Interaction Volumes for Generation of Characteristic X-Rays
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The volume, inside the specimen in which interactions occur while being struck with accelerating electrons, is called interaction volume. This volume depends on several factors such as atomic number of the materials of the specimen, accelerating voltage of the electron beam, and angle of the incident electron beam, because the materials with higher atomic number absorb or stop more electrons (having a smaller interaction volume), higher voltages penetrate farther into the sample and generate larger interaction volumes, and the greater the angle (further from normal) the smaller the volume. Figure 4598 shows the interaction volumes for generation of characteristic X-rays. For comparison, this figure also shows the interaction volumes for generations of secondary electrons, Auger electrons, backscattered electrons, continuum X-rays, and secondary fluorescence (X-rays).

The expressions developed from Bethe equation can give the range in which the X-rays are produced, suggesting the generation depth of characteristic X-rays is roughly equal to penetration depth of incident electrons, given by Kanaya-Okayama Formula [1],

         Kanaya-Okayama Formula --------------------------[4598a]

       R -- The depth penetration,
       A -- The atomic weight (g/mole),
       E0 -- The incident beam energy (keV),
       Z -- The atomic number,
       ρ -- The atomic density (g/cm)2.

The interaction volumes for generations of secondary electrons, Auger electrons, backscattered electrons, characteristic X-rays, continuum X-rays, and secondary fluorescence (X-rays).
Figure 4598. The interaction volumes for generations of secondary electrons, Auger electrons, backscattered electrons, characteristic X-rays, continuum X-rays, and secondary fluorescence (X-rays).

In SEM mode, the EDS spatial resolution depends mainly on the beam size and the interaction volume due to elastic and inelastic scattering. The radius (r) of the interaction volume from which X-Rays are generated is given by,

        interaction volume -------------------- [4598b]
where,
         ρ -- The material density,
         Ec -- The critical excitation energy for the characteristic X-Ray of interest.

For instance, when an incident electron beam at an accelerating voltage of 20 kV irradiates a copper material, the generation depth and width of X-rays are ~ 1.5 µm and ~ 1 µm, respectively. The generation width determines the spatial resolution of X-ray based measurements, e.g. EDS.

 

 

 

 

[1] K. Kanaya, S. Okayama, J. Phys. D., J. Appl. Phys. 1972, 5, 43.

 

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