Photoemission of Valence Electrons from Metallic Solids in the One-Electron Approximation

Abstract

Solids are characterized with respect to the size of the energy gap between valence and conduction band as insulators, semiconductors or metals. In PES and IPES experiments, only metals possess an experimentally accessible (and generally accepted) zero of energy, namely the Fermi energy. The Fermi energy generally shows up as a step in the EDC 1 and therefore it is a very convenient experimental reference point. In insulators and semiconductors (although they of course also have a Fermi energy, it does not usually show up clearly in the PE data) the top of the valence band or the bottom of the conduction band are often taken as the experimental zero of energy. These energy points, however, are not very well defined in the experimental spectra. In order to treat only the simplest possible case, the discussion in this chapter will be restricted to metals. The generalization to insulators or semiconductors is often straightforward. In the most naive view, a metal can be considered as a sea of conduction electrons. The simplest excitations in this metal are the "plasmons". These are collective excitation modes, which one can view as oscillations of the conduction electrons against the cores ofthe positively charged ions [6.2]. The best way to investigate these plasma oscillations is via inelastic electron scattering whereby both the energy and the momentum vector can be measured. The photoelectrons on their way to the surface may also produce such excitations and these show up as side bands to the primary photoelectron spectrum (Chap. 4). In the next step of sophistication the energy states of a metal are characterized by the single-electron energies E and their wave vectors k; this E (k) relation is called the band structure. 2 In the band-model interpretation PES (IPES) measures transitions between states in occupied (empty) and empty (empty) bands. These transitions are vertical in a reduced zone scheme (energy and wave-vector conservation) and therefore occur without 1 This statement is not correct for one dimensional metals [6.1] which do not show a step in the measured spectra but rather a gradual increase in intensity starting at EF (therefore, the valence electrons in these systems are sometimes called Luttinger liquid). 2 k designates the wave vector of the Bloch states in a crystal; K designates the wave vector of the photoexcited electrons within the crystal and pin designates the wave vector of the photoelectrons outside the crystal in the vacuum.