Electron microscopy
Shape of X-ray Peak in EDS Measurements
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The EDS measurement with Si (silicon) detectors is highly linear when calibrated over the energy range from 1 keV to 10 keV. In general, for X-ray peaks above 1 keV, it is sufficient to evaluate the X-ray intensities by considering the measured X-ray peaks as a Gaussian distribution for a single photon energy. In this case, the intensity as a function of energy is given by (see Figure 1755),
         Gaussian distribution of the shape of X-ray peaks -------------------------- [1755a]
         FWHM = 2.355·σA ------------------------ [1755b]
                      ∝(C2E + N2)1/2 -------------------------- [1755c]
         C = 2.35•(Fε)1/2 -------------------------- [1755d]
          AA -- The maximum X-ray intensity as shown in Figure 1755.
          EA -- The average peak energy.
          E -- The X-ray energy in a specific channel.
          σA -- The standard deviation used in statistics.
          FWHM -- The full width at half maximum as a measure of "peak broadening", which increases with E.
          C -- The uncertainty of the formation of charge carriers (electron-hole pairs) in the EDS detector.
          N -- The FWHM of the electronic noise of the amplification process.
          F -- A constant that is also called Fano factor (about 0.1 for Si).
          ε -- 3.8 eV for Si.

In fact, most software available on commercial EDS systems uses the Gaussian approximation to describe the observed shape of an X-ray peak.

Gaussian distribution of X-ray peak

Figure 1755. Gaussian distribution of the shape of X-ray peaks.

According to the Hyperment function, the asymmetry of the X-ray peaks measured from the photon-detector interactions can be theoretically obtained by adding two analytical expressions S(E) and D(E) to describe the spectroscopic features. [1] Therefore, the measured X-ray line shape P(E) as a function of the analyzed photon energy E, can be given by,
         P(E) = S(E) + D(E) + G(E) ------------------- [1755e]
         S(E) -- The Compton scattering of the photons within the detector.
         D(E) -- The incomplete charge collection in the dead layer of the detector.
         G(E) -- The major Gaussian peak.

Note that the peak height of characteristic X-rays is inversely proportional to the energy resolution of the detector.






[1] J. L. Campbell, A. Perujo and B. M. Millman, Analytic description of Si(Li) spectral lineshapes due to monoenergetic photons, X-Ray Spectrometry, 16(5), 195–201, 1987.