CliffLorime (k) Sensitivity Factors in EDS  Practical Electron Microscopy and Database   An Online Book  

Microanalysis  EM Book https://www.globalsino.com/EM/  
If the TEM sample is infinitely thin, then the absorption and fluorescence effects are negligible in Equation . Therefore, the Xray intensity collected by the EDS detector should equal to the Xray intensity generated from the sample by the electron beam. This is normally not true because of Xray absorption within the sample and due to absorption in the Xray detector. However, the discussion below simply ignores the effects of the absorption and fluorescence effects. Quantitative Xray measurements, e.g. EDS, in analytical electron microscopy involves the use of CliffLorimer k_{AB} factors [8] to relate the measured Xray intensities from elements A and B to their composition. Here, the subscript of k_{AB} indicates that the values of the k factors for the intensity of each element A is ratioed to the intensity of element B. The selection of element B has to reduce the uncertainty of k factors due to the variations in the efficiency of individual energy dispersive spectrometers, and thus makes the values of kfactors more universally applicable. Here, k_{AB} is given by,  [4624a] where, Note k_{AB} is a factor that accounts for the relative efficiency of production and detection of the Xrays. Therefore, k_{AB} is a constant for a given accelerating voltage and the efficiency of a specific EDS spectrometer at the relevant xray energies, and is independent of specimen thickness and composition, which is socalled 'thinfilm criterion'. This criterion assumes that the Xrays are neither absorbed nor fluoresced in the specimen. The k_{AB} factors for the K_{α} Xray peaks of the elements from about Mg (Z=12) to Zn (Z=30) is about 1. However, below or above this range of atomic numbers the k_{AB} factor gradually increases as shown in Tables 4624a and 4624c. The k_{AB} factors are experimentally determined from wellinvestigate, homogeneous standards and are normally stored in a lookup table in EDS software. The quality of EDS analyses depends significantly on the accuracy of the k_{AB} values so that it is very important these values are carefully quantified using several standards for each element. For the elements with atomic numbers greater than 12, the k_{AB} factors can now be determined with an error in the range of 1 to 4%, while the determination of k_{AB} factors for light elements is normally less accurate. For a system with many elements, the elemental concentrations can be evaluated with a set of equations. For instance, in a ternary system with three elements A, B and C, the elemental concentration can be evaluated with the following equations: Kfactors vary from instrument to instrument significantly as shown in Tables 4624a4624d and the excel file. The k_{ASi} factors listed in Tables 4624a and 4624b are most useful to geologists and semiconducting engineers where silicon is often the major component element after oxygen, while for metallurgists it is often more useful to display k_{AFe} factors where element B is iron as listed in Tables 4624c and 4624d.
Figure 4624 shows the plots of K_{ASi} Factors listed in Table 4624a. From the figures, we can know that the Kfactors for a specific element are not constant even though at the same accelerating voltage (e.g. 100 keV) because the Kfactors are not only determined by the relevant elements but also affected by the characteristics of the EDS systems. Those differences will affect quantification if no calibration was done on the particular EDS system.
Furthermore, it is better to use the k factors with Fe as the standard, namely k_{AFe}, instead of k_{ASi}, for elemental evaluations because of two reasons. Firstly, the error of the detected Si xray intensity, due to Si K_{α} absorption in the specimen, is larger than that of Fe K_{α}. Secondly, the EDS detector is almost 100% efficient for the detection of Fe K_{α} Xray, while for Si K_{α} xray the detection efficiency is significantly degraded due to xray absorption in the detector itself. If a proper standard containing the two elements (A and B) of interest cannot be found, k_{AB} factors can be obtained from two standards, k_{ASi} = k_{AB} * k_{BSi}  [4624f] In Equation 4624h, it is most difficult to accurately calculate Q and ε. The extraction of the k_{AB} values for K lines above 1.5 eV in energy is in error of ~10 to 15% mainly due to the inaccurate estimation of Q. For the same reason, it is not recommended to calculate the k_{AB} values for light elements Z < 11 or for L lines. Note that at a constant accelerating voltage of a given incident beam the kfactors are independent of specimen thickness and the complexity of compositions in a thin specimen. If the peaks of many elements are measured simultaneously, the measurements are independent of variations in the probe current. The k_{AB} factors depend upon the composition of the specimen and the thickness of the detector window, and change if contamination builds up on the window of the detector, so that they are not constants. However, k_{AB} values for a particular EDS instrument can be stored in a computer and used for a long time. Therefore, no standardization of k_{AB} factors is normally needed at the time of analysis. Table 4624e lists the K_{MoO} factors for Mo L_{α1} and O K _{ } Xrays at accelerating voltages from 15 keV to 30 keV. The Xrays are collected from a bulk sample in an SEM system. At the lower voltage 15 keV, both intensities of Mo L_{α1} and O K _{ } Xrays are higher and the K_{MoO} factor is lower.
Note that, in general, kfactors obtained by experimental methods are normally more accurate than those determined by theoretical calculation:
[1] Lorimer, GW, AlSalman, SA and Cliff, G 1977 The Quantitative Analysis of Thin Specimens: Effects of
Absorption, Fluorescence and Beam Spreading in Developments in Electron Microscopy and Analysis
369–371 Ed. DL Misell The Institute of Physics Bristol and London.


