ELECTRON SPECTROSCOPY OF SURFACES

Characterization of Solid Surfaces and Thin Films byPhotoelectron and Auger Electron Spectroscopy

F-Praktikum in den Masterstudiengangen PhysikVersuch Nr. 35

Lehrstuhl E20, Raum 229

Betreuer: Francesco Allegretti

1 Introduction

Electrons are well suited probes for the investigation of the electronic and geometric prop-erties of clean and adsorbate-covered surfaces. Consequently, the use of electrons is thebasis of a plethora of experimental techniques commonly employed in surface science.This experiment focuses on two techniques, Photoelectron Spectroscopy (PES) andthe photon induced Auger Electron Spectroscopy (AES), which both entail the detec-tion of ejected electrons and are well-suited for investigation of the electronic propertiesof atoms, molecules and solids and for elemental and chemical analysis of surfaces.

One of the main reasons for the widespread use of electrons as probes in surface scienceis their short inelastic mean free path (λe) in solids (Fig. 1). This quantity describes theaverage distance that an electron can travel through the material without suffering energylosses by inelastic scattering; it therefore provides an indication of the electron escapedepth. For electrons with kinetic energy in the range between 10 and 1000 eV, λe canvary between 5 and 30 A depending on the material and thus amounts to only a few atomiclayers. This ensures that in a typical experiment based on electron emission only electronsemitted from a narrow region at the solid-vacuum interface can reach the detector withoutenergy loss. As a result, the PES and AES methods are highly surface sensitive.

During the experiment, the students will become familiar with the fundamental princi-ples, the basic operation and methodology of PES and AES and will get an insight into theunderlying physics. The potential of the techniques and the range of information that canbe gained will be illustrated by considering a prototypical application, the condensationof a magnesium film onto a tungsten surface and its subsequent oxidation. It will also beshown that these nondestructive techniques are of relevance for a vast range of systemsnot only in condensed matter physics, chemistry, and materials science, but also in appliedphysics and even biophysics. The technical basis of the experiment encompasses:

• basics of ultra-high vacuum (UHV) technology

• generation of X-ray radiation

• analysis in energy and detection of electrons

• sample preparation: deposition of a Mg film by evaporation in UHV and subsequentoxidation by molecular oxygen

Figure 1: Inelastic mean free path of electrons as a function of kinetic energy for various elements.

• computer control of the measurements; acquisition of a comprehensive data set

Gaining insight into the analysis and interpretation of the data and drafting a short scien-tific report (in German or English) are further achievements of this FOPRA experiment.

2 Photoelectron Spectroscopy

2.1 Basic principles

PES is based on the photoelectric effect, which was first observed experimentally by Hertzand Hallwachs in 1887-1888 and explained theoretically by Einstein in 1905 [1]. Althoughthe effect has been well known for a long time, it took more than six decades of experi-mental developments before Siegbahn and coworkers succeeded in establishing PES as astandard analytical tool in atomic, molecular, and solid state physics. The basic process isillustrated in Fig. 2a: an incident photon of energy ~ω is absorbed by an electron system(e.g., by a solid surface), promoting an electron from an occupied electronic level intoan unoccupied state. If this unoccupied state lies above the vacuum level, the electroncan escape into the vacuum and be detected by an energy sensitive analyzer. The energybalance is the following:

~ω + Ei(sys) = Ekin + Ef (sys) (1)

where Ei(sys) and Ef (sys) are the total energies of the system (atom, molecule, cluster,or solid) before and after photon absorption, respectively, and Ekin is the kinetic energy ofthe emitted photoelectron. In a simplified one electron picture (i.e., neglecting the energyof mutual electron-electron interactions) the difference Ef (sys) − Ei(sys) can be simplyregarded as the binding energy of the ejected electron:

Eb = Ef (sys)− Ei(sys) = ~ω − Ekin (2)

For a solid surface (Fig. 2b), binding energies are conventionally measured with respect tothe Fermi level rather than to the vacuum level, and the previous relationship is writtenin the form:

Eb = ~ω − Ekin − Φw (3)

where Φw represents the work function of the material.

