Quantification by XPS – A Perspective
JVST, A38, 041001 (2020)
XPS: A perspective on quantitation accuracy for composition analysis of homogeneous materials
We present a perspective on the use of XPS relative peak intensities for determining composition in homogeneous bulk materials. Non-homogenous effects, such as composition variation with depth or severe topography effects (eg in nanoparticles) are not discussed. We consider only use of laboratory based instruments with X-ray sources, Alkα or Mgkα. We address accuracy (not precision, which is much more straight forward) using Relative Sensitivity Factors, RSFs, obtained either empirically from standards (e-RSF), or from use of theoretical cross-sections, σ, (t-RSF). Issues involved are a) the uncertainty of background subtraction of inelastically scattered electrons, b) the accuracy of the RSF’s, and c) the role of XPS peak satellite structure, which affects both a) and b) above.
The XPS of materials tends to fall into two broad classes: where the signals being used for quantification are “main” peaks which are narrower and more symmetric, followed by a relatively low background with only weak satellite structure; and where the “main” peaks are broader and often asymmetric, followed by backgrounds that are higher and have stronger satellite structure. The former generally will yield better accuracy, more easily, than the latter. The latter comprises all compounds containing elements with open valence shell electrons. These are mostly the 3d, 4d, and 5d transition metals, the lanthanides, and the actinides. Compounds involving only the first row elements, Li to F, where the 1s BE is used for quantitation, are those where the best accuracy is potentially achievable.
We specifically address the issue of long-claimed serious discrepancies between e-RSF’s and t-RSF’s, which were interpreted as indicating calculated σ’s, used as a parameter in t-RSF’s, were seriously in error. We conclude this claim to be untrue and that, if done correctly, there is no disagreement between the two approaches within the limits of accuracy claimed.
Finally, we suggest protocols for rapid element composition analysis by obtaining relative XPS signal intensities using only low energy resolution.
Introduction – Perspective on the use of XPS for bulk analysis
Following the discovery, more than 50 years ago, of Chemical Shifts in the core-level BE’s of atoms, thereby allowing distinction between different bonding situations for a given element atom, it was initially hoped that XPS would become a general chemical analysis technique for solids, hence the original acronym, ESCA, Electron Spectroscopy for Chemical Analysis, coined by Siegbahn . However, although already understood that XPS probed close to the surface, it was not initially realized just how surface sensitive.
It soon became clear that, using the laboratory sources of AlKa and MgKa soft X-Rays, the technique probed mostly only down into the top 10 to 100A of material (dependent on the material, the KE of the photoelectrons being measured, and the detection angle with respect to the surface). In fact, for emitted electrons of similar kinetic energies there is little difference in probing depth between electron impact Auger Spectroscopy and XPS . Given that the top 10 to 50A depth for most classes of air exposed materials are often unlikely to be representative of the bulk solid, it became clear that XPS was not going to provide, non-destructively, a bulk general chemical analysis, and for the next 30 years the emphasis was on playing to its strength in studying, often under UHV conditions, clean surfaces, ambient reaction at surfaces, and controlled adsorption and reaction on clean surfaces, ranging from sub-monolayer through to situations that went deeper, such as the early stages of oxidation and corrosion.
Information beyond the natural probing depth was obtained by combining XPS with sputter depth profiling using rare gas ions (usually Ar or Xe). This, of course, is a destructive analysis, which often introduced serious artifacts, such as the preferential sputtering of elements, induced chemistry changes, knock-on intermixing, and surface roughening. The one general class of materials where the non-destructive approach could (and did) provide relatively straight forward chemistry information on the bulk was for those organic polymers which a) have the same surface composition as the bulk, and b) are inert enough not to suffer significantly from surface contamination or ambient reaction . Such material samples could be measured “as received” and/or scrapped or cut before insertion into the instrument vacuum. For most other material cleaving/fracturing/scribing/grinding in the UHV vacuum of the instrument, or at least preparing this way in an attached glove box or HV entry loadlock, was necessary to provide bulk composition analysis .
Over the last ~25 years, however, several developments have led both to an ever increasing use of XPS and also a change in the mix of usage and of users. One is the general trend in many types of technology to thinner and thinner layers, so that total thickness of a layer to be analyzed is often in the ballpark of the natural probing depth of XPS. Another is development of a variety of Cluster Ion Beams , for which, for specific classes of materials, sputtering conditions can be found (cluster size, energy, sample temperature, impact angle) where the depth profiling artifacts mentioned above can be eliminated, or greatly reduced, making bulk analysis possible. The third is simply the vast improvement in instrumentation, automation, and turnkey data analysis. The final factor, which is based on the third, is the encouragement by instrument vendors for XPS users, the majority of whom are no longer experts, to now think of XPS as a straight forward, easy, and quantitative technique generally applicable for elemental and chemical state analysis of solid materials (exactly as Siegbahn might have wished!), particularly if that solid material is actually a thin film of only a few nm thickness.
This then begs the questions “how quantitative” and “how generally applicable”, and “how easily”, which in turn leads us to a discussion of how to turn the relative intensities of XPS signals (absolute XPS intensities are rarely used in XPS) from different elements, or different chemical states of a given element, in a solid sample, into a compositional analysis, or, if you like, a stoichiometry. This is the subject of this perspective.
Our general opinion is that, even for “perfect samples” (flat, homogenous in depth and laterally), accurate quantification is often not easy, and is strongly material dependent. At one extreme it is much easier for polymers containing only 1st row elements, where better than +/-4% accuracy has been routinely demonstrated , than the other extreme of oxides of the transition, lanthanide and actinide elements, where, in cases involving complex spectra with strong satellite structure, it may be problematical to achieve better than +/-20% routinely. This paper and our perspective considers the fundamental issues involved concerning accuracy, but only goes as far as considering flat bulk, homogeneous material. Other situations, such as a varying composition with depth, or samples with strongly structured surfaces (eg nanoparticles) present additional complications that are not discussed in this paper.
We should stress that this perspective does not at all address precision of XPS measurements. It is well established that high precision can be achieved in XPS peak intensity measurements, allowing, for instance, determination of very small fractional changes in both thickness and composition of homogeneous films which have a thickness compatible with the probing depth of the technique. In industrial applications, particularly in quality control, this is often more important than knowing accurately what the true thickness or composition is. Basically it allows a materials processing tolerance control.
Photoemission Intensities and Sample Composition
There are two fundamental factors limiting the accuracy in converting photoemission intensities from solid samples into atomic concentrations. These are:
- Subtraction of the Extrinsic Extrinsic is defined as the intensity that has been lost from the generated photoelectron signal, into the background at lower KE, by inelastic electron scattering, as the photoelectrons pass through the solid, escape the surface, and are detected.
- Knowledge of the spectral distribution of the intrinsic photoelectron signal concerned. Intrinsic is defined as that part of the observed spectrum resulting from the initial photoemission process ejecting an electron, which escapes the solid without having undergone inelastic scattering. For quantitation, using XPS peak relative intensities, it is the intrinsic component we use.
The Photoionization Process and Quantitation
Fig 1a is the hypothetical schematic spectrum of gas phase LiF, using the simplest approximation of the photoemission process – that is that if an individual X-Ray photon interacts with an individual LiF molecule in an ensemble of molecules, it may, with some probability, cause the ejection of an electron (the photoelectron), from one of the LiF quantum energy levels (Molecular Orbitals) in that molecule, according to the Einstein Photoelectric Equation:
KE = hν-BE Equation 1
where hν is the X-Ray energy, BE is the Binding Energy of the electron in the orbital concerned (the energy required to remove it to infinity), and KE is the resulting Kinetic Energy of the ejected photoelectron. In the simplest approximation it is also assumed that when the particular core level electron concerned is ejected other electrons in other molecular orbitals do not respond in any way (the frozen orbital approximation). Knowing hν and measuring KE thus allows determination of BE. If the orbital concerned is a core-electron, meaning deep enough to not be involved directly in the bonding between different atoms (in this case Li and F atoms) then the BE measured is unique to the element concerned. This is the basis of XPS atomic ID. So called Chemical Shifts are slight changes in a core-level BE that are due to major changes in the valence levels caused by bonding between atoms – ie chemistry. This is the primary basis of chemical state ID by XPS, but it is only one of several effects that can, and should be, exploited for bonding information 
The Li atom has a full 1s atomic core level (two electrons) and one valence electron in the 2s orbital. Atomic F has full 1s and 2s orbitals and five electrons in its 2p valence orbitals. In the XPS of an ensemble of LiF molecules the spectrum should then consist of a Li 1s signal, an F 2s signal, an F 1s signal, plus a signal from the valence region consisting of the 6 valence electrons involved in the bonding between Li and F, approximated in chemistry parlance as an ionic bond, Li+F– where the Li 2s electron has been transferred to the F2p orbital.
