Download Atom-size gaps and contacts between electrodes

APPLIED PHYSICS LETTERS
VOLUME 80, NUMBER 13
1 APRIL 2002
Atom-size gaps and contacts between electrodes fabricated
with a self-terminated electrochemical method
S. Boussaad and N. J. Taoa)
Department of Electrical Engineering and Center for Solid State Electronics Research,
Arizona State University, Tempe, Arizona 85287
共Received 18 September 2001; accepted for publication 29 January 2002兲
We describe a method to fabricate atomic-scale gaps and contacts between two metal electrodes.
The method uses a directional electrodeposition process and has a built-in self-termination
mechanism. The final gap width and contact size are preset by an external resistor (R ext) that is
connected in series to one of the electrodes. If 1/R ext is chosen to be much smaller than the
conductance quantum (G 0 ⫽2e 2 /h), a small gap with conductance determined by electron
tunneling is formed. If 1/R ext is comparable or greater than G 0 , a contact with conductance near a
multiple of G 0 is fabricated. © 2002 American Institute of Physics. 关DOI: 10.1063/1.1465128兴
Continued advances in nanoscience and nanotechnology
demand methods to fabricate various nanostructured materials and devices.1–3 This letter describes a self-terminated
electrochemical method to fabricate atomic-scale contacts
and gaps between two metallic electrodes. The conductance
of the contacts varies in a stepwise fashion with a tendency
to quantize near the integer multiples of the conductance
quantum (G 0 ), a phenomenon that has been observed in metallic nanowires fabricated by both mechanical4 and electrochemical methods.5 The conductance of the gaps is determined by electron tunneling. Electrodes separated with such
a gap may be used to connect a small molecule to the external world, but fabricating such electrodes is beyond the reach
of conventional methods.2 Several unconventional methods
have been reported.6 –9
Unlike the previously reported electrochemical
methods,8,9 the present method is not only simpler but also
has a built-in self-termination mechanism. The principle of
this method is sketched in Fig. 1. It starts with a pair of
electrodes separated with a relative large gap in an electrolyte or even pure water. When applying a bias voltage between two electrodes, metal atoms are etched off the anode
and dissolved into the electrolyte as metal ions, which are
then deposited onto the cathode. As we have found experimentally, the etching takes place all over the anode surface,
but the dissolved metal ions are guided by the electric field
and deposited onto the sharpest point of the cathode. Consequently, the gap decreases to the atomic scale and then completely closes as the two electrodes form a contact. In order
to fabricate an atomic gap or contact in a controlled fashion,
the etching and deposition processes must be terminated
promptly once a desired gap or contact is formed.
We introduce a simple self-termination mechanism by
connecting one electrode to an external resistor (R ext). The
effective voltage 共or overpotential兲 for etching and deposition is given by
a兲
Author to whom correspondence should be addressed; electronic mail:
[email protected]
V gap⫽
R gap
V ,
R gap⫹R ext 0
共1兲
where R gap is the gap resistance between the two electrodes,
and V 0 is the total applied bias voltage. R gap is determined by
electron tunneling across the gap and by ionic conduction
共leakage current兲 between the electrodes. Coating the electrodes with an insulating layer of epoxy can reduce the leakage current. The gap is initially large and the electron tunneling is negligible, so R gapⰇR ext , and V gap⬃V 0 , or the
entire applied voltage is used for etching and deposition.
Consequently, the etching and deposition processes take
place at the maximum rates. As the gap narrows, the tunneling current rises exponentially and R gap decreases, which re-
FIG. 1. 共a兲 Schematic drawing of the setup. Metal atoms etched off the left
electrode are guided and deposited onto the right electrode by applying a
voltage between the electrodes with an external resistor in series. As the gap
between the two electrodes shrinks, the gap resistance decreases, which
results in a drop in etching/deposition voltage and eventually terminates the
etching/deposition processes. 共b兲 Snapshots of an experiment that started
with a pair of 25 ␮m Cu electrodes separated with a ⬃20 ␮m gap.
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© 2002 American Institute of Physics
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Appl. Phys. Lett., Vol. 80, No. 13, 1 April 2002
S. Boussaad and N. J. Tao
2399
sults in a decrease in V gap 关see Eq. 共1兲兴 and, therefore, a
slowdown in the etching and deposition rates. Eventually,
when R gapⰆR ext , V gap⬃0, which terminates the etching and
deposition and results in a gap whose width depends on R ext .
