Accuracy Limitations – LiF as example



Accuracy limitations for composition analysis
by XPS using relative peak intensities:
LiF as
an example


J. Vac. Sci. Technol. A 39, 013202 (2021);

 C.R. Brundle
C.R. Brundle and Associates
4215 Fairway Drive, Soquel, CA 95073, USA

 B.V. Crist
The XPS Library Institute – NFP
1091 Vineyard View Way, Salem, OR 97306, USA


Paul S. Bagus
Department of Chemistry
University of North Texas
Denton, Texas 76203


Keywords: XPS, Sensitivity Factors, photoionization cross-sections, quantification accuracy



Although precision in XPS can be excellent, allowing small changes to be easily observed, obtaining accurate absolute elemental composition of a solid material from relative peak intensities is generally much more problematical, involving many factors: background removal; differing analysis depths at different photoelectron kinetic energies; possible angular distribution effects; calibration of the instrument transmission function, and variations of the distribution of the photoelectron intensity between “main” peaks (those usually used for analysis) and associated substructure following the main peak, as a function of the chemical bonding of the elements concerned. The last item, coupled with the use of photoionization cross-sections and/or relative sensitivity factors, is the major subject of this paper, though it is necessary to consider the other items also, using LiF as a test case. The results highlight issues relevant, in differing degrees, (rewrite needed) to most XPS analyses, demonstrating challenges to highly accurate XPS quantification.

LiF, using the Li1s and F1s XPS peaks, appears, at first sight, to be an ideal case for high accuracy. Only 1s core-levels are involved, removing any possible angular effects, and it is a wide band-gap material, resulting in the main Li1s and F1s peaks being well separated from the following scattered electron backgrounds.  There are, however, two serious complications: 1) the main F1s and F2s levels have a major loss of intensity diverted into satellite substructure spread over ~100ev KE from the main line, whereas the Li1s level has very much less diversion (of intensity); 2) there is serious overlap of the substructure from F2s (~30ev BE) with the main line of Li1s at ~55ev.

We report here a detailed analysis of the LiF XPS, plus a supporting theory analysis of losses of intensity from Li1s and F1s to satellite structure, based on cluster models of LiF.  We conclude that, if the overlap from F2s substructure is correctly subtracted from Li1s, and the intensity from satellites for F1s and Li1s properly estimated, the (atom% or quantitative) composition of the single crystal LIF may be recovered to within 5%, using the photoionization cross-sections of Scofield, Inelastic Mean Free Path Lengths based on Tanuma, Powell, and Penn, and the calibrated instrument Transmission Function. This refutes the claim by Wagner, et al, based on their empirical determination of Relative Sensitivity Factors, RSF’s, (which applied only to the instruments and analysis procedure they used, in 1981) that Scofield values are too low in general and, for Li1s in particular, are low by a factor of ~2. This is important because Wagner based RSF’s (sometimes modified and sometimes not) are still embedded in quantification software on modern commercial instruments, and so analysts need to be aware of how those RSF’s were obtained/modified. Incorrect use can lead to large quantification errors.



Recent emphasis on the reliability and reproducibility of physical sciences data [1] has encouraged a reexamination of the usage of XPS for materials analysis and characterization, especially as this is now the most commonly used method for thin material (up to a few 100A thickness) and is often performed by non-experts in a turnkey manner. One of the issues concerns the reliability of absolute accuracy determination (as opposed to precision) of elemental composition [2]. Precision, on the other hand, can be very good, allowing small percentage changes in composition or film thickness to be quickly and easily obtained [3]. We hope to reach both practical analysts, to help them appreciate the proper claims of accuracy for their analysis, and to reach surface scientists to help them appreciate possible limitations in reports of elemental compositions based on XPS. We urge the interested reader to also read our prior publication [2], which is a more general perspective of quantitation accuracy in XPS. The present detailed analysis for LiF follows on from that work.

The usual method for obtaining elemental composition from homogeneous materials is to use the relative intensities of core level XPS signals measured for the key peaks in the spectrum, and then normalize by dividing these by Relative Sensitivity Factors, RSF’s. We note here that this is the proper definition for “Relative Sensitivity Factors”. They are the numbers by which the measured XPS signal intensities must be divided to yield the relative atomic concentrations of the atoms concerned. This might seem self-evident, but there is often confusion concerning what is included in the term.

Historically two approaches have been used:

  • Use of standards (ie material of known composition) to establish, entirely empirically, Experimental Relative Sensitivity Factors, e-RSF, for all elements, normalized against either C1s or F1s set to unity [4]. No theory is involved, but the e-RSF values obtained this way are for the specific procedure used for measuring signal intensities in a specific instrument, under specific operating conditions and data analysis procedures. Composition of unknowns are then established by normalizing the measured signal intensities by the e-RSF’s. However, these RSF values are not valid for different measurement procedures or instruments with different transmission characteristics, unless appropriate corrections have been made, which can be difficult if the true characteristics of the instruments used to derive the original e-RSF’s are not well known.
  • Use of theoretical equations for the photoionization intensities to provide Theoretical Relative Sensitivity Factors, t-RSF. The partial photoionization cross-section, σ, of the element core level concerned is the most important parameter, since it varies by over 100 across the periodic table for the core-levels used [5]. Variation of the Inelastic Mean Free Path Length for Inelastic Scattering, 𝜆, is also important [6,7], because it depends on the KE of the photoelectron, so that XPS signals of different BE’s come from different depths and a correction for this must be made. A calibrated analyzer Transmission Function, T, is also required, though on modern commercial instruments this is usually provided by the vendor and may not be apparent to the operator [8].

It was originally claimed [4] that serious discrepancies existed between the two approaches, blamed at that time on grossly incorrect theoretical values of σ’s used in the t-RSF method. A recent reassessment of that work [2], however, indicated that the disagreement was caused by other factors, leading to an incorrect comparison, and that a) there is no strong evidence for huge errors in the calculated σ’s across the periodic table, and b) there is close agreement between the two methods for determining the composition of compounds consisting of first row elements, Li to F, provided the two methods are used correctly.

The major problem with both approaches, once one asks for the ultimate accuracy possible, stems from the fact that in XPS not all of the photoemission intensity from a given core-level ionization goes into a single peak, but is spread over the “main” peak and intrinsic substructure associated with it at lower KE. This reflects the fact that the ionization process is not strictly a one electron process, with no response from the other electrons in the system [9-11]. Fig1 illustrates, schematically, example spectra. In Fig 1a a single XPS core level peak is depicted, well separated from the subsequent scattered electron background caused by the photoelectrons passing through the solid after photoionization. The background is drawn here as being a featureless step, but it may have structure.  This represents the closest to a one electron process for an insulating material with a band gap as shown. Clearly there is no problem in measuring this intrinsic signal intensity in the peak.