The relative photoelectron peak intensities are controlled by the relative probability for each orbital level to undergo photoionization at the hν value being used (either Alkα at 1486.6ev or Mgkα at 1254.4 ev for standard laboratory based XPS instrumentation). These probabilities, which are known as Partial Photoionization Cross-sections, σ, can be very different for different orbitals of a given atom, and from atom to atom. They depend on the overlap between the X-Ray wave function and the orbital wave function. Fortunately we do know the calculated theoretical relative values. The XPS signal intensities in fig 1a are drawn assuming these theoretical σ values  to be correct. If we knew the values exactly and if we assume that all the intensity resulting from photoionizing a 1s electron of Li and a 1s electron from F, goes into the peaks as drawn in fig 1a (the frozen orbital approximation), plus there is no background and no instrument artifacts (such as a Transmission Function, T, varying with the electron KE), then it would be straight forward to turn the measured intensities (the areas under the peaks) into relative atomic concentrations by normalizing (dividing) each peak intensity by its σ value.
2a. Extrinsic Background Subtraction
Figure 1b is the equivalent hypothetical XPS for solid LiF. The obvious difference from the free molecule spectrum is that there is now a background. There is a step increase in intensity of that background after each peak. The step is drawn (realistically) as about 5% of the peak height for F1s. It is barely observable for the other core-levels, but is still there. The intensity of this background step is intimately related to the surface sensitivity of the technique.
The peaks originate from photoelectrons which have exited the solid without any energy loss caused by inelastic scattering on passing through the LiF matrix on the way out. They are, therefore, intrinsic electrons. Because the average distance an electron, of these energies, can travel without being scattered (the Inelastic Mean Free Path Length, IMFP, or λ), is very small ), most (but not all, because we are talking average distances)) of the electrons in the peaks must, therefore, have originated from very close to the surface. The background step, on the other hand, is the inverse of this. It is made up of those photoelectrons which have suffered inelastic collisions and lost energy on the way out (the extrinsic photoelectrons), so have been removed from the intrinsic peak. They may be scattered once, twice, or many times, losing more and more energy, and so the background step extends 100’s ev to lower KE. Most (but not all) must, therefore, come from deeper in the solid. It is also worth noting that since the X-Rays going in penetrate many 100’s of times deeper than the average inelastic scattering distance of the photoelectrons coming out, the total intensity in the extrinsic background step is actually far larger than that in the intrinsic peak. This may be annoying from an analysis point of view, but is a direct consequence of the surface sensitivity of the technique.
The Devil is always in the details, of course, so a reader unfamiliar with XPS should be asking what exactly is meant above by “most” and “very near the surface”. Fig 2 is instructive. It shows , for a collection angle normal to the surface, the fraction of the intrinsic XPS signal escaping the surface, as a function of the distance travelled (which for collection normal to the surface is the depth of origination). The decaying exponential functional form is derived from the well-known Beer’s Law for attenuation of light by absorption through a medium. Inelastic scattering of electrons can be treated similarly. Beer’s Law states that the absorption (scattering) goes as the inverse exponential function, e-d/λ, where d is the light (electron) path length and λ is the mean absorption (inelastic scattering) length. So for a path length of d=λ, the fraction of the total detected intrinsic signal (measured normal to the surface) that originates from a depth d=λ, is 1-1/e, or 63.8%. For d=2λ the amount is 1-1/e2, or 86.5%, d=3λ it is 1-1/e3 or 95.02%, and so on and it will never quite reach exactly 100%. 3λ is often referred to as the Analysis, or Information, Depth, defined as the depth from which, for normal emission measurement, 95.02% of the detected intrinsic signal originated. The values of λ have been determined experimentally in many cases, but have also been calculated quite accurately . Over most of the KE range for which we are concerned in XPS (1486.ev down to about 300ev when using an AlKα laboratory X-Ray source), λ varies as KE~x, where x varies between, 0.6 and 0.75, and also with the nature of the material. It can range from a few A for some metals to ~50A for some organics (the material variability depends on density, amongst other things). Readers should refer to the article by Powell in this issue for further discussion of the effects of inelastic scattering and elastic scattering on XPS measurements .
Note that in fig1b the step is drawn with a gap between it and the peak it follows. This is because our example, solid LiF, is an insulator and has essentially no scattering mechanisms for energies smaller than the band gap. If the solid had been a conductor, say a metal, the spectrum would look very different, as drawn schematically in fig 1c for the 2p3/2 XPS peak of Fe metal. There is no longer a gap because scattering with involving levels close to the Fermi level, leading to small incremental energy losses, is possible. Also, there may be discrete extrinsic structure on the step because specific scattering processes of given energies may have high probability, such as plasmon-like excitation (a plasmon is a collective oscillation of conduction electrons in a free electron metal). The photoelectron peak itself may be asymmetric on the high BE side, as drawn in Fig1c.
The point of all this, as related to our subject matter, accuracy of stoichiometry quantitation in XPS, is that if one adopts even the simplest (and often quite poor) assumption that all the XPS intrinsic intensity is in one “main peak” (the frozen orbital approximation), as implied in fig 1, the ability to separate the intrinsic photoelectron peak from the onset of the extrinsic background following it, is limited and can be very different for different XPS signals. In our example in fig 1b, it is easy and reliable for the insulating LIF, but less so for the conductive metal case, Fig1c.
Two approaches to subtracting a background have been extensively used in XPS when trying to establish stoichiometry from relative intensities, both empirical. The first is simply drawing a straight line from where you think the peak starts to where you think it finishes. In Fig 1b this is an easy task as the background before the peak and after is almost the same. The area under the peak is almost unaffected by small variations in where one picks the start and end. For fig 1c however, it is not obvious exactly where the peak ends and small variations in choice make a more significant difference.
The second method is the so-called Shirley background subtraction , which again requires picking start and finish points, and then calculating the scattered background between them assuming the intensity of the scattered background at any BE is proportional to the integrated total signal intensity up to that BE. The end point, by definition, assumes the signal at that point is now totally from the background (ie the intrinsic signal has finished). For fig1b there is no significant difference between the two approaches because start and end points have (nearly) identical intensities. In fig 1c the two approaches are significantly different, even if identical start and end points are picked. In reality things are often much more complex than even fig1c, because all of the XPS intensity may not go into one well-defined main peak, as discussed in section 2b.
There is a third method for removing a background, the Tougaard Background approach . Unlike the straight line and Shirley background approaches it is not entirely empirical, but attempts to calculate the actual inelastic scattering events using parameters derived from other experiments. Using those parameters often results in a much reduced background removal compared to Shirley [12, 13] because the end point, which is not picked by the operator but comes from the calculation, is shifted much further to lower KE (several 10’s ev in the original 2 parameter formalism). It can be arbitrarily forced to coincide with a defined end point by changing the parameters to unrealistic ones, in which case it becomes more similar, but not identical to Shirley. Currently it is our opinion that it is not known whether Shirley or Tougaard is more correct and this may vary with the spectrum being analysed. In general Shirley tends to strip out too much intensity, so underestimating the intrinsic signal, whereas Tougaard does the opposite. What is important for quantitative analysis is that the same method, covering appropriate energy ranges (start to end points) be used for the XPS signals being ratioed. This is discussed in more detail later.
2b. Spectral Distribution of the Intrinsic Photoelectron Signal.
The idea that photoemission is a one electron process is a first order assumption (the frozen orbital assumption), and often not a very good one, as we will see. There are (at least) two specific final state effects that are important here. A final state effect means it is specific to the final state of the atom resulting from the photoionization, which is a positively charged ion with an electron missing from a specific core-level. The two effects are known as “shake structure”, and “multiplet splitting”. Both “steal” intensity from an XPS “main line” and distribute it at lower KE, as described below.
Fig 3a is the XPS of an ensemble of Ne atoms acquired in the gas phase . The “one electron” description of photoionization part of this is the “main peak” at ~818ev BE (~618ev KE). It represents that fraction of the atoms in the ensemble that simply undergoes removal of a 1s electron without any other electrons changing orbitals. At higher apparent BE, spread over at least 100ev, are peaks from those Ne atoms which have undergone 1s electron removal, plus a “shake-up” process, meaning that in addition to the 1s electron removal, another electron, or even two electrons, in the valence levels of the atom, have been excited to a higher unoccupied quantum energy level, using up an extra amount of the available X-Ray photon energy, hν, and so result in a peak at lower KE than the main peak.
The relative intensity of all the shake-up process peaks is ~12% of the main peak. In addition, “shake-off” processes occur, where in addition to 1s removal another electron is also removed. This gives intensity in the form of an intrinsic step, starting at about 47ev below the main peak in this case. The fractional intensity is estimated as ~16%. So in terms of fractions of the total photoemission from the 1s level, 78% of the atoms undergo a one electron transition, the Ne 1s removal only (the main peak), 9% undergo 1s removal plus shake up, and 13% involve 1s plus shake off. All the shake processes for Ne atoms are, of necessity, intra-atomic, meaning they all occur within the Ne atom. For molecules there are greater opportunities for shake structure because neighboring atom valence electrons can be involved. In solids there will be even greater opportunities owing to increased coordination of atoms in a lattice.
