Silicon is a nonmetallic element (number 14 on the periodic table) found in the earth’s crust. The element is a major component in semiconductors, and its high conductivity makes it useful in solar power cells.
Silicone is a class of silicon-based chemical compounds used in paints, adhesives, lubricants, and breast implants, among other applications.
So, while silicon is the correct word in relation to computer electronics and solar energy (and hence is the spelling used in Silicon Valley), silicone is usually correct in relation to other types of manufactured items.
Currently, the cost of electricity from silicon solar cells is about ten times that of other energy sources. [Wired]
Oxidation involves the growth of a layer of silicon dioxide on a silicon wafer. [Fundamentals of Semiconductor Devices, M. K. Achuthan]
Brass brains have been succeeded by silicon chips, which calculate that high water at London Bridge yesterday was at precisely 3.30pm. [Telegraph]
Plastic surgeons readily adapted the silicone implants for post-mastectomy chests. [Atlantic]
For the inert surface of silicone rubber, the former requires the generation of high-
energy species. [Current Topics in Elastomers Research, Anil K. Bhowmick]