Full-range solution for the measurement of thin-film surface densities with proton-excited x rays

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Abstract
A Fredholm‐integral expression for characteristic x‐ray production by proton bombardment is developed relating multicomponent elemental thin‐film concentration profiles to proton‐stopping power, x‐ray‐production cross section, and x‐ray attenuation. The thickness of Al2O3 and Ta2O5 films on their respective metallic substrates were measured with 20‐ to 80‐keV protons with an accuracy of 5% for thick films (1200 Å) and 25% for thinner films (30 Å). Nonlinear regression analysis of the data indicated that all parameters of interest, including the zero‐voltage anodization potential, can be determined from the raw data. With exception to the oxygen K‐shell x‐ray attenuation coefficient, the parameters were determined with good to reasonable accuracy. A general concentration profile could not be determined by numerical methods as a result of insufficient variation in the kernel of the integral equation.