Why does this matter for quantitation? In compounds the fraction of a photoelectron signal from a given orbital (eg the 1s of Ne used as the example here) that goes into the main peak can, and does, vary with the chemical state of the atom concerned and also varies from core level to core level for a given atom in a given chemical state ). The classic solid-state example of this, well-known for over 40 years, is the difference between the Cu 2p XPS of Cu2+ compounds and Cu+ compounds. Owing to the strong difference in the valence level electronic structure in these two oxidation states (Cu2+ is 3d9; Cu+ has a closed shell, 3d10), much greater intensity is transferred from the “main” peaks into shake-up structure for Cu2+ than in Cu+, as shown in figs 3b and 3c, for the 2p3/2,1/2 spectra from CuO and Cu2O . These are the peaks normally used for quantitation, because they are the strongest and narrowest peaks in the Cu XPS. The Cu2+ species has ~ 50% of its total intrinsic intensity in the observed shake satellites, whereas there is very little (but not zero) for Cu+. So, if one attempted to use, say, just the “main” Cu2p3/2 peak to O1s peak intensity ratio to determine the stoichiometry difference between CuO and Cu2O, one would obviously be seriously wrong. In this case of Cu2+/Cu+ the problem of varying spectral distribution with chemistry is very obvious and so cannot be (and has not been) ignored by analysts, so that the Cu2+ shake intensity is usually included in the total (but that for the the Cu+ is, incorrectly, often not!). In general, though, separation of any intrinsic spectral intensity of shake satellites from the extrinsic background can be more subtle and complex than the Cu2+ and Cu+ case here. This presents a very real limitation to the accuracy of quantification in many cases.
The second final state effect which steals XPS signal intensity from a “main” peak is Multiplet Splitting. It is most easily explained by looking at the N1s spectrum of the NO gaseous molecule, fig 4a. . Even though there is only a single N atom there are two peaks, separated by about 1.5ev. NO is a paramagnetic molecule, having a single electron with unpaired spin in its valence levels. N1s photoionization results in an unpaired electron left in that orbital, which can couple either parallel (high spin state) or antiparallel (low spin state) with the unpaired valence electron, with the theoretically expected 2:1 probability (reflecting the relative number of ways this coupling can occur). These two final states are separated by ~1.5ev energy (high spin states are always lower in energy than low spin states), explaining the spectrum. The O1s XPS is similarly split, but the magnitude of the splitting is less.
In more complex situations, such as the 3d transition element compounds, where there can be up to 5 unpaired valence d electrons, the coupling is more complex (owing to more possible coupling arrangements). For the 2p and 3p XPS spectra there is also the angular momentum leading to spin orbit splitting, S-O, resulting in the 2p3/2 and 2p1/2 components in the 2p XPS structure of CuO in fig 3b. The multiplet splitting broadening of Cu2+ is superimposed on this, and is not identical for the two spin–orbit components. The Cu+ 2p spectra of Cu2O, on the other hand, has no multiplet splitting, because there are no unpaired valence d electrons, and so the main peaks are much narrower than in CuO. When valence f electrons are involved (lanthanides and actinides), the situation can be even more complex because there can be up to 7 unpaired electrons.
Another example of multiplet splitting is shown in Fig 4b, the 2p spectrum of solid Fe2O3 . The expected positions and intensities of the multiplet components, calculated, ab initio, using an FeO6 cluster model with Fe in the Fe3+ oxidation state, are also shown also in Fig 4c . Those features not explained by the multiplet splitting components in the cluster calculation are shake features, which are not included in the calculations. Altogether the intrinsic spectrum is very complex and sits on a large extrinsic background. Just as shake features are chemistry dependent, so are multiplet spittings; strongly on the oxidation state for the transition metals (since this controls the number of d electrons present) and less so on the ligand (connected to the degree of covalency involved).
Converting XPS relative intensities into stoichiometry
Two methods have been extensively used for over 40 years to turn relative XPS intensities into stoichiometries. One is based on using the theoretically calculated σ values to normalize intensities and derive a Theoretical RSF, t-RSF. The other establishes empirical Relative Sensitivity Factors, e-RSF, valid for a given instrument, using reference standard materials of known composition measured on that instrument. How each works in practice is discussed below.
Theoretical Cross-section, σ, based RSF’s, t-RSF
In 1972 Scofield  published tabulated calculated σ values for all orbitals of most elements in the periodic table, at photon energies of 1487ev (Al Kα radiation) and 1254ev (Mg Kα radiation), normalized against C1s as unity. For a short while this was the second most referenced paper in the physical sciences. This was not because of originality or sophistication of the calculations. They were standard atomic quantum physics calculations. Some had been published by Scofield earlier, while others (notably Nefedov’s group in Russia ) had performed similar calculations. They were cited so often because the relative σ values allowed, in principle, a simple approach for converting XPS relative intensities into material stoichiometries.
It is very clear that if one plots Scofield calculated values against Z, there is a smooth variation with Z, so that one can interpolate any missing values. The catch is that that a calculated σ value for a given orbital is for the total photoemission intensity originating from that orbital, ie in the Ne case of fig 3a it is the total of the “main” peak and all shake up and shake off satellites. If only the “main” peak intensity was included, it would represent only 78% of the σ value. In the case of Fe2O3 (fig4b) to use the calculated σ value for Fe 2p, or Fe3p to normalize the XPS Fe signal intensities to the O1s XPS signal requires inclusion of the all multiplet splitting components and all shake components, and separation of these from the extrinsic background .
The full equation for photoemission intensity generation in a solid  is given by:
I = nFσφyTλ Equation 2
I is the number of photoelectrons detected per second from the orbital concerned, going into the measured XPS peak
n is the concentration of the atom concerned (atoms/cm3)
F is the X-ray flux (photons/cm2)
σ is the partial ionization cross-section for the orbital concerned
y is the fraction of σ retained in the measured peak ( ie it would be 0.78 for Ne atoms if only the main peak intensity at 618 ev KE in fig 3a was measured)
φ is an angular distribution term (see below)
T is the efficiency of detection of the spectrometer (the Transmission Function, a function of KE)
λ is the IMPF (a function of KE of the photoelectron, as already discussed, though the use of the Experimental Attenuation Length, EAL, which includes the modifying effect of Elastic Scattering is more accurate )
For atoms a and b then, in a given spectrum, where F drops out, the stoichiometry is derived from
na/nb = Ia/σaφayaTaλa Ib/σbφbybTbλb Equation 3
So, since an RSF is defined as the factor a measured XPS signal intensity must be normalized by to obtain relative atom intensities, σφyTλ is the RSF of the atom concerned.
The behavior of φ for free atoms is well understood . It is a function of the angle between incoming X-Rays and outgoing photoelectrons, and also depends on the angular momentum quantum number of the orbital concerned (s, p, d, f), and the atomic number, Z. For all s orbitals the angular behavior is the same so φa/φb becomes unity if ratioing s level intensities. In addition, there is a “magic angle”, 54.7 deg, for which φa/φb is unity for all orbitals, so if measurement is made at this angle, φa/φb drops out of the equation. Unfortunately it is not at all clear for solids whether any significant angular effect has ever been observed (it must at least be reduced by elastic scattering, which changes the direction of the emitted electrons), and the assumption is usually made that there is none (φa/φb becomes unity), or that the effect is smaller than other errors, so is ignored.
The behavior of T, which is a function of KE, is usually well- characterized in modern commercial instruments. It is corrected for by “removal at source” in some instrument software (ie the spectrum you see has already been corrected for T). If not, it should be corrected for after acquisition. In older instruments, and publications, T might not have been very well known and not have been corrected properly, if at all.
The behavior of λ as function of KE has already been addressed above . It goes as ~ KEx, where x is between 0.6 and 0.75 for most compounds. Note it is not important, for RSF’s, what the actual λ’s are, only what the value for x is. At low KE, the behavior of λ can become anomalous and may not follow this simple relationship, so we do not recommend using XPS peaks below ~300ev when attempting quantification (see the discussion in Powell ).
Making the usual assumption that the T effect has been corrected for, and that φa/φb is unity we now have
na/nb =Ia/σayaλa Ib/ σbybλb = Ia/Ib σbybλb/ σayaλa = Ia/Ib x σbyb/ σaya x (KEb/KEa)x Equation 4
Assuming the measured peaks capture all the signal (ie including all satellite intensity), then y =1. Alternatively, if y is not 1, but is the same for both a and b, then it still drops out and we have for either case:
na/nb =Ia/Ib x σb/ σa x (KEb/KEa)x Equation 5
I α nσKEx Equation 6
This is the most commonly used theory equation for converting a relative intensity, Ia/Ib, into a stoichiometry, na/nb and so σKEx is the reduced version of t-RSF, ignoring the possibility of any non-cancelling φ, non-cancelling y, and incorrectly characterized T.