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ω

vacuum level

in vacuum final state

initial state

Fermi level

(a) (b)

photon

photoelectron

sample

z

y

x

Ekin

Eb

Φw

ωhe-

φp

φe

θe

θp

ωh

Figure 2: Schematic view of the photoemission process: (a) a photon of energy ~ω impinges on asolid surface, and after absorption of the photon an electron is ejected in a given direction (θe, φe)with respect to the reference system; (b) corresponding energy balance within the framework ofthe single particle (or one electron) picture. The work function is the minimum energy requiredto remove an electron from the solid; it can be seen as the energy barrier that electrons have toovercome in order to escape from the surface into the vacuum.

For a given photon energy, recording the number of photoelectrons as a function of theirkinetic energy yields a spectrum of distinct lines, which reflects - in the first approximation- the energy distribution of occupied orbitals of the electron system under investigation.Since the binding energies of the occupied orbitals and their sequence are different for(and therefore characteristic of) each chemical element, photoemission spectra can serveas “fingerprints” of the respective elements (Fig. 3). This renders PES a very usefulanalytical tool, making it possible - for instance - to determine the composition of anunknown sample and to assess the degree of cleanliness of solid surfaces.

Depending on the photon energy we discriminate core level PES (electrons excitedfrom inner shells → Eb ≥∼ 40 eV) and valence electron PES (electrons excited fromouter shells → 0 ≤ Eb ≤∼ 40 eV). The latter is named UPS (Ultraviolet PhotoelectronSpectroscopy) because UV photons from gas discharge sources or UV synchrotron beam-lines are commonly used. PES with soft X-rays (~ω below 2-3 keV), which can excitecore level electrons, is labeled XPS (X-ray Photoelectron Spectroscopy). Typical lightsources are X-ray tubes with or without an additional monochromator, and soft X-raysynchrotron beamlines. In the present experiment, XPS measurements will be performed

Figure 3: Photoemission spectra of the 1s core levels of the second row elements (taken fromRef. [2]).

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using the characteristic X-ray radiation from an aluminium anode (the Al Kα line at ~ω= 1486.6 eV).

2.2 Spectral features and quantitative aspects of core level PES

2.2.1 Binding energy and the chemical shift

When comparing the binding energies of core electrons of a distinct atom in differentsystems (i.e., in different molecules, compounds or solids), one finds that the exact value ofthe binding energy depends on the chemical environment of the atom and that energy shiftsmay occur when inequivalent atoms of the same elemental species are present (Fig. 4).These energy shifts are termed chemical shifts. By comparison with data from well-known “standard” substances the values of these shifts can be used in many cases forthe determination of oxidation states and of the nature of the chemical bond formed bythe atoms. This application of XPS, which is denoted by the alternative name ESCA(Electron Spectroscopy for Chemical Analysis), is an important application of core levelPES in chemistry, surface physics and materials research.

(a)

(b)

Figure 4: (a) Chemical shifts in isolated molecules (C 1s and N 1s levels); (b) 4f7/2 core level shiftfor a W(111) surface. In (b) the surface component at lower binding energy is clearly discerned,whereas the component arising from the first sub-surface layer can only be detected by means ofa more sophisticated analysis. This special type of chemical shift originates from the differentcoordination (→ different chemical environment) of surface atoms relative to bulk atoms: it isusually referred to as surface core level shift. Panels (a) and (b) are both taken from Ref. [2].

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2.2.2 Initial and final state effects in photoemission

In the analysis of the energy shifts in core level photoemission one can separate differentenergetic contributions arising from distinct effects and different physical processes. Theseeffects can be classified depending on the fact that they act, respectively, on the initial stateof the system under study or on the final state reached after the photoelectron ejection [3].

Initial state effects

• Ground state effects:Ground state effects are those contributions to the observed energy shifts that aredue to variations of the distribution of valence electrons depending on the chemicalenvironment, i.e. that are due to the electronic part of the potential. Experimentallyobserved chemical shifts are only partly due to ground state effects. So-called finalstate effects (see below) can also contribute to chemical shifts, and although theircontribution is often assumed not to be dominant, it cannot be neglected a priori.

