Sensitivity factors

Fig. 15. Auger sensitivity factors relative to the Ag MNN Auger transition as a function of atomic number (19).

In order for a solution for the systems of equations expressed in equation 11 to exist, the number of sensors must be at least equal to the number of analytes. To proceed, the analyst must first determine the sensitivity factors using external standards, ie, solve equation 11 for Kusing known C and R. Because concentration C is generally not a square data matrix, equation 11 is solved by the generalized inverse method. K is given by... 

Once the criticai zones aiong the rotor axis have been identified, the sensitivity factors of those pianes must be caicuiated. If unbalance sensitivity factors of those pianes must be caicuiated. If unbalance sensitivity factors are not avaiiabie for the baiance pianes and sensors at the speeds of interest, triai weight runs are required. Thermai stabiiization times become important, since the process can consume significant periods of time. If the sensitivities are avaiiabie, then corrections may be caicuiated based on... 

The number of Auger electrons from a particular element emitted from a volume of material under electron bombardment is proportional to the number of atoms of that element in the volume. However it is seldom possible to make a basic, first principles calculation of the concentration of a particular species from an Auger spectrum. Instead, sensitivity factors are used to account for the unknown parameters in the measurement and applied to the signals of all of the species present which are then summed and each divided by the total to calculate the relative atomic percentages present. 

Pragmatically, the relative concentrations of elements are determined from the measured ion beam ratios by the application of relative sensitivity factors, which are determined experimentally from standard samples ... 

Vieth and Huneke have recendy presented a thorough discussion of GDMS quantitation, including the measurement of relative GDMS sensitivity factors and a modeling of glow-discharge source processes to enable semiempirical estimates of... 

Figura 2 Elamantal ralativB sensitivity factors as a function of chamical grouping in the...

In principle, therefore, the surface concentration of an element can be calculated from the intensity of a particular photoelectron emission, according to Eq. (2.6). In practice, the method of relative sensitivity factors is in common use. If spectra were recorded from reference samples of pure elements A and B on the same spectrometer and the corresponding line intensities are and respectively, Eq. (2.6) can be written as... 

Thus, as for XP S, the average surface concentration Na can, in principle, be calculated by measurement of the Auger current, according to Eq. (2.13). Again, as in XPS, relative sensitivity factors are generally used. The Auger current for the same transition XYZ in a standard of pure A is measured under the same experimental conditions as in the analysis of A in M, whereupon the ratio of the atomic concentrations is... 

Sa is the relative sensitivity factor. Normally, values of Sa are derived empirically or semi-empirically. Tables of such sensitivity factors have been published by Payling... 

Because measuring A can be problematic, quantification is normally performed by relative sensitivity factor (RSF) methods. If a species A on the surface is detected by the ion X , the ratio of the detected ion current /a(X ) to the primary ion current 7pi and the surface density 9 (A) is called the practical sensitivity factor Sp (X (A)) ... 

The most accurate - and most popular - method of quantifying matrix effects is to analyze the unknown sample with a similar sample of known composition. The relationship between measured intensity and the content of each sample is, usually, defined by the relative sensitivity factor (RSF) ... 

Fig. 3.36. Experimental, Fe-related HF- calculated according to [3.74] from plasma SNMS sensitivity factors S(pe)x Ref [3.71] (salts) [3.72] alloys, [3.73] with elements X ordered according to round robins (r.r.). their post-ionization probabilities...

The absolute sensitivity factors Sx must be determined for this procedure by integrating intensities over time while sputtering suitable pure element samples and determining the crater volume for HF-plasma SNMS the weight loss can also be measured. 

Values of Y (X (A)) for elements typically range from 10 to 10 in NR-laser-SNMS, and from 10 to 10 in R-laser-SNMS. If the experimental conditions are not well known, the concentration of A can also be quantified by using the relative sensitivity factor (RSF) method (Eqs (3.8) and (3.9) in Sect. 3.1.3). 

Tab. 3.1. NR-laser-SNMS Relative sensitivity factors S (Me, ESi) and detection limits DL for metals on Si wafer surfaces.

The usefulness of Eq. (3.41) depends crucially on whether or not the sensitivity factor rjA depends on the presence of other elements in the surface ( matrix effects ). It is an experimental finding that in general neutralization depends only on the atomic number of the scattering center, and matrix effects occur rarely. An instructive example is the neutralization of He by A1 in the pure metal and in alumina. The slopes of the neutralization curves turn out to be the same for both materials, i. e. matrix effects are absent [3.143]. This is a strong indication that in the neutralization process not only the valence/conduction electrons, but also atomic levels below the valence/ conduction band are involved. 

In principle GD-MS is very well suited for analysis of layers, also, and all concepts developed for SNMS (Sect. 3.3) can be used to calculate the concentration-depth profile from the measured intensity-time profile by use of relative or absolute sensitivity factors [3.199]. So far, however, acceptance of this technique is hesitant compared with GD-OES. The main factors limiting wider acceptance are the greater cost of the instrument and the fact that no commercial ion source has yet been optimized for this purpose. The literature therefore contains only preliminary results from analysis of layers obtained with either modified sources of the commercial instrument [3.200, 3.201] or with homebuilt sources coupled to quadrupole [3.199], sector field [3.202], or time-of-flight instruments [3.203]. To summarize, the future success of GD-MS in this field of application strongly depends on the availability of commercial sources with adequate depth resolution comparable with that of GD-OES. 

Similar to other sputter-based techniques, a sensitivity factor can be determined ... 

If relative sensitivity factors are used, reference measurement of standard samples is not necessary. The ratio of two different elemental concentrations in one sample is given by ... 

The ratio Db/Da is a so-called relative sensitivity factor D. This ratio is mostly determined by one element, e. g. the element for insulating samples, silicon, which is one of the main components of glasses. By use of the equation that the sum of the concentrations of all elements is equal to unity, the bulk concentrations can be determined directly from the measured intensities and the known D-factors, if all components of the sample are known. The linearity of the detected intensity and the flux of the sputtered neutrals in IBSCA and SNMS has been demonstrated for silicate glasses [4.253]. For SNMS the lower matrix dependence has been shown for a variety of samples [4.263]. Comparison of normalized SNMS and IBSCA signals for Na and Pb as prominent components of optical glasses shows that a fairly good linear dependence exists (Fig. 4.49). 

In this expression. Si is the sensitivity factor for element i and the sum in the denominator is taken over all elements that are detected [21]. 

However, the spatial resolution of AES is mueh greater than that of XPS and ean approaeh approximately 25 nm. This makes AES a powerful technique for constructing high-resolution maps showing the distribution of chemical species across a surface. Because of the small analysis area, it is an easy matter to combine AES with inert gas sputtering to construct depth profiles showing the distribution of chemical species as a function of distance away from the surface and into the bulk of the solid. Quantitative analysis can be done using sensitivity factors and an equation similar to Eq. 17. 

Fig. 8.75 Relation between (k — l)/n) and tj in 1% NaCl, where k is the ratio of fatigue strength in air to that in a corrosive environment, the notch sensitivity factor on fatigue strength, the corrosion current density at start of fatigue cycling, and jy the total life in...

This test has possible advantages over the notched Izod test. The notch sensitivity factor is eliminated, and energy is not used in pushing aside the broken portion of the specimen. The test results are recorded in ft-lb/in.2 (kJ/m2). This allows for minor variations in dimensions of the minimum in cross-section area. 

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