The pressure dependence of the deposition rate in a magnetron sputtering system

An analytical expression is obtained for the pressure distance product parameter that defines the pressure dependence of the deposition rate of sputtered atoms in the Keller-Simmons formula. The generalized Keller-Simmons formula is proposed, which can be used in the case when the 1D approach is not suitable for the simulation of the flux of sputtered atoms to a substrate. The generalized Keller-Simmons formula using the pressure distance product derived from the analytical expression allows one to simulate the pressure dependence of the deposition rate of sputtered atoms for different target materials and to simulate the chemical composition of a multicomponent film at different pressures and distances from a compound target to the substrate. Results of simulations using the generalized Keller-Simmons formula are in good agreement with the experiment.