Escape probability of signal photoelectrons from non-crystalline solids: influence of anisotropy of photoemission

The escape probability of photoelectrons as a function of depth of orgin haa been studied experimentally, analytically and by the Monte Carlo (MS) technique. The depth distribution function (DDF) describing the probability for an electron emitted at a certain depth to leave a surface without being scattered inelastically has been obtained by solving a kinetic equation in the transport approximation. The analytically derived DDF is a universal function of the ratio of the inealstic to the transport mean free paths and the asymmetry parameter. In the directions of minima of the angular distribution, this function is no longer exponential, but it may be essentially nonmonotonic, reaching its maximum value at the depth comparable with the inelastic mean free path. The maximum value of the DDF exceeds its surface value by about 50% for the asymmetry parameter being equal to 2 in the emission directions close to that of X-ray propagation. Under the same conditions, the mean escape depth of electrons may be several times larger than the value predicted by the usual XPS formalism. Such behaviour of the escape probability is explained by elastic scattering of photoelectrons.The solution to the kinetic equation for a uniform target is generalized for a sample with an arbitrary depth profile and depth-dependent elastic and inelastic scattering cross-sections under the condition of the ratio of the inelastic to the transport mean free paths being independent of depth. Analytical formulas for the photoelectron yield from overlayer/substrate structure have been derived and studied in detail. The analytical predictions are compared with the experimental and Monte Carlo simulation data obtained for aluminium oxide/aluminium specimen. A satisfactory agreement is observed between the experimental and theoretical results.