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Suspended Gold Nanowires:
Ballistic Transport of Electrons
Kunio Takayanagi
Tokyo Institute of Technology, Graduate School of Interdisciplinary Science and Technology,
4259 Nagatuta, Midori-ku, Yokohama, 226-8502 Japan

Yukihito Kondo1) and Hideaki Ohnishi 2)
Particle Surface Project of ERATO, JST,

Abstract
Gold nanowires a few atomic diameters
wide are observed by ultra-high vacuum transmission electron microscopy, and their conductance measured simultaneously using a scanning tunneling microscope built into the electron microscope. A strand of gold atoms suspended between electrodes is directly observed
to have a conductance of 2e2/h (=(12.9 kΩ)-1),
where e is the electron charge and h is Planck’s
constant. This conductance quantization resultsfrom ballistic transport of electrons through a
conduction channel of the strand.

strands of gold atoms are coiled around theaxis of the nanowire.14)

2. Conductance quantizationkΩ)-1). Moreover, the conductance is no longer
dependent on the length of the wire. The conductance of a narrow constriction formed between two electrodes is generally understoodby the Landauer formula:15)
G = (2e2/h)∑Tj,(1)where Tj is the electron transmission probability for the j-th conductance channel. Since
Tj=1 for ballistic transport, G=(2e2/h)N for ananowire (constriction) with N conduction
channels.
Provided the constriction has width W, as
shown in Fig. 1, the momentum px and py of

1. Introduction

Every material has a definite conductivity,
so that the conductance of a wire is inversely
proportional to the length of the wire. On theother hand, as the length scale of the wire is
reduced to the mean free path of electrons,
the electron transport mechanism changes fromdiffusive to ballistic, as shown in Fig. 1. When
the width of the wire is further reduced to thenanometer or Fermi wavelength scale, the conductance between electrodes connected by thenanowire is quantized in steps of 2e2/h (= (12.9As the scale of microelectronic engineering continues to decrease, the nature of electron transport through one-dimensional nanometer-scale channels such as quantum
wires1) and carbon nanotubes2,3) has become
important. Quantum point contacts (QPCs) are
structures in which a “neck” of atoms a few
atomic diameters wide bridges two electrodes.
Metal QPCs were formed by connecting two
metal electrodes using a scanning tunnelingmicroscope (STM)4-7) a mechanically controllable
breaking junction (MCB) 8-11) and relay switch12)geometry. These QPCs typically display a
stepwise conductance change as the contact
is withdrawn, with a conductance step of 2e2/h, where e is the electron charge and h is
Planck’s constant.
A metal QPC’s structure and conductancewere directly observed by using an ultra-highvacuum transmission electron microscope(UHV-TEM) which has a miniaturized STM atthe specimen position. A gold nanowire formed
between the gold STM tip and gold sample was
directly observed by TEM at atomic resolution,with the conductance of the QPC measured
simultaneously. The gold QPC showed conductance quantization with a step of 2e2/h during
withdrawal of the STM tip.13) Gold nanowires
have helical multi-shell structures, in which

Fig. 1 Diffusive (a) and ballistic (b) transport of electrons in one-dimensional wires. λ is the mean free path of theelectrons, and λF is the Fermi wavelength.

the electron waves confined in the wire is quantized. The momentum is given by hn/2W, for

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Fig. 2 STM-TEM instrument. A miniaturized scanning tunneling microscope (STM) is included at the specimen position of a UHV high-resolution transmission electron microscope(HR-TEM). A nanowire is formed between the gold STM tip and a gold substrate.

integral values of n. Then, electrons of energy
E (mass m) can not be transported through theconstriction if pz2=2mE-(px2+py2) is negative. The
largest number of n defines the number ofconduction channels N. N is determined so thatthe maximum px can not exceed h/λF, where λF
is the Fermi wavelength of the electrons in theelectrodes. For a potential difference of eV between the electrodes, electrons having energies from Ef to Ef+eV contribute to the conduction current, where Ef is the Fermi energy. Taking spin degeneracy into account, then, G=2e2/
h is obtained for each conduction channel. The
number of conduction channels depends on
the width of the nanowire, so the conductancedecreases stepwise as the nanowire isthinned.16)
Conductance quantization has been discussed theoretically more rigorously for atomicnanowires.17-19) Transmission properties that depend on electron-electron interactions or spin
degeneracy are interesting. The former reduces
Tj,20) while the latter produces the e2/h conductance step.21)

3. UHV transmission electron
microscope with built-in STM
Fig. 3 Electronic circuit for measuring the conductance of a gold nanowire. A gold substrate deposited on a Cu rod anda gold STM tip are biased by Vb. The conduction current It is measured as It=Vout /RF. The conductance between the electrodes(tip and sample) is calculated by G=It /Vb.

