Diploma - Max Planck Institute for Solid State Research

12 2 Theoretical foundation
Figure 2.4: photoemission models – left: three-step model, dividing the photoemission process
into (1) excitation, (2) transport and (3) transmission to the vacuum; right: one-step model,
quantum mechanical description of the excitation process by calculating the transition propability
between the bound state and the unbound free state whose tail decays into the solid [28,
p. 245]
routine methods to obtain ultra-high vacuum (UHV) have been developed to establish
the precondition for analyzing clean surfaces [28, p. 8] which enabled the community
for the first time to distinguish surface and bulk originated spectral features. Since the
discovery of the high-T c compounds and the development of devices capable of angular
resolved photoemission spectroscopy (ARPES) , the interest in PES is regrowing.
Photoemission (PE) is basically a “photon in – electron out” process granting access
to the electronic structure of solids. Measuring the emission angle and the energy of the
electron one is able to analyze the manybody transition. Initial states will be marked
by the index i, final states correspondingly by f. In the following the two major models
are sketched (a detailed description is given in [28]).
2.2.1 Three-step model
The originally single-step quantum mechanical PE process is devided into three steps,
which will be discussed below. Nevertheless, this approximation is purely phenomenological
and has been described in detail in [29, 30].
(i) Optical excitation
The incoming photon (excited electron) is characterized by the energy E ph (E e )
and the momentum p ph (p e ), respectively. Neglecting the photon’s momentum
(since p ph ≪ p e ≈ 100p ph , this is only valid for ω ≪ 500 eV) and respecting
momentum conservation allows only “vertical” transitions – where the electron’s
momentum changes by plus / minus a reciprocal lattice vector. In principle, one
should deal with the extended zone scheme because elsewise one is not able to