• Reference level effects:Shifts of the reference level for the kinetic energy scale may also contribute to exper-imentally obtained initial state shifts. In order to be able to compare Eb values, allphotoemission spectra have to be calibrated against identical reference levels. Thiscan be difficult for atoms in different environments. For gas phase measurements Ebvalues are commonly referenced to the vacuum level, while - as noted before - forsolid state investigations the Fermi level is the commonly adopted zero point of thebinding energy scale. Therefore, if gas phase and solid state data are compared onehas to know the energy separation between the vacuum and the Fermi level ( = thework function Φw, see Fig. 2b).

Final state effects

• Relaxation shift :A very important final state effect is the relaxation of the electron system in responseto the creation of a core hole (= the vacancy in the inner shell) upon photoemission.The core hole represents a positive charge acting on the remaining electrons, whichtherefore rearrange themselves to shield the electron vacancy and to minimize thetotal energy of the ionized atom. The screening of the core hole typically comprisesan intra-atomic and an extra-atomic contribution. The intra-atomic part is due tothe relaxation of the electrons (essentially, the outer shell electrons) of the excitedatom itself. For isolated atoms this is the only contribution. For atoms bound inmolecules or solids the electrons of the neighboring atoms are also polarized by thecreation of the core hole, although to a lesser extent, thus giving rise to the extra-atomic component of the relaxation. Due to the energy conservation the relaxationof the electron system reduces the apparent binding energy Eb measured for thephotoelectron. The energy balance before and after photoemission is, in fact:

~ω + Ei(N) = Ekin + Ef (N − 1) =⇒ Eb = Ef (N − 1)− Ei(N)

where Ei(N) is the energy of the ground state of the atom with N electrons andEf (N − 1) the energy of the final state of the ionized atom. If relaxation takesplace, the minimization of Ef (N − 1) leads to a decrease of the expected binding

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energy. Because the screening of the core hole depends on the electronic environ-ment1, relaxations shifts differ from system to system for a specific core level line.This difference, in combination with the initial state effects (see above), contributesto the chemical shift.

• Multiplet splitting :Removal of a core electron may create different final state configurations with differ-ent spin and orbital angular momentum, and therefore different binding energies inPES (= different lines in the spectrum). In particular, multiplet splitting occurs ifthe initial state of the photoionized atom contains unpaired electrons. For instance,in the N 1s photoionization of an isolated NO molecule two lines are obtained, whichcorrespond to parallel or anti-parallel orientation of the spin of the residual 1s elec-tron with respect to the unpaired electron in the molecular 2π orbital (triplet andsinglet final states, respectively).Another example is given by some transition metal ions, such as Mn2+ [3]. Mn2+

has a high spin configuration, S = 5/2, in which all five 3d electrons in the outershell are unpaired and with parallel spins. If a photoelectron is ejected from the 3slevel, the exchange interaction between the spin of the remaining 3s electron andthe total 3d spin produces different binding energies for the two possible final statesS ± 1

2 = 3, 2. As a consequence, the 3s photemission line is split into a doublet,where the 7 : 5 intensity ratio of the two components stems from the ratio of therespective mS degeneracies.

• Spin-orbit coupling in the final state:In the photoemission from p, d and f inner subshells the spectral lines are split intotwo-component peaks (Fig. 5a). This splitting arises from spin-orbit coupling effectsin the final state [4, 5]. While in the initial state the inner subshells are completelyfilled (for example, the configuration of the inner shells in gold is: (1s)2 (2s)2 (2p)6

... (4f)14 ... ), in the final state one electron has been removed and an unpaired spinis left behind. The spin can be oriented up or down, and if the core hole belongsto an orbital with non-zero orbital angular momentum (l > 0) there will be a cou-pling between the unpaired spin and the orbital angular momentum: the two statesj+ = l + 1/2 and j− = l − 1/2 are not degenerate and a spin-orbit split doublet isobserved in the photoelectron spectrum.The intensity ratio of the two spin-orbit components is dictated by the ratio of the

respective multiplicities: (2j+ + 1)/(2j− + 1) = (2l + 2)/2l (Fig. 5b), which deter-mines the relative probability of transition to the two states upon photoionization.Generally, in the photoemission spectrum from a given subshell the core level sub-peak with maximum j is detected at lower binding energy. Obviously, no spin-orbitsplitting occurs in the photoemission from s core levels.

