Effect of porosity on thickness uniformity of MgF₂ films on spherical substrates

Simulation based on Knudsen's law shows that film thickness uniformity above 99% can be realized on spherical substrates with optimized profiles of shadowing masks. However, a type of optical thickness nonuniformity is revealed when the masks are applied for thickness correction of MgF₂ films experimentally. The optical thickness nonuniformity depends on steepness of the spherical surfaces and reaches 5% approximately for surfaces with CA/RoC = 1.22. Porosity of the MgF₂ film is superimposed on Knudsen's law to interpret the optical thickness nonuniformity. For theoretical simulation, the influence of porosity on optical thickness distribution is characterized by a new parameter that describes nonlinear dependence of deposition rate on cosine function of molecular injection angles in Knudsen's law. Utilizing the optimized deposition model, optical thickness uniformity of MgF₂ films approaching to or above 99% has been achieved for surfaces of different steepness in a single coating run.