Assuming, then, that φ, y, and T present no issues, the accuracy of a determined stoichiometry, based on σ values, obviously depends on the accuracy of the theory for σ. Scofield reviewed agreement of his calculations with experimentally derived information available at that time from X-Ray absorption data (not XPS). He concluded general agreement within 5% except for high Z elements for his calculated total cross-sections (ie the sum of all the partial values). For H to to Ne the 1s partial photoionization cross-section dominates the total, so one expects within 5% accuracy for the XPS 1s values.
Standards based e- RSFs
In the prior section it was shown that t-RSFs are given by σφyTλ, but in practice are usually reduced to σKEx, with the assumption that T has been accounted for by the instrument software, or corrected for after measurement, and that φ and y are unity, or are at least the same for all the photoelectron peaks used to establish the RSFs.
For RSFs, based on a standard containing atoms A and B, with composition AnaBnb:
e-RSFA/e-RSFB = IA/na x nb /IA Equation 7
Where IA and IB are the XPS intensities experimentally measured for the standard on a given instrument. Thus e-RSFA/e-RSFB for a given instrument, under given acquisition conditions, is determined directly from IA/IB. No knowledge of σ, φ, T or λ is required.
Unless the experimental intensity measurement includes both the “main peak” and all satellite intensities, which is hard to know, it is, however, still an assumption that y does not change for the given element in different compounds; that is the fraction of the total intensity captured in the measured peak(s) remains constant . If it does change, then the e-RSF determined is strictly valid only for the specific chemical state of the atom in that standard. In addition, of course, the values are only valid for the instrument on which the standards were run. They will not be valid for measurements on other instruments having different geometries and analyzer transmission functions.
Reconciling apparent discrepancies between historical e-RSFs and t-RSF’s
Though Scofield’s work is so old his values are still used, as is, by many analysts today to provide material composition, sometimes with the appropriate λ corrections, sometimes not. His tabulated values, relative to C1s as 1.00, are given to 3 significant figures, unfortunately allowing an analyst, applying them to analysis of solid material, to quote composition to 3 figures, which is clearly totally unjustified given the other uncertainties.
Other authors calculated σ values to a similarly expected level of accuracy as Scofield (ie a similar level of physics was included). A check of Scofield against Lindau and Yeh , indicates agreement at hv = 1486 ev to within 6% across the periodic table, with the Scofield values being consistently slightly the higher. For Z <20 the calculated values are remarkably close.
In 1982, Wagner, et al , put together, from 135 standards, a database of relative peak intensities for 62 elements in the periodic table. The data included new measurements (primarily fluorides) and previous values already published by Wagner, and by others. The values were normalized to F1s as unity, either directly or through secondary standards. Two early commercial instruments (Varian and PHI) were used, and, on the basis of not finding any consistent trends in differences between instruments, it was assumed that instrument characteristics were similar, values transferable, and there were no angular effects. The database included, for some elements, multiple measurements on multiple samples on both instruments, and at the other extreme only a single measurement (Be 1s derived from BeF2).
There was a wide spread in the values obtained, normalized to F1s as unity (the values unfortunately were quoted to 2 or even 3 significant figures, however). For example, for 4 measurements on LiF, Li 1s varied by ~35%; Na 1s by a factor of 2 for the 8 measurements; Zn 2p by 35% over 3 measurements. No significant trends in the variations were found from instrument to instrument or lab to lab.
Wagner took these values and plotted them against the KE of the XPS peak on a log log scale, separating them into 1s, 2p, 3d, and 4f curves. He then fitted the results to straight line segments and generated a second table of e-RSF values, derived from these straight line fits (note: not from the average of the actual data points for a given element). Despite the obvious limitations of this approach, which essentially is introducing interpolation between elements even when the experimental data disagreed with this, these e-RSF values were given to 2 significant figures (though some were bracketed to indicate “rough”). The Wagner 1s plot for Li to F is redrawn in fig 5a.
These “Wagner” e-RSF values have persisted down through XPS quantification for 37 years, sometimes being adjusted in a highly questionable manner for differing T and φ characteristics of other instruments, sometimes not, and sometimes being quoted to 3 significant figures! This is not the fault of the original authors, who clearly understood the issues, and whose goals were to establish, empirically, the trends and to compare to the σ derived results for t-RSF. However, in addition to later misrepresentations of their data, there are serious issues concerning the original measurements:
- Wagner’s paper does not provide information on whether the bulk known composition of the standards is maintained in the XPS analysis depth. The authors took what care they could to minimize air exposure and poor vacuum effects, but today we would consider these methods inadequate to guarantee unreacted surfaces.
- The most frustrating issue, and the one most relevant to today’s concerns about “irreproducible data”, is that no actual spectra were reported. Only derived peak intensities were given, without adequate information on background subtraction, or what part of the spectral distribution was and was not included. In general, it seems that in most instances, but not all, only main line intensity was included (ie excluding satellites). If the actual full spectra had been reported we would be able to establish whether samples were degraded, or contaminated, and how backgrounds were drawn.
- No distinction was made between Al kα and Mg kα X-Ray source generated data, though the ratios of σ values, normalized to F1s values, certainly changes by up to as much as 5% between the two sources, depending on the BE level concerned .
In addition, though it was clearly appreciated that y was not unity for paramagnetic compounds because of multiplet splitting, the importance of shake intensities, which is not limited to paramagnetic materials, was not considered. Neither was it appreciated (or at least not discussed) that y may vary substantially with the chemical state of an atom (eg Cu2+ versus Cu+, fig 3b and 3c). In such cases e-RSF based on “main peak only” intensity would be strictly valid only for the atom in that particular chemical state.
Wagner compared the e-RSF values, which were specific for the Varian and PHI instruments of that era, to σ based t-RSF values. This comparison could be done in one of two ways.
- By either removing the effects of λ, T, y and φ from the empirical measurements, leaving only the σ dependence, or
- By adding in the λ, T, y and φ corrections to the σ values to give a t-RSF.
They chose to do the latter and presented sets of comparison plots for 1s, 2p, 3d, and 4f levels for the 135 compounds in the study. In this comparison the λ correction used, with λ being proportional to KE0.66, is appropriate and small variations are insignificant compared to other inaccuracies, but the validity of T as a function of KE is less certain. φ was assumed to be unity on the basis that there was no evidence for any difference in results between the Varian and PHI instruments, which had differing geometries that would be expected to produce different results if φ correction was significant. Y was set at unity for all the comparisons because, though it was appreciated that it was less than unity in some cases, there was no information on what the values might be.
1s BE’s: Elements Li to F
The general conclusion of Wagner, et al, across the periodic table, was that the relative Scofield calculated σ values, normalized against F1s as unity, were “significantly in error – as much as 40% in some cases for strong lines and far more than that for some of the secondary lines”. Though this might not have been too surprising for high z elements (more electrons; d and f states) it was, and still is, very surprising for the much simpler situation of the 1s only levels in the first row elements, especially as the Scofield claim of 5% accuracy for this set was supported by other experimental evidence. In addition, there can be no differential φ behavior as function of Z for 1s orbitals, so no concern in setting it as unity. In their comparison plot of e-RSF versus t-RSF, redrawn in fig 5a, it is the Li1s t-RSF value (based on the Scofield Li1s σ value) which appears to be “40% or more in error” (actually more like a factor of 2), with the interpolated Be value of the empirical curve also considerably different from theory (but note that the single measurement involved here, on BeF2, is actually closer to t-RSF and far from the value assigned for e-RSF by the curve drawn).
There are 4 factors that could contribute to the discrepancy between the authors’ e-RSF’s and t-RSF’s in fig 5a:
- The calculated σ values could be seriously in error, as claimed by the authors
- The assumption that y = 0 for these elements in the compounds measured is incorrect and it is neither zero nor the same for each element
- The transmission function assumed, proportional to KE-1, is incorrect, which is possible based on the report  that Seah suggested it should be KE-0.5 for at least part of the KE range involved.
- The effect of hydrocarbon contamination, which was considered, is far greater than the authors thought.
To test factor 2) above it is instructive to reexamine, in a modern instrument, the spectrum of LiF, which was the compound used to establish the Li1s e-RSF value. Fig 6 shows a modern XPS survey spectrum (corrected at source for T), with good statistics, for a LiF crystal . Higher resolution expanded regions are shown as insets for the F1s and the F2p/F2s/Li1s regions respectively. It is important to note that the BE range acquired for these high resolution spectra is far wider than is normally used in XPS analysis (20 to 30ev is usual), in order to capture all observable satellites. The F1s spectrum clearly shows the position of the start of the expected extrinsic background as a step at ~13ev. Superimposed on this background is a series of peaks, labelled 1 to 10, spreading out over the full 100ev of the scan. They constitute about 12% of the total F1s intensity. This is quite consistent with the expected shake contribution, judged from the atomic spectrum of the next element in the periodic table, Ne, in fig 3a. From that spectrum we would expect a similar amount of step-like shake-off contribution, which in the LiF solid case may be spread out and undetectable on the extrinsic background. So we estimate that a “main line” only measurement of F1s in LIF underestimates the total F1s intensity by ~25%.
