The charged particle experiences Coulomb interactions with the nuclei and the orbital electrons of the atoms in a matter when it travels through the matter. As shown in Figure 4688a, these interactions can be divided into three categories depending on the impact parameter b compared with the atomic radius a: a) Interaction with the external nuclear field (bremsstrahlung production) for b << a; b) Interaction with the orbital electrons for b ≈ a (hard collision); c) Interaction with the orbital electron for b >> a (soft collision).
Figure 4688a. Radiative (a), hard (b) and soft (c) collisions. b is the impact parameter and a is the atomic radius.
On the other hand, two types of X-rays are induced by the electron beam: characteristic X-rays and bremsstrahlung X-rays as shown in Figure 4688b. A continuum of bremsstrahlung X-rays is produced in the low energy regimes if an electron is decelerated by the nucleus. However, the bremsstrahlung can actually be any value from 0 up to the incident electron energy. The bremsstrahlung X-rays are normally broad and are featureless background to characteristic X-rays. Bremsstrahlung X-rays are useful and convenient to the biologist, but usually annoys most materials scientists.
Figure 4688b. Schematic showing X-rays of a sample element.
Table 4688 shows that electrons interact with 1 electron, many electrons, 1 nucleus, and many nuclei in solids.
Table 4688. Effects of interactions of electrons in solids.
||Interaction with electron(s)
||Interaction with nucleus/nuclei
||Electron Compton effect; electron excitation (from 50 eV to a few keV: EDS and EELS)
||Plasmon excitation (< 50 eV, ~100 nm TEM specimen); Cerenkov effect
||Rutherford scattering; phonon scattering (< 1 eV, heat)
The intensity of the bremsstrahlung x-rays (Ib) at an energy (Ev) is quantified by Kramers' law,
Based on Equation 4688, the x-ray continuum intensity decreases with increase of the photon energy, yielding zero at the energy of the incident electron beam. At low X-ray photon energies the intensity increases rapidly due to the greater probability for slight deviations in the trajectory caused by the Coulombic field in the atoms.
Z -- The average atomic number of the specimen,
E0 -- The incident beam energy,
I -- The electron beam current,
Ev -- The continuum photon energy.
The main inelastic scattering mechanisms are:
i) Phonon excitation (heat).
ii) Plasmon excitation (valence electrons).
iii) Single electron excitation (inner and outer shell scattering).
iv) Direct radiation losses (Bremsstrahlung radiation due to deceleration of the electron beam in the Coulomb field of an atom).
v) Excitation of conducting electrons leading to secondary electron emissions.
Furthermore, EDS has relatively low peak-to-background ratio in electron microscopes due to the high background coming from bremsstrahlung radiation emitted by electrons suffering deceleration on scattering by atoms. This background continuum makes it unable to detect characteristic X-rays from components below the 0.1-0.05% level. Even though trace elements down to ~500 ppm of oxides can be detected by SEM-EDS, their quantification is not accurate. Note that collecting EDS data for longer time only slightly improves the detection limit.