VUV Spectroscopy of Atoms, Molecules and Surfaces

92 Chapter 5. Femtosecond VUV core-level spectroscopy ...
plying an increase in the core-level binding energy for a metal with a less
than half filled valence-band and vice versa. For the transition metals with
a partly filled d-shell the valence-band narrowing is dominating while for the
simple sp metals the two contributions are almost equal, resulting in a small
(∼100 meV) shift towards lower binding energy for Al(100) and no shift for
Al(111) [83].
The natural width of a core-level depends on the probability that the corehole
will be filled by an electron decaying from an outer (valence) shell. This
probability is, in general, larger the larger the number of electrons occupying
the outer shells but this picture may be modified by correlation effects and
particularly strong decay channels [84]. Typically, the core-level widths vary
in the 0.1–2 eV range between different elements with comparable core-level
binding energies [85]. For example, the Al 2p level with a core-level binding
energy of ∼73 eV has an unusually narrow width of ∼50 meV, as reflected
by the presence of only three electrons in higher-lying shells. At the other
extreme, the widths of the 3p and 4p levels of the first- and second-row
transition elements, spanning a 30–90 eV binding-energy range, are 2–4eV,
with the lowest value attained at the left of the periodic table [85, 86]. The
natural Lorentzian width is often masked by Gaussian contributions from
phonon broadening and the experimental resolution of the electron-energy
analyzer (each contributing at least ∼50 meV) [87]. In addition, there will
be a tail on the low-kinetic energy side of the core-level peak arising from
intrinsic- and extrinsic excitation processes taking place during- and after the
photoionization process, respectively. The most important intrinsic losses
are due to electron-hole pair excitations which give rise to an asymmetry of
the core-level peak. The extrinsic losses arise from inelastic scatterings of
the photoelectrons travelling towards the surface and their contribution will
be minimum when the escape depth is smallest possible, i.e. for a ∼50 eV
kinetic energy of the core-ionized electrons (which contribute the most to the
spectrum). Considering all these contributions, a measured core-level peak
is most often fitted with the so-called Doniach-Sunjic line-shape [88]
D(E) =
E−EB
Γ(1 − α)cos[πα/2+(1−α)arctan(−γ )]
(1 + (E−EB)2
γ2 ) (1−α)/2
(5.1)
convoved with a Gaussian representing the combined effects of the phonon
broadening and experimental resolution, and added to a polynomial background
representing the intrinsic- and extrinsic losses. Here, EB is the
core-level binding energy, γ the natural width (HWHM), α an asymmetry
parameter accounting for electron-hole pair excitations and Γ the Gamma
function.