Looking at the F2s, F 2p, and Li1s high resolution spectrum, in Fig 6, one can identify the same step initiation of the extrinsic background at ~13ev after each main line. One also sees that exactly the same series of shake satellites found for F1s is present on the F2s spectrum. The overlay comparison, where F1s and F2s main lines are aligned, makes it clear that the shake-up positions are identical in F2s and F1s. Note that satellites 2 and 3 from F2s lie right under Li1s, causing the experimental intensity of the Li1s line to be overestimated by about 7%. As far as we can tell there is little or no discernable satellite intensity associated with Li1s. The structure after Li1s comes mainly from the overlapping satellites of F2s. The lack of significant shake structure for Li1s is actually expected from simple argument, as Li+ has no valence electrons to be excited into higher lying orbitals. Full ab initio theory supports these arguments, calculating a 1.4% loss to satellites for Li+, but 22.7% for F– . In solid LiF both losses would be expected to increase slightly because of the availability of screening electrons from the surrounding lattice.
Thus the corrections necessary to the experimentally determined F1s and Li1s intensities to compare to theory, requires an increase of ~25% for F1s (ie y is not unity, but is 0.75) and a reduction to the Li1s intensity of ~7% due to the overlapping F2s structure. The total correction of ~32%, renormalized to F1s as unity, to the e-RSF value for Li1s is marked in fig 5b and a corrected e-RSF curve drawn, based on a straight line fit to the data.
We initially expected that the losses of intensity to satellites from the main 1s line to gradually increase on moving from ~0 for Li 1s (y=1.0) through Be, B, C, N and O to the ~25% value for F1s (y=0.75), simply on the basis that there is a smoothly increasing number of valence electrons available for shake up. Preliminary unpublished work by the present authors on BeF2 and (CF2)n does not support this however. Both the F1s and the Be1s in BeF2 spectrum have backgrounds with some superimposed structure, but they seem to be of roughly similar intensities. F1s and C1s in (CF2)n behave similarly. This may be because these compounds have much greater percentage covalent bonding, with only LiF being fully ionic, leading to the completely different satellite behavior for the F1s and the Li1s.
Considering item 3) above, changing the KE dependence of T significantly will make a large difference in the Wagner t-RSF curve plotted in Fig 5a. The normalization to F1s of course dictates that the t-RSF and e-RSF are identical at F1s, so the two curves must meet and cross there if they have different slopes, as they do in fig 5a. Changing the KE dependence from KE-1 to KE-0.5 for the t-RSF plot makes it indistinguishable from the corrected e-RSF plot in fig 5b.
Hydrocarbon contamination, item 4 above, was considered by Wagner. They showed that even assuming significant amounts (~8A) were present on their standards, corrections of less than 10% relative to F1s would occur by including the effect on the t-RSF curve. For freshly prepared samples it is not likely that more contamination is present and it would take much more to significantly alter their plot.
Summarizing, it appears likely that the uniqueness of Li+ (no satellite losses for Li1s), plus an incorrect T behavior as function of KE, account for the apparent discrepancy between the e-RSF and t-RSF curves in Fig 5a, especially when considering the actual wide spread in these old individual e-RSF measurements. We also note that recent experimental values of σ, determined, by removing the T and λ effects, using modern instruments with hugely increased sensitivities and well-characterized T functions, do not find significant disagreement with the Scofield calculated σ values for the 1st row elements. There is typically a +-7% scatter around the theoretical values , which might be improved upon with detailed information on what satellite intensities were included.
What does all this mean in practical terms for XPS quantification for 1st row elements? First it supports the extensive work on polymers involving C, N, O, and F, over many years, where reasonable agreement with known bulk composition has been obtained using Scofield σ values such that if all observable satellites are included, better than 4% accuracy has been demonstrated . Second for the whole 1st row, if one wants to use standards based on main line intensities only, this will work provided the losses are the same for the elements in the analysis (ie y is identical but not necessarily 1.0). However, using this method, the preferred one by practical analysts because it is much faster than looking for genuine satellite intensity spread over large energy ranges, accuracy will, of course, degrade with any variation of y between the elements being compared (such as in LiF).
2p BE’s: Mg (Z=12) through As (Z=33),
excluding the transition elements Sc (Z=21) to Zn(Z=30).
The 2p BE’s are the XPS lines usually used for analysis in this section of the periodic table because they are the strongest. Fig 7a redraws the Wagner plots for e-RSF and t-RSF for these elements. Again there is a large spread in the data, and their fitted line, from which the Wagner e-RSF values were derived, comes nowhere near the actual data for either Mg. The slopes of the two curves differ substantially, just like in the 1s plots of fig 5, so that by K and Ca the difference from t-RSF is reduced from about a factor of 2 to only about 40%, and by Ge and As the curves have crossed and e-RSF is apparently smaller than t-RSF. The transition elements, Sc to Zn deviate strongly from a straight line fit, as expected because of the strong satellite structure not included in the intensities measured. They are discussed separately below.
The crossing point of the Wagner e-RSF and t-RSF curves is at about 700ev, which is exactly what is expected if the difference in slopes is due to an incorrect T dependence on KE, normalized to the F1s BE energy. As for the 1s plot in fig 5, changing the T dependence used in deriving t-RSF from KE-1 to KE-0.5 would bring the two curves essentially into agreement, given the wide spread of the e-RSF values. Also, just as for the 1s BE’s, modern experimental values of σ, extracted from e-RSF by removing the T and λ dependence, do not at all agree with the Wagner conclusions. Extracted values, using main line intensity only, indicates a 5 to 25% discrepancy with the Scofield calculated σ values, with no particular trend , and this may be reduced if satellite intensities are included. We conclude again that the apparent very large errors in Scofield calculated σ values claimed by Wagner, et al., for 2p are incorrect and caused by an incorrect assumed T dependence on KE.
There is one aspect where there does appear to be major errors in the calculated σ values, however, and that concerns the 2p/2s ratios. Since the BE’s of 2p and 2s are close together, neither T nor λ effects can make any significant difference to these ratios, so measured peak area ratios are directly comparable to the theoretical σ ratios. For Al, Si, and P the measured ratios are close to the Scofield σ ratios, but they deviate substantially for S, Cl, K, and Ca. An example is shown in Fig 8 for the Cl2p and 2s region of NaCl . The ratio of the 2p/2s peak intensities is 1.3 times greater than the Scofield σ ratios. This does not change significantly if the satellite intensity at ~20ev is included, since it is roughly the same, relative to its parent line, for both 2p and 2s. We have no explanation for the discrepancy, which was actually suspected by Scofield  from the fragmentary XPS experimental data existing at that time, but note that it is unlikely to be caused by a differing angular term, φ, between 2p and 2s, because the current measurement was made fairly close to the magic angle of 54.7 deg. (centered at 60 deg. with an angular spread of +/- 8 deg.).
2p BE’s of The Transition elements Sc (21) to Zn (30)
The 2p levels are, again, the usual ones used for study and quantification of compounds of these transition metal elements. Many of these elements can exist in two or more different oxidation states, meaning that the number of unpaired electrons in the valence 3d levels will vary. The presence of unpaired electrons means there will be multiplet splitting of XPS peaks, which may, or may not, be resolved, or simply broaden the “main” line. Variation in the number of unpaired electrons leads to variation in the multiplet splittings, both in positions and intensities. Though not directly related to this, variation in the number of unpaired valence electrons also results in variation in losses from “main” peaks to shake structure. Finally, since the spin-orbit split components, 2p3/2 and 2p1/2 are resolved but not separated by large energies, the multiplet components and satellites originating from each S-O component can actually spread enough to overlap the other.
Cu2+ versus Cu+ is the classic extreme example of variation in multiplet splitting and shake with oxidation state, as shown in Fig 3. Cu2+ has an open shell 3d9 configuration, leading to strong multiplet splitting effects, which, though not resolved, broaden the XPS “main” 2p lines, and also an unusually strong and apparently well-resolved shake satellite structure, as shown in Fig 3b for CuO. Cu+, on the other hand, has a closed 3d10 structure, meaning multiplet splitting is impossible so there is no broadening of the “main” lines, and very much weaker and differently positioned shake structure, as in Cu2O (fig 3c). Cu2+ and Cu+ with different ligands (eg OH, F, etc) will behave similarly, but not necessarily identically.
