The method of finite element analysis is used to calculate oxygen-concentration profiles and oxygen-absorption rates at the substrate and along the shields in an rf magnetron reactive sputtering system having a 12-inch-diameter magnetron. Results for several shield arrangements are calculated as a function of oxygen flow rate. The approach used assumes the following: (i) The target is being sputtered in the metallic state; (ii) the oxygen-concentration profile in the system can be calculated from the diffusion equation; (iii) the maximum amount of oxygen that can be absorbed at any point in the system is proportional to the metal deposition rate at that point; (iv) the target absorbs no oxygen as long as it is in the metallic state. The relative metal deposition rate along the substrate and shields is calculated, normalized to the measured deposition rate at the substrate, and used as a boundary condition for the diffusion equation. The calculated oxygen flow rate for the formation of stoichiometric substrate films agrees with experimental results to within 15%. The critical flow rate at which the target oxidizes, Qc , is measured experimentally and when used in the model gives an oxygen partial pressure of about 0.31 · 10−6 torr at the sputtering track.
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