I've graduated, the thesis is online and the hard bound copies have arrived. It's time to talk about my thesis.
First of all, my PhD thesis is called "Physical Properties of Graphene Nano-devices", it's theoretical and you can download it from the Loughborough University
The abstract is as follows:
"In this doctoral thesis the two dimensional material graphene has been studied in depth with particular respect to Zener tunnelling devices. From the hexagonal structure the Hamiltonian at a Dirac point was derived with the option of including an energy gap. This Hamiltonian was then used to obtain the tunnelling properties of various graphene nano-devices; the devices studied include Zener tunnelling potential barriers such as single and double graphene potential steps. A form of the Landauer formalism was obtained for graphene devices. Combined with the scattering properties of potential barriers the current and conductance was found for a wide range of graphene nano-devices. These results were then compared to recently obtained experimental results for graphene nano-ribbons, showing many similarities between nano-ribbons and infinite sheet graphene. The methods studied were then applied to materials which have been shown to possess three dimensional Dirac cones known as topological insulators. In the case of Cd3As2 the Dirac cone is asymmetrical with respect to the z-direction, the effect of this asymmetry has been discussed with comparison to the symmetrical case."
What isn't mentioned in the abstract is what I really wanted from the thesis. Whenever I would read a scientific paper a method or term would be used and simply referenced, there was no real information on where it came from and (especially when starting a new topic) this can cause some real confusion. That is what I wanted to avoid in my thesis; the thesis will include *everything*.
The thesis focuses on graphene electronics, specifically transistors and diodes. Due to how the physics of transistors work, to *fully* derive how to build a graphene transistor you need to start at the atomic level with the fact that graphene is a two dimensional sheet of hexagons. After you have figured out hexagons, you just need a tight binding approximation to obtain the Hamiltonian, then solve a potential barrier problem, and use the result in the Landauer formalism to find current. You can now predict what will happen when you plug the thing into the whatsit. A real result.
Which leads to the second important point. The thesis should be accessible, so there are no big scary leaps in the maths. This thesis should be readable by an undergraduate, maybe even someone with just an A level in maths. It may get science-y at points, which it has too, but the maths should be followable.
Of course, there is far more to the thesis than just 'build a graphene transistor from hexagons' there are plenty of additional problems, calculations and analysis which extend in to other materials, not just graphene, but you'll see that if you decide to give it a read.