If R ext is smaller than ⬃12.7 k⍀, a contact between the electrodes is formed and the tunneling is replaced with ballistic
transport.
The self-termination effect is further enhanced by the
exponential dependence of the etching and deposition current
density, J, on V gap , according to11
J 共 V gap兲 ⬀exp共 ␣ eV gap /k B T 兲 ,
共2兲
where ␣ is usually around 0.5, e is the electron charge, k B is
the Boltzman constant, and T is temperature.
The starting electrodes in our experiment were prepared
from a 25 ␮m Cu, Au, or Ag fibers 共99.999%兲 coated with
epoxy on a glass substrate. The initial gap between the electrodes was 10–20 ␮m, created by carefully cutting the metal
fibers. The electrodes were immediately covered by the
etching/deposition solutions 共e.g., pure water, KCl, HCl, and
H2 SO4 兲. R ext tested in the experiment ranged from 1 k⍀ to 1
G⍀. The etching/deposition voltage was supplied with a
function generator. The current was determined from the
voltage across R ext , which was monitored by an electrometer
共Keithley, model 617兲.
Figure 1共b兲 shows a few snapshots of the formation of an
atomic-scale contact. Applying a 1.2 V voltage (V 0 ) to the
circuit, electrochemical deposition does not occur immediately. Instead, it takes some induction time 共from tens of
seconds to a few minutes兲 before the deposition becomes
visible. Once the electrodeposition starts, it is rather fast and
highly directional with its sharp growing front pointing to the
anode. The growing front reaches the anode within a few
minutes and the process then terminates itself, which is controlled by R ext . We have systematically varied R ext in order
to form contacts of different sizes and gaps of various
widths, and monitored the conductance between the electrodes during the etching and deposition.
Figure 2共a兲 shows the conductance 共normalized against
G 0 兲 between two Cu electrodes during electrochemical etching and deposition in water with R ext preset at 3 k⍀ 共⬍12.7
k⍀兲. The initial conductance due to ionic conduction is negligibly small compared to G 0 . A few minutes after applying
a 1.2 V voltage, the conductance suddenly jumps to ⬃ 2G 0
and the deposition terminates itself as a contact is formed
between the electrodes. However, the initial contact breaks
within seconds and the conductance drops back to zero. The
drop in the conductance reactivates the deposition process,
and the contact with conductance near 1 G 0 is reformed a
few seconds later. While the conductance tends to stabilize, a
large noise 共sharp spikes兲 in the conductance is clearly visible. Zooming in, the noise reveals stepwise fluctuations in
the conductance between ⬃ 1 G 0 and ⬃ 0 G 0 关inset of Fig.
2共a兲兴, corresponding to a constant breakdown and reformation of the contact. We believe that electromigration of the
atoms near the contact causes the breakdown, which is then
reformed by further deposition. Since electromigration depends sensitively on the applied voltage, we have studied the
dependence of the noise on the applied voltage. Figure 2共b兲
shows an example of such studies. The conductance fluctu-
FIG. 2. Choosing a R ext⬍12.7 k⍀, an atomic-scale contact with quantized
conductance can be fabricated. 共a兲 is an example that shows the conductance
change during the formation of a contact 共R ext⫽3 k⍀ and V 0 ⫽1.2 V). 共b兲
shows a similar experiment except that the bias was reduced to 0.2 V from
1.2 V, 20 s after the formation of a contact. The reduction of the bias largely
eliminates the on–off fluctuations. A smaller R ext 共e.g., 1 k⍀兲 results in a
higher conductance contact and the conductance often increases in a stepwise fashion before reaching a final value 共c兲. The current through the contact is linearly dependent on the voltage across the contact 共d兲.
ates violently when setting the voltage at 1.2 V, but the fluctuations are significantly smaller after reducing the bias voltage to 0.2 V, which supports the electromigration
explanation.
We have formed a contact with conductance at a higher
value by using a smaller R ext . During the formation of the
contact, the conductance varies in a stepwise fashion that can
be recorded when the variation is slow enough 关Fig. 2共c兲兴.