Fig 1b represents a conductor or semiconductor without a discernable band-gap. It is now harder to accurately measure the area because of the lack of knowledge of how to correctly separate the signal from the following scattered electron background. Fig1c represents the situation, for an insulator, where a significant fraction of intensity has been diverted from the “main” peak into other intrinsic substructure (often referred to as “intrinsic satellite structure”) superimposed on a featureless background. It is important to realize that this substructure may spread over many 10’s ev to lower KE than the main photoelectron peak (the schematic is drawn for an insulator, but applies equally to a conductor, except there is no bandgap). Fig 1d adds a final complication – structure in the inelastically scattered electron background (often referred to as extrinsic substructure, meaning it is not from the XPS photoionization process), caused by specific high probability inelastic scattering events as the ejected photoelectrons travel through the material and escape. To accurately process the data, our problem is how to separate the intrinsic substructure, which is relevant to accurate quantification, from this extrinsic scattered electron background.



FIG.1. Schematic representation of the core level XPS for:

  1. A one electron photoionization process for a wide band gap insulator. A straight-line background removal is appropriate.
  2. As a) but for a conductor. Two possibilities for removing intensity from the scattered electron background are shown. They will result in differing integrated areas under the peak, and those areas will also change if the assumed position of the end point of the intrinsic spectrum is changed.
  3. Satellite peaks. The main peak represents those atoms that undergo only the core level ionization. The two satellite peaks shown, are from those atoms which have undergone both the core-level ionization, plus excitation of a valence level electron to one of the unoccupied levels available. It is possible to have many such peaks.
  4. As d) but with an extrinsic scattered electron feature added, representing a scattering event with high probability at this loss energy from the main intrinsic peak.

The fraction of signal diverted into satellite structure can, and does, vary from atom to atom, core level to core level for a given atom in a given chemical state, and for different bonding situations of a given atom [10]. It is this variability, and our difficulty in reliably identifying and accurately separating intrinsic satellite structure from the extrinsic background, that is the ultimate limiting factor in using XPS intensities for accurate composition analysis. In the e-RSF approach usually only the main peak is used to generate RSF’s in the standards used [4]. This limits accuracy when an e-RSF, determined for an element in a particular bonding situation in a given standard material, is then applied for differing situations in other compounds. This is true even if measurements are made on the same instrument under the same operating conditions.  In the t-RSF approach, for ultimate accuracy all the intrinsic satellite intensity is required because a calculated σ refers to the total photoionization intensity from the initial quantum level concerned, ie. “main” peak plus satellites [5]. The degree of degradation in accuracy using only main line intensities obviously depends on how large are the losses to satellite structure and how different they are between the XPS main lines being ratio-ed.

In the present study, on a single crystal LiF standard, the situation is, in principle, simplified for three reasons: 1) The band gap results in the main peak being well-separated from the background; 2) the compound is diamagnetic, meaning there are no unpaired valence electrons to spin-spin interact with the unpaired electron remaining in the core level after photoionization, so there can be no multiplet splitting into individual components, which might be widely spread and/or can cause unresolvable main peak broadening [12,13]; 3) there is no relative angular distribution effect when comparing s electrons [14,15].

Any intrinsic sub-structure occurring in the XPS of LiF must, therefore, be the result of shake-up (and shake off) processes (termed “satellite structure”) where a valence electron is promoted to a higher empty level (or, for shake-off, ionized completely) in conjunction with the ejection of the 1s electron, thereby reducing the KE available to the outgoing electron by the corresponding promotion energy [10]. The process is described schematically for an atom in the energy level diagram of Fig 2. It is important to understand that, for any given individual atom in an ensemble of identical atoms, only one core-level electron is removed, per atom, by the photoionization process. Some fraction of the atoms in the ensemble undergo just the core level electron ionization, resulting in the “main” line of Fig 2a, while others emit core level electrons with KE reduced by the energy of a valence level electron excited (shake-up) to a higher level, or removed completely (shake-off) in response to creation of the core-hole, resulting in the peak as in Fig 2b.

The total signal observed from the ensemble is then given by the fraction undergoing just the core level ionization (“main” peak), and (plus) the fraction suffering both core level ionization plus shake, Fig 2c. Of course, there are many shake processes possible, resulting in the possibility of many shake satellite peaks, depending on whether they gain any intensity [9]. Again, this paragraph may appear self-evident to those experienced in the use and interpretation of XPS, but novices sometimes interpret the resultant spectrum of Fig 2c as implying that both peaks come from the same individual atom. Since the theoretically calculated σ represents the sum of all probabilities of photoionization from the initial state, the ultimate accuracy issue depends on determining and including the fraction of signal diverted from the main line into the shake peak, or peaks, which for LiF varies significantly for the Li 1s photoionization compared to the F1s photoionization.


FIG. 2. Schematic energy level diagrams for:

  1. a one electron core level XPS process for an atom; removal of a core electron only
  2. a two electron XPS process involving a valence level excitation (shake process) in addition to the core level ionization
  3. The resultant spectrum for an ensemble of atoms, where 2/3rds undergo just a core electron removal, and 1/3d undergo a core electron removal plus a valence level excitation

We are guided by theory as a check or validation of the reliability of our experimental estimates of satellite structure intensities. A series of rigorous ab initio wavefunctions, WFs, have been determined so that we have reliable knowledge of the fractional losses from the main Li1s and F 1s peaks (termed Li1s(main) and F1s(main) from here on). The results are compatible with our experimental estimates of the satellite intensities in that losses from F1s are predicted to be far greater than from Li1s. We then use the experimentally determined relative intensities to see how closely the known stoichiometry of the compound is reproduced when applying the appropriate equation for relating relative intensities to composition. Since the equation uses the calculated σ values of Scofield [5], and the calculated 𝜆 values of Tanuma, Powell, and Penn (TPP-2M) [6], this also gives us information concerning their reliability. (repeat Ref 1 ?)



  1. Theoretical Methods and Models for Ab Initio MO Calculations

The Sudden Approximation, SA, developed by Aberg [16,17] provides a direct means to determine the losses of intensity from the main XPS peaks into shake satellites. (do we need a reference to explain shake satellites?) These shake satellites have intensity because the orbitals to describe the WFs, for the core ions are different from those that are appropriate to describe the initial, ground state WF of the system before core ionization. For a closed shell system, the initial WF can be represented by a single Slater determinant where all shells are filled while the WFs for the main peaks of the core ions resulting from removal of a core photoelectron are also represented by a single Slater determinant but where an electron has been removed from one of the core shells. However, the latter orbitals change from those of the initial state to respond to the potential arising from the presence of the core-hole; see Ref. [10] for a review of the WFs for XPS core-ions. The SA relative intensity that is found for the main peaks is rigorously obtained from the determinant of the overlap of the variationally optimized orbitals for the ground state and for the ionic state where a single electron is removed from the ground state WF so that both initial and final state WFs have N−1 electrons; see, for example, Ref. [18]. This electron is taken from the core shell of the XPS peak whose intensity losses are of interest. The overlap integrals of this determinant, Si,j can be written as


where 0£Si,j£1 and the SA relative intensity, Irel, to the main XPS peak is simply


If the orbitals for the ground state (GS) and the ion were identical we would have Si,j = di,j and the determinant of the Si,j matrix would be 1 indicating that no intensity is lost to satellites. It is standard to describe losses as a percent of the total intensity that would be obtained if there were no losses from the main peaks to the shake satellites where, for our special case, we have, from Eq.(2),

A useful qualitative way to see whether the losses are significant, and to distinguish the extent of losses for different systems, is to consider just the diagonal Si,i for the valence shells. Then for F as in LiF, the 2p orbitals would contribute a term [S2p,2p]12 to the Irel, where the power is 12 because there are six 2p electrons and the product of the overlap integrals is squared. As a measure of how rapidly losses can become important, if we had S2p,2p=0.95 then the approximation to Irel would be (0.95)12=0.54 or almost half the intensity would be lost. if there were much smaller changes in the 2p orbital from the ground state to the core ionic state with S2p,2p=0.99, the contribution to Irel would still be 0.89 for a more modest loss of 11%. On the other hand, for the 1s ionization of Li+, again as in LiF, where there are no 2s or 2p electrons, the contribution from the 1s shell to the Irel would be simply [s1s,1s]2 which to a good approximation would be very close to 1. Of course, for a proper calculation of the SA Irel for crystalline LiF, it is necessary to include the changes in the orbitals of the surrounding atoms as well as those of the core ionized atom in our discussion above. To correctly describe the LiF compound we use embedded clusters following the procedure that has been used to describe the electronic structure and the XPS of a large variety of oxides as described in Ref. [10].

