My doctoral thesis (part II)

Last time I described the silicon portion of my thesis, and skimmed over the diamond bits. Here is a bit about them…

This goes back to my Honours project, for which I was awarded a scholarship funded by Quantum Communications Victoria (QCV) to pursue models of defects in diamond using density functional theory. Back in 2007, the big defect of interest was the negatively charged nitrogen-vacancy centre (NV), which is much as it sounds like: take one carbon (C) atom out of the diamond (make a vacancy in the lattice), select an adjacent C atom and exchange it for nitrogen (N).

QCV were very interested in this defect for secure communications purposes because when it is hit with a specific type of laser pulse, it generates one and only one photon. This is known as a “single-photon source”, and it is an extremely useful thing to have if you want to implement quantum key distribution (QKD) protocols, such as BB84. These allow you to generate encryption keys (to keep your messages secret) with someone you cannot meet before you want to talk secretly with. I’m sure you can imagine how useful this might be to governments, the military, and financial institutions – and also to journalists, scientists (before they publish their findings) and even the general populace on occasion. They did indeed get a working single photon source generator prototype, and even managed to sell some… but I digress.

The funny thing about diamond is that it has over 500 defects that are known to give out photons of various kinds (blue, green, red, infrared, etc.). The best-studied of these is the NV defect, but others were also of interest for their properties. Since the postdoc I was working with was already modelling NV, I looked at an alternative defect that had recently been of interest in various journals involving xenon (Xe) atoms. We didn’t know much about it, apart from that if you bombarded a diamond with Xe ions using an accelerator, and then annealled the diamonds at a high temperature to repair the damage caused to the lattice, these defects appeared. A study published in 2007 revealed that the atomic symmetry of the defect was trigonal, which is science-lingo for “is a bit like a triangle” in as much as if you spin it 120º about a special axis, it looks the same.

What did I do?

At this point, I started the local computing cluster up… but as is often the case, in Honours you don’t have a lot of time to devote to the project and you usually haven’t had exposure to the skill set required yet — so the model that came out the other end wasn’t all that good (which didn’t stop me from presenting it at an international conference early the next year, since it took me a fair chunk of the following two years to illustrate that). As it turned out, the local computer didn’t have quite enough RAM for the bigger calculation I needed to do (calculations of optical properties are quite intensive), and the low number of cpus (32) weren’t sufficient to complete the job in a timely enough manner for that year’s assessment, either.

When I started out on the PhD the next year, I was of course still interested in this problem, and was hoping to use my year of experience with it to get a head start while I learned all about silicon and quantum computing… but events were not conducive. I got access to the national supercomputer (actually, an older version) through my second supervisor (Prof. Salvy Russo), but they had just uninstalled the software I needed (was familiar with) as nobody else had been using it. Renegotiating the licence took a while – and then I was faced with using the code via the command line on a UNIX cluster, rather than through the polished graphical user interface I’d had on the local system. I realised that this was just another of the skills you pick up along the way through a PhD, but the code was also parallelised in the wrong way (there are two main ways) for the cluster and I was limited to a set number of cpus and their attached RAM — and it just wasn’t enough to perform the calculation I needed (again). So we looked around for something else useful we could study about the system.

We hit on the idea that, if we couldn’t calculate the optical absorption spectrum, perhaps we could establish which type of structure was the most energetically favourable (likely to form). My supervisor had access to plenty of other density functional theory software packages, and so I started learning about those under Manolo Per (one of those bright postdocs I mentioned earlier). We ended up with two candidate models for the defect – one with a Xe atom sitting between two vacant C sites in the diamond (split-divacancy) and one with a Xe atom having replaced a C atom, and three neighbouring C-vacancies (trivacancy). A basic substitutional Xe caused too much strain to the nearby atoms and cost much more energy to make, so this was considered unphysical. We established that the energy cost to make the defect (defect formation energy) was lowest for the split-divacancy defect.

