FEATURE ARTICLE
Fullerene Nanotubes: C1,000,000 and Beyond
Some unusual new molecules—long, hollow fibers with tantalizing electronic and mechanical properties—have joined diamonds and graphite in the carbon family
Boris Yakobson, Richard Smalley
Metal or Semiconductor?
Are nanotubes metallic or semiconducting? This question was
addressed at the Naval Research Laboratory and Massachusetts
Institute of Technology before the first real tubules were sighted.
The answer was "both."
The electrical properties of any material are largely determined by
quantum partitions-bands in the energy scale that electrons occupy.
Some energy levels correspond to states simply incompatible with the
symmetry of the material structure and are not allowed. They create
gaps between the energy bands available for the electrons.
Lower bands are usually full and leave no room for motion. Higher
bands can be partially occupied by electrons, able in this case to
accept a little kinetic energy and get going if an electric field
happens to push them. This partially occupied area is called a
conduction band. The conductivity is found in this
band. The nature of the gap is the key to modern electronics.
Wide-bandgap semiconductors (such as gallium nitride) make more
stable and powerful transistors and can emit the blue color sought
today for flat-panel displays; a narrow bandgap (as in mercury
cadmium telluride) is good for sensing infrared light for night vision.
In planar graphite there is no bandgap between the empty and full
states, but there are only a tiny number of electrons capable of
moving along the graphene sheets. Graphite therefore has weak
conductivity and is called a semimetal. Figure 14 shows
what happens, however, when one rolls it up into a tube. Now the
velocity of an electron (actually, a wave-vector k, but
never mind) has only one direction available, along the tube, rather
than the two directions that were available in the graphene plane.
Motion in the perpendicular direction is now around the tube and has
to satisfy new periodicity conditions. This reduces the azimuthal
freedom of an electron to just a few discrete possibilities, as the
family of curves indicates.
The electrons occupy the states below a certain energy called the
Fermi level (actually, the picture is somewhat blurred by thermal
excitations), which in this case is positioned right at the crossing
of the valence and conduction bands. Therefore there is no gap;
electrons can move, and our (10,10) nanotube should conduct. How
well? For graphite, the low density of such carriers results in poor
conductivity. For a parallel bundle of armchair nanotubes, the
carrier density is tens of thousand times higher, and the
conductivity is like that of a good metal.
Since such analysis depends largely on the corkscrew symmetry of the
tube, however, its conductivity varies surprisingly with helicity.
Only the armchair (n,n) tubes are truly metallic by
symmetry. All other tubes have an energy gap, although it is tiny
for those zigzag (n,0) tubes with n a multiple of
three. The gap decreases in inverse proportion with diameter, and
thus approaches zero for planar graphite. In principle, any
one-dimensional metal is prone to so-called Peierls
instability, when translational symmetry breaks, as in the
hydrocarbon chains in polyacetylene, ...
÷CH÷CH÷CH÷ ... → -CH=CH-CH= ...,
and the alternating spacing results in a nonzero gap. Fortunately,
in the case of nanotubes, even a little thermal motion is sufficient
to smear away this pattern and restore the uniformity, so that
conductivity stays high even without enrichment by doping, the
addition of another element.
In experiments, attaching contacts to a nanotube takes almost as
much dexterity as stretching it mechanically. Reports of successes
in connecting devices from the macroworld to "molecular
wires" came last year from Belgium, then from Harvard and from
NEC, with gradual important progress in probe attachment. The
simpler two-probe scheme makes it difficult to separate the
resistance of the contacts, including a possible Schottky barrier
(an area where current can flow only one way), from the resistance
of the nanotube itself. A nanotube is placed on a substrate with
prearranged gold pads, and then is either contacted by the
cantilever probe tip of a microscope or connected by the metal leads
deposited lithographically across the tube (Figure 15) and
all the way to the pads. Current is put through the external pair of
probes, and the voltage measured on the internal couple tells us
about the conductivity. Variations of resistivity with temperature
and with external magnetic field (magnetoresistance) were
used to reveal the nature of conductance.
In these tests both metallic and nonmetallic nanotubes have been
found, illustrating the profound sensitivity of the electrical
properties to the geometry of a specific tube. However, none of the
nanotubes showed an increase in resistance with temperature, a
classic attribute of a metal, obscured probably by the multiwall
structure and the possible presence of defects. The synthesis of
single-wall armchair nanotubes provided a way out of this
uncertainty. Their resistivity grows with heat, as it does for all
the metal pieces in our home appliances and electric bulbs.
» Post Comment