The choices that we make for cluster models and for cluster WFs for an LiF crystal follows the ideas developed for previous studies of the XPS of MgO [19] and of CaO [20]. To describe the bulk BEs of Li and of F in LiF, we have used two different clusters. For the F(1s) BE, the clusters have a F anion at the center surrounded with a first shell of Li atoms for FLi6 where the Li atoms are placed at their position in the LiF crystal. [21] The Li cations are then surrounded by their nearest neighbor F anions so that each Li cation has 6 nearest F anion neighbors to form a FLi6F18 cluster. Finally, another shell of Li anions is added so that each F atom has its correct coordination of 6 nearest neighbor cations with a cluster of FLi­6F18Li38 where the formula lists the atoms in each shell separately. This cluster is then embedded in a set of point charges following the Evjen procedure [22] to correctly reproduce the Madelung potential. The point charges have the values of Q=±1 for bulk charges and suitable fractions for face, edge, and corner positions to insure a totally neutral cluster; [22,23] all atoms and point charges are placed at lattice positions of LiF. The analogous cluster for the BEs of bulk Li atoms is an Evjen point charge embedded LiF6Li­18F38. The reason for using clusters with several shells of ions is to have a reasonable basis for describing the response of the crystal of LiF to the localized core-hole on Li or F caused by Li1s or F1s photoionization.

Two Hartree-Fock, HF, WFs are computed for each cluster where one is for the initial state and the other one for a configuration with a 1s hole localized on the central ion of the cluster. The choice of two solutions is so that the response of the crystal is taken into account when an XPS core ion is formed with the set of orbitals variationally optimized for the core-hole configuration. The two solutions also allow the calculation of the I(loss) with Eqs. (1)-(3). For an ionic crystal like LiF , or MgO [19] or CaO [20], the main response of the crystal to a core-hole is the polarization of the surrounding ions. For LiF this is principally the polarization of the F anion [24] as opposed to the rather rigid Li+ cation. [24,25] The polarization of anions in CaO as a function of their distance from the ionized center and of their contributions to relaxation energies was examined in Ref. [20]. While our treatment neglects the polarization of more distant F anions, since they are included in the embedded clusters as point charges, the polarization of these ions is reduced because they are more distant from the core-ionized atom. [20] A measure of our treatment of the response to Li+ and F core ionization can be obtained by comparing our calculated value for the difference of the F and Li+ 1s BEs, DBE,

with measured values. The directly calculated DBE for the clusters described above is DBE=629.61 eV but this is for non-relativistic WFs and so does not include relativistic effects. From relativistic Dirac Fock calculations on the 1s BEs of F and Li+ based on four component calculations with a Dirac-Coulomb Hamiltonian, we find relativistic corrections to higher BE of 0.75 eV for the 1s BE of F and 0.01 eV for the 1s BE of Li+. The calculation of these corrections is described in more detail in Ref. [26]. The relativistic corrected calculated DBE=630.35 eV is compared to the measured value of DBE=629.0±0.2 eV determined in the present work. A portion of the 0.2% error in the calculated DBE arises from minor limitations in the basis set used to describe the orbitals [27] and a portion from different errors in the calculation of the 1s BEs of F [28] and Li+. The error in the 1s DBE due to an unbalanced treatment of the crystal environment is estimated to be <1 eV giving strong confidence that the results we report for the different shake losses of the 1s F and Li+ XPS peaks are reliable. In this connection, the study of shake in Ne [9,17] and the study of the anomalous multiplet intensities in NO [18,29] is reliable. In order to explicitly distinguish the contributions to the XPS shakes losses in LiF that arise from the condensed phase environment from atomic effects, we have also calculated the shake losses for the main 1s BE peaks for the isolated Li+ and F ions. All the non-relativistic calculations of WFs and Irel were carried out with the CLIPS package of molecular structure programs. [30] The calculations of relativistic BEs were made with the DIRAC program system. [31]

The shake losses from the main 1s XPS peaks for the isolated ions and for LiF are given in Table 1. As expected from our qualitative analysis, mentioned above, of the overlap of the F(2p) orbitals for the initial and 1s-hole configurations, there is a large loss of 27.5% from the 1s XPS peak of the F anion. This is due in large part to the fact that the overlap of the 2p orbitals variationally determined for GS and 1s-hole configurations of F is <j2p(GS)½j2p(ion)> = 0.981. While this is not much reduced from 1.0, when it is raised to the 12th power to account for the closed 2p shell, the loss to shake satellites becomes substantial. On the other hand, the loss from the XPS 1s peak for the isolated Li+ cation is small at 1.4% because the SA intensity of the main XPS peak for the one-electron 1s ionized Li+ is simply the square of the overlap integral <j1s(GS)½j1s(ion)> = 0.993. Moving to solid LiF, it is interesting that the shake loss of the F(1s) XPS peak is slightly smaller than for an isolated F anion. The reason is fairly clear. The main effect of the Li cations is to force a reduction in the size of the F orbitals because they are not able to occupy the space filled with the Li+ cation charge. A detailed analysis of this compression [32] shows that the effective size of an F anion in the solid LiF lattice is reduced by about 6% from that of an isolated F anion. Thus, the initial state F(2p) orbital in LiF, since it is already somewhat contracted, will have a larger overlap with the F(2p) orbital contracted toward the F 1s core-hole than is the case for the free ion. Since the Li+ cations are rather rigid, they can barely polarize and cannot contribute to the change in overlap integrals needed for shake losses and the polarization of the next nearest neighbor F anions is smaller since they are more distant from the core ionized F; see the discussion in Ref. [20].All this leads to a small reduction in shake losses for the F(1s) XPS peak.


The situation is quite different for the losses of the Li+ 1s XPS peak which is substantially larger, by a factor of about 6, for Li+ in solid LiF than for the isolated ion. Again, this has a clear origin in the polarization of the F charge toward the core ionized Li+ cation, which is most important for the polarization of the 6 F anions that are nearest F neighbors of the core ionized Li+ but where there will also be some contribution from the more distant second nearest neighbors. For the crystal, the losses of intensity from the main Li(1s) XPS peak to shake satellites are not as negligible as they are for the isolated Li+ cation.

