RANDOM UNCERTAINTIES IN AES AND XPS .1. UNCERTAINTIES IN PEAK ENERGIES, INTENSITIES AND AREAS DERIVED FROM PEAK SYNTHESIS

We develop equations for numerically evaluating random uncertainties in Auger and x-ray photoelectron spectroscopies. First, the general statistical theorems involving the chi-squared (chi-2) distribution are clearly stated. These are applied to peak synthesis to determine the standard deviation uncertainties in quantities such as peak intensity, peak energy and peak width. General methods for their incorporation in new software are discussed. In the meantime, we suggest a new method for determining these uncertainty values using existing software provided by instrument manufacturers. These software packages typically give the chi-2 value for the fit of a model spectrum to the experimental data. It is shown that (provided random errors dominate) a change in any adjustable parameter to its one standard deviation limit will cause the chi-2 value for the fitting of all the other adjustable parameters to increase by unity. This provides a method which directly gives the standard deviation for each adjustable parameter.