Polysilicon is the next lowest quality of silicon and is made by the Siemens process. Impurities are removed by distillation in the process, and a pure silicon material is grown by chemical vapour deposition requiring high temperatures. The Siemens process' energy consumption is very high.
An alternative to the Siemens process is the fluidized bed reactors (FBR), which uses lower temperatures and hence consume much less energy. The purity of polysilicon can be as high as 99.9999%.
If the purity of polysilicon is not required, upgraded metallurgical silicon can be made cheaply by blowing gases through the silicon melt to remove impurities.
To make monocrystalline silicon ingots, which are solids that is one big continuous crystal, there are 2 methods. The Czochralski processing method allows doping, orientation of the crystal to (100) or (111), and production of large crystals.
The float zone process allows the creation of ingots with very low densities of impurities like oxygen and carbon. It also allows doping, but the size of the ingot is limited.
Polysilicon (multicrystalline silicon) can also be produced by silicon casting, where melting is done in a dedicated crucible, and the melt is poured into a growth crucible to solidify. If melting and solidification are done in the same crucible, it is called directional solidification.
Finally, 2 methods can be used to create wafers out of ingots. Sawing can be done, but it generates a large proportion of wasted silicon called kerf loss, and requires polishing. Silicon ribbon is the next method. It pulls ribbons of silicon out of silicon melt before cutting them into wafers. Further treatment is needed, but the electronic quality of ribbon silicon is still not as good as monocrystalline silion.
Reference:
4.2 Manufacturing of Crystalline Silicon, Delft University of Technology, https://www.youtube.com/watch?v=Oqk4H2Ji79k
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