My doctoral thesis (part I)

What was my thesis about? (The TL;DR version)
Well, to put it baldly (badly?), I was looking at what happens when you make defects in a semiconductor crystal – and specifically (for four chapters), what happens if you do so in particular high-density regular arrays. Now, while that is a wonderfully compact description for someone who already knows what I did or is in my field, it is utterly woeful for anyone who doesn’t have some very particular background knowledge. Let me tell you part of the story…

Can I get rid of all that jargon? Sure – and here’s a bit of background to help.
I was looking at silicon (Si) in particular because Prof. Michelle Simmons‘ group at UNSW were building some very interesting quantum devices using it within the ARC Centre of Excellence for Quantum Computing Technology (at least, that’s what it was back in 2008 when I started – that wound down in 2010 and was replaced by the ARC CoE for Quantum Computation and Communication Technology). Since my professor (Lloyd Hollenberg) and I were in the theory arm of the Centre, it made sense to try to understand how and why these devices behaved the way they did.  We also reached out to Prof. Salvy Russo at RMIT, an expert in materials simulation, to be my second supervisor.

Silicon is a lovely material that atomically looks just like diamond, except you have Si atoms instead of carbon, and due to having more electrons they are spread a little further apart (about 50% further). If you took chemistry through to the end of high school, you might remember that some atoms bond by sharing electrons (covalent bonding) and that they often try to complete shells of eight electrons (octet rule). Si atoms have four electrons in their outermost shell, and they share with four other Si atoms in what is called a tetrahedral arrangement.

In layman’s terms, if you take some material – such as Si – and remove some atoms from the middle somewhere, you have made defects in the crystal. These are known as “intrinsic” defects, because:
1) they occur naturally within any “pure” silicon, and
2) they don’t involve any other elements.
The next-least complicated defects involve some other type of atom – let’s say phosphorus (P), and these are known as “impurities” for obvious reasons. In fact, most electronics you have encountered in the real world are built from precisely these materials! We use Si as the host because by itself, it doesn’t conduct – but it does form very regular crystals in sizes we can see and touch (Si wafers can be a handspan across).

This isn’t very interesting so far, but when we add the P atoms, they sit in the Si crystal without disturbing it spatially – because P atoms are very, very similar to Si atoms (they only have one extra proton and one extra electron). Thanks to this similarity, they bind into the Si “lattice” (a word that describes the atomic structure of the crystal) almost the same way Si does, except for that one extra electron, which finds itself exiled to the next shell out, where all those other electrons camouflage (screen) the P nucleus and leave only a bit of the extra positive charge from the extra proton “visible” to that lone electron. This makes it look a little like hydrogen (one electron, one proton), and scientists often think of it as such. As you might imagine, this means that last electron can float around quite a distance from its atom (technically, it has a large effective Bohr radius).

By now, you’re probably thinking “whoop-de-doo, why should I care?” – but bear with me a little longer. You’re right: if there were only a few of these P atoms in a big, hand-sized chunk of Si, it would be really boring – but what if we put many of them in? Electronics is based on the idea that all these extra electrons can be put to use by applying electric fields to pull them up to the surface of the Si, or push them away. (Check out a recent form of transistor if you are interested in how this works.) Now, imagine putting even more of these P atoms into the Si, enough so that all those lone electrons that were exiled up to their own shells overlap. You’ve just made yourself a metal! (Remember from high-school science that metals have loose electrons floating around like a gas about all the metal nuclei? It’s the same here.)

What did I actually do?
Now, imagine that we don’t waste much P, because we can put it all into one atomic layer of the Si. We set it up in a regular square grid, where each of those outside P electrons can see lots of P atoms close by – and they can all travel about as they like between them. Of course, they’ll average out to one each (and they’ll repel each other from clumping up most of the time), but we essentially have a thin metal sandwiched between Si on the top and Si on the bottom. One of the beautiful consequences of quantum mechanics is that, when you confine electrons to tiny, tiny spaces like you do here, they behave in odd ways. I modelled this very scenario with the help of some very bright post-docs and professors… I did it using two different theories; effective mass theory (EMT) and density functional theory (DFT).

This took quite a while: first, we had to establish our methods and benchmark them as best we could; second, DFT calculations require significant amounts of computer time; and third, the nature of the loosely held P electrons meant that we had to include a lot of extra Si in the DFT models (which made it even more computer-intensive).

Then we took things a bit further and thought about what might happen if you had two of these layers near each other – how would they interact? What happens as we separate them further; when do they behave like they did on their own? What effects arise from moving one grid around in its plane, relative to the other?

Finally, we thought about pinching off another dimension to make a wire out of this stuff, and brought in another student to the project. At this point, I’d been hanging around plenty long enough, so I wrote it all up (and some other work on diamond) and submitted it as my thesis…

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