Another way to examine the extent of the screening of the core-hole that leads to XPS intensity lost to shake satellites is to examine the relaxation energy, ER, which is the difference between a frozen orbital (Koopmans’ Theorem) BE(KT) [30] and a fully relaxed BE(DSCF)[28]. Specifically, ER = BE(KT) – BE(DSCF) is the difference between the BE(KT) given, for closed shell systems, by the HF initial state orbital energies and the BE(DSCF) given by taking the difference of the variational energies of the initial and core-ion states. The BE(KT) does not include any orbital relaxation (hence the term “frozen orbital approximation”) to screen the core-hole while the BE(DSCF) does fully include this relaxation; see, for example, Refs. [10, 34] for a discussion of the interpretation of relaxation energies. The ER of the F and Li 1s BEs for the isolated ions and for LiF are given in Table 2. As expected, the ER for the 1s BE of the isolated Li+ cation is quite small at 1.5 eV while the ER for the 1s BE of isolated F is more than an order of magnitude larger, 24.9 eV. The large ER for Fis mostly because the F 2p orbitals for the 1s-hole configuration are significantly more contracted than for the initial state of the anion. This is the same reason as for the large intensity loss from the main F 1s XPS peak. The ER of the F 1s BE is smaller for LiF for the very same reason that the shake losses of the F 1s XPS peak are smaller for LiF than for the isolated F anion; the relaxation in LiF is decreased largely because of the compressional effect of the surrounding Li+ change density [32] on the F 2p orbitals. On the other hand, the ER of the Li 1s BE in LiF increases by almost a factor of 3 from the ER of isolated Li+ because of the polarization of the charge distribution of the F anions in LiF. [20, 32]. So, it can be seen that shake losses and relaxation are closely related.



It is important to stress that although we believe we have determined the losses from the 1s(main) peaks quite reliably, we have no information on where the shake satellites are or how the intensity is distributed over the different satellites. It is reasonable to expect that the shake satellites will be spread over a large range of energy and into both shake-up and shake-off peaks [17,11]. In order to understand the distribution of shake intensities, it is necessary to have an understanding both of localized and conduction band excitations. While the nature of shake excited states is known for some atoms [35] and molecules, [36] it is more complex for condensed phase systems. This is especially true for compounds like LiF where there may not be low lying excited states such as exist in systems such as in Ti(IV) compounds where d electrons are involved. [37]


B.  Photoemission Intensities

The full equation [4] for the intrinsic photoemission intensity detected from a core-level, in a solid, is given by:

where I is the number of photoelectrons detected, per second, originating from the quantum shell concerned and going into the measured XPS main 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 main peak (the rest go into the shake peaks), ϕ is an angular distribution term, T is the efficiency of detection of the spectrometer (the transmission function, a function of KE), and λ is the IMFP (a function of KE).


For atoms a and b, then, in a given spectrum, where F drops out, the ratio of Ia to Ib is given by

s orbitals have no angular momentum, so ϕa and ϕb drop out. T in the Thermo K-Alpha instrument is calibrated by the vendor and removed at source (see the experimental section) so T also drops out. Thus


In the present work, if I is the total intensity (main plus satellites) then ya and yb are unity and drop out and we have

so generically, provided T has been removed at source and all intrinsic satellite intensity included, we have


We take the σ values from the original work by Scofield [5] but in the discussion section we review using σ value calculations by other authors. We use the 𝜆 values from Tanuma, Powell and Penn (TPP-2M) [6] as implemented in the Thermo software, but discuss the empirical relationship from experimental measurements that 𝜆 is proportional to KEx where x is somewhere between 0.6 and 0.7. In reality it is the Experimental Attenuation Length, EAL [7], that should be used, which may be as much as 30% shorter than 𝜆. An EAL accounts for the additional effect of elastic scattering. However, it is only the ratio of the EAL’s at the two KE’s concerned that is important. We are assuming here that the EAL ratio is essentially the same as the ratio of 𝜆’s.



A.  Instrument

A Thermo-Scientific K-Alpha Plus XPS spectrometer was used [8]. It is fitted with a monochromatic Al source (hv 1486.ev). The hemispherical analyzer has a maximum resolution of 0.1ev. The X-Ray source contributes 0.16ev. The angle between X-ray input and analyzer is 60deg. The input lens to the analyzer subtends 60deg and is normal to the sample surface. Base pressure achievable after bakeout is ~1e-8 Pa. Normal operating pressure in the analyzer chamber when the X-Ray source is on and data is taken is ~7e-6 Pa and 7e-5 Pa when the flood gun is on. The dual electron/ion flood gun (LaB6/Ar+) used for charge neutralization has a beam size of ~3mm.

The analyzer BE energy scale is calibrated using sputter cleaned Cu, Ag, and Au samples (Cu2p3/2 at 932.62ev, Ag3d5/2 at 368.22ev, and Au4f7/2 at 83.96ev, all +/-0.08ev). It is checked monthly and corrected as needed, but is very stable unless the system is opened and baking is necessary. At 200ev band pass and 0.1ev step size the Ag 3d5/2 resolution is 1.8ev FWHM. For high energy resolution work a band pass of 50ev is usually used (though 20ev or 10ev can be used, there is usually no practical advantage and a great loss of signal intensity), yielding 0.7ev FWHM at 0.1ev step size.

The Ar+ sputter gun produces a standard monatomic Ar+ beam that can be operated between 200ev and 3kv and can be rastered over an area of 4 x 2mm.

The Thermo Scientific software, Avantage v 5.9912, applies a correction to the intensity of acquired spectra for the Transmission Function, T, “at source”, meaning it is done in real time while the spectra are acquired and so is transparent to the operator. The correction can be removed later if wanted [38].

B.  Sample

A single crystal LiF sample, 10x5x1mm, was obtained from SurfaceNet (lot # 869220119). It was cleaved roughly orthogonal to the nominal (100) crystal orientation in laboratory cleanroom air (20% relative humidity) and was mounted on double-sided adhesive tape mounted on an Al stub. The stub was then mounted on the 60x60mm copper-bronze stage and inserted into the load lock. All this took ~5minutes. It was pumped down to 7e-4 Pa, which took another 5 minutes, and then transferred to the analyzer chamber, but not to the analysis position.

C.  Data Collection parameters

The X-Ray source was turned on at a power of 72watts and a 400um spot size. The flood gun was turned on and set to an e-beam energy of 1ev, 300um current, and an Ar+ energy of 5ev. The sample was then moved to the analysis position and the F1s intensity monitored in unscanned SnapshotTM mode (20ev BE range) while the stage z axis was adjusted for maximum sensitivity. The XY position of the charge neutralization gun was adjusted to give the lowest BE for F1s compatible with no obvious peak asymmetry and a minimum FWHM. The total exposure to X-rays at this point was ~5minutes. A single survey scan at 200ev band pass energy was acquired at 1ev step size to observe initial contamination levels (~0.8% atomic nominal for both carbon and oxygen). A set of spectra (C1s, O1s, F1s, Li1s FAuger, F2s and O2s, and Valence Band) were taken using a mixture of 200ev, 100ev and 50ev band passes and step sizes. The Ar+ sputter gun was then turned on at 500ev and raster size 4x2mm for 5sec (nominal removal 5A, based on an SiO2 etch rate) and a second set of data taken. The total collection time was 18,000sec.

