Diploma - Max Planck Institute for Solid State Research

2.2 Photoemission Process 15
in eq. 2.16. The best compromise between complexity and feasible computational effort
for initial and final states has been found with inverse Low Electron Energy Diffraction
(LEED) states. Since in LEED a valid description for initial, transmissible and
reflected electron states (which respect the low mean free path of electrons as well as
the vacuum / solid transition by a potential step) has been developed, the left task is
to reverse the transmitted (incoming) LEED beam and to add the photon receiving the
initial and final states for photoemission.
2.2.3 General remarks
As it has been sketched, PE spectra reflect the transition between two eigenstates and
hence differ fundamentally from ground state Kohn-Sham eigenenergies [31]. At least
for Hatree-Fock theory Koopmans stated, that the energy of the highest occupied orbital
is approximately the ionization energy (with negative sign) [32]. A more detailed review
is given in [31]. However, for a qualitative description of valence band photoemission
of metals one can use DFT results hence the final state almost resembles the initial
state because the photoexcitation hole is delocalized – which means well-screened. In
contrast, core level or localized electron photoemission depend strongly on the relaxation
of the final state.
Besides, since the inelastic mean free path of electrons is in the order of the lattice
constant, the k ⊥ component is not conserved. Thus, one has to partially integrate
over k ⊥ for initial states. The former and the finite lifetime of final states cause the
emergence of projected band structure in photoemission.