MEAN ESCAPE DEPTH OF SIGNAL PHOTOELECTRONS FROM AMORPHOUS AND POLYCRYSTALLINE SOLIDS

The mean escape depth (MED) of the signal photoelectrons in x-ray phot oelectron spectroscopy (XPS) is a useful measure of the surface sensit ivity in WS measurements. The MED has previously been given by the pro duct of the inelastic mean free path for the signal electrons and the cosine of the photoelectron emission angle, but, due to anisotropy in photoemission and to the effects of elastic electron scattering, evalu ation of MED has become more complex. The theoretical formulation pres ented here is based on the solution of a kinetic equation within the t ransport approximation. This approximation allows us to solve the boun dary-value problem with simplifying assumptions for the scattering pro perties of atoms constituting an amorphous or polycrystalline solid. T o illustrate this approach, MED values have been computed for the 2s, 3s, and 4s subshells of aluminum, silver, and gold, respectively, for a large number of possible experimental configurations, and compared w ith corresponding MED values obtained from Monte Carlo simulations; sa tisfactory agreement has been obtained. Similar comparisons have also been made for the 3p and 3d subshells of silver, again with good agree ment. It has been found that the MED is strongly affected by elastic s cattering of electrons on their way out of the solid. The MED Values a re up to about 30% less than the values expected from the oversimplifi ed formalism (where elastic electron-scattering effects are neglected) for near-normal emission angles although MED Values can be much large r (by up to about a factor of 2) than those from the simple theory for near-grazing emission angles or for certain other experimental config urations. These calculations show that MED values can deviate substant ially (typically by +/-30% for common measurement conditions) from tho se expected from the simple formalism due to combined effects of elast ic electron scattering and of anisotropy in the photoionization proces s. MED values can be calculated much more rapidly, by orders of magnit ude, with the new formalism than from Monte Carlo simulations.