Final States and Initial States

 

Initial and Final State Effects

by C. Richard Brundle, Brundle & Associates, Soquel, California, USA

 

XPS can provide a wide variety of physics and chemistry information, but it must be remembered that the Photoemission Process involves a transition from the initial, neutral, electronic state of the species concerned, to a final, positively ionized state.

Because of this the XPS information obtained is always, at some level, a mixture of effects in both states, though in some cases it is mostly ground state related and in others mostly final state related. A list of phenomena or effects involving XPS and related subjects is given below, with an indication of whether the phenomena or effect mostly address the initial state (IS) or the final state (FS) of the species, or both, or whether it is irrelevant (IRR) to the subject concerned. Each has a link to a description elsewhere on the website.

 

      • Atomic composition determination (IS and FS)
      • Atomic geometries (IRR)
      • Auger chemical shifts (FS)
      • Auger parameter (IS and FS)
      • Auger process (FS)
      • Auger spectroscopy (FS)
      • Auto-ionization (FS)
      • Born-Haber cycle (IS and FS)
      • Charge distribution (IS and FS)
      • Configuration interaction, CI  (IS and FS)
      • Core hole lifetimes (FS)
      • Core level Chemical shifts (IS and FS)
      • Core level multiplet splitting (FS)
      • Coster-Kronig transitions (FS)
      • Density of States (IS)
      • Electronic structure, electron configuration (IS and FS)
      • Extrinsic energy losses (IRR)
      • Film thickness (IRR)
      • IMFP (IRR)
      • Intrinsic losses (FS)
      • Ionicity, covalency (IS and FS)
      • Ionized MO energy levels (FS)
      • Jahn-Teller splitting (IS and FS)
      • J-J coupling (FS)
      • Joint Density of States (IS and FS)
      • Neutral MO energy levels (IS)
      • Peak asymmetries (FS)
      • Peak FWHM (Gaussian part, instrument effect) (IRR)
      • Peak Lorentzian width of FWHM (FS)
      • Phonon broadening (FS)
      • Photoelectron diffraction (IRR)
      • Photoionization cross-section (IS)
      • Plasmon losses (IRR)
      • Quantum levels (IS and FS)
      • Relaxation energies (FS)
      • Russell-Saunders coupling (FS)
      • Shake-off structure (FS)
      • Shake-up structure (FS)
      • Spin-orbit splitting (IS)
      • Surface Core level chemical shifts (IS and FS)
      • Surface Electronic structure (IS and FS)
      • Surface sensitivity (IRR)
      • Vibrational effects (FS)
      • Work function (IRR)
      • XPS BE’s (IS and FS)
      • XPS core level natural line widths (FS)

 

 

Organization of Initial State and Final State Effects

From Paul van der Heide book:  X-ray Photoelectron Spectroscopy – An introduction to Principles and Practices

 

 

Initial State Effects:

These describe the effects induced by the bonding that occurs with other atoms/ions in the neutral ground state.  Although only valence electrons take part in bonding, all electrons (valence and core electrons) experience the change in electron density induced (configuration interaction). These effects are primarily responsible for the ability of XPS to derive the speciation of photoelectron emitting atoms/ions.

Initial state effects arise from neutral ground-state polarization (bonding) and spin orbit splitting. The former can be subdivided into interatomic effects (those from neighboring atoms/ions) and intra-atomic effects (those from within the atom/ion).

Initial state effects describe any effect that results from the electronic structure of an atom/ion undergoing photoelectron emission that was present prior to the photoelectron emission process. These effects are split into two subgroups:

  • Spin-induced interactions present within the photoelectron emitting atom/ion
  • Coulombic interaction present within the photoelectron emitting atom/ion

Spin-induced interactions describe the effect a spinning charge following a nonsymmetric orbit (those with l > 0) has on the B.E.XPS values of emitted photoelectrons. This is typically referred to as spin orbit splitting.  Spin orbit splitting can be influenced by multiplet splitting.