• Multi-electron excitations and satellites:The reorganization of the electrons upon creation of the core hole can lead to elec-tronically excited final states. Because of energy conservation this excitation energyis missing in the kinetic energy of the photoelectron: the corresponding satellite lines

1For example, the screening ensured by electron rearrangement is typically more effective in metals thanin ionic solids, thanks to the availability of valence electrons (called conduction electrons) that are free tomove inside the material. Accordingly, the magnitude of the binding energy reduction due to relaxation ismore pronounced in metals than in ionic materials.

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(a) (b)

Subshell

Total angular

momentum j

components

Ratio of the

degeneracies

(g = 2j +1)

s

p

d

f

1/2 -

4/2

6/4

8/6

3/2, 1/2

5/2, 3/2

7/2, 5/2

Au 4f5/2

Au 4f7/2

Binding Energy (eV)

Co

un

ts

Figure 5: (a) Spin-orbit coupling leads to a splitting of the 4f photoemission line of gold into adoublet [2]. (b) Table listing spin-orbit split components and intensity ratios for different subshells.The notation n[l-subshell]j is commonly used (e.g., 4f7/2).

are therefore shifted to higher binding energy relative to the main core level line2.Different processes can be identified. Shake-up satellites occur when an additionalelectron is promoted from an occupied energy level into a bound unoccupied state,whereas shake-off satellites when the additionally excited electron is promoted intoa state in the continuum above the vacuum level (Fig. 6). Other possible satellitesare related to plasmon excitations. Plasmons are quasi-particles arising from thequantization of plasma oscillation, i.e. of the collective oscillation of the free elec-tron gas density with respect to the positively charged ion cores. Plasmon satellitesappear displaced to higher binding energy from the “elastic” line by amounts n(~ωp)+ m(~ωs), where n and m are integers and ~ωp and ~ωs are the energy of a bulk anda surface plasmon, respectively. Finally, interband satellites in solids correspond totransitions of additional electrons into unoccupied states above the Fermi level andto the creation of electron-hole pairs. They may show up as discrete lines in somecases, but commonly they give rise to an asymmetric broadening of the high bindingenergy side of the photoemission peaks.

970 950 940 930960

CuO

Cu 2p1/2

Cu 2p3/2

shake-up structure

binding energy (eV)

shake-offshake-up(a) (b)

Figure 6: (a) Schematic of the shake-up and shake-off transitions; (b) Shake-up loss structure inthe Cu 2p spectrum of copper (II) oxide (CuO), adapted from Ref. [6].

2Additional satellites in PE spectra occur when the photon source is not monochromatic (see §5.2).

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2.2.3 Surface sensitivity and collection geometry

As noted in section 1, the surface sensitivity of photoelectron spectroscopy stems from theshort inelastic mean free path of electrons. While X-rays interact only weakly with matterand consequently can penetrate deeply into a solid (1000 nm or more at ~ω ∼ 1 keV),electrons with energy in the range 5-1500 eV readily lose energy by inelastic scattering.XPS experiments are mainly concerned with the intensity of emitted photoelectrons thathave suffered no energy losses: therefore, the XPS sampling depth refers to a characteris-tic length over which electrons can travel without undergoing inelastic scattering events.This quantity is the inelastic mean free path λe plotted in Fig. 1, which is defined asthe average distance that an electron of given kinetic energy Ekin travels between twosuccessive inelastic collisions [4]. In other terms, the probability for an electron to cover adistance z in the solid without losing energy can be written as an exponential decay:

P (z) ∝ e− z

λe =⇒ < z >=

∫zP (z)dz = λe

If an electron experiences energy losses, but still has enough energy to escape from thesurface into the vacuum, it will not contribute to the main photoemission line but ratherto a background signal on its low kinetic energy side. For the correct determination ofpeak areas, peak positions and peak widths this background is always substracted3.

If one considers for simplicity the electrons emitted in the direction perpendicular toa solid surface, the previous considerations imply that a small element of thickness dz ata distance z from the surface (z = 0 denotes the surface plane) gives a contribution dI tothe measured intensity:

dI ∝ e− z

λe dz (4)

For the total intensity I coming from a thin film of thickness t right underneath the surfacethis yields (i.e., by integrating Eq. (4) between 0 and t):

I = I0 [1− e−t/λe ] (5)

The sampling depth of the XPS experiment is often defined as 3λe, which means that 95%of the photoemission intensity of the core level line comes from the corresponding region(3λe thick) below the surface [4].

