# Determination of the Primary Excitation Spectra in XPS and AES

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{2}, respectively, and the quantification of the two-hole final states contributing to the L

_{3}M

_{45}M

_{45}Auger electron emission of copper. These examples illustrate the procedure, that can be applied to any homogeneous isotropic material.

## 1. Introduction

## 2. Theoretical Model

- (a)
- A non-local dielectric description of the material response [9]. This allows for a straightforward analytical evaluation of the energy loss probability of swift emitted electrons in presence of a positive stationary charge;
- (b)
- Elastic scattering is neglected. This is justified by the fact that it is of minor importance for the description of energy losses lower than ~30 eV [13], which are mostly considered here.

_{sc}is the electron inelastic mean free path defined as the inverse of the area of ${K}_{eff,av}^{XPS}\left(\u0127\omega \right)$. If ${K}_{eff,av}^{XPS}\left(\u0127\omega \right)$ is known, F(E) can be evaluated by Equation (1), which is also one of the cases implemented in the QUASES Quantitative Analysis of Surfaces by Electron Spectroscopy software package [15].

_{0}and emission angle θ, while the core hole is stationary (infinite lifetime). The effective inelastic electron scattering cross section ${K}_{eff}^{XPS}\left(x;\mathit{\u0127}\omega \right)$ defined as the probability that the electron, excited at depth x, loses an energy ħω per unit energy loss and per unit path length traveled inside the solid can be evaluated from the induced potential ${\Phi}_{ind}\left(x;\mathit{k},\omega \right)$ created by the static hole and the moving electron according to the expression [9]:

**k**is the transferred momentum,

**r**the electron position, ρ

_{e}(

**r**,t) the charge density of the electron, t the time (at t = 0 the electron-hole pair is created), and Re{} refers to the real part of the quantity in brackets. ${\Phi}_{ind}\left(x;\mathit{k},\omega \right)$ is obtained within the surface reflection model [9]. The detailed final analytical expression for ${K}_{eff}^{XPS}\left(x;\mathit{\u0127}\omega \right)$ is rather involved (c.f. ref. [9]). At this stage, it is worth emphasizing that the material response is included in Equation (2) through its complex dielectric function required to evaluate ${\Phi}_{ind}\left(x;\mathit{k},\omega \right)$. Thus, the electron energy losses caused by the sudden electron-hole pair creation and subsequent photoelectron transport out of the material gives rise to both collective excitations (i.e., plasmons) and interband electron transitions.

_{i}, ħω

_{0i}, ħγ

_{i}and α

_{i}denote the strength, position, width and dispersion parameters of the i’th ELF oscillator. The step function θ(ħω − E

_{g}) (θ = 1 for $\hslash \omega >{E}_{g}$; θ = 0 for $\hslash \omega <{E}_{g}$) is included to describe the band gap energy E

_{g}in semiconductors and insulators. The parameters describing the energy loss function may be taken from the literature [16,17], or they can conveniently be determined from analysis of reflection electron energy loss spectroscopy (REELS) measurements [18].

_{0}and the angle of emission θ of the photoelectron, and the parametrized energy-loss function, which characterizes the dielectric response of the material.

_{i}(E) peaks that account for the local quantum effects not included in the dielectric description of the material, such as spin-orbit, multiplet splitting and shake-ups.

## 3. Case Studies

_{2}[25], respectively. The last example reports the quantification of the two-hole multiplet final states contributing to the L

_{3}M

_{45}M

_{45}Auger emission from metallic copper [26]. In these case examples, the analysis of electron emitted spectra has been performed according to either Equation (1) or Equation (5) depending on the convenience to illustrate particular effects of the material under study.

#### 3.1. Angular Dependence of Al 2s Photoelectron Emission from Aluminum

#### 3.2. Ag 3d Photoelectron Emission from Silver

_{5/2}and Ag 3d

_{3/2}peaks, shake up contributions shifted by 13.2 eV and 18.0 eV from the main 3d peaks that account for approximately 1–3% of their intensity. This result agrees with quantum mechanical calculations that assigned similar contributions to 4d → 5p and 4d → 5s final state shake-ups [29]. Note that the quantification of these features would hardly be possible with straight line or Shirley background analysis typically applied to isolate photoelectron peaks.

#### 3.3. Ce 3d Photoelectron Emission from CeO_{2}

_{2}has also been rather controversial in the past due to the complex photoemission spectra of this material [30,31,32,33]. Figure 4 shows raw experimental XPS data of this emission together with the primary excited spectra obtained after subtraction of the inelastic background determined within either the Shirley method [11], or the present model using the effective inelastic-scattering cross section for XPS, ${K}_{eff,av}^{XPS}\left(\u0127\omega \right)$, considering both extrinsic and intrinsic material-specific excitations. Note that the choice of the procedure for inelastic background subtraction clearly influences the relative intensity of the different features within the primary spectrum. We emphasize that even though the Shirley modeling of background correction often gives reasonably “good looking” results when used to isolate peaks, it is questionable to apply it for complex photoemitted peak line shapes, such as Ce 3d from CeO

_{2}[34].

