NanoVision 2020

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PHYS 2235 Physics of NanoMaterials S. J.
Xu Department of Physics (Lecture 7)
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Coulomb Blockade Effect and Single Electron
Tunneling

• Contents of Lecture 7
• Principle and functions of Scanning Tunneling
  Microscopy
• Coulomb Blockade Effect and Single Electron
  Tunneling
• Carbon Nanotubes
• References

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Scanning Tunneling Microscopy
Perhaps scanning tunneling microscopy (STM)
is the most powerful tool for the nanoworld. It
was invented by G. Binnig and H. Rohrer who wan
the Nobel prize in 1986. The heart of a STM is a
fine metal wire, called the tip, placed in close
proximity to a conducting surface as
shown in Fig. 1. If the STM tip is close
enough to the surface then an applied voltage
between the tip and sample will cause electrons
to tunnel through the barrier.
Fig. 1. Basic schematic of a STM.
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Notice that the tunneling current is
exponentially dependent on the barrier width
(actually the distance between the tip and the
surface of sample) and increases by decade per
Angstrom as the tip is brought closer to the
surface. In typical systems a tip-sample
separation of 4 Å will produce tunneling currents
of 1 nA for biases of 1 V.

• Microscopy

By scanning the tip along the surface and
monitoring the tunneling current, one can image
the surface morphology with atomic resolution.
The tip scanning can be controlled using
piezoelectric materials. In typical scanning
modes, the current is kept constant as the tip is
moved laterally along the surface. The r figure 2
shows a STM image of Ag (001) surface taken in
this manner. Each bright spot corresponds to a
single Ag atom.
Fig.2. STM image of Ag(001).
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• Spectroscopy

When the dependence of the tunneling current on
position reveals the
geometric structure of the surface, the
dependence of current on voltage gives
information about its electronic structure. It
can be shown that the tunneling current is
approximately proportional to the integral of all
the electronic states between the Fermi energy to
the tunneling bias, as schematically shown in
Fig. 3. Notice that the first-order derivative of
the tunneling current with respect to voltage
(dI/dV) is thus proportional to the local density
of states underneath the tip, at the given
voltage.
Fig.3. Electronic state distribution of sample
and electron tunneling.
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Thus by measuring dI/dV as a function of voltage,
one can probe the electronic states at that
particular point on the surface.
Figure 4 represents the simulated current I
and dI/dV as a function of voltage for the state
distribution shown in Fig. 3. In general, the
peaks in the spectrum of dI/dV correspond to the
electronic resonances, such as atomic states, of
the system being probed. One can go a step
further and combine STM microscopy and
spectroscopy, to image the spatial distribution
of the observed electronic states. For example,
well-known quantum corrals shown in Fig. 5.
Fig.4. Simulated I and dI/dV as a function of
voltage for the case in Fig. 3.
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Quantum Corrals
Fig. 5. Stadium corral. Iron on copper (111). M.
F. Crommie et al., Surf. Rev. Lett. 2, 127 (1995).
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• Manipulation

Another powerful STM capability is the ability to
move atoms and
molecules. This is achieved by placing the tip
close enough to the surface adsorbate so that the
dip-adsorbate attraction is comparable to the
surface corrugation barrier. In this regime, the
atom or molecule will follow the tip wherever it
is moved along the surface. One can then retract
the tip, without causing the atom or molecule to
desorb from the surface. Thus one can construct a
desirable nanostructures. Fig. 6. Schematic
diagram of molecule manipulation with STM.
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Atom Manipulation with STM
Fig. 8. Xenon on Nickel(110). D.M. Eigler, E.K.
Schweizer. Nature 344, 524-526 (1990).
Fig. 7. Iron on Copper(111). Lutz Eigler
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Coulomb Blockade Effect Single Electron
Tunneling
The Coulomb Blockade Effect (CBE) can be
described as discrete changes in charging energy
of an ultrasmall capacitor due to Coulomb
interactions between electrons.
e
Fig. 9. Principle of the CBE.
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The charging energy
where C is the effective capacitance of the
capacitor, e the electron charge.
The quantum resistance
The two criteria for observation of the CBE
Single electron tunneling is characterized by the
discrete current resonant peaks in the I-V
curves. Figure 10 shows a typical experimental
current-gate voltage curve of an artificial
quantum dot at 50 mK. The curve consists of a
number of single-electron tunneling peaks or
Coulomb Oscillations.
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Typical CBE SET Experimental Curves
Fig. 10. Measured I-V curves of electron
tunneling through an artificial quantum dot. S.
Tarucha et al., Phys. Rev. Lett. 77, 3613 (1996).
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Carbon Nanotubes
Carbon nanotubes are a typical family of
nanomaterials, which have been demonstrated to
exhibit many novel electrical, mechanical and
optical properties. They are expected to have
many potential applications including conductive
and high-strength composites energy storage and
energy conversion devices sensors
field-emission displays and radiation sources
and nanometer sized semiconductor devices,
probes, and interconnects. Some of these
applications are now realized in products. Others
are demonstrated in early to the advanced
devices. Two main types of carbon nanotubes
single-walled nanotubes (SWNTs) and multi-walled
nanotubes (MWNTs). SWNT consists of a single
graphite sheet seamlessly wrapped into a
cylindrical tube while MWNT comprises an array of
such tubes that are concentrically nested like
rings of a tree trunk. Figure 11 shows typical
structures of carbon nanotubes.
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Carbon Nanotubes
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If you could slit open the nanotube pictured
above, by cutting all the bonds along any
straight line parallel to its axis, it would
uncurl to form this strip of graphite.
The lattice vector connecting the sides of
the strip is (N,M) (10,10). This vector
completely characterizes the tube. There are an
infinite number of other possible tubes
characterized by different lattice vectors. If N
M ("armchair" tubes) or M 0 ("zigzag" tubes),
there is N-fold rotational symmetry. Otherwise,
the tube has helical symmetry (it is chiral.)
Theory says that "armchair" tubes, having N M,
should be 1D metals. Those with N-M ? 3n should
be narrow-gap semiconductors, and the rest should
be insulators.
Fig. 12
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References

• R. H. Baguhman, A. A. Zakhidov, and Q. A. de
  Heer, Carbon NanotubesThe Route towards
  Applications, Science 297, 787 (2002).