From S. Tougaard, JVST A 39, 011201 (2021)
Tougaard Background Details
The Tougaard background relies on a quantitative description of the physical processes that lead to the background. It comes in various forms depending on the situation and the simplest algorithm is where C = 1643 eV2. The factor B1 is adjusted to give zero intensity in a region between 30 and 50 eV below the characteristic peak structure.
For polymers, and other materials (such as Si and Al) with a obvious plasmon structure, the three-parameter Tougaard background algorithm is more accurate,
where C and D depend on the material. The kernel in the integrals reflect the cross section for inelastic scattering in the material, and for complex systems, where the photoelectron may pass layers of material with widely different scattering properties, a mixture of the corresponding cross sections gives a more accurate description of the background. Figure 3 shows the full Al Kα excited spectrum from a Cu foil analyzed by Eq. (2). As can be seen, the inelastically scattered electron background is described with good accuracy over the full 1000 eV energy range. Note also that the peaks extend to ∼30 eV on the low energy side of the characteristic peaks. The intensity in this energy range arises from the intrinsic (or shake-up) electrons. As was described above, when this method is applied to a single peak, a straight line is first fitted to the spectrum on the high energy side of the peak, and then subtracted from a region of the spectrum whereby the peak and background intensity originating from a given core level is isolated. Such straight line backgrounds are shown in the figure below.
Figure 4 shows the Si2p,2s spectra from SiO2 (Ref. 24) analyzed by Eq. (2) (with C = 1643 eV2) (upper) and by Eq. (3) [using C = 542 and D = 275 eV2, valid for SiO2 (Ref. 28)] (lower). SiO2 has a narrow plasmon at ∼23 eV, and while Eqs. (2) and (3) both give consistent and good background correction beyond ∼40 eV from the Si 2s peak, Eq. (3) accounts better for the intensity in the plasmon energy loss structure. This illustrates that while Eq. (2) has been shown to be good for many transition metals, their alloys, and oxides, Eq. (3) is better when the material has sharp plasmon loss features.
Since Eq. (2) accounts so well for the background in Fig. 3 it is obvious that it gives a quite accurate description of the inelastic scattering processes that are responsible for the background. Equation (2) does, however, only apply for homogeneous and exponential atom depth distributions. For other depth distributions, different and more complex algorithms apply as discussed in Secs. V C and V D. Although the Shirley and straight line methods are not based on physical models and have been found to be less accurate they still give a reasonably accurate relative measure for the peak area. The two methods have the advantage that only the main peak region (typically of width less than 5 eV) needs to be analyzed, while proper use of the Tougaard background requires a wider energy range. In practice, the Shirley and straight line backgrounds are widely used.
In this guide, we first discuss the problem with standard quantitative XPS analysis which, based on measured peak intensities, calculates and reports the composition as atomic concentrations of the surface. We point out that these numbers can be highly misleading and very inaccurate and that a meaningful quantification cannot be made unless the attenuation factor is also taken into account. In Secs. IV A–IV C, we then discuss the advantages and limitations of different ways to do that. We emphasize the interplay
between XPS peak intensity, inelastic background, and depth distribution of atoms and describe how this can be used to significantly improve the accuracy and greatly enhance the amount of information that can be extracted from XPS. The quantification then involves the analysis of both the peak intensity as well as the distribution of inelastically scattered electrons in the background that accompanies the peak. This has resulted in several practical methods and algorithms that involve spectral analysis at different levels of complexity as described in Secs. V A–V D. Finally, Sec. V E gives details on how the best peaks are selected for analysis by these methods.