Then, because those calculations had all assumed a temperature of absolute zero (0 K), we included atomic vibrations (which is how temperature manifests in real solids) under the quasi-harmonic approximation. This means that we treated all the bonds like perfect springs, but adjusted the size of the box they were in… and you can see the maths in the paper if you’re keen. The vibrations contribute to a temperature-dependent free-energy term, and we reported the relative defect formation free energy for the two candidates. Again, the split-divacancy defect was more stable at any temperature we cared about. This was a solid prediction… but how could someone test it?

Well, as part of the calculation, we’d had to specify the vibrational density of states (the allowed vibrations, mapped against energy) for each defected diamond. When we projected the vibrational modes back onto the Xe atom, we found that one defect had one mode, and the other had two (well, really three, but two of them had the same energy so their peaks combined). Further, these modes were “local vibrational modes”, where the nearest C atoms participated about 10% as much as the Xe, and the falloff from there was pretty steep. Aha! Here was a potential way the defects could be distinguished – all someone had to do was measure the local vibrations of a defect involving about 7 atoms…

I got talking to a friend and colleague, Paul Spizzirri (another post-doc… aren’t they wonderful?), who was one of the local experts in Raman spectroscopy (which probes atomic vibrations in solids). He suggested that the optical transition believed to originate from one of these defects might enhance the vibrational signal, and that though it might be pushing the boundaries of Raman spectroscopy, a careful experiment might be able to see the signal if there were enough of these defects all vibrating at once.

All this was enough for a paper, and so we published one. A “little later” (in science, when projects often run over several years, twelve months can seem like the blink of an eye — it’s a bit like how people in the country where towns are few and far between often consider distance differently, thinking comparatively little of driving 200 km to see a friend on the weekend, while city folk can sometimes think that 50 km is a long way) Paul and I decided that taking a look for the defect might be fun on a Friday night. The problem was where to find a Xe-implanted diamond… Happily, my wife had been looking at one as part of her studies not too long before, and it was still in the department — and its overseas owner (we did the right thing and asked) was happy to let us use it.

The first session, as you might expect, was a bit of a bust. We tried conventional Raman spectroscopy, and couldn’t see any hint of a feature in the right spectral region. Got the usual signal from the diamond, so we knew the equipment was working… Turning up the laser intensity and collecting for more time didn’t help, either. The detectors just saturated (like a gauge going off the end of the scale) so we got no useful information. Trying again with a different laser, and with polarising filters in the line showed no effect.

This problem was really like the proverbial finding a needle in a haystack. The defects we were looking for take up less than a cubic nanometer, while the laser spot illuminated an area of about a square micron to a depth of several microns — a total volume over a billion times larger. This means that we were seeing a whole lot of diamond for not very much defect (even though there were probably several in the spot, they were all concentrated up near the surface and there weren’t all that many on the kind of scale of the number of C atoms in that much diamond). We had to scratch our heads and leave it for that night…

The second try, though, was a bit different. Paul had adapted a technique to make nanoparticles of silver, with which we carpeted the diamond surface. These nanoparticles enhance the local light intensity around themselves on a tiny scale – we conjectured that if our desired defects were close to the particles, their Raman signal should be magnified by several orders of magnitude (powers of ten). Hopefully this would make them comparable to the other features we were seeing from all that diamond underneath.

In fact, the first spectrum we took that second night showed a feature right in the target zone. We then spent some time trying to optimise its collection to maximise our signal-to-noise… and also took spectra from other locations on the diamond (pristine, supposedly unimplanted, and the two regions we considered likely to show Xe signal). Everything worked as we expected, and the feature showed up in all the right regions (and none of the wrong ones).

Further analysis showed that the feature was made up of two vibrational peaks just as I had predicted for the most stable structure (rather than one peak, which corresponded to the other structure, or three peaks which would be a combination of them). This was enough to write up and submit my thesis, so that’s what happened next.

I can’t really describe the feeling of personally confirming a prediction that you made. It suffices to say that I’ll probably spend the next forty years (given that I can secure funding and/or positions, of course) chasing it as hard as I can, whether that’s in a university setting, or on the outside. Beats a runner’s high hands down (although I like that feeling too).

As of today, I’m still trying to translate that last piece of work into an article. There are a couple of subtleties to explore still in the data, and I might need to try things in another sample. I’ll discuss them once I iron them out and get that paper accepted…

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