically within this frequency window (Figures 1 and 6). DOI: 10.1021/la902026e
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For this experiment, a parallel set of electrodes (Figure 1c, Supporting Information) on a glass substrate was used with an electrode distance of 4 μm. An ac signal of 10 V was applied between the electrodes corresponding to the electric field value of Erms = 2.26 104 V/m. Different frequencies (1 MHz, 500 kHz, 300 kHz, 100 kHz, and 30 kHz) were applied chronologically for 1 min each, as shown in Figure 6. Each of the panels in Figure 6a-f shows the electrode structure after the application of the particular frequency for the indicated period of time. As shown in Figures 6a,b, no wire formation happened at the higher frequencies of 1 MHz and 500 kHz, respectively, even after 1 min. An extremely small assembly could be observed at a frequency of 300 kHz (Figure 6c). The growth kinetics is faster at 100 kHz, and we could see the metal assembling immediately between the electrodes (Figure 6d), which grew with time to give a denser structure after 1 min (Figure 6e). The growth kinetics was extremely fast at a frequency of 30 kHz, and a dense structure was formed between the electrodes immediately within a fraction of a second (Figure 6f). This shows that the process builds up as we move from high frequencies to low frequencies. Because of the parallel structure of the electrodes, the wires are confined within them so they grow laterally and join with the neighboring branches, giving a dense structure as shown in Figure 6e,f. The frequency region can be divided into three domains with respect to the dielectrophoretically led assembly, viz., the highfrequency domain, the optimum frequency region at which patterned wires are formed, and the extremely low frequency domain. Both particles and media have their own characteristic dielectric relaxation times. At high frequencies, the time period of the external electric field is smaller than the relaxation time of the dielectric particle. At such frequencies, there exists a constant phase shift between the external electric field and the polarization of the particle. This leads to negative dielectrophoresis, thus inhibiting the assembly. Within the optimal frequency window, the counterion cloud has enough time to react to the external field and hence dipoles are formed in phase with the external field. These dipoles then drift into the dielectrophoretic force field and hence assembly can occur. At very low frequencies, we fail to form wires but get random depositions. This could be explained by the fact that in an ac field the positive and negative charge centers of the ion-counterion complex can be assumed to vibrate about the mean central position (thus bringing about the time-dependent dipole moment) and hence the net electrostatic drift of either of the charge centers can be assumed to be zero. This zero electrostatic drift can be assumed to occur only when the displacement of the ion (and also the surrounding counterion) in the half cycle (δxhc) is small enough that the electric field can be considered to be homogeneous in that region [i.e., (E(x þ δxhc) ≈ E(x)]. When the ionic displacement (δxhc) over the half cycle is larger than the distance over which the field can be considered to be homogeneous, the ion may not return to the original position in the next half cycle. Thus when E(x þ δxhc) 6¼ E(x), there would be a net electrostatic drift of ions even in the ac case. In the microelectrode systems, high spatial field inhomogeneities exist. Hence the electrostatic drift of the ions can commence at low frequency because the net ionic displacement in the half cycle is inversely proportional to the applied frequency (δxhc 1/f). Once the movement of the ions is governed by the electrostatic drift rather than the dielectrophoretic drift, metal deposition can no longer occur in a patterned way on the basis of the selfalignment mechanism due to near-field enhancement at the tip, as discussed in Figure 5b. Consequently, the wire-formation process is disturbed, which requires self-aligned material deposition brought about only by the dielectrophoretic force. 558 DOI: 10.1021/la902026e
Ranjan et al.
Figure 7. Ag microwires grown at a different potential at a constant frequency of 30 kHz for the stated period of time. (a) The electrode 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 the application of 5.0 V. The electrode distance is ∼4 μm.
