The escape probability of Al 2s photoelectrons leaving an aluminum oxide sa
mple (Al2O3) has been studied as a function of depth of origin. It has been
found that the escape probability (the so-called emission depth distributi
on function - DDF) depends strongly on the photoelectron emission direction
with respect to that of the incident X-ray beam. In particular, in the emi
ssion direction close to that of photon propagation, the DDF differs substa
ntially from the simple Beer-Lambert law and exhibits a nonmonotonic behavi
or with a maximum in the near-surface region at a depth of about 10 Angstro
m. Experimental results are in good agreement with theoretical predictions
based on Monte Carlo simulations of the electron transport and with analyti
cal solution of the linearized Boltzmann kinetic equation with appropriate
boundary conditions. Both theoretical approaches take into account multiple
elastic scattering of photoelectrons on their way out of the sample. It is
shown that the commonly used straight line approximation (SLA), which negl
ects elastic scattering effects, fails to describe adequately experimental
data at emission directions close to minima of the differential photoelectr
ic cross section.