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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].
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v. Nano Lett. 2003, 3, 1019–1023. (b) Monica, A. H.; Papadakis, S. J.; Osiander, R.;
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552 DOI: 10.1021/la902026e
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.
Langmuir 2010, 26(1), 552–559
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
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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.
554 DOI: 10.1021/la902026e
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.
556 DOI: 10.1021/la902026e
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,
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Ranjan et al.
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.
Langmuir 2010, 26(1), 552–559
Article
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
557
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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
Ranjan et al.
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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