Because in this particular 3d element case (Cu2+ and Cu+) the shake structure appears to be well-separated from the main lines, a materials composition analyst might make one of two choices for quantification of Cu compounds in use of e-RSF values:
- Establish separate e-RSF’s for Cu2+ and for Cu+ using standard samples (maybe CuO and Cu2O) using only the “main” 2p3/2 line only and then apply this to other Cu2+ and Cu+ compounds
- Establish an e-RSF by integrating the areas over the whole Cu 2p3/2,1/2 region, out as far as satellite structure is observed, and apply this to determine composition of other Cu compounds.
The second approach is, in principle, going to be the more accurate, because it takes into account any changes in multiplet splitting and shake structure with change in ligand, and also because it is likely that the shake structure and main lines are not really completely separated (ie there is some genuine intrinsic intensity between them). But it requires taking data over a much larger energy range, which takes longer.
If, instead of using e-RSF values, one relies on the accuracy of the Scofield 2p σ value for Cu (which is not oxidation state dependent), for t-RSF, the analyst really has no choice but to integrate the Cu 2p intensity over the whole region.
The large dip from a straight line for e-RSF in the Wagner plot for the elements Ti to Ni in fig 7b is a direct consequence of excluding satellite intensity. The authors knew this, but incorrectly ascribed it to only multiplet splitting effects. In reality it is due to both multiplet and shake, with shake effects being dominant in some cases. Because the S-O splitting is fairly small, ranging from ~6ev for Ti to ~17ev for Ni, and the shake and multiplet effects spread over this or greater range, it is generally not realistic, unlike the Cu examples, to try and separate out “main” line only intensities to establish e-RSF’s, and integration over the whole 2p region must be used for best accuracy. Nefedov and coworkers  also reported results (but not actual spectra) for these transition elements. Though they did not state which compounds were used, they did claim to have taken into account satellite intensities in deriving their values for the experimental σ. Their values fall roughly on the dotted line between Ca and Cu in Fig 7b, as would be expected if satellite intensity were included.
An example of the futility of trying to separate just the 2p3/2 “main” peak intensity in some cases is given for the well-studied case of Fe2O3 [12, 24-27], for which a partial survey scan is shown in fig 9a, and a higher resolution Fe2p spectrum in Fig 4b, for a single crystal sample of hematite . Clearly, as pointed out by Bravo-Sanchez, et al (12), trying to fit any type of background to just the 2p3/2 region will result in the removal of a significant amount of genuine intrinsic signal. With the background (Shirley type) subtracted in the manner shown in Fig 9a, and with the specific start end points shown, an experimental σ value of ~14.5 for Fe 2p can be extracted from e-RSF determined by ratioing the total Fe 2p intensity to that of O1s (backgrounds as drawn). This compares to the Scofield σ value of 16.4, so 12% low. However, the necessity of integrating over the large energy range for Fe2p, with structure throughout it, exacerbates the problem of appropriate background subtraction. The end point is somewhat arbitrary. Here, and in some publications, it is chosen to be where it is in fig 9a, because there is a small peak at ~743ev, which is considered to be a shake component, and we want to include that. In other studies, authors have picked the end point to be ~728ev , excluding this peak. This, of course makes a difference, and the degree of difference actually depends a lot on what version of Shirley Background (traditional, iterated, “active”) is used. A conventional Shirley background cannot be extended beyond the point where the total signal starts to decline, without assuming a component of genuine intrinsic signal exists in the declining region. An iterated Shirley background requires a few points of flat background at the end point to correctly finish, which is why ~728ev is sometimes chosen as the signal there passes through a brief flat region. The “active” approach  involves, amongst other things, the possibility of adding a downward sloping background at some point. This is, however, also arbitrary and in essence is saying “I know it is all background from here on, with no intrinsic signal”. This is might be correct, but is an arbitrary assumption. The current authors believe, but cannot prove, that there may be intrinsic signal contribution beyond 743 ev in fig 9a, based on the fact that the downward slope of the signal is much larger than would be expected for just extrinsic background (eg compare to after the O1s peak). Also in the spectrum of Fe metal, there is a slight, but clear, break in the slope at ~ 760 ev in the Mg K alpha recorded spectrum , which may indicate the true end of the Fe2p signal. This region is masked using an Al Kα X-ray source because of the start of the overlapping Fe Auger signal.
There is yet an additional catch if wanting to use Scofield cross-sections for the analysis. A careful examination of the O1s signal at high resolution, (fig 9b), reveals there is considerable intensity in structure spreading over a 70ev range after the main peak (the majority is within 30ev though). In the compositional analysis one is comparing intensities of Fe2p to O1s. If one uses Scofield σ values for quantification and includes shake intensity for Fe2p, then the shake intensity for O1s should be included. The fractional intensity in the structure after the main O1s is about 35% of the total, as determined by an iterated Shirley Background fit . If all this is shake, excluding it, while including the satellite structure in the Fe2p (unavoidable), would result in a 35% error in stoichiometry determination! Of course, we do not know how much of this structure represents genuine shake structure. The peaks are broad and flat and some of it may well be extrinsic structure. Given this complication, a claimed accuracy for a Fe2O3 analysis as Fe2.00+/-0.005, done by including all Fe 2p satellite structure, but without including any O1s satellite structure, is surprising .
The rest of the periodic table
The discussion above concerning the spectral distribution of intrinsic signal for the 3d transition metal elements is valid also for the elements Y(39) to Pd(46) (4d valence electrons) and La(57) to Pt(78) (5d valence electrons). The Lanthanides, Ce(58) to Lu(71), and Th(90) and U(92) are even more complex because of the potential involvement of 4f and 5f open valence shells. An extreme example, the 3d spectrum of Ce 4+ in CeO2, is given in fig 10 . The assignment of the peaks, as marked, to the S-O components and related shake satellites , has not been verified by any theory, but is very plausible. The percentage of intensity in shake structure is much more intense than that in the “main” peaks. From a theory point of view this means that the one electron picture of photoemission has completely broken down. So far it has not been possible to come very close to describing the spectrum from ab initio cluster calculations, even when including significant many body interaction terms by Configuration Interaction in the final state , but they do agree with experiment in that there is far more intensity lost to satellite structure than in the “main” lines. From a quantitative analysis point of view, the intensity over the whole Ce3d spectrum must be used. Though, from just looking at CeO2 in fig 10, it might seem feasible to just use the leading peak to provide an e-RSF, we know this is not the case, because changing the ligand from O to F, (CeF4), results in large changes in relative intensities throughout the whole spectrum, as can be seen in Fig 10.
Of course, there is much of the periodic table that we have not discussed at all: the heavier elements in groups IA and IIA, and the heavier elements in groups IIIA through VIIA. These all have closed valence shell structures, so there are no multiplet splitting effects. The problem of potentially significant shake intensity remains, however, and it is also likely that the Scofield σ values are less accurate than for the lighter elements.
We have reviewed two approaches, e-RSF and t-RSF, used for quantification in XPS using relative peak intensities. The original goal of one of the authors (CRB) was simply to try and establish whether there was justification to the Wagner et al claim  that Scofield’s calculated σ values  were seriously in error. Our conclusion is that for the 1st row elements they are not and the reason for the reported discrepancy was a combination of not including satellite intensities when necessary in e-RSF, and a wrong transmission function, T, value when deriving σ from t-RSF. We believe the calculated Scofield σ values for the 1s level of the 1st row elements are accurate to +/- 5% as claimed by Scofield. So if an analyst’s work involves only these elements (eg much polymer and biomaterials work, and a few ceramics) using Scofield σ values will not cause greater errors than this. Background subtraction and satellite structure are not major issues either for such material, except for the unique case of LiF. However, if structure identifiable as shake is present, it improves accuracy by including it (eg. the well-known π to π* shake of C1s for aromatic compounds ).
For non-transition elements, where the 2p BE’s peaks are usually used for quantification (Na to As), there is also no evidence of huge discrepancies in σ, but for some of the elements, P to Ca, it seems certain that the calculated 2p/2s ratio is in significant error, with 2p being perhaps up to 15% high and 2s up to 15% low, suggesting some mechanism that transfers intensity from 2s to 2p.
For the elements later in the periodic table with d or f valence shells, quantification accuracy is likely to be much poorer in situations where d or f valence shells are open, leading to large multiplet splitting and shake effects. These effects can vary considerably with oxidation state (variation of the number of unpaired valence electrons), and also significantly with ligand (variation of covalency), but there is no strong evidence that Scofield values are hugely in error. Owing to the variation in multiplet and shake intensities and positions, accuracy in quantification is severely limited if attempts are made to use only the “main” line part of the spectrum and a generic e-RSF for that element. Intensity generally spreads over the whole 2p region and well beyond and it is necessary to integrate intensity over the whole region to improve accuracy. This however increases the effect, on measured intensities, of variability in background subtraction using different procedures.
For elements where open f shells are involved (lanthanides and actinides), the one electron approximation of photoemission becomes untenable in some cases (eg Ce). Shake effects can become so large that the “main” line is no longer that – satellite intensity swamps it, and also can vary a lot with change in ligand. Quantification requires integration across the whole spectral region. There is not enough data available to evaluate Scofield cross-section inaccuracies, but it is reasonable to suspect they are significantly worse than for the 1st row elements.
