Thus, the “suboptimal” results (somewhat higher RSDs) that are obtained when constraints are applied to less-than-perfect peak shapes are often preferable because they prevent a fit from yielding unphysical or unchemical results. As shown in multiple examples, while unconstrained, less-than-optimal peak shapes may produce lower RSDs, they often lead to incorrect results. These constraints may include fixing the relative full width at half maxima (peak widths), area ratios, and/or the relative positions of fit components. However, because this ideal peak shape is often unknown, constraints on the components of a fit are usually necessary to obtain good fits to data. Here, we show that optimal XPS peak fitting is obtained when the peak shape (the synthetic mathematical function that represents the chemical states of the material) best matches the physics and chemistry of the underlying data. Peak fitting is typically based on the minimization of a figure-of-merit, such as the residual standard deviation (RSD). Peak fitting of x-ray photoelectron spectroscopy (XPS) data is the primary method for identifying and quantifying the chemical states of the atoms near the surface of a sample.