Eight (8) months later, after analysis of the original data taken, the sample was reinserted and a further set of data, all at 50ev bandpass and 0.1ev step size, were acquired to improve statistics and resolution, but only for a survey, the F1s region (now run out 130ev to higher BE after the F1s main peak, and the 0 to 160ev BE region, which encompasses the VB, F2s, and Li1s region, run out to 130ev beyond the main Li1s peak. These extended ranges are required to capture all observable substructure.

D.  BE Calibration of Spectra

Since the sample is a wide band gap insulator the charge neutralizer was on (see above), but this does not guarantee complete charge removal and in fact it is set up to minimize charge broadening. BE calibration was done using the observed adventitious carbon surface contamination with C1s set at 285.0ev (a ~1.5ev correction from the experimental value). No drifts were observed and the Li1s and F1s corrected values agree with literature values, though the absolute BE’s have no bearing on the quantitative analysis.



Fig 3 is a survey spectrum recorded at 200ev pass energy. It was taken during the first run in 2009. In addition to the expected LiF features, trace O1s and C1s are observable. There are no following background steps associated with these features (expanded spectra, not shown) unlike after the genuine LiF features (F1s, F2s, Li1s and the valence band, VB), indicating no inelastic scattering through LiF and that these features represent very minimal surface contamination.

The expanded F1s insert, Fig 3(b), shows clearly resolved F1s substructure. It extends at least 130ev to lower KE, up to the start of the F Auger signal, though most of the intensity is concentrated in the first ~65ev. The presence of such substructure is clearly evident also in early literature survey scans. Complex substructure spread over a wide range is also evident in the 0 to 120ev BE range, encompassing the VB, F2s and Li1s regions, though this can only be seen in the expanded spectrum (Fig 3c).



FIG. 3. A survey XPS spectrum, (a), of an LiF single crystal, taken at low resolution (200ev band pass), and expanded spectra, (b) and (c) from the same survey.


A.  The F1s region

Fig 4 is a high-resolution spectrum (50ev band pass) of the F1s region. 12 individual substructure features are assigned, sitting on the general inelastically scattered background, which starts sharply at ~11ev energy loss from F1s (main), in agreement with values of the band gap for LiF [39]. If there are no impurity states in the band gap, no inelastic scattering is possible below the band gap energy, which means the intensity in F1s (main) can be correctly determined by using an almost flat straight-line background, Fig 4.


FIG. 4. High resolution (50ev band pass) F1s region of the XPS of LiF. The band gap of ~11ev determines where the start of the scattered electron background begins. Peaks 1 to 12, with the exception of 3, are considered to be intrinsic satellites of L1s(main). Peak 3 is considered to be an extrinsic background feature, see text.


The background to the substructure peaks has also been approximated using straight-lines in the expanded spectrum, Fig 4(b). The suggested background under peaks 1 and 2 is based on a comparison with the Li1s background (see later, Fig 8). In terms of quantification the doublet peaks, 3 and 4, are the strongest and so most important. This region has been peak fit with 4 components, 2 for each peak (Fig 5a), which was found to be the minimum number necessary to give a good fit, in order to estimate the individual areas of the doublet peaks.


FIG. 5. a) peak fitting of peaks 3 and 4 of the F1s substructure. b) peak fitting of the Li1s XPS to remove the overlapping F2s substructure, based on a), see text. The start of the scattered electron background has an apparently delayed onset in b), owing to overlap from the peak preceding it


The difficult task is to establish which of features 1 to 12 are genuine intrinsic shake structure satellites associated with F1s (main) and which are features of the extrinsic scattered electron background.   Any peak structure representing extrinsic scattering must appear at exactly the same energy loss after every intrinsic photoemission peak, since they all simply involve ejected photoelectrons passing through the same LiF material, though intensities may vary as a function of KE. The band-gap step is an example of this, being found at an identical value, ~11ev, after all the main features, F1s, F2s, Li1s and VB (Figs 4 and 6). On this basis peak 3 in F1s is assigned as an extrinsic scattered feature in the background, because it also appears at the same loss position, ~25.5ev, after F2s, Li1s, and the VB (see Fig 6). On the other hand, any genuine shake satellite substructure would, at first sight, not be expected to be at the same loss positions from Li1s(main) as from F1s(main), though that from F2s(main) might be expected to be very similar to that from F1s(main). We will return to the task of separating intrinsic and extrinsic substructure features after consideration of the Li1s spectrum.

FIG. 6. a) 0 to 160 ev BE region of the XPS spectrum of LiF at high resolution (50ev bandpass). b) b) vertically expanded spectrum. The start of the scattered electron background at ~11ev and the position of the extrinsic scattered electron peak at ~25.5ev is marked after each main peak, VB, F2s, and Li1s.


B.  The 0ev to 160ev BE region (VB, F2s, and Li1s)

Fig 6 shows the 0 to 160ev BE range at high resolution (50ev band pass). We are primarily interested, for quantification, in extracting the intrinsic Li1s intensity. There is clearly structure overlapping Li1s(main). It is substructure associated with the F2s signal, as fully discussed below with reference to Fig7, but for Fig 6 we just want to note a) that the start of the scattered electron backgrounds can be identified by the sharp step increase in intensity at ~11ev after Li1s, F2s, and the valence band, VB, which is the same as the step after F1s in Fig 4, and b) there is a pronounced peak at 25.5ev loss energy from Li1s(main), at ~80ev, which is the same loss value found for peak 3 in Fig 4 for F1s and therefore also identified as an extrinsic plasma loss feature of the scattered background. If this is a correct assignment, then this 25.5ev loss feature should also be present after F2s(main) and after the VB. It can be seen that, indeed, such a feature is present in both cases. The 25.5ev loss from F2s overlaps the Li1s(main) leading edge, and the 25.5ev loss from VB overlaps F2s the (main) on the trailing edge.

In Fig 7 the central spectrum is a vertically expansion of Fig 6. The spectrum below it is the F1s spectrum of Fig 4, but shifted in BE so that F1s(main) aligns exactly with F2s(main). One would expect the substructure following F2s(main) to be very similar, if not identical, to F1s(main), so the alignment shows how the F2s substructure interferes with the Li1s spectrum. The possible interfering peak positions, 1 to 12, are marked by the vertical upward dotted arrows connecting the bottom spectrum to the middle.

FIG. 7. Comparison of the F1s spectrum with F2s (bottom) by aligning the two main peaks, and the F1s spectrum with Li1s (top) by aligning the F1s(main) with Li1s(main, showing the match up of features. The up dotted arrows indicate where substructure from F2s should lie. The down dotted arrows indicate where intrinsic substructure from Li1s may contribute. The estimated amounts of the possible intrinsic Li1s substructure are indicated by the vertically hatched areas. The extrinsic background scattering feature at 25.5ev loss from Li1s (main) is represented by the shaded area, as is the same feature following F2s(main) and VB. See text.


