Core level spectroscopy

CASTEP can calculate spectroscopic properties of solids that are due to electronic transitions from a core level of an ion to the conduction band (X-ray absorption) and from the valence band to a core level (X-ray emission). This can be used to describe a wide variety of experimental results connected to such processes. Core holes can be created by X-ray or electron incident radiation.

The core level is localized, so core level spectroscopy provides a detailed element-specific picture of the local electronic structure around a given atomic site. There is no contribution from the other atoms in the system, so the electronic states for a specific atom can be investigated.

In the case of anisotropic systems, angular-dependent experiments enable the separation of states with different symmetries for the involved orbitals. An important consequence is that symmetry states, which result solely from chemical bonding, can be studied.

Emission spectroscopy

X-ray emission spectroscopy (XES) is a classical technique used to study the electronic structure of bulk samples. It is ideally suited to these systems due to the large information depth (around 0.1 m for soft X-rays). In XES the core hole created by an X-ray absorption process is filled by the decay of a valence electron. For this process energy is conserved by the emission of an x-ray photon of matching energy. A selective, resonant excitation of a core hole state at the atomic center of an adsorbate can be used to probe surfaces.

Absorption spectroscopy

Electron energy-loss near-edge structure (ELNES or EELS) and x-ray absorption near-edge structure (XANES) spectroscopies provide information on the unoccupied electronic states by exciting one electron from a core level into an unoccupied state. Scanning transmission electron microscopes with an electron energy-loss spectrometer attached have been used extensively in the study of nanoscale materials, providing information on local composition, structure, and electronic structure. However, the probing electron or x-ray interacts with a system that has been perturbed by the probe itself. The system being studied has had an inner-shell electron removed, leaving a core hole.

Core hole effects

The relaxation of a system with a core hole will affect the observed core level excitation spectra so that interpretation of the experimental spectrum becomes a more challenging task. A satisfactory theory of optical spectra or core excited spectra should calculate two particle electron-hole interactions in a reliable and accessible way. In the core level excitation process, the core hole is localized on a single atomic site. Using an atom with a reduced occupation in the core level in a supercell approximation has been a good and popular description for the calculation of core level spectroscopy using standard density functional theory (DFT).

Recent developments in core-level spectroscopy calculations using the Bethe-Salpeter equation or time-dependent DFT (or a combination of the two) provide more rigorous approaches for a core-level spectra calculation. In these methods many-body effects, such as the broadening of spectra due to electron-hole lifetime, can be taken into account in a natural way. While good agreement with experimental results has been achieved, this necessarily comes with a much greater computational burden in comparison to standard ground state calculations.

A systematic observation of core hole effects and a quantitative estimation of the core hole strength in materials can assist in the simulation and interpretation of core level spectra. Applying empirical rules, a core-level spectrum is not likely to be heavily influenced by core-hole effects, so information on the ground electronic structure of a material can be inferred directly from the experimental spectrum. In this case, traditional ground state calculations should predict the main features of experimental results and allow interpretation of the spectrum. If this is not the case, inclusion of the influence of the core hole is essential in the theoretical simulation. Analysis of experimental results should take into account that near-edge fine structure includes influences in the core excitation processes beyond the ground state electronic structure.

There is an open question regarding the best way of handling the charge of core holes; depending on the nature of the system it might be appropriate to treat the system either as having lost an electron and thus having a charge of 1 or as neutral. Materials Studio assumes the former treatment.

Energy broadening

The ELNES calculation can be performed with an energy resolution far better than that used to obtain experimental results. Therefore, the calculated ELNES must be broadened before comparing it with the experiment. The broadening observed in the experimental spectra has three origins: the lifetime of the core hole, the lifetime of the excited state, and instrumental broadening. A good description of this subject was given by Hebert (2007).

Instrumental broadening is easiest to simulate: it can be modeled by a Gaussian with a FWHM given by the instrument. For a TEM equipped with a field emission gun, this is usually about 0.6-0.7 eV. Some instruments are equipped with a monochromator to improve energy resolution to about 0.1 eV. In nearly all cases the energy distribution can be modeled by a Gaussian curve.

The broadening by the core hole lifetime depends on the atom and the edge. Values for lifetime broadening are tabulated and can be found in the literature, see Fuggle and Inglesfield (1992). Broadening due to the lifetime of the core hole is, however, relatively low for edges accessible in EELS (about 0.2 eV for the Ni or Cu L3 edge). The broadening of core hole lifetimes can be modeled by a Lorentzian (Fuggle and Inglesfield, 1992).

The broadening by the excited state lifetimes is more complicated. At the edge onset (where the lifetime of the excited state approaches infinity) the broadening is zero and increases with increasing energy. Different methods have been employed to obtain the broadening factor, see Hebert (2007) for a comparative review. An empirical linear function Γ(E) = 0.1 E (where E is the energy above the threshold) gives good results when compared to the experiment - this is the option employed in CASTEP.

Spin-orbit splitting

Experimental spectra record transitions involving core states that are split as a result of the spin-orbit interactions; so one should distinguish between states such as p_1/2 and p_3/2 and so on. The CASTEP implementation lacks spin-orbit terms, so the calculations can only produce "generic" spectra for p, d, or f states. In spectroscopic terms this means producing (for example) L_2,3 spectra rather than just L₂. The simplest, albeit slightly approximate, way to model experimental spectra is to modify the calculated spectrum as follows:

Find the experimental value of the spin-orbit splitting of the core states.
Generate an approximate L₃ spectrum by shifting the L₂ spectrum.
Apply intensity scaling based on the occupancy of the respective electronic shell. The intensity ratios for L spectra are 2:4 and for M spectra 4:6, and so on.
Add the two shifted and scaled spectra together.