Re: What IS the physics then?
Before launching into the Physics, how can I upvote the strapline?
How many .. to change a light bulb, I LOVE it.
As is mentioned above, blue light needs more energy per photon. GaAs was used for red LEDs originally, and alloying it with Indium and Gallium in various ratios causes the bandgap of teh material to increase and therefore we can reach yellow then yellow/green, and these days, pure green - of the sort one can hold in one's own mortal hand.
For Blue we need to find a material with more bandgap than GaAs, InGaAs, InGaAsP, InGaAlAsP and all that lot - you can see that the choice of material variants has grown, testament to the work that has been put into this market.
GaN and SiC are both contenders, early blue LEDs used SiC but the brightness is limited, it is an indirect band-gap material - a phonon is needed to carry away some excess momentum when the photon is emitted, reducing the probability of emission and wasting some energy.
Both SiC and GaN are exceedingly hard to grow in pure form, being riddled with screw dislocations, threading dislocations, foreign atom inclusions and many more nastys. GaN is the worst, we need defects per cm2 of a few hundred, typical bulk materials have 10^6 to 10^9.
To solve this we need to grow thin layers on a substrate that we can make decent crystals of, like sapphire (Al2O3) or SiC or even GaAs. The substrate order will force the thin layer to be defect-free. Unfortunately all the substrates have a different lattice constant, the mismatch needs to be accommodated somehow through interposing layers.
It is in this area where the Nobel Laureates excelled, Akasaki and Amano used sapphire with a buffer layer of AlN, whilst Nakamura found a way to grow GaN starting at low temperature then increasing the deposition temperature, spreading the strain across some distance.
It is all to do with the temperatures and gas compositions, including different dopants - and finally the sequencing to build crystalline thin layers that can cool down from the forming temperature (800-1400'C) to room temperature without shattering.
Since then there have been many more developments, like quantum dots, plasmonic resonators - and all sorts of means to get the light out of the crystal, but these are not part of the prize-winning research.