Inelastic interactions

Electron energy loss spectroscopy

In electron energy loss spectroscopy (EELS) a material is exposed to a beam of electrons with a known, narrow range of kinetic energies. Some of the electrons will undergo inelastic scattering, which means that they lose energy and have their paths slightly and randomly deflected. The amount of energy loss can be measured via an electron spectrometer and interpreted in terms of what caused the energy loss. Inelastic interactions include phonon excitations, inter and intra band transitions, plasmon excitations, inner shell ionizations, and Čerenkov radiation. The inner-shell ionizations are particularly useful for detecting the elemental components of a material. For example, one might find that a larger-than-expected number of electrons comes through the material with 285 eV (electron volts, a unit of energy) less energy than they had when they entered the material. It so happens that this is about the amount of energy needed to remove an inner-shell electron from a carbon atom. This can be taken as evidence that there's a significant amount of carbon in the part of the material that's being hit by the electron beam. With some care, and looking at a wide range of energy losses, one can determine the types of atoms, and the numbers of atoms of each type, being struck by the beam. The scattering angle (that is, the amount that the electron's path is deflected) can also be measured, giving information about the dispersion relation of whatever material excitation caused the inelastic scattering.

History

The technique was developed by James Hillier and RF Baker in the mid 1940s but was not widely used over the next 50 years, only becoming more widespread in research in the 1990s due to advances in microscope instrumentation and vacuum technology. With modern instrumentation becoming widely available in laboratories worldwide, the technical and scientific developments from the mid 1990s have been rapid. The technique is able to take advantage of modern aberration-corrected probe forming systems to attain spatial resolutions down to ~0.1 nm, while with a monochromated electron source and/or careful deconvolution the energy resolution can be 100 meV or better. This has enabled detailed measurements of the atomic and electronic properties of single columns of atoms, and in a few cases, of single atoms.

EELS and EDX

EELS is often spoken of as being complementary to energy-dispersive x-ray spectroscopy (variously called EDX, EDS, XEDS, etc.), which is another common spectroscopy technique available on many electron microscopes. EDX excels at identifying the atomic composition of a material, is quite easy to use, and is particularly sensitive to heavier elements. EELS has historically been a more difficult technique but is in principle capable of measuring atomic composition, chemical bonding, valence and conduction band electronic properties, surface properties, and element-specific pair distance distribution functions. EELS tends to work best at relatively low atomic numbers, where the excitation edges tend to be sharp, well-defined, and at experimentally accessible energy losses (the signal being very weak beyond about 3 keV energy loss). EELS is perhaps best developed for the elements ranging from carbon through the 3d transition metals (from scandium to zinc). For carbon, an experienced spectroscopist can tell at a glance the differences among diamond, graphite, amorphous carbon, and "mineral" carbon (such as the carbon appearing in carbonates). The spectra of 3d transition metals can be analyzed to identify the oxidation states of the atoms. Cu(I), for instance, has a different so-called "white-line" intensity ratio than does Cu(II). This ability to "fingerprint" different forms of the same element is a strong advantage of EELS over EDX. The difference is mainly due to the difference in energy resolution between the two techniques (~1 eV or better for EELS, perhaps a few times ten eV for EDX).

Variants

There are several basic flavors of EELS, primarily classified by the geometry and by the kinetic energy of the incident electrons (typically measured in kiloelectron-volts, or keV). Probably the most common today is transmission EELS, in which the kinetic energies are typically 100 to 300 keV and the incident electrons pass entirely through the material sample. Usually this occurs in a transmission electron microscope (TEM), although some dedicated systems exist which enable extreme resolution in terms of energy and momentum transfer at the expense of spatial resolution.

Other flavors include reflection EELS (including reflection high-energy electron energy-loss spectroscopy (RHEELS), typically at 10 to 30 keV) and aloof EELS (sometimes called near-field EELS, in which the electron beam does not in fact strike the sample but instead interacts with it via the long-ranged Coulomb interaction; aloof EELS is particularly sensitive to surface properties but is limited to very small energy losses such as those associated with surface plasmons or direct interband transitions).

Within transmission EELS, the technique is further subdivided into valence EELS (which measures plasmons and interband transitions) and inner-shell ionization EELS (which provides much the same information as x-ray absorption spectroscopy, but from much smaller volumes of material). The dividing line between the two, while somewhat ill-defined, is in the vicinity of 50 eV energy loss.

High resolution electron energy loss spectroscopy, in which the electron beam is 1eV to 10eV, and highly monochromatic.

Thickness measurements

EELS allows quick and reliable measurement of local thickness in transmission electron microscope. The most efficent procedure is the following:

  • Measure the energy loss spectrum in the energy range about -5..200 eV (wider better). Such measurement is quick (milliseconds) and thus can be applied to materials normally unstable under electron beam.
  • Analyse the spectrum: (i) extract zero-loss peak (ZLP) using standard routines; (ii) calculate integrals under the ZLP (I0) and under the whole spectrum (I).
  • The thickness t is calculated as mfp*ln(I/I0). Here mfp is the mean free path of electron inelastic scattering, which has recently been tabulated for most elemental solids and oxides.

The spatial resolution of this procedure is limited by the plasmon localization and is about 1 nm, meaning that spatial thickness maps can be measured in scanning transmission electron microscope with ~1 nm resolution.

Pressure measurements

The intensity and position of low-energy EELS peaks is affected by pressure. This fact allows mapping local pressure with ~1 nm spatial resolution.

  • Peak shift method is reliable and straightforward. The peak position is calibrated by independent (usually optical) measurement using a diamond anvill cell. However, the spectral resolution of most EEL spectrometers (0.3-2 eV, typically 1eV) is often too crude for the small pressure-induced shifts. Therefore, the sensitivity and accuracy of this method is relatively poor. Nevertheless, pressures as small as 0.2 GPa inside helium bubbles in aluminum have been measured.
  • Peak intensity method relies on pressure-induced change in the intensity of dipole-forbidden transitions. Because this intensity is zero for zero pressure the method is relatively sensitive and accurate. However, it requires existence of allowed and forbidden transitions of similar energies and thus is only applicable to specific systems, e.g., Xe bubbles in aluminum.

Notes

The technique of EELS was originally proposed and demonstrated by Hillier and Baker (J. Appl. Phys. (1944) 15, 663)

  • Brydson, Rik. (2001). Electron energy loss spectroscopy. Garland/BIOS Scientific Publishers. ISBN 1859961347.

See also

References

External links

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