When detecting photoelectrons emitted at an angle θe away from the surface normal(see Fig. 2a), one has to consider the effective path z/cosθe of the electrons in the solid,and Eq. (4) becomes:

dI ∝ exp[− z

λe · cosθe] · dz (6)

Hence, in grazing emission geometry the sampling depth of XPS is reduced to 3λe · cosθeand the surface sensitivity is strongly enhanced (e.g., θe ∼ 80◦ =⇒ cosθe ∼ 0.17).

2.2.4 Quantitation

From the previous discussion it is clear that an extended X-ray photoelectron spectrumcontains peaks that appear superimposed on a smooth background and can be associatedwith the different elements (except H and He) present in the outer ∼50 A or less of thesample. Determination of the peak areas (appropriately corrected to take into account

3Particularly at low kinetic energies (< 100 eV) the inelastic electron background is large due to theincreasing number of secondary electrons emitted in “cascade” processes.

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instrumental factors) allows, in principle, an estimate of the elemental ratios, such thatthe composition of the sample can be determined semi-quantitatively. To this purpose,the absolute intensity I of the photoemission line i from an element A is usually expressedas [4]4:

Ii,A = K · J0 · σi,A(~ω) · T (EA) ·Li,A(γ) ·∫∫∫

nA(z) exp[− z

λe(EA) · cosθe] dx dy dz (7)

Here, K is an instrumental constant; J0 is the incident photon flux, which is assumed forsimplicity to be independent of the (x, y, z) position inside the sample; σi,A(~ω) representsthe photoionization cross-section of peak i from the element A, related to the probabilityof creating a photoelectron in the orbital i of A at the photon energy ~ω; T is the trans-mission function of the electron analyzer; Li,A(γ) describes the angular dependence of thephotoemission process (γ = angle between the incident X-ray beam and the direction ofthe ejected electrons); nA(z) is the density of atoms A at a distance z below the surface(neglecting lateral variations, i.e. parallel to the surface plane), and λe(EA) is the inelasticmean free path of electrons of energy EA in the material.

In most cases, calibration of absolute intensities based on Eq. (7) is not possible, sinceinstrumental factors may be difficult to determine. However, measurements of relativeintensities are valuable in practical experiments where elemental ratios are important,such as - for instance - for the detection of relative surface coverages of adsorbates andcontaminants or for the determination of the stoichiometry of a compound.

2.2.5 Peak width of core level lines

The observed line shape of a given photoemission peak results from the convolution ofdifferent contributions. These are related: i) to the equipment used in the experiment(instrumental resolution); and ii) to the photoemission process itself (lifetime of the corehole, presence of satellite features). To i) contribute primarily the linewidth and lineshapeof the photon source used for the excitation, and the energy resolution of the electronenergy analyzer employed to analyze in energy the distribution of photoelectrons. Anessential contribution to ii) is the peak broadening due to the finite lifetime of the corehole; broadening by coupling to the nuclear motion (intra-molecular vibrations includingrapidly dissociating antibonding states, and phonons) and due to the presence of shake-upsatellites, electron-hole pair excitation and multiple splitting effects may be in many casesnon-negligible.

The spectral lineshape due to the core hole lifetime τ is Lorentzian [7]:

I(E) = I(Ec)Γ2

(E − Ec)2 + Γ2(8)

where I(E) is the intensity at the energy E, and Ec is the center of the Lorentzian peak(when the spectrum is plotted in the binding energy scale, Ec is the binding energy Ebof the “main line” satisfying the energy conservation law with the relaxation shift takeninto account). The energy broadening is therefore quantified by the the full-width at half-maximum (FWHM) of the line, 2Γ, which is called intrinsic or natural linewidth and isrelated to the lifetime through the following expression [8]:

2Γ =~τ

=6.58× 10−16 eV · sec

τ [sec](9)

4Photoelectron diffraction effects arising from coherent scattering of the photoelectron wavefield byneighbouring atoms are neglected in formula (7). This is correct, for example, in amorphous or polycrys-talline samples and for angle-integrated mesurements.

