Diploma - Max Planck Institute for Solid State Research

2.2 Photoemission Process 11
Figure 2.3: mean free inelastic scattering path of electrons in solids; only weak material
dependence [28, p. 8]
b) the Neumann function (regular at r → ∞) in the interstitial region.
Those basis functions and their derivatives are by generation smooth at the
sphere’s boundary. Furthermore, assuming that only closed packaged structures
(corresponding to tightly bound compounds) will be regarded, the atomic spheres
can be extended until the interstitial part vanishes completely (ASA). The major
drawback of the LMTO code is its dependence on ASA which does not yield good
approximations for anisotropic or “open” structures not to mention slab calculations.
In principle, one has to take care of each setup by manually adjusting
the spherical overlap, eventually even introducing “empty spheres” (an additional
atomic sphere without a nuclei potential but with local basis functions), to obtain
valid configurations.
All calculations will be labelled as (lmto 5.01.1, parameters and approximations
used).
Since the applied approximations and the basis sets are different for LMTO and FPLO,
their spherical contributions (l, m projection) can differ severely although the converged
charge densities are approximately the same. Due to the fact that LMTO is based on
ASA and a spherically-averaged potential the results are in principle less accurate than
the ones obtained by FPLO, thus the latter has been used for most of the calculations.
Nevertheless, to estimate the hybridization strength it was necessary to extract the
coefficients from LMTO (see ch. 4.2).
2.2 Photoemission Process
Photoemission spectroscopy (PES) has been one of the first techniques which allowed
to study the quantized nature of electrons inside solids, but due to the small electron
escape depth (see fig. 2.3) the interpretation of the spectra was difficult. The interest
in electron-based spectroscopy has risen in the 1970s (especially for solids), because