Coulombic interactions describe the influence of the charge density within the photoelectron emitting atom/ion on the B.E.XPS values of emitted photoelectrons. This is controlled by the local chemical environment the photoelectron emitting atom/ion resides in and the electronic structure of the atom/ion itself. The former is referred to as an intra-atomic effect, whereas the latter is referred to as an interatomic effect. These effects are most commonly seen in the scaling of B.E.XPS values with the following:

  • Oxidation state of photoelectron emitting atom/ion
  • Bond distance of photoelectron emitting atom with neighboring atoms/ions
  • Madelung potentials (values only exist for ionic crystals and are only applicable to systems displaying the same structure)
  • Electronegativity of neighboring atoms/ions (only applicable to systems of similar structure)

With the exception of spin orbit splitting, all initial state effects can be understood within the context of the charge potential model. This model is useful in that it describes from a classical standpoint, the interplay between intra-atomic and interatomic effects.

 

Final State Effects:

These describe the effect induced by the perturbation of the electronic structure resulting from photoelectron emission, particularly when core levels are involved. Since such effects also depend on the initial electronic structure (that from bonding), they too can be useful in revealing the original speciation of the photoelectron emitting atom/ion.

Final state effects can be seen to stem from photoelectron-induced polarization and rearrangement effects. Although interatomic and intra-atomic effects are apparent, these are more closely intertwined. The same can be said for excitation and rearrangement. Shake-up effects can influence multiplet splitting.

Final state effects vary as a function of:

  • The core hole lifetime (shorter lifetimes result in stronger final state effects since these are more likely to occur within photoelectron emission timescales)
  • The coupling that exists between electrons in different stationary states (increased coupling results in stronger final state effects), hence the enhanced final state effects noted from elements on the lower right-hand side of the periodic table (cf. Russell–Saunders vs. j–j coupling arguments)

 

 

Initial State Effects that exist before Photoelectron Emission Process 

  • Ground state polarization
    • Coulombic interaction effects – Intra-atomic behavior – due to charge density of local chemical environment of the photoelectron emitting atom
    • Coulombic interaction effects – Interatomic behavior – due to charge density of the electronic structure of the photoelectron of the atom/ion itself
  • Spin-Orbit splitting
  • Oxidation state
  • Bond distance
  • Madelung potentials for ion crystals
  • Electronegativity

The problem in the use of binding energies as a probe for local structures in the electron distribution is connected with the fact that the binding energy is the difference between the energy of an initial and a final state.

 

FINAL State Effects that exist after Photoelectron Emission 

  • Excited state polarization
    • Coulombic  effects – intra-atomic
    • Multiplet splitting  (also known as exchange splitting)
  • Rearrangement effects (lifetime ~10-15 seconds)
    • Shake-up (excitation of valence band electrons)
    • Shake-off (loss of valence band electrons)
    • Plasmons – surface and bulk (excitation of conduction band electrons)
    • Auger peaks
    • Peak asymmetry

Final state effects in XPS describe any effect resulting from the perturbation to the electronic structure of an atom/ion undergoing photoelectron emission, that is, any effect (interatomic and intra-atomic) resulting from core hole formation. Final state effects can vary as a function of core hole lifetimes, and can be subdivided into two groups, these being

  • Core hole-induced polarization (instantaneous electrostatic and magnetic effects)
  • Core hole-induced rearrangement (subsequent excitation and relaxation processes)

Core hole-induced polarization is an instantaneous effect that results from the removal of a spinning charge (the photoelectron) from an atom/ion. This not only results in an electrostatic effect (all electrons have unit charge) but also in a magnetic effect (spinning charges produce magnetic fields). These can influence the recorded B.E.XPS in a number of different ways.

Rearrangement effects stem from the energy transfer associated with the dissipation of the core hole produced during the photoelectron emission process. Since this and any subsequent electronic rearrangement can occur within the timescale of photoelectron emission, these can introduce new rearrangement-specific spectral features. Examples of these include

  1. Satellite peaks and photoelectron peak asymmetry
  2. Plasmon loss peaks
  3. Auger electron peaks (since these are X-ray induced, they also appear in XPS spectra, but not vice versa)

Note: Satellite peaks and photoelectron peak asymmetry are considered together since both stem from the same source; only the transition energies differ.

 

 

 

Sequence of Actions – Starting from Initial State and Ending in Final State

 

 

 

Koopmans’ Theorem

The BE of an electron is simply the difference between the initial state (atom with n electrons) and final state (atom with n-1electrons (ion) and free photoelectron)

If no relaxation* followed photoemission, BE = – orbital energy, which can be calculated from Hartree Fock.

*this “relaxation” refers to electronic rearrangement following photoemission – not to be confused with relaxation of surface atoms