Owing to the almost exact overlap of peak 3 from F2s (the extrinsic background plasma-like scattered electron loss peak at 25.5ev loss) with Li1s (main), removing its intensity correctly is critical. For this we refer back to Fig 5, where a detailed comparison is shown. First in Fig 5b we draw a straight-line background along the top of the F2s inelastic scattering step, starting at 47ev and finishing at 67ev, in a like manner to that drawn in Fig 5a for F1s. The method used to position the overlapping peaks under Li1s(main) relies on knowledge, from Fig 5a, as to their expected positions. The (c) component of peak 4 is constrained to be at the same loss from F2s(main) as it is from F1s(main), 29.5ev. The separation of component (c) and (b) is constrained, at 4.2ev+/-0.2ev, to be the same as for F1s, resulting in (b) being centered exactly under Li1s(main). The positions of (a) and (d) are not constrained, but the widths are constrained to be ≤ than 3.2ev FWHM. Li1s(main) is centered at 56.5ev and is fit with an L/G ratio of 30/70, with the width allowed to float, resulting in a FWHM value of 1.7ev identical to the measured value for F1s (we have tried other L/G ratios, 10/90 and 20/80, but 30/70 gives the best fit).

An excellent visual fit, Fig 5b, is obtained, but it is obvious that component (a) of peak 3 from F2s carries much greater intensity than it does in the F1s spectrum, Fig 5a. We do not know the reason, but it is clear there is extra overlap intensity here that should be removed in any quantitative analysis using Li1s.

The spectrum at the top of Fig 5 is the F1s spectrum shifted so that F1s(main) aligns with Li1s(main). It shows that peaks 1,2, 4 and 7 in F1s have no match in Li1s, as expected, but in addition to the match at 25.5ev for peak 3, as expected for its assignment as an extrinsic scattering loss, the positions (but not intensities) for peaks 5, 6, 8, 9 and 10 do seem to be possible matches, as identified by the downward dotted arrows.  So, though at first sight possibly surprising, we cannot rule out that these weak features in the Li1s spectrum may include some genuine shake satellite peak intensities from Li1s(main), which have the same loss energies as satellite peaks in F1s and F2s, in addition to the identified overlap contributions from F2s substructure which need removing. In Figs 6 and 7 the backgrounds have been defined by straight lines, in a like manner to F1s (Fig 4).


C.  Quantification using F1s and Li1s Intensities.

The derived XPS determined compositions, from peak relative intensities are given in Table III, using different assumptions concerning which substructure features represent intrinsic shake satellites from F1s(main) and Li1s(main), and with and without removing the overlap F2s substructure peaks from the Li1s intensity. To convert intensities to %age composition equation (10) is used, which assumes that all necessary intensity has been included in IF(1s) and ILi(1s). The 𝜆 ratio is from TPP-2M values for LiF, and the σ values are those of Scofield for atomic Li and atomic F.

Table III. Derived composition (atom %s) from F 1s and Li 1s peak intensities using varying assumptions about substructure assignments:  Column A – main only, overlap not removed from Li 1s; Column B – same as A, but F 2s overlap removed from  Li 1s (main); Column C – same as B, but F 1s intrinsic satellite intensity  included; Column D – same as C but all possible Li 1s intrinsic satellite intensity included; Column E – same as D, but suspected impurity intensity (14-150 eV) of Li 1s removed; Column F – same as B, but intensities re-normalized according to theory of total intrinsic losses;



Six columns, A to F, are shown. Column A simply uses the areas under Li1s(main), drawing a straight-line background, Fig 5b, without any removal of the F2s overlapping substructure, and the measured area under F1s(main), also with a straight-line background, Fig 4. We include this column because it is most likely to mimic what was actually measured in the Wagner paper [4], where the energy resolution would not be high enough to have separated the overlapping substructure from F2s on Li1s, and a background was said to be constructed using a “baseline drawn tangent to the base at both sides of the peak”. As can be seen the result vastly overestimates the total Li1s intensity because of the non-removal of the overlap, and vastly underestimates the F1s intensity because of lack of inclusion of the obvious F1s satellite intensities.

Column B removes the overlaps to Li1s, but still does not include the F1s satellite intensity. It greatly improves the determined stoichiometry compared to column A, but is still significantly in error.

Column C adds the F1s satellites, but excludes peak 3 as an extrinsic loss peak (its area is estimated as 55% of peaks 3 plus 4, see Fig 5b). The Li/F ratio is now 49.93/50.07. This exact match to LiF stoichiometry is entirely fortuitous, because, though our measurement of the area of F1s(main) is quite precise, and the overlapping F2s structure for Li1s(main) has been removed as accurately as possible, the determined intensities of  the F1s intrinsic satellite structures are only estimates based on the straight line backgrounds and the separation of the intrinsic peak 4 from the extrinsic peak 3 (Fig 5a). In addition, theory tells us that there should be some intrinsic satellite intensity for Li1s (Table I), but none is included in column C.

In column D we now include all of the substructure intensity following Li1s(main) which cannot be accounted for by F2s overlap, or the extrinsic peak at 25.5ev loss (Fig 7), and so could possibly be intrinsic satellite intensity. The Li/F ratio now changes to 52.27/47.73. In column E we have done the same thing, except the Li1s small substructure doublet at~ 150ev, which we think is probably an unknown impurity (the nearest match we can find, which is not very good, is Gd3+), has been removed. The ratio then changes slightly to 51.60/48.40.

In arriving at the values in columns C, D and E we believe the straight-line backgrounds, as drawn, are the most reasonable that can be achieved, but there is one area where the reader would be justified in claiming arbitrariness without some further explanation. That is the background drawn under peaks 1 and 2 in the F1s spectrum (Fig 4). Fig 8 shows a comparison of the leading edge of the extrinsic background step at ~11ev loss, for both Li1s and F1s. The comparison clearly shows that peaks 1 and 2 are not present for Li1s, with the extrinsic background rising and curving over smoothly before the start of the extrinsic 25.5ev structure. We have tried to mimic this background in the F1s spectrum with the straight-line as drawn, resulting in the contribution of 1.05% from peaks 1 and 2, as shown in Column C. Obviously, it could be drawn somewhat differently, thereby either increasing or decreasing the total F1s intensity, but not significantly.


FIG. 8. Detailed comparison of the start of the extrinsic scattered electron background for Li1s and F1s, justifying how the background for F1s in this region was established, and the areas of peaks 1 and 2, were estimated.


The bottom line conclusion then, from processing the experimental data, is that using the Scofield calculated σ values, the determined stoichiometry is somewhere between Li1.00F1.00 and Li1.00F0.91,which supports Scofield’s claim of 5% accuracy for the Li1s and F1s σ values, and refutes the claim by Wagner, et al, that the calculated σ value for Li1s, relative to F1s, is low by a factor of 2.

In the final column, F, we explore the use of the calculated losses from Li1s(main) and F1s(main) from Table I. The theoretical predictions are that Li1s(main) retains 91.1% of the total Li1s intensity and F1s(main) retains 74.9%, see Table III. In column F we have normalized the experimental results of column B (main line intensities only) using these theoretical retention values, resulting in an Li/F ratio of 50.2/49.8. Again, the almost exact agreement to the known stoichiometry must be fortuitous, but the result implies the calculations are quite accurate, and that the LiF stoichiometry can be determined using main line intensities only, plus theory, to the same level of accuracy as doing it entirely experimentally by trying to include all intrinsic satellite intensities.