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Metal QPCs are made by withdrawing
electrodes bridged by a nanowire. During thewithdrawal, the nanowire is thinned and elon-Cutting Edge 1

gated until it ruptures. The current passing between the electrodes under a constant bias
voltage is used to measure the conductancestep. Conductance changes are displayed on
an oscilloscope for each withdrawal. Experiments are done progressively for a number ofmetals, such as Au, Ag, Cu, Pt, Al, Fe, Ni, Co,Bi, Pb, Hg, and Na. The conductance steps measured for many withdrawal experiments are displayed in histograms, whose peaks appearedat around Ne2/h ( where N=1 and 2), suggesting quantization of the conductance. The structure of these QPCs has not been examined except by computer simulation, however.
To simultaneously study structure and conductance, we developed a UHV high-resolution
transmission electron microscope (HR-TEM)
with a miniaturized STM at the specimen position, as shown schematically in Fig. 2. The UHVHR-TEM was equipped with a field emission
gun operated at 200 kV. Operating the UHVHR-TEM at 10-8 Pa enabled clean fabrication ofgold tips and samples in-situ, thereby eliminating any effects of contamination on the structure and conductance. A mechanically sharpened gold tip was brought close to a gold island that had been deposited on a very thincopper wire, as shown in Fig. 3. The gold tip
was dipped into the gold island and then withdrawn by a shear-type piezoelectric transducer.
The tip was withdrawn slowly, at a constant
speed under computer control. Structuralchanges in the gold QPC were observed continuously during withdrawal by using a video
monitor. The conductance of the gold QPC wasmeasured simultaneously by the electrical connections shown in Fig. 3. The structure and conductance of the QPC were simultaneously recorded in each frame of the video images at
33-ms intervals.

Fig. 4 Transmission electron microscope images of a gold nanowire during withdrawal. The tip and sample are oriented
in the [110] direction, and the dark lines appearing in them are (002) lattice fringes spaced at 0.2 nm. The dark lines (ordark line) connecting the tip and sample are the nanowires.

4. Conductance and structurechanges of gold nanowire
Successive structure and conductancechanges of gold QPCs were observed using theSTM-TEM. The structure of QPCs is dependent
on the orientation of their electrodes. A QPCwith electrodes oriented along the [110] crystalline axis is shown in Fig. 4, and the corresponding conductance is shown in Fig. 5. Figures 4(a)-(f) are electron microscope images
during the withdrawal of the gold STM tip, and(002) lattice planes with a 0.2-nm spacing canbe seen. The dark lines in the gold nanowire
represent rows of gold atoms spanning the distance from the gold substrate to the tip. Thenanowire thins in Figs. 4(a)-(e) and has ruptured

Fig. 5 Conductance steps observed for the withdrawal process shown in Fig. 4. The arrows labeled (a)-(f) showcorrespondence to images (a)-(f) in Fig. 4.

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Fig. 6 Structural models of (a) a double strand and (b) a single strand of gold atoms, which span electrodes oriented in the [110] direction. The imaging electron beam is along the [1-10]
direction. The distance between P and Q is 0.89 nm.

in Fig. 4(f). The dark lines disappear one-byone, and at each disappearance the nanowire
appears to be reorganized into a stable structure so that it maintains a regular and uniform
diameter. The atomic structures of eachnanowire have not been determined directlyfrom these images. It is worthnoting that thedark lines in Figs. 4(a)-(e) (especially in Fig. 4(e))
have an enlarged spacing relative to the (002)lattice spacing of the tip and substrate, whichindicates that new structures formed at thenanowire (see the following section).
The conductance, shown in Fig. 5,changed stepwise in accordance with the structure changes shown in Fig. 4. The nanowire
withdrawal steps shown in Figs. 4(a)-(f) thus
correspond to the conductances labeled by arrows (a)-(f) in Fig. 5, with the conductancechanging in steps of n(2e2/h). The plateaus in6

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Fig. 5 for each stable nanowire structure in Figs.
4(a)-(e) indicate one-to-one correspondence
between the structure and the conductance.
Scattering of the conductance values for eachplateau follows any scattering of the local structure of the nanowire, or of the contact between
the nanowire and the electrode.
More than 300 experiments provided clear
evidence that a linear strand of gold atoms hasa unit conductance of G0=2e2/h. Experiments
also gave evidence that a double strand of gold
atoms has a conductance twice the unit conductance. Figures 6(a) and (b) show structure
models of the double strand and single strand,
deduced from quantitative analysis of brightdark image contrast like that in Fig. 4(e). Since
the electrodes are in the [110] direction, eachstrand is coherent with the [110] atomic rows
in the electrode bridges. Electron microscope

images, which gave a distance from P to Q aslarge as 0.89 nm, suggest that the gold atoms
in the strand have the same nearest neighbordistance (0.29 nm) as in the bulk gold crystal.
Thus, we verified that a QPC with [110] electrodes forms a nanowire at the contact, withthe conductance quantized in steps of N(2e2/h) for each step of structural change in thenanowire.

