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Selected topics in graphene, part 2: need for speed

There seemed to be at least some interest in my previous post regarding seeing graphene on SiO2, so I'm back for round two of 'not entirely useful, but still somewhat interesting information about graphene'.


You have probably heard, if you've been following some of the graphene-related developments in the past few years, that graphene electronics are really fast. You may have even heard the (terrible, but popular) phrase "graphene superhighway". What you may not have come across is a detailed description of what it is about graphene's structure that makes it so fast or, for that matter, what "fast" even means in this context. If I've just piqued your curiosity, read on.

I'll start by defining fast. In the context of electronics, what we're talking about is charge mobility. And charge mobility is how fast charges (electrons/holes) move in response to an applied bias. Electrons are moving around randomly all the time, but that's not what we're interested in here. The mobility is the speed they all move together in one direction when a voltage is applied to the electronic device.

Just how fast is graphene? Well silicon, our electronics standard-bearer, has a charge mobility* of around 1,400 cm2/Vs. Organic materials are lucky to hit 40 cm2/Vs. Graphene, under the right circumstances, can have a charge mobility measuring up to 1,000,000 cm2/Vs. Even with not-ideal conditions, 20,000 cm2/Vs is not uncommon for graphene. That is a pretty substantial improvement. So why is this so?

If you've ever seen a drawing of graphene's structure, it may have looked something like Figure 1A below, a hexagonal lattice with alternating double and single bonds. Where the bonds intersect is a carbon atom. In chemistry, when double and single bonds alternate like that, we call it "congujation". It has been shown that in these conjugated systems, there actually aren't any true double and single bonds; instead, the electrons making up the bonds are shared across the conjugated system and form a series of 1.5 bonds. So in reality, Figure 1B is a truer picture of graphene's structure.


To see what effect this conjugation has on the electrons in graphene, we need to take a closer look at what is going on at the atomic level. Let's discuss atomic orbitals. They need not be complicated, despite what your nearest chemistry undergraduate might say. We all know Bohr's basic model of the atom right? A nucleus at the center with a bunch of electrons orbiting it. The atomic orbital is just the region around the nucleus in which you are most likely to find an electron. We tend to picture orbitals as spherical, which is true for certain electrons, but for bigger atoms with more electrons, like carbon, they can take other shapes. Take a look at Figure 2. That's a drawing of the atomic orbitals around a single carbon atom in the graphene lattice. It has three orbitals in the lattice plane (green) and one above and below the plane (red) which is called the p-orbital. This seems really esoteric, but it's all about the come together, I promise.


In Figure 3A, I have made a bond between two carbon atoms in a hexagonal lattice. See how the in-plane orbitals are overlapping? That's a single bond. The two carbons are sharing electrons. But what about the two p-orbitals? What happens to them? Well, in a conjugated system, they sort of join together (think of them as prisoner + wife/husband in a conjugal visit scenario: same word, same idea) to form a big cloud of shared electron density above and below the plane of the lattice which makes the additional 'half bond'. Like in 3B. Do you see where I'm going with this? In a giant conjugated system like graphene, there is a giant p-orbital cloud above and below the lattice plane that electrons can just zip around in unimpeded! Silicon doesn't have this. In a silicon crystal, all the bonds are single bonds and the electrons moving around keep running into silicon atoms and being slowed down. And that's why graphene is so fast in comparison.


There you go, atomic orbital theory: actually, occasionally, a useful way to explain things.


I'm not sure what to reference here, because the above information is a weird combination of graphene literature and my brain and 1st year chemistry, but here are a couple of good graphene review articles. The Scientific American one is even pleasantly readable.

Geim, AK & Kim, P. Carbon Wonderland. Scientific American (April 2008), 298, 90.

Allen, MJ. et al. Honeycomb Carbon: A Review of Graphene. Chem. Rev. 2010, 110, 132.


* In semiconductors, there are actually two separate charge mobilities: hole mobility and electron mobility and they are usually not equal (though in graphene, they are). I am too lazy to keep specifying, so when I say "charge mobility" in this article, I am referring to the larger of the two.

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