Thanks for your comment, it really helps piece it together. I'm familiar with semiconductor/transistor theory but the article was light on details. Also, I was mostly lost reading Wikipedia. What I've found: there's quite a long list of band-gap semiconductors [1], and the blues fit in chronologically by coming after the reds/greens (Gallium-Arsenide GaAs stuff). The blues center around Gallium-Nitride (GaN) [2] semiconductors.
> They found out you could grow GaN by flowing hot gasses containing Ga and N on top of an artificial sapphire film, which would act as a template for the crystal to grow.
This must be what [3] refers to. Mix molten gallium with nitrogen at 100 atm, 1000 ˚C. Alternatively, mix gallium with ammonia. Get a powder of GaN, then vapor deposit it into layers.
> The problem is that GaN crystals and sapphire crystals are slightly different sizes (the gaps between their constituent atoms is different) so they don't match up exactly
Right, several articles mention matching lattice constants. Seems to be a big problem. In fact, [2] mentions that the first substrates used for growing GaN were sapphire, zinc oxide, and silicon carbide. A chart [4] shows lattice constants, which I don't fully understand, but GaN's 3.186 Å is pretty close to SiC's 3.086 Å. So this seems to make sense.
How do you compare a single lattice constant like ZnO: 4.580 Å with a pair like GaN's 3.186 Å, 5.186 Å?
> This must be what [3] refers to. Mix molten gallium with nitrogen at 100 atm, 1000 ˚C. Alternatively, mix gallium with ammonia. Get a powder of GaN, then vapor deposit it into layers.
Not quite. If you want something to search for, search for "metalorganic vapour phase epitaxy" (MOVPE) or "metalorganic vapour deposition" (MOCVD).
> How do you compare a single lattice constant like ZnO: 4.580 Å with a pair like GaN's 3.186 Å, 5.186 Å?
This is a harder question than it might seem!
You can easily calculate a lattice misfit as a percentage if the crystals are the same shape: (a_substrate - a_film)/a_film. If it's low, the films will be strained, if it's higher then the films will have to relax through some deformation process resulting in disruption and defects at the interface. It's a complex process, and there's no easy rule for what will happen (keyword to search for is "Matthews Blakeslee" who came up with a model to predict how thick a film could be for a given lattice misfit before you get these defects, but in practice it's quite limited).
Care must be taken to directly compare lattice parameters though. To pick a simple example, imagine you have one crystal with a lattice parameter exactly twice that of another. On paper, that'd be a lot of misfit, but because they tile perfectly in practice it might work really well. Likewise, you can imagine lining up two square crystals, you could imagine being able to line up the diagonal of one crystal with the sides of the other crystal if one lattice parameter if the ratio of their lattice parameters is 1:sqrt(2). So it's not as simple as just looking to see how similar two numbers are, you have to consider the geometry of the crystals too.
This is where it gets a little complicated. For your specific example of ZnO and GaN, the ZnO value you have is for cubic ZnO so its three lattice parameters are the same (a=b=c like the sides of a cube) which is why only one is quoted (a = 4.580 Å) whereas GaN is hexagonal (a=b!=c) which is why two are quoted (a = 3.186 Å, c = 5.186 Å).
[Aside: GaN is often grown on its c-plane, in which case we can neglect the c parameter for working out the lattice misfit. This is something that's difficult for me to explain in words, but if you're interested in understanding it a bit better, search for "Bravais lattices" so you more easily visualise what these lattice parameters refer to. This means we only need to consider the a values when working out the misfit.]
So you'd want to compare the 4.580 Å value to the 3.186 Å value and ignore the 5.18 6Å value. But because the GaN crystal is not just a different size but also different shape to the ZnO crystal (hexagonal vs. cubic), it's actually more complicated. However, luckily for you, ZnO also exists in a hexagonal form just like GaN and in that case has lattice parameters a ~= 3.25 Å and c ~= 5.21 Å, so the misfit between ZnO and GaN in this case would be about 2%?
If you're curious, it seems like people do grow ZnO on GaN and vice versa, so you picked a good example to ask about :)
> They found out you could grow GaN by flowing hot gasses containing Ga and N on top of an artificial sapphire film, which would act as a template for the crystal to grow.
This must be what [3] refers to. Mix molten gallium with nitrogen at 100 atm, 1000 ˚C. Alternatively, mix gallium with ammonia. Get a powder of GaN, then vapor deposit it into layers.
> The problem is that GaN crystals and sapphire crystals are slightly different sizes (the gaps between their constituent atoms is different) so they don't match up exactly
Right, several articles mention matching lattice constants. Seems to be a big problem. In fact, [2] mentions that the first substrates used for growing GaN were sapphire, zinc oxide, and silicon carbide. A chart [4] shows lattice constants, which I don't fully understand, but GaN's 3.186 Å is pretty close to SiC's 3.086 Å. So this seems to make sense.
How do you compare a single lattice constant like ZnO: 4.580 Å with a pair like GaN's 3.186 Å, 5.186 Å?
[1] https://en.wikipedia.org/wiki/Light-emitting_diode#Ultraviol...
[2] https://en.wikipedia.org/wiki/Gallium_nitride
[3] https://en.wikipedia.org/wiki/Gallium_nitride#Bulk_substrate...
[4] http://sector7.xray.aps.anl.gov/calculators/crystal_lattice_...