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04/16/2008
Speedy Electrons in Thin Carbon
Last week’s column dealt with asthma, nitric oxide and carbon
single-walled nanotubes, SWNTs. I had planned to discuss
another form of carbon, graphene, but realized that this material
deserved a full column to itself after reading an article titled
“Carbon Wonderland” by Andre Geim and Philip Kim in the
April 2008 issue of scientific American. Geim and Kim are
professors at Manchester University in England and Columbia
University, respectively, and both have been in the forefront of
research on this remarkable material.
What is graphene? Let’s look at some graphite, the stuff in your
“lead” pencil. A bit of history – it wasn’t until the 1500s that the
English discovered a large deposit of pure graphite, then known
as “plumbago”, Latin for “lead ore”. The “lead” ore was quickly
recognized as being useful for making marks on things and the
lead pencil was born. I find it astonishing that it wasn’t until
1779 that a Swede, Carl Scheele, proved that plumbago was
carbon, not lead. Later, a German, Abraham Gottlob Werner,
coined the name graphite for the material, after a Greek word
meaning “to write”.
But I digress. We’ve discussed before how graphite consists of
layers of carbon only loosely held together by a weak force
known in the trade as the van der Waals force. We also have
talked about how this van der Waals force is involved in the
gecko’s ability to walk on ceilings. If we look at the layers of
carbon in graphite we see that the carbon atoms are arranged in a
hexagonal structure that looks like chicken wire. Last week we
noted that carbon nanotubes have this same hexagonal chicken
wire structure rolled up into a tube. Unroll a single-walled
carbon nanotube and you have a flat layer of hexagonally
arranged carbon atoms just like a single layer of carbon in the
graphite structure. The ultimate single layer of graphite only one
atom thick is called graphene.
So, how do we make graphene? We probably all have made bits
of graphene without knowing it whenever we’ve written on a
sheet of paper with that “lead” pencil. The graphite layers that
slide off the graphite in the pencil may include some bits of
layers that are indeed only one atom thick. Being so thin,
graphene is transparent and, even with a high-power microscope,
bits of it would be difficult to spot amongst the debris of graphite
left on your paper.
So, let’s try a bit more sophisticated type of writing – let’s make
a “nanopencil”, as did Philip Kim and a graduate student at
Columbia. We’ve talked in the past about the atomic force
microscope in which a very small sharp tip of a material is more
or less dragged across a surface and in the best case actually
reveals the structure of the surface atom by atom. In this case,
let’s make the tip out of graphite and write on the surface of a
silicon wafer. Under the right conditions, what happens when
we write lightly on the wafer is that rows of little “pancakes” of
graphene are wiped off onto the silicon surface. Actually, when
Kim and Zhang did it the pancakes were not really graphene but
graphite a few tens of layers thick.
It was deemed highly unlikely that a single atom thick layer of
graphene could be achieved and that it would be stable.
However, in 2004, Geim, working with postdoc Kostya
Novoselov and co-workers at Manchester, went at the problem in
a much less sophisticated way. They just took some debris left
over after splitting graphite into flakes and sandwiched the flakes
between folded plastic adhesive tape and pulled the tape,
cleaving the flakes in two. They repeated the process and the
flakes got thinner and thinner. Finally, examining their
handiwork, they were amazed to find some pieces that were only
one atom thick. Not only had they made graphene but the pieces
of graphene were chemically stable at room temperature. They
found the graphene to be strong and stiff.
It’s amazing that these intrepid scientists were able to make and
work with any material only an atom thick. But there’s more. It
turns out that electrons travel faster in graphene than any other
known material. Whoa! This property makes physicists and
electrical engineers drool over the possibilities of making
graphene transistors or other devices. We’ve talked about
Moore’s law and the fact that transistors are reaching such small
sizes that piling more and more transistors on that silicon chip
may be reaching a fundamental limit. Could graphene, only an
atom thick with its great electrical properties, extend Moore’s
law another decade or more?
Warning! Here’s where things get rough and I don’t pretend to
understand what follows, namely, the concept of “tunneling”.
Actually, I should be ashamed of the preceding statement
inasmuch as I once was an expert in making materials related to
a device known as the Esaki tunnel diode, named after its
inventor, Leo Esaki. …….(Sorry, I just spent an hour reading a
paper I published on the subject back in 1960 and was carried
away by how much I knew then and how little I know today!)
Tunneling. If you’re driving your car and come to a hill, it takes
energy in the form of burning your precious fuel to climb the hill.
Going down the hill you get part of that energy back, especially
if you coast down the hill. In physics the “hills” are energy
barriers. When an electron come to one of these barriers, the
weirdness of quantum mechanics comes into play. The electron
doesn’t necessarily have to climb over that barrier to get to the
other side. Good old Heisenberg’s uncertainty principle says that
you can’t pin down the location of an electron precisely and
there’s a good chance (more than zero and less than 100 percent)
that it’s on the other side of the barrier; that is, it can “tunnel”
through the barrier. Obviously, your car can’t tunnel through
that hill unless you’ve brought along some sort of borer and extra
fuel to power it.
Now take the case of our graphene and the speedy electrons.
Apparently, graphene is such a wondrous material that it’s a new
ball game when it comes to tunneling. Notice in the preceding
paragraph that I said the chances of the electron tunneling to the
other side are less than a hundred percent. It seems that in
graphene the electrons are traveling so fast that Einstein comes
into play and the electron becomes a “relativistic” particle.
According to the Scientific American article, it also seems that
physicists have for years wanted to find some means of testing
the validity of the “Klein paradox”.
Given the right conditions, when one of these relativistic
particles encounters a potential energy barrier the Klein paradox
is that this particle can tunnel through the barrier no matter how
high or how wide. The tunneling probability is 100 percent –
“perfect” tunneling. Again according to the article, physicists
had thought such quantum effects would only be observable in
such places as black holes or very high-energy particle
accelerators. Now it seems as though the high electrical
conductivity in graphene may be due to this perfect tunneling;
when the electron comes to the barrier it just sails right through.
So much for the latest chapter on the wondrous world of carbon.
I’m sure there will be more. Meanwhile, it’s back to care giving.
For those interested in the latest news on my wife, we’ve just
been to a knee replacement surgeon and it looks like a single or
double knee replacement is in the offing!
Allen F. Bortrum
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