Suggested Protocols for Rapid XPS Analysis aimed at quantifying elemental composition.
Finally, some brief comments concerning the practical analyst’s dilemma to quantitation – “do I have time to do the job thoroughly, or can I get the desired level of accuracy in a fraction of the time by a restricted default approach that uses RSF’s”. We certainly do not advocate making “perfect” the enemy of “good enough”, but, of course, “good enough” should be defined before the measurement is made. In the experience of one of the authors (CRB) it is not unusual for a customer to ask for accuracy well beyond what he/she can justify needing, but at least that is a better starting point than just “please analyze this”.
The goal of the other author (BVC) is to provide an analysis procedure which a typical “in the trenches” analyst can live with and still generate reliable quantitation. Given that the effects of background subtraction, and the uncertainties of changing multiplet and shake structure with chemistry, are not generically well documented across the periodic table, even a close to perfect job in collecting the data, involving much individual input per analysis, is not going to guarantee a high level of accuracy in stoichiometry, except for the first row compounds (where it might be +/-4% or better). For compounds where open d or f shells are involved, there is probably no advantage in going beyond a properly set up low energy resolution survey spectrum (enough points per ev; enough S/N statistics) for a stoichiometry analysis of the bulk of a homogeneous material. In any case a survey spectrum should always be the default first step (and repeated as the last to see if anything has changed during the analysis). This will require defining the start and end points of the background fits to the peaks being used for quantitation in the survey, and being consistent in this for the XPS level being considered. Of course, if detailed information relating to chemistry is required, that is entirely another matter and high energy resolution scans are required over whatever energy range encompasses the main signal and satellites that may carry chemical state information on that element.
If the analyst chooses not to go beyond the survey spectrum for quantitation by measuring key XPS peaks at higher energy resolution, then the spectral range actually acquired should not be limited to the conventional 20 or 30 ev for each element, but rather should be great enough to capture any significant satellite structure. This range will vary, but could be as much as 80ev, as in Fig 9b, for O1s. The survey spectrum in fig 9a was acquired using a 200ev pass energy, with only 1 point per ev, and took <3 minutes. Acquiring just high energy resolution scans of Fe2p and O1s, generating the same S/N statistics, over the 80 ev wide range needed, takes ~10 times longer, and does not significantly change the ratio determined Fe/O stoichiometry.
Changing the end point of the background subtraction, and/or the method of subtraction (Shirley, Tougaard, or modifications of either) may produce more significant variation in determined composition. Again it is important to be consistent in the approach to background subtraction for the peaks being ratioed.
For a sample of unknown Fe/O composition and chemistry using this default survey spectrum approach, combined with e-RSF’s measured the same way on appropriate pure standards (eg Fe2O3, hematite crystal), is recommended. Using e-RSF’s established for different oxidation state standards (in this case Fe0, Fe2+ and Fe3+) will improve accuracy if differing fractions of the total photoemission are captured in the defined energy range, which, generally is going to be hard to know a priori. If standards are not available and t-RSFs, based on Scofield σ values are used, then all significant satellites should be included in the measured intensities.
In the Appendix we provide a suggested protocol for establishing a procedure of measurement that will return a correct stoichiometry, using Scofield σ values, for chemical compounds (standards) of known composition, but remember this is somewhat arbitrary in nature, relying on adjustment of start and endpoints, and the method of background subtraction. Once these have been established for the standard, it can then be used for the unknown containing the same element. We are currently testing this approach for robustness for transition metal compounds.
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- Paul S. Bagus, Connie J. Nelin, C. R. Brundle, N. Lahiri, Eugene S. Ilton, Kevin M. Rosso, JCP accepted for publication
- I. Nefedov, N. P. Serguishin, I. M. Band, and Trzhaskovskaya, J. Elec. Spec. 2, 383, 1973; V. I. Nefedov, N. P. Serguishin, Y. V. Salyn, I. M. Band, and M. B. Trzhaskovskaya, J. Elec. Spec. 2, 383, 1975
- D. Wagner, et al, Surface and Interface Analysis. 3, 211, 1981
- J. Yeh and I. Lindau, Atomic Data and Nuclear Data Tables, 32, 1, 1985
- S. Bagus unpublished
- V. Crist σ values, website https://xpslibrary.com/crist-empirical-rsfs-scofield-base/ https://xpsdata.com (accessed Dec 16, 2019); Thermo σ values, https://xpslibrary.com/crist-empirical-rsfs-scofield-base/ https://xpsdata.com (accessed Dec 16, 2019)
- R. Brundle, T. J. Chuang, and K. Wandelt, Surface Science, 68, 459, 1978
- Pauly, F. Yubero, J. P. Espinos, and S. Tougaard, Surf. Interface Anal. 2018, page 1
- Aronniemi, J. Sainio, and J. Lahtinen, Surface Science, 578, 108, 2005
- Doubray and S. A. Chambers, Phys. Rev. B 64, 205414, 2001
- Handbook of X-Ray Photoelectron Spectroscopy, J.F. Moulder, W. F. Stickle, P. E. Sobol, and K. D. Bomben, PHI, 1992
- Peter Sherwood, private communication
- J. Nelin, P. S. Bagus, E. S.Ilton, S. A, Chambers, H. Kuhlenbeck, H. J. Freund, Int. J. Quant. Chem., 110, 2752, 2010
Fig 1a Schematic hypothetical XPS spectrum expected for gas phase LiF
Fig 1b Schematic XPS spectrum for solid LiF
Fig 1c 2p3/2 XPS spectrum for Fe metal
Fig 2 Relative Intensity of an XPS signal, per unit depth, emerging normal to the surface at its unscattered original KE.
Fig 3a XPS of the Ne atom showing shake-up and shake-off contributions spreading over 100ev KE 
Fig 3b XPS 2p spectrum of CuO
Fig 3c XPS 2p spectrum of Cu2O
Fig 4a N1s spectrum of the NO free molecule showing the multiplet split components
Fig 4b XPS 2p spectrum of single crystal haematite, Fe2O3, showing multiplet broadening of the main 2p3/2 and 2p1/2 peaks, plus shake-up features
Fig 4c Calculated multiplet splittings of the 2p spectrum of Fe2O3. The envelope is sum of all components 
Fig 5a Redrawn fig 3 from Wagner , comparing e-RSF curve to t-RSF curve for elements Li to F.
Fig 5b Proposed correction to the e-RSF curve due to a 32% correction in the Li/F ratio (see text). Changing the T dependence on KE from KE-1 to KE-0.5 brings the t-RSF curve into coincidence with the e-RSF curve (see text).
Fig 6 Survey spectrum of LiF single crystal. Inset (left) shows a high resolution spectrum of the F1s region with 10 identifiable satellite features. Inset (right) shows a high resolution spectrum of the F2s and Li1s region (upper) and an overlay of the F1s spectrum on the F2s (lower) showing the overlap interference of the F2s satellites with the Li1s spectrum.
Fig 7a Redrawn from part of Fig 4 from Wagner  comparing their 2p e-RSFs to t-RSFs for Mg through to As.
Fig 7b Showing the transition element region in more detail. Some Nefedov values for the transition metals  lie roughly on the dotted straight line joining the e-RSF’s of Ca and Cu (See text for discussion).
Fig 8 The Cl 2s and 2p region of a single crystal of NaCl. Scofield σ normalized intensities give a ratio of 1.3 instead of the expected 1.0 (see text)
Fig 9a Survey spectrum of single crystal hematite, Fe2O3, with Shirley backgrounds.
Fig 9b High resolution spectrum of O1s of the hematite sample with fully iterated Shirley background  extended to cover all observable satellites
Fig 10 The Ce 3d XPS spectrum of CeO2 and CeF4.
Data Collection and Processing Protocols for Generating Correct Stoichiometry in a Homogeneous Bulk Standard material, which can then be used to establish unknown compositions for materials containing the same elements.
