Core Levels and Final States
Photoemission produces a final state that is lacking one electron with respect to the initial state. Therefore, PES always measures final-state energies which can be related to initial-state energies only after some theoretical considerations. The problem
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Photo emission produces a final state that is lacking one electron with respect to the initial state. Therefore, PES always measures final-state energies which can be related to initial-state energies only after some theoretical considerations. The problem is illustrated in Fig. 2.1. On the left-hand side are shown the one-electron orbital energies -E in the ground state of the neon atom. On the right-hand side are the final state configurations, as measured by PES for the same atom. 1 These are, of course, hole-state energies. The relation between these two sets of energy levels is far from trivial. However, one should add that the orbital energies (left side) cannot be measured. In general, one can only measure the energy levels given on the right-hand side, which are (many-body) hole-state energies [2.1]. These statements have to be modified for wide valence bands in solids. The PES final state in the valence band of Cu metal agrees well with the result of a one-electron band structure calculation (Chap. 7). In this case the screening of the photohole is almost perfect and therefore the final state energy equals the initial state one-electron energy. Thus, except for the case of valence states in wide-band solids, the most elementary "final-state effect" in PES is observed in the binding energy. If we consider, for example, a molecule with N electrons, the kinetic energy (with respect to the vacuum level Ev) of a photoelectron is given by (2.1) For the sake of clarity we have to add a short word concerning energyreference points. Although it may seem somewhat inconsistent, the energies of free atoms and molecules will be given with respect to the vacuum level (Evac) and those of solids with respect to the Fermi level (EF). The logical way of referencing would be to refer the energies of solids also to the vacuum level. This, however, would be contrary to general usage. As far as (2.1) is concerned, this means that for a solid the work function ¢ has to be subtracted on the right-hand side. 2 1
2
These energies are sometimes just called the orbital energies. The term orbital here does not mean that the spin gives no contribution to the energy. Here, ¢ is the smallest energy required to take an electron from inside the solid to the vacuum level.
S. Hüfner, Photoelectron Spectroscopy © Springer-Verlag Berlin Heidelberg 2003
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2. Core Levels and Final States
~,
EVQC
JEB
-E (2 P312)4 (2p 112) 2 {2S)2
(2p 312)3 /P 312 (2p112)1,2P 112 ( 2S)1,2S 112
(1s )1/S112
(1 S)2
Initial State
Final State
one electron
many body
orbital energies
binding energies
Fig. 2.1. Orbital energies and final (hole) statl] energies for neon. On the lefthand side one sees the orbital energies. The right-hand side shows the energy level obtained after ejection of an electron by a photon. The resulting electronic configurations (they are all one-hole states) are also indicated. The left-hand diagram is only of theoretical interest since the orbital energies themselves cannot be measured. The right-hand energy level include th
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