This may account for the random particle deposition at low frequencies. The deposition of the nano- and microwires was found to depend on the magnitude of the applied ac field, and we found that in each case a minimum threshold of electric field (and hence the dielectrophoretic force) is necessary to initiate the process.11 We estimated the minimum threshold values of the electric field required for the dielectrophoretic deposition of patterned Ag microwires. In this experiment, we applied a 30 kHz frequency and varied the applied voltage between a parallel set of electrodes with a 4 μm distance. We applied in ascending order for 1 min each of the following voltages: 0.5, 1.5, 3.0, and 5.0 V. Nothing appreciable happened for the first three values, as shown in Figure 7a. The wires were immediately seen to be formed when the applied voltage was 5.0 V (Erms = 1.13 104 V/m). Figure 7b shows that the wires formed immediately within the first 1.5 s of the application of 5.0 V. The wires grew denser with time, and after 1 min, the entire space between the electrodes was covered by them. This shows that there exists a threshold voltage/field below which the kinetics is too small to detect anything noticeable. The electric field is calculated by assuming flat electrode surfaces placed opposite to each other and gives a value for the bulk solution. A detailed calculation individually taking into account the potential drop across the double layer and the bulk solution is reported in the Supporting Information. Local geometrical inhomogeneities at the electrode surface and growing tips enhance the field up to various extents, depending on their shape, and bring about localized nucleation and growth wherever the threshold is crossed. These two experiments prove that noticeable assembly occurs at some optimized values of frequency and voltage. When any of these parameters lie outside their respective domains, no assembly is observed.
Conclusions We have introduced a dielectrophoretic model for the growth of metallic nanowires from their aqueous salt solution. Most of the experiments were performed on the growth of silver microwires, observed in situ using a light microscope. Ions with the surrounding counterion clouds behave as neutral particles responding to the dielectrophoretic force field. The assembly could be divided into nucleation and growth phases. Kinetic parameters related to these processes have also been reported. Our calculations show that the dielectrophoretic assembly is not feasible by a simple energy consideration, with the thermal energy being orders of magnitude higher. An additional effect of the electric field enhancement is needed, which is brought about by two different factors. First a double layer formed at the foremost front of the growing electrode seems to enhance the field 2 to 3 orders of magnitude higher than that of the bulk. Second, the electrode asperities and the growing tip enhance this field by many orders of Langmuir 2010, 26(1), 552–559
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magnitude because of their extremely small radius of curvature. These two factors have a profound effect on the growth whereas the conditions of the bulk solution have no effect on the assembly process. The thermal energy is too high throughout the bulk solution and keeps the concentration homogeneous. We showed that there exists an optimum window of frequency within which the wires can assemble. There also exists a threshold voltage below which the wires fail to form. This process of nanowire formation has potential implications on the future development of the bottom-up assembly of nanomaterials. Beyond the formation of metallic nanostructures, there could be many other options for the organized deposition of nanostructures by dielectrophoresis. A proper understanding of the theory will help in exploiting the process over much wider areas of bionanotechnology. Acknowledgment. We are grateful to Daniel Sickert and Gerald Eckstein (Siemens AG), Munich, Germany, for the preparation of the electrodes. We thank Anja Bl€uher for her
Langmuir 2010, 26(1), 552–559
Article
support with SEM imaging and Markus P€otschke for help with the FEM simulations. This work was supported by BMBF (contract 13N8512), DFG, and European ERA NANOSCIENCE NET (project S5; ME 1256/11-1) grants to M.M. Supporting Information Available: Electrode structure. Setup for dielectrophoretic deposition. Schematic view of electrodes dipped in a solution for a closed circuit and the equivalent circuit for the electric current between the two electrodes. Images of deposited Ag microstructures, depending on the applied dc voltage. Images of a silver microwire growing from the corner of one electrodes to the other in the aqueous silver acetate solution. Movie showing the deposition of silver micorwires from the aqueous silver acetate solution. Explanation of the Poisson equation approximation. Calculations for silver wires. This material is available free of charge via the Internet at http:// pubs.acs.org.
DOI: 10.1021/la902026e
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