^{4+}oxidation state in CeO

_{2}is often subdivided into 6 peaks labelled v, v″, v‴, u, u″ and u‴ [30], v and u referring to the 3d

_{5/2}and 3d

_{3/2}spin–orbit components, respectively. The doublet v/u corresponds to the final state Ce3d

^{9}4f

^{2}O2p

^{4}, while v″/u″ are assigned to Ce3d

^{9}4f

^{1}-O2p

^{5}and v‴/u‴ to Ce3d

^{9}4f

^{0}-O2p

^{6}, respectively [32]. The interpretation of the v/u components has been rather controversial in the past. Thus, for example Skála et al. [33] proposed either the use of asymmetric tails for v and u, or the modeling of v and u by two symmetric peaks. They found better consistency for the second interpretation that, in fact, is supported by Dirac–Fock and configuration-interaction wave-functions calculations [35]. This last interpretation is consistent with the analysis reported in Figure 4.

#### 3.4. Cu 2p Photoelectron Emission from CuO

^{10}L (c denotes a core hole and L a hole in the ligand) final state in which an electron is transferred from the ligand into the Cu 3d level. On the other hand, the shake up is attributed to a c3d

^{9}final state in which no charge transfer occurs [36].

#### 3.5. L_{3}M_{45}M_{45} Auger Emission from Copper

_{3}M

_{45}M

_{45}Auger emission from copper excited with Mg Kα X-rays. It mainly arises from the L

_{3}(2p

_{3/2}) core-hole decay via the Auger process involving two M

_{45}(3d) electrons resulting in a final 3d

^{8}configuration. We then may expect to observe, due to L-S coupling, a multiplet emission with five terms namely

^{3}F,

^{1}D,

^{3}P,

^{1}G and

^{1}S. This contribution is referred to as the “normal” Auger contribution to the measured L

_{3}M

_{45}M

_{45}transition. It comes out that the observed spectrum has extra features compared with the theoretically evaluated “normal” Auger emission [38]. In fact, there is some contribution in the low kinetic energy part of the L

_{3}M

_{45}M

_{45}spectrum [38,39,40,41] due to a L

_{2}L

_{3}M

_{45}Coster–Kronig transition. Indeed, after a L

_{2}L

_{3}M

_{45}Coster–Kronig transition, a L

_{3}M

_{45}M

_{45}process takes place with a third hole in the M

_{45}level of the final state. This extra L

_{3}M

_{45}M

_{45}process is thus shifted to lower kinetic energy because of the Coulomb interaction between this M

_{45}spectator vacancy and the Auger electron. The multiplet structure associated with such an Auger vacancy satellite transition corresponds to a 3d

^{7}configuration. We will refer to this contribution as the “extra” Auger contribution to the measured L

_{3}M

_{45}M

_{45}transition.

## 4. Summary and Concluding Remarks

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic representation of the process to obtain average effective inelastic scattering cross sections within the dielectric model outline above. (

**Left**): ${K}_{eff}^{XPS}\left(x;\u0127\omega \right)$ for 1000 eV photoelectrons excited at several depths x in Silicon. (

**Right**): The corresponding ${K}_{eff,av}^{XPS}\left(\u0127\omega \right)$ evaluated according to Equation (4) as illustrated in the upper right part.

**Figure 2.**(

**a**) Theoretical and (

**b**) experimental (adapted from Biswas et al. [27]) evaluation of Al 2s photoelectron emission from aluminum for several emission angles. (

**c**) Corresponding ${K}_{eff,av}^{XPS}\left(\u0127\omega \right)$ cross sections together with their decomposition into extrinsic (dashed lines) and intrinsic (dashed-dotted lines) contributions.

**Figure 3.**Blow up of the shake-up structure corresponding to the Ag 3d photoelectron emission of silver. The figure includes experimental data (red dashed line), model calculation (blue dashed-dotted line) and the corresponding initially excited F(E) spectrum considered in the calculation (full black line). The spectra are normalized so the Ag 3d

_{5/2}peak has unit area.

**Figure 4.**(

**a**) Experimental J(E) spectra (thick solid line), and corresponding primary excitation spectra F(E) evaluated by means of Shirley background correction or using Equation (1). (

**b**) Decomposition of F(E) in its Ce 3d

_{5/2}(v, v″ and v‴) and Ce 3d

_{3/2}(u, u″, and u‴) components.

**Figure 5.**(

**a**) Experimental and simulated J(E) spectra of the Cu 2p emission from CuO. (

**b**) Primary excited spectrum F(E) used to evaluate J(E) compared with the corresponding charge transfer multiplet calculation with CTM4XAS software [8].

**Figure 6.**Experimental and simulated J(E) spectra of the L

_{3}M

_{45}M

_{45}Auger emission from copper. In addition, the corresponding primary excited spectrum F(E) is included together with their most intense final state terms (full lines: 3d

^{8}normal Auger emission; dashed lines: 3d

^{7}extra Auger vacancy satellite structure). Bottom: relative energy and intensity of the 3d

^{8}individual terms contributing to the Auger emission.

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**MDPI and ACS Style**

Pauly, N.; Yubero, F.; Tougaard, S.
Determination of the Primary Excitation Spectra in XPS and AES. *Nanomaterials* **2023**, *13*, 339.
https://doi.org/10.3390/nano13020339

**AMA Style**

Pauly N, Yubero F, Tougaard S.
Determination of the Primary Excitation Spectra in XPS and AES. *Nanomaterials*. 2023; 13(2):339.
https://doi.org/10.3390/nano13020339

**Chicago/Turabian Style**

Pauly, Nicolas, Francisco Yubero, and Sven Tougaard.
2023. "Determination of the Primary Excitation Spectra in XPS and AES" *Nanomaterials* 13, no. 2: 339.
https://doi.org/10.3390/nano13020339