- Fresh HOMOGENOUS Bulk is exposed (see below) by fracture, cleave, scrape,
or grinding of sample using freshly cleaned scraping/cutting/grinding tools
- Original Scofield SFs are correct
- Software uses unmodified, original Scofield SFs
- Carbon on surface is due only to normal adventitious (AMC) carbon
- Once sample bulk is produced, the sample will be loaded immediately into sample load lock (<5 minutes)
- Sample has NOT been exposed to any gases, siloxane, or metal coatings before receipt
- Analysis area has NOT been exposed to SEM electron or Ion beams
- X-ray source is Monochromatic
- Instrument is <20 years old⁰
- Software provides Iterated Shirley Background fit
- Software removes transmission function effect
- X-ray to Lens angle is ~ 55⁰ to negate angular asymmetry effects
- Software provides IMFP correction or allows change of IMFP
- Pass energy does NOT saturate detector in 500-1300 eV range
- Detector system is a pulse counting A/D electron collector, not optical
- Detector system has a minimum of 5 channels
- Dead-time correction is turned OFF
- Electron take-off-angle relative to surface plane is >30 deg
- Lens-field-of-view area is NOT (or is only slightly) dependent on electron lens voltages
- X-ray spot is very near the center of the lens field-of-view
- Charge control gives FWHM for polypropylene <1.2 eV with no shoulders
- Sample is NOT degrading during the time of the analysis
- X-ray flux is NOT degrading sample during time of analysis
- Sample is NOT reacting with the gases in the analysis chamber
- Sample is NOT emitting solvent or water molecules into analysis chamber
- Vacuum of analysis chamber is <5 e-8 torr
- There are no spike noise peaks
- X-ray source is stable during analysis time
- Electron collection angle is between 20-60 degrees in width
- Magnetic lens, if present, is turned OFF, unless essential
- Software does NOT modify raw data except to remove TF
- Analysis of fresh exposed Teflon bulk gives a 66:33 atom% ratio with <5% error
- Using an Argon filled glove box (bag) for sample preparation is preferred, but not essential
Sample Preparation Method Produces Reasonably Clean Pure Bulk Chemistry (general, not just for bulk standards)
- Plastic sheet: Use a clean single edge razor to scrape the surface
- Plastic bead: Use tweezers or pliers to hold bead, and use a clean
single edged razor to cut bead in half
- Fiber/hair: Tape fiber down, use a clean single edge razor to cut fiber
- Wafer: Scribe 1-2 mm line at edge, and then cleave using pressure from a scribe on the line or glass cleavers
- Lump: Mark outside with black or blue Sharpie pen,
place in clean plastic bag, place bag on a metal
sheet, hit with hammer
- Glass sheet: If sheet is 1-3 mm thick, scribe a line from edge to
edge, and use glass cleavers to cleave the sheet
- Natural mineral: Mark outside with black or blue Sharpie pen
place in clean plastic bag, place bag on a metal
sheet, hit with hammer
- Metal sheet: Scrape surface with single edge razor blade, or
Scrape surface with a carbide or diamond tip
- Ceramic sheet: If sheet is 1-3 mm thick, scribe a line from edge to
edge, and use glass cleavers to break the sheet.
Alternatively, if sheet is >5 mm thick, mark outside with
black or blue Sharpie pen, place in clean plastic bag,
place bag on a metal sheet, hit with hammer
- Fine powder: Using a clean mortar & pestle, grind the powder enough
to expose fresh bulk
- Granular pieces: Place inside clean plastic bag on a metal sheet, hit with hammer
to form small grains, then try to grind in clean mortar & pestle
Data Collection Protocol
- Survey Window Size: -10 to 1100 eV (very rarely increase 1300 eV)
- Step Size for Survey: 7 to 1.0 eV per step
- Points/eV in full O (1s) peak: 1.3 pt/eV (provides 10 pts/8 eV endpt-endpt)
- Points/eV in full Fe (2p) peak: 1.3 pt/eV (provides 58 pts/46 eV endpt-endpt)
- Total Number of Channels (Points): 1,300 data points
- Dwell Time per Voltage Point: 50 msec per voltage (data) point
- Total Number of Scans: 2 scans for full survey
- X-ray Power: maximum
- Ion etching: none (scrape/cleave/grind are acceptable)
- Pass Energy: use maximum PE recommended by maker
- FWHM for clean Ag 3d5: should get ~1.8 – 2.0 eV using maximum PE
- FWHM for O (1s) for max PE = should get ~2.0-2.2 eV using maximum PE
- Total Time for 2 scan Survey: <4 minutes for 2 scans (to avoid X-ray damage)
Data Processing Protocol for Two Major Peak Types
There are two extreme situations:
- A single narrow symmetrical peak that is far from any related peaks from the same element (eg spin-orbit components, Auger signals), and is far from a peak from any other element present
- An overlapping spin-orbit coupled peak envelop (such as Fe 2p) that clearly has overlapping spin-orbit peaks or nearby shake-up structure (such as Cu2+2p)
- This protocol is designed for use on survey spectra only. Step size is usually 0.7-1.0
- This protocol uses iterated Shirley background method for peak area integration, and recommends peak area baseline ranges that are at usually 40-50 eV wide
- The recommended maximum range for any baseline range is an 80 eV spread
- This protocol should incorporate all significant Shake-up and Multiplet splitting signals.
- Do not use this protocol for high resolution spectra
- The Iterated Shirley baseline should never be allowed to cross over the baseline of the spectrum
- Use (select) iterated Shirley type background method (do NOT use special modes) to integrate peaks
- Use (select) 5-10 iterations and 0.01-0.001 convergence
- Use (select) a 1.0 eV range or 5 data points for baseline (background) endpoint averaging
For Peak Type #1 – a single narrow symmetrical peak – that is well separated from any spin-orbit or other peak
- USING an O (1s) peak as an Example: Locate BE of O (1s) peak max (usually 530-532 eV)
- Add baseline start and endpoints that are very close to the nearly symmetrical peak being integrated (e.g. 5 eV below and 5 eV above the peak maximum counts)
- Place the two endpoints close to base of the peak where the background intensity is at a minimum.
- If possible, adjust (define) upper BE endpoint to be 8-15 eV above O 1s peak max BE (e.g. 538-545 eV).
- If however the Iterated Shirley baseline shows a bad fit (crosses the spectrum signal), then move the upper endpoint to lower BE toward the O 1s maximum until you locate a minimum intensity position
- Vertically expand (zoom) lower BE endpoint region to clearly see and check endpoints selected and noise
- If lower BE endpoint is located on a flat bottom region, then adjustment of lower endpoint position is finished. (Note: Placement of the lower BE endpoint is usually easy.)
- Now look at the upper BE endpoint.
- If upper (higher) BE endpoint is located on a flat bottom region, then adjustment of upper endpoint position is finished. In this case, stop. Peak integration of 1st peak is done.
- If, however, the upper endpoint is not located on a flat bottom region, then visually inspect the region of the spectrum that is 30-50 eV higher in BE
- Locate a low point in that extended 30-50 eV region, and move the upper endpoint to a point having lowest count
- Vertically expand (zoom) upper BE endpoint region to clearly see the upper endpoint selected and the noise.
- If upper BE endpoint is located on a flat bottom region, then you are finished. If not, then move upper endpoint to nearest point having lowest count.
- When upper BE endpoint is located at a flat bottom region, then stop. Peak integration is done.
For Peak Type #2 – eg an spin-orbit coupled peak envelop (such as Fe 2p) having overlapping spin-orbit peaks or nearby shake-up structure (such as Cu2p 2+)
- USING Fe (2p) as an Example: Locate BE of Fe (2p) peak max (usually 709-711 eV)
- Add baseline start point to be roughly 8-10 eV below the peak maximum counts (e.g. 695-688 eV in the case of Fe2p)
- If possible, adjust (define) upper BE endpoint to be 35-40 eV above spin-orbit lower peak max BE (e.g. 735-745 eV in the case of Fe2p)
- Vertically expand (zoom) upper BE endpoint region to clearly see endpoint selected and noise
- If upper BE endpoint is located on a flat bottom region, then you are finished.
- If not, move the upper endpoint toward higher BE to the nearest point having a valley or a minimum. Do not move more than 5-10 eV higher.
- When upper BE endpoint is finally located at a flat bottom region, then stop.
- If you have reached the maximum acceptable upper endpoint range (80 eV), then stop. You are finished.
Next Step – Generate Atom% values and Empirical Formula
- Generate atom% values by applying the t-RSF method using unmodified, original Scofield SFs and an IMFP exponent ~0.66
- If resulting atom% values match the expected theoretical atom% (ratio), then finished.
- If resulting atom% values differ by more than 10% from theory, then look at upper BE baseline endpoints. If there is no possibility of overlap with another signal, then try increasing upper BE endpoints by 5-10 eV until you locate a new minimum in the spectrum.
- Check expected ratio and atom% values again. If atom% values still deviate by more than 10% from theory, then the sample may have significant levels of contamination in the bulk or on the freshly exposed surface.
- If there is no bulk contamination, then consider the possibility that the sample might truly be a different chemical compound (homologue) and truly has different stoichiometry.
- If the 80 eV peak area integration range for either of the 2 signals has a significant overlap with another XPS signal from the same element (e.g. Fe 3s overlaps upper BE range of Fe 3p), then join the peak area integration of those two peaks (e.g. Fe 3s-3p), increment the SF to reflect the addition, and increase the upper BE baseline endpoint to be 20-30 eV above the BE max of the higher BE, secondary XPS signal.
Cross-Checking by Processing Alternate Minor Peak(s)
- To cross-check the atom% empirical ratio obtained, use an alternate secondary XPS peak to measure atom%, but use the same protocol defined above, eg for Fe in Fe 2O3, both the Fe (3p+3s) and O(2s) can be used