Effect of the Silicon Drift Detector


SNIP [6]. Mathematical background methods are not suitable for P/B based quantification [4] because the absorption jumps at large peaks are not easily determined, but knowledge of them is required for correct calculation of proper P/B values. Peak deconvolution is performed with a probability-theory- based Bayesian algorithm [7,8]. Background calculation and peak deconvolution procedures are also core components of the EXpertID initial qualitative analysis of measured spectra. Also required are incomplete charge collection and pile-up corrections to the spectrum; these are related to the detector properties and the pulse processing electronics. Corrections for matrix effects. Two methods are avail-


radiation (ch) and ci ments i, is:


ai ch


,,


able in EDAX soſtware to convert the raw data (P or P/B) to element concentrations for bulk samples: the net-counts pro- cedure called eZAF and the P/B-based termed PeBaZAF. Both correction procedures employ aspects of the well-known ZAF corrections [9]. Te ZAF abbreviation stands for atomic num- ber correction (Z), absorption correction (A), and secondary fluorescence correction (F). ZAF method basics. A classical (very simplified) formula, stands for the measured net-counts of characteristic are the unknown weight fractions for ele-


where Ni


N cit d qZ AF 4


=ε π ωΩ where εi


ai iiiai ch


(), (1)


electron microscope beam-current, the measurement time, and the solid angle. Te index a stands for “all” elements and indi- cates those values that depend on the amounts of the other ele- ments in the specimen. ωi


is the fluorescence yield, the fraction


of ionizations that result in emission of an X-ray photon, and qi is the transition probability of an evaluated line in a line series


(for example, the Kα part of K-series). An iteration is required to solve the equation system. In Equation 1, the Z describes the generated X-rays by primary electron interactions inside of the sample. Te A and F factors consider the loss of X-rays due to absorption in the sample and the enhancement by secondary flu- orescence caused by other generated X-rays with higher photon energies. But with classical standards-based notation, the mea- sured net counts of the unknown sample are always related to the measured net counts from a standard sample; this is the k-ratio of standards-based analysis. We can modify Equation 1 to:


N N kc ZAF


ai s


, i st ai ,, ai


() == ()


ai s


, ZAF st i (2)


Where s is for the sample and st stands for standard, usually a pure element standard, measured under the same conditions. Several factors cancel out because they are usually the same for measurements of the standard and the sample. With further simplification Equation 2 becomes:


kc ZAF ai ai = ()′ ,, ai, (3) Te ZAFʹ factors are now all correction factors relative to


the pure element standard. It is possible to take the k-ratio and divide by ZAFʹ factors to get the weight fractions of the elements in the unknown. Te ZAFʹ notation of Equation 3 is still used in


36


is the detector efficiency, and it dΩ 4π is the product of the


standardless quantification results to keep it somehow consistent with the classical standards-based formula. Nevertheless, since no standards were measured, the pure-element-related k-ratio is actually calculated via a model; it is not a really a measured value. Te eZAF method. In this article a generically standard-


less-based correction factor notation is always used. Te atomic number correction Z, which is in two parts, is no longer a “cor- rection” but a calculation of primarily excited X-rays [9]. Tere is a calculated integral over energy-dependent cross sections that considers the stopping power for electrons in the sample, the energy lost from incident electrons. Tis is the S-factor calcula- tion for all electron-generated X-ray photons. Te second part of the Z factor is a separate backscatter “correction,” the R-factor [3,9], which compensates for electrons escaping the sample and not generating X-rays. One can derive from Equation (1):


N cit d qS RA F 4


ai ch


,, ,, =ε π ωΩ


ai iiiai ch


()


ai ch


(4) Te dead-time corrected measurement time is known, but


it is not usually possible to determine the beam-current exactly in an SEM. Tere is one more unknown parameter than the available equations, thus it is necessary to use the additional constraint that the sum of all concentrations must equal 100%. But it is possible to determine the unknown parameter indi- rectly with a separate reference measurement on a pure ele- ment sample under the same conditions. In the latter case, the results can be calculated as un-normalized compositions. Te eZAF method uses a Z and R calculation that follows


the fundamental work by Love & Scott [10]. Te absorption cor- rection used is based on the Sewell/Love/Scott “Quadrilateral” model for estimating the curve of generated X-rays as a func- tion of depth [11]. In the absorption correction, a more recent database of mass absorption coefficients (MACs) by Elam et al. [12] is also used. Tis is important because these MAC values can strongly affect the absorption correction. Te fluorescence correction is based on [13]. Figure 2 shows a HfNi sample spectrum, and Figure 3


shows the evaluation of the spectrum with a k-ratio-based result presentation versus generic standardless notation. Te internal correction calculation is same using identical models. Terefore, the results are same. Te difference in the upper table is that the k-ratio notation is assuming smaller corrections in relation to an estimated pure element measurement. But this measurement was actually not performed and therefore the algorithm has cal- culated the k-ratio, based on a theoretical model. In the lower table of Figure 3, the correction factors in relation to generated X-rays are actually greater because standard measurements were not performed. Based on different estimated corrections, the calculated systematic error estimations are different. In the standardless notation, all R- and A-corrections are less than 1.0 (a loss from primary excited X-rays), and all F-corrections are greater than 1.0 (an enhancement of primarily excited X-rays). Tis is not what happens with k-ratio of ZAFʹ notation where everything is compared to pure element standards. In the stan- dardless case, the k-ratio is a fake. It was never really measured. Te P/B method. Te EDAX PeBaZAF is a P/B-method


following the basic ZAF approaches, but in this case a pre- cise measurement must be made of the bremsstrahlung back- ground. Te basic relation is given by writing Equation 4 for


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