Shake loss intensities in x-ray photoelectron spectroscopy: Theory, experiment, and atomic composition accuracy for MgO and related compounds

The relative intensities of XPS core levels, scaled by their photoionization cross sections, are regularly used to determine sample atomic composition. Cross sections, however, give the intensity to all possible final states for the core ionizations, not just to the main peak. This includes all intrinsic satellite structure (shake states and, for open shell systems, the different ionic multiplets). In practice, for solids, this is usually experimentally impossible to determine accurately because such a satellite structure sits on the inelastically scattered electron background and cannot be easily separated. Therefore, usually, only the intensity of the main peak is used. This limits the ultimate possible accuracy of XPS composition determination. The purpose of the present paper is to examine the contributions that a theoretical analysis of losses of intensity can make to improve quantitation. For an MgO single crystal, we show that the correct stoichiometry of 1:1 can be recovered using the theoretical analysis of the experimental MgO peak ratio intensities. For materials with a sufficient bandgap for the XPS main peaks to be separated from the scattered background, the intensity of main peaks can often be accurately determined. Thus, if one uses theory to calculate that fraction of the total intensity lost from a main peak into all its satellite structure, the intensity of just main peaks could then be used to more accurately determine relative atom % composition. This work tests this approach using a single crystal MgO (50% Mg, 50% O) standard. Ab initio electronic structure theory of representative MgO clusters is used to determine Hartree–Fock wave functions for the ground state and final ionized states corresponding to the main Mg 2p and O1s XPS peaks of the oxide. The sudden approximation, SA, is used to determine the fractional losses from these main peaks to shake satellites, which is found to be greater for O1s than Mg2p. This results in predicted “apparent composition” for stoichiometric MgO of 55.2% Mg, 44.8% O instead of the true 50% Mg, 50% O. Equivalent theory for CaO results in a predicted apparent Ca value of 53.4%. Experimentally, using Mg2s or 2p intensity ratio to O1s, we find values between 52.2% and 56.0% Mg using two crystals and four different instrument electron pass energies. The average value of the measurements is 54.5% Mg when corrected for the presence of an adventitious carbon overlayer and slight surface hydroxide. Though this agreement with theory may be somewhat fortuitous, given the potential experimental errors, which are fully discussed, it is similar to that in our earlier study on LiF. We also present preliminary experimental data on Mg(OH)₂ and MgSO₄, which show a similar trend of apparently higher than 50% Mg, but we have no theory values. We are not yet able to experimentally test for validation of the difference between apparent composition for MgO (55.2% Mg) and CaO (53.4% Ca), owing to significant carbonate formation at the surface of the single crystal CaO. An important conclusion is that the theoretical determination of shake losses, obtained with ab initio wavefunctions and the SA, is likely to be a useful way to calibrate the accuracy and reliability of compositions obtained from XPS intensities and merits further study.