ESTIMATION OF DEPTH PROFILES FROM INELASTIC BACKGROUNDS IN XPS .1. GENERAL RELATIONSHIPS

The accuracy by which an unknown concentration profile can be found By analysis of XPS spectra is investigated theoretically by analytical a nd numerical techniques. The problem of determining the profile is ref ormulated as an optimization problem. By use of analytical techniques we obtain qualitative statements about the depth resolution and we der ive fundamental relationships between the different parameters that in dicate their relative importance. In order to illustrate the various d ependencies of the variability of the model parameters, we derive anal ytical expressions for the standard errors of the model parameters for two simple models: a delta layer and an exponentially decreasing prof ile, Furthermore, the complete probability distribution of the model p arameters for a rectangular model is investigated numerically.