Then you have the actual crystal growth portion where you shove all those wafers into an evacuated chamber, heat them to a thousand degrees, spin them around, and spray them toxic pyrophoric gases. This process takes multiple hours to grow just a few microns of light producing crystals.
Then you have to grind the wafers down to the appropriate die thickness, go through multiple stages of etching, add a phosphor for white LEDs, deposit gold and ITO for electrical contacts, and use lasers to cut them into individual die. Then, finally, you can ship them to the people in the linked article. Honestly, this article is the most boring part of the whole process.
Source: I used to work in R&D for an LED manufacturer.
and a lab to get a better feel for how band gaps affect the spectrum: http://electron6.phys.utk.edu/phys250/Laboratories/Light%20e...