D.  Quantification using F2s and Li1s Intensities.

An alternative to using Li1s/F1s ratios to establish stoichiometry would be to use Li1s/F2s. This has the potential advantage that the 𝜆 and T values for Li1s and F2s in equations 5 and 6 are essentially identical, because the KE hardly changes, and so drop out. We are, however, unable to measure the total intensity of F2s as accurately as F1s because of the overlapping substructure from the VB region on F2s(main), and the overlapping of the F2s substructure with Li1s (Fig 7). Fig 9 shows an attempt to determine the intensity of just F2s(main) by removing the overlap structure from VB. If we take the determined intensity of F2s(main) and assume it represents a retained 74.9% of the total (Table I), as was calculated from theory for F1s, and the determined intensity of Li1s(main) and assume it represents 91.1% retained, the composition resulting is Li/F = 48/52. This should be compared to Column F in Table 3 where F1s was used and the value was 50.2/49.8. Though not identical, which it should not be because the intensity losses from F2s would not be expected to be identical to those from F1s, it is very close and assures us that there are not serious errors in the 𝜆 and T ratios used when comparing F1s to Li1s.



FIG. 9. Showing the method of removal of the VB substructure from the F2s(main) peak, see text




A.  Calculation of photoionization cross-sections, σ

We have used the atomic σ values of Scofield [5] because a) they are considered the most reliable; b) they are the most used and cited; c) they are embedded as options in the software used with several commercial XPS instruments; d) they are the values Wagner, et al, [4] criticized in their comparison of t-RSFs to e-RSFs. There are several other sets of calculations in the literature covering various atomic number ranges, using h𝜐 values that include 1487ev (Alkα) and 1256ev (Mg kα). Those of Lindau and Yeh[40], and of Nefedov, et al., [41] (up to z = 30), incorporate the same level of physics calculated the same way. Those of Trhaskovska [42] used a somewhat different approach likely to be less accurate. All of these papers provide absolute σ values, but for the present work all we need is the ratio of Li1s to F1s. These are shown in Table IV. We note that the ratio varies from ~5% lower than the Scofield value to ~ 3% higher. Nefedov [41] also calculated the value for ions in addition to neutral atoms for the first-row elements. Except for Li and Be, one would expect a completely insignificant difference, because for elements B to F the orbital concerned in forming an ion is the 2p valence level, which has zero electron density at the 1s radius. This is exactly what Nefedov found (identical values for atom and ion to the 3rd significant figure). For Li+ and Be+, however, where it is the valence 2s level that is involved, the 2s orbital has a very small, but non-zero, density at the 1s orbital, so a small difference in 1s σ values might be expected for the ion compared to the atom. Nefedov actually found a surprisingly large effect (5% difference) for Li+, Table 4, but no effect for Be+.  We have no explanation for this.



B.  Calculation of the escape depth correction

In equation 9 the correction made to the intensities of Ia to Ib to account for the different probing depths of the F1s and Li1s XPS lines is given by the inverse ratio of the 𝜆 values for the two KE’s concerned. 𝜆 values provided by the TPP-2M calculations [6] are considered very reliable, and we used their ratios, as implemented in the Thermo software [43], in deriving the determined LiF compositions in Table 3. Prior to such calculations being available it was common to use experimentally determined variations of 𝜆 as a function of KE through a solid, where it was observed that they were proportional to KEx over the KE range normally used in XPS for analysis (a few 100ev to 1486ev). x varied somewhere between 0.5 and 0.8 in such studies [44]. The 𝜆 correction term in equation 9 for the Li/F ratio then becomes

Wagner, et al, used a value of x=0.66 in their paper [4]. For LiF, using this relationship instead of the TPP-2M values, makes less than 1% difference, so 0.66 was a very appropriate choice. In a recent paper by two of the present authors [2] we used, generically, x=0.6 for a variety of materials. Compared to TPP-2M (or x = 0.66) for LiF, this weaker dependance on KE underestimates the difference in probing depth between F1s and Li1s, compared to using TPP-2M or x= 0.66, resulting in a 4% worsening (increase) of the determined Li/F ratios for LiF in Table 3.


C.  Use of e-RSF’s for XPS Quantitation

There are 3 contributing factors to the large error in the Wagner comparison of e-RSF to t-RSF for Li1s, normalized to F1s.

The first was an incorrect determination of the experimental intensity of Li1s(main), caused by not removing overlapping substructure from the nearby F2s peak. Simply doing this appropriately changes the ratio of Li/F from 1:0.64 to 1:0.82, using just the Li(main) and F1s(main) peaks and the Scofield σ values (Table III, comparison of column A to B).

The second factor was the failure to consider the significant shake satellites and so not including them in their attempt to derive a t-RSF to compare to their e-RSF. As we have shown, properly including the satellite intensities of F1s and Li1s, which spread more than 100ev to lower KE, changes the determined t-RSF based stoichiometry to somewhere between 1:0.94 and 1:1.00, depending on the assumptions made, using the Scofield σ values (Table III, columns C to F). We cannot narrow this range further because of the difficulty of establishing exact satellite intensities.

The third reason was the use of an apparently incorrect instrument transmission function, T, when converting the Scofield σ values into t-RSFs to compare to the e-RSFs of the instruments being used at that time.  We have not discussed this factor in this paper, but it has been explained in reference 1. It can be a very significant correction, because it applies not just to Li1s and F1s in LiF but to all the comparisons made by Wagner of their e-RSFs to Scofield σ based t-RSFs. The further apart in KE the XPS peaks being compared, the greater the error introduced by an incorrect T, as it is a function of KE.

Taken all together the three factors above combined to create an apparent discrepancy of a factor of ~2 (too low) in the Scofield calculated Li1s σ value when Wagner tried to match a t-RSF using Scofield with their e-RSF.

Of course, none of the above precludes using the e-RSF of Wagner, as long as it is used in an identical manner, which means main peaks only; straight-line background (but there is no information on the start and end BE’s for this); and an instrument of identical analyzer transmission characteristics. (We are not recommending the use of e-RSFs because the original work is missing essential spectra with BGs and other issues.) However, since LiF is a unique compound in having the F2s substructure lying under Li1s, and has sharper and more intense F1s satellites than in other compounds, a main line only e-RSF for Li1s, based on LiF as the standard from which it is acquired, is a poor choice. When trying to quantify any other Li containing compound it cannot be very accurate. If applied to other LiF samples using instrumentation with an identical T behavior, of course it should (and does) return the correct stoichiometry [45], but this does not help for other unknown composition Li compounds.



One of the goals of this work was to establish, as accurately as possible, the true value of σ for Li1s, because of the claim that the calculated value was too low by a factor of ~2. We have shown that the theoretically calculated value appears, in fact, valid to the accuracy claimed (5%) and therefore the stoichiometry of Li F, determined by XPS using the calculated σ values of Li1s and F1s, should be accurate within 10%, that is between Li1F0.9 and Li0.9F1, provided there are no errors in the Transmission Function, T, or the ratio of 𝜆 values used for correcting for the different depths probed by Li1s and F1s . The stoichiometry we actually return by the three alternative valid data analysis procedures (columns D to F in Table 3) range from Li1F0.99 and Li1F0.91. The invalid procedures of not removing peak overlaps on Li1s, and not including satellite intensities in (columns A and B, Table 4) return stoichiometries far from LiF, as expected.