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2Γ is typically larger for inner shell orbitals, because these can be filled rapidly by electronsfrom the outer shells. Therefore, for a given element 2Γ tends to increase with increasingbinding energy (for example: the natural broadening increases in the order 4f < 4d <4p < 4s in gold). In a similar way, for a given core level orbital (e.g. 1s) 2Γ increasesas the atomic number Z increases, due to the higher valence electron density in heavieratoms.

At variance with the Lorentzian broadening produced by the core hole lifetime, instru-mental effects and vibrational broadening yield Gaussian lineshapes. In metals electron-hole excitations at the Fermi edge can cause additional asymmetric line broadening, withan asymmetric tail on the low kinetic energy side of the photoemission peak. Multiplesplitting and shake-up satellites also contribute with asymmetric broadening: dependingon their binding energy and the instrumental resolution they may or may not be resolvablefrom the main photoemission peak.

The contributions of intrinsic and instrumental effects to the experimentally observedlinewidth can be combined to a first approximation into a quadratic sum [4]:

FWHM2tot = (2Γ)2 + FWHM2

X + FWHM2A (10)

with the second and third term on the right side due to the X-ray source and analyzerresolution, respectively.

3 Auger Electron Spectroscopy

3.1 Decay of a core hole

Photoionization of inner shell levels creates electronically excited states. These excitedstates can decay via two different de-excitation routes:

(a) The hole in the inner shell X is filled by an electron from an outer shell Y , anda photon is emitted. This is the well-known X-ray emission process or fluorescentdecay. The energy balance is:

~ω = Ei(X)− Ef (Y ) (11)

where ~ω is the energy of the fluorescence photon, and Ei(X) and Ef (Y ) are thetotal energies of the system with holes in the shells X and Y , respectively.

(b) The hole in the inner shell X is filled by an electron from an outer shell Y as in theprevious case, but the excess energy is transferred to a third electron from an outershell Z, which is emitted. The process, called Auger decay, involves three electrons:the electron knocked out in the initial ionization (photoelectron), the electron thatdecays to fill the inner shell vacancy, and the emitted electron from the outer shell(Auger electron). As a consequence, the final state is a doubly ionized state. Sincethe energy is conserved during the transition, the kinetic energy of the emitted Augerelectron, measured with respect to the Fermi level EF , is:

Ekin,F = Ei(X)− Ef (Y,Z) (12)

Here, Ei(X) and Ef (Y,Z) represent the total energies of the system with one holein shell X, and two holes in shells Y and Z, respectively. The non-radiative decay is,of course, only permitted for Ekin,F > 0; this condition limits the number of possibleX,Y ,Z combinations.

The branching ratio of processes (a) and (b) is governed by the respective decay cross-sections. For the binding energy range below 1.5 keV, as in the present experiment, andespecially for the lighter elements, the non-radiative decay by far prevails.

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3.2 Important aspects of AES

In most cases, core ionization and core hole decay can be treated as independent (two-step process). Besides via photoionization, the primary core hole can be also createdby inelastic electron scattering. One can thus distinguish between XAES (X-ray inducedAuger Electron Spectroscopy) and EAES (Electron induced Auger Electron Spectroscopy),depending on whether the primary hole has been created by photoionization or by electronscattering. Excitation by electrons is very popular in conventional laboratories, becauseelectron sources are much cheaper than photon sources and the experimental set-up canbe relatively simple [9]. Moreover, electron guns can have very small beam spots enablingelement-specific Auger electron microscopy. Photon induced core ionization, on the otherhand, has the advantage that the concomitant rate of valence excitations is lower than inthe EAES case. Valence excitations are the main sources of irradiation damage, thereforeXAES is a less destructive tool. Because of this, XAES is an important technique forinvestigation of radiation sensitive layers on surfaces.

As in the PES case, discrete, element-specific lines associated with Auger transitionsappears in AES spectra (see Fig. 7 for a survey of the different processes in photoexcitedelectron spectra). Similarly to PES, therefore, Auger spectra can be used for elementalanalysis. Moreover, chemical specificity is ensured by the occurrence of chemical shiftscaused by shifts in the inner shell energy levels due to changes in the bonding. It shouldalso be noted that the emitted Auger electrons carry a well-defined kinetic energy, whichdirectly reflects the sequence of energy levels involved in the Auger transition and doesnot depend on the energy of the photons/electrons used to create the primary hole inthe inner shell. At variance with core level peaks in PES, which are characterized by aconstant binding energy (→ the kinetic energy increases linearly with the photon energy),Auger lines are better identified by their distinctive kinetic energy and AES spectra aretherefore commonly plotted on the kinetic energy scale.

