Initial State and Final State Effects – D. Wayne Goodman

Koopmans’ theorem predicts that the XP spectra observed represents the electronic states of electrons in the analyte atom before the photoemission process, i.e., the initial state. Spin orbit coupling is an example of an initial state effect, in which spectral features arise from the inherent unpaired electron make-up of the atoms prior to the photoemission event. In this scenario, peak splittings due to energy differences between singlet and triplet states via interaction of the spin and orbital magnetic moments occur whenever there are unpaired electrons in the valence shells. If the electron ejected is parallel (triplet state) to that of the valence electrons, it can undergo exchange interaction and result in a lower kinetic energy (higher binding energy) than the case for an anti-parallel spin (singlet state). The result is a doublet in the XP spectrum. Splittings due to spin orbit coupling are generally not observed (resolved into 2 peaks) for low atomic number elements (Z ≤ 20). A Ca 2p core level (Fig. 11), for instance, gives two photoemission peaks: 2p_1/2 (l = 1 and J = 1 − 1/2) and 2p_3/2 (l = 1 and l = 1 + 1/2). Similarly, d and f orbitals can split upon photoionization. The relative intensity ratio of the 2 peaks of a spin-orbit-coupled doublet is determined by the 2 J + 1 multiplicity of the levels. For example, the relative intensity of J = 3/2 and J = 1/2 components of a 2p is 4:2 = 2:1; for that of 5/2 and 3/2 peaks of a 3d level, it is 6:4 and for the 7/2 and 5/2 peaks of the 4f level, it is 8:6.

FIGURE. The XP spectrum of Ca 2p level showing spin-orbit-coupled l ± s = 1/2 and 3/2 peaks.

Binding energy shifts from initial state effects can be interpreted using the charge potential model:

where Eⁱ_b = the binding energy of an electron from an atom i, q_i is the charge on the atom, k = constant, q_j = the charge on a neighboring atom j, r_ij = the distance between atom i and atom j, and E^ref_b = the energy reference. The kq_i term indicates that binding energy increases with increasing positive charge on the atom from which the photoelectron emanates. The ∑jqjrij term, known as the Madelung sum, in ionic solids negates the contribution from the kq_i term, since the neighboring atom has an opposite charge.

During the photoionization process, changes in the electronic environment due to the creation of the core-level vacancy leading to final state effects play a large role in influencing the binding energy. In order to properly interpret the XPS binding energy value, perturbation of the electronic environment during the photoemission must be accounted for. For instance, let N = the number of total electrons in the atom before photoionization. The atom in its initial state conditions Eⁱ_N absorbs a monochromatic photon of energy, hν, causing the ejection of a photoelectron with kinetic energy, E_k. The adsorption process takes place in approximately 10⁻¹⁷ sec. Approximately 10⁻¹⁴ sec later, the atom itself has one less electron and a core-level vacancy. The energy balance between initial and final states of the atom before and after photoionization can be expressed as:

where Eⁱ_N = total energy of the atom with N electrons in the initial state (i.e., before photoionization), E^f_N−1, l = the total energy of the atom with N – 1 electrons and a hole in the core level, l, in the final state. It should be emphasized that the N − 1 remaining electrons in the final state atom and electrons in neighboring atoms are influenced by the presence of the core shell vacancy, relaxing to lower the total energy of the of the atom by ΔE_relax. The relaxation energy should be accounted for in the determination of the kinetic energy of the photoelectron. The binding energy is not simply the energy of the orbital from which the photoelectron is emitted (i.e., initial state effect), but rather the difference in energy resulting from the perturbation of the remaining electrons upon removal of a core level electron. These photoemission processes occur at time scales sufficiently slow to influence exiting electrons via attraction of the core-ionized atom, known as the adiabatic limit. In the other extreme, photoelectrons can be emitted before the core-ionized atom relaxes. Photoemission during these “fast” processes (known as the sudden limit) often result in extra peaks in the XP spectrum. Shake-up and shake-off losses are final state effects which appear in the XP spectrum resulting from a photoelectron imparting energy to another electron within the atom. These features arise from the perturbation process (final state effects) caused by photoemission. The energy associated with relaxation may be sufficient to excite a valence level electron to higher energy. The electron receiving energy either ends up in a higher unoccupied state having discrete energy (shake-up) or an unbounded state (shake-off). Since photoemission and relaxation occur simultaneously, the outgoing photoelectron loses kinetic energy. These shake peaks, due to kinetic energy losses, appear at higher binding energy relative to the main core-level peak. Discrete shake-up losses are pronounced for metal oxides. Pronounced intensities are typically found for compounds having unpaired 3d or 4f electrons. Shake-up features that show up in the XP spectra of the Cu 2p core levels in Cu oxide stand out as a notable example (Fig. 12), providing noteworthy diagnostic tool for detecting the Cu²⁺. The CuO spectrum shows pronounced shake-up satellite features (top) due to the fact that Cu²⁺ ([Ar]3d⁹) has an open shell configuration. In contrast, Cu₂O (bottom) lacks these features since Cu⁺ ([Ar]3d¹⁰) has a closed shell arrangement.

FIGURE. The XP scans of Cu 2p core levels of CuO (top) with pronounced shake-up satellites.
[Reprinted from Chemical Physics Letters, Vol. 63, M. Scrocco, p. 53, Copyright © 1979, with permission from Elsevier Science.]