We have measured the I–V characteristics of the contacts.
Figure 2共d兲 is an example of the I–V curves for a contact
with conductance near 1G 0 . The current is linearly proportional to the bias voltage, a simple Ohmic behavior.12
By increasing R ext above 12.7 k⍀, we have fabricated
atomic- scale gaps between the electrodes. Figure 3共a兲 shows
the conductance 共normalized against G 0 兲 in logarithmic scale
during the etching and deposition processes (R ext⫽1 M⍀).
The initial finite conductance is due to leakage current. Following the gradual increase in leakage is a jump in the conductance, which we attribute to the tunneling current that
changes exponentially with the gap width. The conductance
jump results in a sudden drop in the etching/deposition voltage and terminates the processes. The conductance, consequently, stabilizes at a finite value that depends on R ext .
Fluctuations in the conductance of the gaps are, in general,
much less than those in atomic-scale contacts 关e.g., Fig.
2共a兲兴, but stepwise fluctuations are often observed 关Fig.
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Appl. Phys. Lett., Vol. 80, No. 13, 1 April 2002
S. Boussaad and N. J. Tao
FIG. 4. Histograms of the terminal conductance with R ext preset at various
values. Despite the run-to-run variations, the trend that the terminal conductance increases as 1/R ext is clearly shown.
FIG. 3. Choosing a R ext⬎12.7 k⍀, an atomic-scale gap between two electrodes can be fabricated. 共a兲 shows an example with R ext⫽1 M⍀, and V 0
⫽1.2 V. The conductance 共in natural log scale兲 increases sharply and then
stabilizes at a final value. 共b兲 is an experiment under similar conditions. The
large fluctuations may be attributed to the etching and deposition of individual atoms in the gap. 共c兲 is the I–V characteristic that shows an exponential dependence of the tunneling current on the bias for a gap formed
with R ext⫽10 M⍀, and V 0 ⫽1.2 V.
3共b兲兴. Similar stepwise fluctuations have been observed by us
previously and attributed to the etching and deposition of
individual atoms.10
We have measured the I – V gap characteristics of the gaps
关Fig. 3共c兲兴. The exponential dependence of the current on the
bias is in sharp contrast to the simple Ohmic behavior of the
atomic-scale contacts shown in Fig. 2共d兲. The current is also
several orders of magnitude smaller than that for the atomicscale contacts. Repeated cycling of the bias voltage does not
show any hysteresis in the current, indicating that the current
is not due to polarization or electrochemical reactions. Furthermore, the exponential dependence is in good agreement
with electron tunneling across a square barrier. The above
observations lead us to believe that the I – V gap characteristics
of the gaps are due to electron tunneling.
We have varied R ext from 1 k⍀ to 10 M⍀ and found that
the conductance of the terminal contact or gap decreases as
R ext increases. Figure 4 plots the histogram of some of the
measurements, which shows clearly the trend despite run-torun variations. We have attempted to use R ext greater than 10
M⍀ 共e.g., 1 G⍀兲, but with less success because the tunneling
current becomes comparable to the leakage current. This
limit in R ext may be overcome by further reducing the leakage current using microfabricated metal electrodes that have
smaller exposed electrode area.
In order to examine the possible effects of oxide formation, we have carried out the experiment with Cu electrodes
in 0.5 M HCl and in 0.5 M H2 SO4 . The dependence of the
final contact or gap conductance on R ext is similar, but the
etching and deposition are significantly faster for a given
applied voltage in the acid solutions. Although the increased
etching and deposition rates can speed up the fabrication
process, the increased ionic concentration results in a higher
leakage current. We have also performed the experiment with
Au and Ag electrodes. Unlike Cu and Ag that work in both
electrolytes and pure water, Au cannot be etched easily in
water and electrolytes such as 0.2 M HCl must be used.
In summary, we have demonstrated an electrochemical
method to fabricate atomic-scale gaps and contacts between
two metal electrodes. In contrast to the previously reported
methods, the present method has a self-termination mechanism that allows us to quickly form a desired gap to fit a
small molecule and an atom-size contact with quantized conductance.
The authors would like to thank AFOSR 共F49620-99-10112兲 and NSF 共CHE-9818073兲 for financial support.
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