Deviation of photoelectron intensity from Beer-Lambert law in near-ambient pressure hard x-ray photoelectron spectroscopy

In near-ambient-pressure photoelectron spectroscopy, the photoelectron intensity is assumed to follow the Beer-Lambert law, that is, the intensity decreases exponentially with distance d between the sample and the aperture cone. In this study, the gas pressure dependence of photoelectron intensity is systematically studied in a wide range of d values from 0.3 up to 5 mm. The experimental results were reproduced by replacing d with d + do (do is a constant) in the Beer-Lambert law. The do value was evaluated as similar to 1 mm, which is considerably larger than the normal d value of 0.3 mm. Fluid dynamics simulation results obtained using a structural model with a size close to that of the actual differential pumping system suggested that the residual gas in the long pumping path caused a large do value.