5. Gold magic-nanowires
suspended in vacuum
The structure of a gold QPC was studied
at atomic resolution. A very thin gold film wasplaced on the specimen stage of the UHV-HRTEM and bombarded with a very strong (~100A/cm2) electron beam in order to bore holes inthe film. As the holes were enlarged, a freestanding nanobridge of gold film was formed

Cutting Edge 1in vacuum. By thinning the nanobridge further,it turned into a nanowire or into a single strandof atoms with a regular structure. The thinning
process of the gold film and the formation of ananowire or single atomic strand were recorded
at atomic resolution, on videotape. These phenomena have never captured before.
Long gold nanowires could be formed inthe [110] direction by using a gold (001) film,
as shown in Fig. 7. The thinnest wire shown inFig. 7(a) had a diameter (width) of around 0.6
nm. For each image, we can see wave-like lines
along the wire axis (view the images from thewire axis at the grazing angle). These wavelike images can not be explained if thenanowires have a crystalline structure. Afterelaborate computer simulation based on theseimages, the gold nanowires were found to havehelical multi-shell structures, as illustrated in Fig.
8. Each shell is tubular, made of atomic strands
that coil around the axis of the tube, and characterized by the number of atomic strands. An
L-M-N shell structure thus has three coaxial
tubes, and the outermost tube has L atomicstrands. The observed images were characterized as 7-1, 11-4, 13-6, and 14-7-1 multi-shellstructures. The circumferences of the outer andinner tubes have a difference of 7d for all
nanowires (d: lattice constant), indicating“magic number” of seven. Because of the odd
magic number, gold nanowires must always
have helical structures, so they have chirality
similar to that of carbon nanotubes. AlthoughFig. 7 Transmission electron microscope images of gold nanowires. The dark dots represent gold atoms. We view theimages at the grazing angle from the wire direction. Note also the diameters of the nanowires: 1.3 nm, 1.1 nm, 0.8 nm,
and 0.6 nm.

Fig. 8 Helical multi-shell structures of gold nanowires. Models (a) - (d) show the 7-1, 11-4, 13-6, and 14-7-1 structures. Each shell(tube) is helical and characterized by the number of atom
strands (n). The n-fold helix of each shell is composed by a tube with triangular close-packed network of gold atom.

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Cutting Edge 1

0.4nm

(a)

(b)

Fig. 9 Transmission electron microscope image (a) and model (b) of a single strand of gold atoms. The gold strand is in the [100] direction, and the imaging electron beam is along the[011] direction. Note that the gold atoms in the strand are spaced at approximately 0.4 nm.

we have not yet observed a single-shell gold
nanowire, 6-0 and 5-0 single-shell structuresare very likely to exist.
The thinnest nanowire is a single strandof atoms (a linear chain of atoms). Figure 9shows an image of a single strand, which wasmade from a gold thin film of the (011) orientation. The strand extends along the [100] direction. This [100] strand contrasts with strands
in the [110] direction, such as those shown in
Fig. 7. The [100] strand in Fig. 9 has been elongated to have an inter-atomic distance of 0.4nm, which is unexpectedly long compared with
the nearest neighbor distance (0.29 nm at roomtemperature). A single strand of atoms which
is suspended in vacuum (Fig.6b) has a conductance of (12.9 kΩ)-1. Therefore, a single strand
passes a current as large as 1 A with a bias
voltage of 13 mV. High current density on theorder of 107 A/mm2 thus results from ballistic
electron transport.

6. Quantum Architecture byInvisible
Conductance quantization of electrons
passing through a narrow constriction wasdemonstrated not only for electrons, but alsofor QPCs in a two-dimensional electron gas(GaAs/GaAlAs) system.22) In both cases electron8

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transport is ballistic, since a nanowire has awidth comparable to the Fermi wavelength andmuch shorter than the mean free path of electrons. Therefore, quantization of electronic conductance is common nature for all one-dimensional materials.
Because of ballistic transport, nanowires
are thought to have zero resistance, with little
energy dissipation such as Joule heating. In thisrespect, the quantization or quantum limit ofthermal transport might become important,23,24)
since it restricts heat dissipation from thesystem. As the scale of electronic circuits decreases further, we should encounter thesequantum limits. One-dimensional nanowires
displaying quantization of electron, phonon,and entropy transport should then play important and useful roles. Quantum architectureusing nanoscale materials is an invisible world,
but “there is plenty of room at the bottom” insuch invisible world which will be realized in
the 21 century.

Present address:1) EMG Electron Optics Division JEOL LTD.
3-1-2, Musashino, Akishima, Tokyo 196-8558 JAPAN2) Research Center for Ultra-High Voltage Electron Microscopy
Osaka University
7-1, Mihogaoka, Ibaraki, Osaka 567-0047, JAPAN

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