Silicon, chemical symbol Si, is an abundant chemical element. It occurs commonly in sand, numerous minerals, and in clays. It most often occurs as silicates or as silicon dioxide, also called silica or quartz.
In the production of polysilicon, a purified grade of silica or quartz is heated in an electric furnace (where large carbon electrodes burn off oxygen) to metallurgical grade silicon. Using proprietary technology, this intermediate is then converted to chemical derivatives for purification (usually by distillation). They are then converted back to silicon, then zone refined and sliced into wafers as polysilicon.
According to “Forty Years of Firsts: The Recollections of a Dow Corning Pioneer,” by Dr. Earl L. Warrick, McGraw-Hill, 1990, in 1959, Dow Corning entered the high purity silicon business for use in semiconductors by licensing the Siemens-Westinghouse process. Metallurgical grade silicon made by reduction of high purity quartz in an electric furnace with carbon electrodes was reacted with hydrogen chloride to form trichlorosilane. The silane was purified by careful distillation. Then it was decomposed at high temperature in the presence of silicon to add layers of new silicon (with hydrogen as a by-product). This polycrystalline silicon was then zone refined to single crystal silicon. By 1966, Dow Corning had become the world’s largest producer of polysilicon.
According to an article in the May 4, 2015 issue of C&EN, the Siemens process requires heating rods of silicon with trichlorosilane in large vacuum chambers at 1100 C for several days. The silicon rods that grow must then be crushed and zone refined. Newer processes are said to use fluidized bed technology to produce silicon granules. Wacker, REC Silicon, Sun Edison, and GCL-Poly are all reported to have improved processes in development. The new processes reduce production costs to $10 to 15/kg vs $12 to 20/kg for the Siemens process.
For additional perspective of the extensive processing used to create silicon wafers for the microchip industry, see the MEMC 50 year book. 
The April 29, 2011, issue of C&EN listed producers' global market share as: Hemlock (subsidiary of Dow-Corning, subsidiary of Dow Chemical and Corning Glass Works) 16%, OCI, 15%, GCL-Poly, 11%, Wacker Chemie, 9%, and others 49%.
MEMC claims to be the second largest producer of polysilicon in the US.
A bit more about MEMCs processing technology was revealed in the obituary of Bob Walsh, the "Father of Polishing." [] His process for smoothing the rough surface of wafer slices used a combination of chemical etching and mechanical polishing.
Numerous producers have announced new production capacity leading some to predict over supply of polysilicon in 2012.
In February, 2012, BusinessWeek reported that polysilicon prices had fallen by 65 percent last year to $26.52/kg. 
In January, 2013, C&EN reported that Hemlock, Renewable Energy Corp. (REC of Norway), and Wacker were reducing production and delaying new plant openings due to falling prices. Hemlock has main plant in Hemlock, MI near Midland, cutting production. Delaying startup of new plant at Clarksville, TN. REC plant is at Moses Lake, WA. Reducing production. Wacker delaying start-up of new plant at Charleston, TN. No mention of MEMC (ticker WFR) whose stock is recovering from a recent bottom. []
In 2014, Hemlock announced a decision to write-off the new plant in Clarksville, TN at a cost of $1.6B, split between Dow Chemical and Corning Glass Works at $500M each. The new Wacker plant in Charleston, TN still plans to open late in 2015.
In 2015, Wacker created Siltronic as its silicon wafer subsidiary and sold 42.2% of its shares to the public. Siltronic is the world's third largest producer of hyperpure silicon wafers for the semiconductor industry.
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