I think your question was, and correct me if I'm paraphrasing incorrectly: "Raw materials suppliers to foundries" and "Equipment suppliers to foundries".
Silicon is supplied by SUMCO and SunEdison. SOI (silicon on insulator) wafers are supplied by Soitec. Most foundries use either silicon or SOI, although silicon is currently much more dominant.
Silicon wafers are processed using chemicals. I'll use the chemical formulas for compactness. HF, H2SO4, HNO3, H2O2, NH4OH, HCl, KOH, IPA, CuSO4 are used in huge quantity and high purity forms. N2, Argon, NF3, NH3, WF6, and organometallics are some gas-phase chemicals. Solids include tantalum, copper, titanium, and tungsten.
Wet chemical manufacturers who supply foundries include KMG, Honeywell, Sumitomo Chemical, and Hitachi Chemical. Gas manufacturers who supply foundries include Air Products and Air Liquide. Metals manufacturers who supply foundries include Tosoh SMD and Cabot Corp.
The vendors who make equipment to spread the chemicals (solids, liquids, or gases) on silicon wafers are in two categories: Traditional and new. The traditional vendors are Applied Materials, Lam Research, and Tokyo Electron. The new vendors are fragmented, tightly controlled by one foundry and a single Asian country, and pursue a low-cost strategy.
The final equipment vendor I'll mention is ASML. This one is different. While other parts of the fab spread chemicals on silicon, ASML spreads light on photoresist, using proprietary techniques they invented and control. They have no competitors, and directly control the entire industry.