Page 420 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN012C-568 July 26, 2001 15:32

70 Photoelectron Spectroscopy

single-particle approximation. Two facts, however, clearly theoretical model. It can be described, however, by a su-
+
show the limitations of this type of interpretation: (1) the perposition of the eigenstates M of the ion, where each
k
deviations from KT [Eq. (7)] and (2) the appearance of of these states contributes with a certain weight factor g k :
shake-up and shake-off satellites. + ∗

M = g k M + (11)
From these two observations, it is obvious that we can- i k
k
not completely neglect final state effects. Using KT as a
first approximation, we can write In the high-energy limit where the electron leaves the ion-
ized system very quickly (sudden limit), the probability
(10)
of a transition to a final state M is equal to g . The main
E B (i) =−ε i − R i + 2
k k
+
where R i is called the “relaxation energy.” The meaning contribution usually comes from a state M that has the
i
of Eq. (10) can be understood by the following Gedanken same orbital occupation as the hypothetical frozen orbital
+ ∗
experiment. We separate the photoemission process into state (M ) . However, because of the presence of the hole,
i
two steps. In the first step, we use the FOA and remove one the orbitals of M i + differ somewhat from the orbitals of
electron from a given orbital i, leaving all other electrons the initial state M 0 . Since the weight factor g i is usually
unperturbed. To remove the electron we need the energy greater than 0.5, we normally can give an assignment of
−ε i . In the second step, we consider the reaction of the the main bands or main lines of a PE spectrum in terms
remaining electrons to the presence of the hole created in of KT, as discussed in the previous section. The remainder
the first step. The system will “relax” to a new, energeti- of the weights is frequently distributed over a variety of
+
cally favorable situation. Therefore, the relaxation energy final states M including the continuum states, thus ex-
k
is usually positive. Only in rare cases can specific quan- plaining shake-up satellites and the shake-off continuum.
+
tum mechanical effects (so-called correlation effects) lead When we are able to describe M to a good approximation
k
to small negative values of R. In Table III we have com- by a single 2h1p state, we reach a situation as discussed in
pared experimental binding energies to calculated orbital the previous section in connection with Fig. 9, where sev-
energies. The relaxation energies derived from these two eral of the observed shake-up satellites could be assigned
sets of data vary from orbital to orbital. R is much larger to specific electronic excitations in the core ionized sys-
for core electrons than for valence electrons; however, rel- tem. For larger systems, where the number of possible
ative to the magnitude of the binding energy, R is similar electronic excitations becomes very large, we will be able
for all shells. to identify the shake-up satellites only in cases where the
From our Gedanken experiment, we suggest that R i will remaining weight is not distributed more or less equally
be connected strongly to the mobility of the electrons in over a large number of final states. When g k has a some-
+
the system. If the orbital from which the electron is re- what larger value for a specific final state M , we will
k
moved is highly localized, as in a core orbital or a lone observe a characteristic shake-up satellite even for an ex-
pair orbital, the most efficient stabilization of the hole tended system. An example of such a situation will be
state will be achieved by transfer of negative charge to discussed in Section IV.D.
the vicinity of the hole. If a direct transfer is not possi- We now turn to binding energy shifts. From Eq. (10)
ble, the stabilization can be achieved only by polarization we obtain
of the surroundings. From this consideration we expect
E B (i) =− ε i − R i (12)
larger relaxation energies for the core ionization of met-
als, where the electrons in the valence band move almost Binding energy shifts depend as much on initial state ef-
freely, than for the core ionization of insulators, where the fects (via ε i )ason final state effects (via R i ). Often we
polarization of the nearest neighbor atoms yields the most are specifically interested in initial state effects, because
important contribution to the relaxation. For delocalized we want to derive information on the electronic structure
holes that result from the photoionization of π electrons of of the initial system M 0 and its dependence on variations
unsaturated molecules or valence electrons of solids, the in chemical constitution. This information, however, can
relaxation contribution is expected to be smaller and less be derived only if R is negligibly small or if we are
dependent on the individual orbital. This is in accordance able to obtain independent information on R. The re-
with the data shown in Table III; for formaldehyde, for laxation contribution itself also contains valuable infor-
example, the smallest relaxation energy is found for the π mation, since it is connected with electronic relaxation
orbital 1b 1 . processes that can take place during a chemical transfor-
The considerations discussed above can also be viewed mation. In a wide variety of chemical reactions the transi-
+ ∗
in a somewhat different manner. The ion state (M ) tion state is charged. The better this charge can be screened
i
formed in the FOA is not a real state (eigenstate) of the by a relaxation of the whole electronic system, the lower
investigated system. It exists only in the framework of the the energy of the transition state.