The nomenclature of Auger transitions follows the electron shells contributing to the

Figure 7: Features of photoexcited electron spectra. From right (high kinetic energy) to left(low kinetic energy): d) photoionization of valence band levels; c) Auger transitions; b) core levelexcitation; a) inelastic loss processes.

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Figure 8: Explanation of different types of Auger decay processes based on the energy leveldiagrams: a) KLL decay; b) LMM decay; c) Coster-Kronig transition; d) Auger decay involvingvalence band levels of a solid. Figure taken from Ref. [10].

decay. An Auger line labeled XY Z corresponds to a primary hole in the X shell thatdecays into final holes in the Y and the Z shells (see Fig. 8). Commonly, the X-raynomenclature is used for identification of the holes: the K shell denotes 1s electrons, whileL1, L2, L3 indicates 2s, 2p1/2, and 2p3/2 electrons, respectively, etc. The decay cross-section is maximum if one of the two final holes has the same principal quantum number(i.e., is from the same shell) as the primary hole. These XXZ processes are called Coster-Kronig transitions. For super Coster-Kronig decays all participating holes have identicalprincipal quantum numbers (e.g., N4N6N6 and N5N7N7 for tungsten). When the atomin which the Auger process takes place is bound in a solid, extended electronic bands canbe involved in the decay and the label V is used. For example, a L3V V transition occurswhen an electron from the valence band de-excites into the L3 core hole, with the excessenergy being transferred to another valence band electron. Because strong redistributionof valence electrons may occurr upon formation of new chemical bonds, valence bandAuger transitions supply chemical information.

Similarly to PES, satellite lines occur in AES. Multiplet features are even richer forAES in comparison to PES because of the doubly ionized final state, i.e. there are at leasttwo holes which interact with each other. Depending on the atomic number Z, L−S (forlow Z) or j− j coupling (for large Z) prevails. Possible final states of KLL transitions arepresented in Fig. 9. Decay satellites, such as shake-up or shake-off processes triggered upondecay, can render the situation even more complicated. Characteristic energy losses due toexcitation of plasmons and asymmetric peak broadening caused by interband transitionsare also frequently observed in solids. For all these reasons, Auger lines appear - in general- broader than typical core level photoemission peaks, and they may also exhibit a morecomplex shape.

Calculation of the kinetic energies of Auger electrons according to Eq. (12) can be dif-ficult for electron systems larger than isolated atoms. Hence, approximations are required.One possibility is to take the binding energy for the energy level X of the primary hole,remove from it the binding energy of the decay electron from shell Y in order to quantifythe de-excitation energy, and finally subtract the binding energy of the level Z from whichthe Auger electron is ejected [11]. Inserting an additional term Uh−h that accounts for the

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Figure 9: Relative KLL Auger energies from theory (lines) and experiments (points) as a functionof the atomic number Z. Light elements (left side): L − S coupling, heavy elements (right side):j−j coupling; intermediate coupling case in between. The doubly ionized electronic configurationsare indicated in brackets, preceded by the spectroscopic notation (1S0, 1P1, etc.). See Ref. [9].

interaction of the two holes in the final state, one can write:5

Ekin,F = EPESb (X)− EPESb (Y )− EPESb (Z)− Uh−h (13)

By neglecting Uh−h, one obtains the approximate kinetic energy range of the Auger tran-sition. Uh−h can be determined experimentally by comparison with the measured Ekin,F ,thus providing important information about the interaction energy of the two holes.

4 Adsorption on surfaces

The term “adsorption” indicates the process of trapping and binding of foreign species(atoms or molecules) onto a surface by condensation from the gas phase. The energyreleased in this process is called energy of adsorption Uads or also binding energy (notto be confused with the binding energy in PES). The term “substrate” refers to the solidsurface onto which adsorption occurs, while “adsorbate” is used to indicate the species thatare adsorbed onto the substrate. Adsorption can be associative (if a particle or moleculeis adsorbed as a single unit) or dissociative (if the particle or molecule is dissociated uponadsorption), and moreover adsorption processes may be reversible or irreversible.

