At its core, REELS measures the energy distribution of electrons that have been elastically reflected from a sample surface after inelastic scattering events. The intensity of electrons at a particular energy loss $\Delta E$ reflects the probability of exciting a specific electronic, vibrational, or collective mode in the target material. It is based on EELS, which had been in use for many years with electron microscopy systems before the reflectance (REELS) mode was developed.

In electron energy loss spectroscopy, an electron beam interacts with a sample – and the resultant energy losses are measured. The specific energy losses relate to the atomic excitations within the atoms studied, and provide information on the bonding, chemical state, and electronic structure of the atoms in question.

Compared to EELS, REELS uses much lower energies (< 3 keV, vs 80 – 300 keV). This limits the electronic transitions which can be probed (we are really only looking at valence electrons here), but enables surface sensitivity.

The mathematics of Electron Energy Loss Spectroscopy (EELS) involves describing the probability and energy distribution of inelastic scattering events when electrons interact with a material. Here are some key mathematical elements:[4]

Energy Loss Calculation:
The energy lost by an incident electron is given by:

where E₀ is the initial kinetic energy of the electron and E is the kinetic energy after passing through the sample.

Differential Cross Section:
The key quantity in EELS is the double differential scattering cross section, which gives the probability of an electron losing an energy ΔE and scattering through an angle θ:

Here, q is the momentum transfer related to scattering angle and electron wavelength, and $ϵ(q,\Delta E)$ is the dielectric function of the material describing its electronic response.

Energy Loss Function:
The energy loss function — the imaginary part of the inverse dielectric function —

encodes the probability that an electron loses energy ΔE at momentum transfer q. This function peaks at characteristic energies corresponding to excitations like plasmons, interband transitions, or ionization edges

Modern REELS instrumentation consists of three main components:

Electron Source: Field emission or Schottky sources provide a stable, narrow energy spread beam, crucial for achieving the high energy resolution required for REELS (≤0.5 eV, or lower with cold emission sources). In XPS based REELS systems this will typically be the charge neutralisation system gun.

Spectrometer/Analyzer: The energy of reflected (backscattered) electrons is typically measured by an energy analyser based on electrostatic sector elements, such as toroidal or hemispherical analysers. In advanced REELS designs:

• • Electrons are retarded by electrostatic fields, lowering their kinetic energy before entering the analyser to enhance resolution.

  • Energy pass windows are finely tuned; for example, predicted energy resolutions of 0.4 eV at a 10 eV pass energy and 0.2 eV at a 5 eV pass energy are possible.

  • The spectrometer aligns with the incident beam and collects electrons at defined polar angles, optimizing sensitivity to specific surface modes.

Detector: Electron multipliers (e.g., microchannel plates) convert the energy-resolved electron signal into a measurable current with high sensitivity.

A major characteristic of REELS data is an elastically scattered, zero loss peak. This should be aligned to 0 eV.

The peak area of this peak can also be normalised for comparison of datasets.

Sven Tougaard has developed two important pieces of software for REELS analysis:

QUASES-XS-REELS #

• Quantitative cross section determination in absolute units
• User friendly data handling of spectra taken
  under four different operations of the REELS experiment
• Spectral smooth (Savitzky-Golay)
• Saving, printing, and plotting of cross section data
• File handling

QUEELS-ε(k,ω)-REELS #

Determine dielectric function from REELS data

After the spectra has been normalised, the onset of inelastic loss represents the energy at which the REELS beam has begun to promote electrons across the band gap.

Vos et al[1] identified this, and demonstrated how this could be used to record band gaps for aluminium nitride, and some other wide gap semiconductors.

This method requires a high enough energy electron beam (1 keV or above), so that the asymmetry of the elastic peak due to excitations within the band gap, caused by surface effects, is removed.

At high energies, the elastic loss peak is heavily affected by recoil effects, and is broad and asymmetric, obscuring the onset of loss and rendering the method unusable.

The ideal energies for this method are between 5 and 20 keV – although many XPS systems with REELS capabilities offer lower energy systems, since they use the flood gun charge neutraliser. These will still record band gaps, although for small band gap systems it may be very hard to measure the loss properly. Isaacs et al have successfully used this to measure titania systems, although they found the resultant band gaps slightly higher than by DRUVS – ascribed to DRUVS measuring the lowest energy threshold for exciton formation, whereas REELS measures the bandgap as the separation between the valence and conduction bands.[5]

REELS distinguishes between bulk and surface plasmon excitations—surface plasmon peaks are generally downshifted compared to bulk.[2]

The plasmon energies are sensitive to the material’s electron density and can be quantitatively analyzed using Drude theory, considering band gap and effective mass.

REELS is crucial for studying collective excitations in correlated materials, layered systems, and nanostructures.

REELS reveals shifts or broadening in plasmon and interband transition peaks due to amorphization, irradiation, or lattice disorder.

For example, irradiated SiC shows a significant downward plasmon shift due to density and band gap changes, which can be quantitatively analysed.[2]

Ito et al, showed that REELS can be very useful in identifying lithium compounds, with similar accuracy and capability to Li K-edge XANES.[6] They found that operating in the 3 kV mode,  they could speciate the lithium with much better accuracy than by using XPS alone.

Since REELS is measuring electron loss processes, it can effectively measure and simulate loss processes following a photoemission process – and aid in the construction of Tougaard backgrounds with the correct cross-sections.[7,8,9]

Tahir and Tougaard found that optical properties of polymers, including band gap and dielectric function, could be obtained using REELS with very low energy beams (300 – 500 eV). Higher energy beams were found to damage the sample, and in fact REELS itself could be used to detect surface damage.[10]