A further goal of the present paper was to compare the experimentally determined total intensity losses from Li1s and F1s to shake satellites with the theoretical predictions from representative cluster model ab initio MO calculations. While the absolute values from theory are higher, which is not surprising since we have little chance of experimentally observing and distinguishing shake off structure (as opposed to shake up) from the background, if the theoretical calculated losses are used to normalize the Li1s(main) and F1s(main) experimental values for losses, the resultant Li/F ratio using just the main lines is very close to unity, validating the theory for total losses (column F, Table 4). It might be possible with the aid of similar theoretical studies on other systems to obtain general rules for satellite losses that would allow reliable quantification using main peak only intensities and σ.

A final cautionary conclusion for analysts is that, while in the case of LiF we can return an accuracy of within ~5% in composition using σ values, this is not going to be true in general, though it may be for compounds consisting of only elements Li through to F. For cases where there is not a clear separation between the main line and the scattered background, which is all situations where there is a band gap of less than a couple of ev, the accuracy of separating the intensity of the main line from the start of the scattered electron background will degrade. In addition, for any compounds where there is an open shell in the valence levels, ie all paramagnetic material with d and f valence electrons, multiplet splitting of core lines will occur with the multiplets both broadening the “main” line and possibly spreading up to 30ev to higher BE for some core levels [46]. These same materials also tend to have strong shake intensities superimposed over the same range. Both effects reduce potential accuracy, not least because it also becomes more difficult to consistently remove a background, or even know over what energy range it is appropriate to remove a background. When other core levels are nearby, such as the 2p1/2 spin-orbit partner to 2p3/2 levels, or the 3s near to 3p, in the 3d transition metal series, it is clear, however, that substructure from the lower BE level often overlaps the higher one and the only valid way to subtract a background for quantitation purposes is to include both levels. Whether a Shirley type background [47] or a Tougaard [48] type is the more appropriate remains to be seen, but in either case the analyst has to bias the removal by picking the end point of the background, which means a belief that the intrinsic structure has all been captured by then, and beyond that point (higher BE) there is only background [2]. We are attempting to address this issue of background removal using a series of Fe oxide standards of different stoichiometry, which removes concerns about σ, 𝜆, and T accuracies since the same peaks (Fe/O) are ratio-ed in the different compounds.

Owing to the above issues analysts who are interested in absolute accuracy of better than ~20% in stoichiometry, and are using software embedded RSF values, the analyst is recommended to should carefully check where these values come from, what they include, and how they were obtained and/or modified. They should also treat reported claims of great quantitative accuracy with caution. The following should be kept in mind:

  1. For most elements there is significant intrinsic intensity well away from the “main” peak. This can be true even for apparently simple situations like LiF.
  2. Because these loss peaks can spread several 10’s of ev, they may contribute to overlaps which complicate determining the intensity of even other “main” peaks.
  3. The full use of cross-section based t-RSF’s, which requires measuring the total intensity, is limited by the need to separate intrinsic loss peaks from background, but the calculations of the cross-section values themselves are quite reliable.
  4. Theory may, eventually, be able to provide guidance as to what fraction of the total intensity remains in the “main” peak, so that it can be more accurately used for quantification.
  5. “Packaged” e-RSF’s have often been obtained ignoring all or parts of intrinsic loss features. Because intensity lost from “main lines” into these features changes with chemical environment, this limits the accuracy (and usefulness) of such e-RSF’s. Analysts should determine their own e-RSF’s using standards of similar chemistry to their unknowns if they require greater accuracy. ISO Standard 18128 partially addresses this [49].


As Prof. Charles Fadley once said about XPS “any student of mine claiming an absolute accuracy of better than 10% – heck even 20%, had better be prepared to prove it.”



PSB acknowledges support from the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences (CSGB) Division through its Geosciences program at Pacific Northwest National Laboratory (PNNL). PNNL is a multi-program national laboratory operated for the DOE by Battelle Memorial Institute under contract no. DE-AC05-76RL01830. The samples and all spectra used in this work were supplied by The XPS Library.



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27T. Van Mourik, A. K. Wilson, K. A. Peterson, D. E. Woon, and T. H. Dunning, Jr., Adv. Quantum Chem. 31, 105 (1999).
28P. S. Bagus, Phys. Rev. 139, A619 (1965).
29P. S. Bagus, C. Sousa, and F. Illas, Theor. Chem. Accounts 138, 61 (2019).
30CLIPS is a program system to compute ab initio SCF and correlated wavefunctions for polyatomic systems. It has been developed based on the publicly available programs in the ALCHEMY package from the IBM San Jose Research Laboratory by P. S. Bagus, B. Liu, A. D. McLean, and M. Yoshimine.
31DIRAC, a relativistic ab initio electronic structure program, Release DIRAC08 (2008), written by L. Visscher, H. J. Aa. Jensen, and T. Saue, with new contributions from R. Bast, S. Dubillard, K. G. Dyall, U. Ekström, E. Eliav, T. Fleig, A. S. P. Gomes, T. U. Helgaker, J. Henriksson, M. Iliaš, Ch. R. Jacob, S. Knecht, P. Norman, J. Olsen, M. Pernpointner, K. Ruud, P. Sałek, and J. Sikkema (see the URL at, 2008).
32J. Q. Broughton and P. S. Bagus, Phys. Rev. B 30, 4761 (1984).
33T. Koopmans, Physica 1, 104 (1933).
34P. S. Bagus and F. Illas, Catal. Lett. 50, 2457 (2020).
35S. Svensson, B. Eriksson, N. Martensson, G. Wendin, and U. Gelius, J. Electron Spectrosc. 47, 327 (1988).
36H. J. Freund W. E. Plummer, W. R. Salaneck and R. W. Bigelow., J. Chem. Phys. 75, 4275 (1981).
37P. S. Bagus C.J. Nelin, C. R. Brundle, and S. A. Chambers, J. Physical Chemistry C 123, 7705 (2019). https://doi:10.1021/acs.jpcc.8b05576
38Turning Transmission Function correction ON and OFF in Avantage Software – transmission-function-2/ last access Sept 25, 2020
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42M. B. Trzhaskovskaya and V. G. Yarzhemsky, Atomic Data and Nuclear Data Tables, 119, 99 (2018)
43 TPP-2M used for Quantitation in Avantage software – last access Sept 25, 2020, Avantage Help file: Index search  – TPP-2M
44C. D. Wagner, L. E. Davis, and W. M. Riggs, Surf. Interface Anal. 2, 53 (1980).
45C. Ro and R. W. Linton Surf. Sci. Spec. 1, 277 (1992)
46P. S. Bagus, C. J. Nelin, C. R. Brundle, B. V. Crist, N. Lahari, and K. E. Rosso, to be published
47D. A. Shirley, Phys. Rev. B. 5, 4709, (1972); A. Procter and P. Sherwood, Anal. Chem. 54, 13 (1982).
48S. Tougaard, Surf. Interface Anal. 25, 137 (1997).
49ISO 18118: Surface chemical analysis – Auger electron spectroscopy and X-ray photoelectron spectroscopy – Guide to the use of experimentally determined relative sensitivity factors for the quantitative analysis of homogenous materials, (ISO, Geneva Switzerland 2002).