The reverse process, the removal of adsorbed species from the surface, is called “desorp-tion”. Desorption may be stimulated by heat (thermal desorption), by electrons (electronstimulated desorption), or by photons or ions (photon or ion stimulated desorption).

4.1 Types of adsorption

Physisorption:Physical adsorption (= physisorption) is governed by weak Van der Waals interactions withthe surface. The adsorption energy Uads is small, typically < 30 kJ/mol or 0.3 eV/particle.Formation of multilayers (condensates) is possible at sufficiently low temperatures.Example: He on noble metal surfaces at cryogenic temperatures.

5To express E samplekin,vacuum the work function has to be substracted from Ekin,F in Eq. (13).

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Chemisorption:Chemical adsorption (= chemisorption) involves the formation of a chemical bond betweenthe adsorbate and the surface, e.g. transfer of electrons and/or formation of covalent bonds(hybrid molecular orbitals). In most cases the adsorption energy is much larger than 30kJ/mol, ≥ 100 kJ/mol or 1 eV/particle. Chemisorption is often dissociative and may beirreversible; activation barriers are possible, and chemisorbates form typically only a sin-gle layer (= direct contact of surface atoms and the chemisorbate is required). Moreover,specific binding sites may be favoured because of the highly corrugated surface potential.Examples: CO and oxygen chemisorption on transition metals at room temperature.

4.2 Adsorption order

First order adsorption:One particle from the gas phase yields one particle of the adsorbate, i.e., the impingingparticles are molecules that do not dissociate upon adsorption. The reverse process is firstorder desorption.Examples: CO/nickel (CO chemisorbs on Ni surfaces molecularly with Uads ∼ 120 kJ/mole);Ar/Ruthenium (Ar physisorbs on Ru with Uads ∼ 10 kJ/mol).

Second order adsorption:A molecule dissociates upon adsorption. One particle in the gas phase yields two particleson the surface. The reverse process is associative desorption or second order desorption.Example: H2/Nickel (H2 dissociates into two H atoms on Ni, Uads ∼ 90 kJ/mole).

4.3 Nomenclature

Other concepts that are common in adsorption studies in the realm of surface science:

• Surface (relative) coverage Θ: Θ ≡ Nads

Nsubwith Nads = number of adsorbate particles per unit area; Nsub = number of particlesper unit area in the substrate surface layer(s). Θ is typically expressed in monolayersor as a fraction of a monolayer (ML), 1 ML corresponding to an adsorbate surfacedensity equal to the surface density of substrate atoms.

• Collision rate ν:it is defined as the number of particles hitting a surface per unit time and unit area.The Hertz-Knudsen equation following from the gas kinetic theory states that:

ν =p√

2πMkBT[particles · s−1 ·m−2]

with P = pressure [N· m−2 = Pa]; M = particle mass [Kg]; T = temperature [K];kB = Boltzmann constant.

• Sticking coefficient s:

s =dNads

dt

/dNcoll

dt0 ≤ s ≤ 1

probability that a particle colliding with the surface is adsorbed and stays on it.

• Exposure:measure of the amount of gas that a surface has been exposed to; more specifi-cally, the product of the gas pressure and the time of exposure. Normal unit is theLangmuir, where 1L = 10−6 Torr ·s (1 Torr = 133.3 Pa = 1.333 mbar).

14

5 Experimental set-up

The experimental set-up, schematically depicted in Fig. 10, consists of an ultra-high vac-uum (UHV) chamber on which the PES apparatus and the equipment for sample insertion,preparation and manipulation are mounted.

5.1 Vacuum system

The UHV chamber is maintained at a base pressure lower than 1× 10−9 mbar (1× 10−7

Pa). The pressure is measured by an ion gauge (hot filament ionization gauge) mountedinside the chamber. Pressure in the UHV regime is required in order to permit electrondetection (avoiding scattering of the photoelectrons between the sample surface and thedetector) and to ensure that atomically clean surfaces can be prepared and maintainedfree of contaminants during the experiment. The chamber is pumped by an ion getterpump directly mounted inside the chamber. Auxiliary pumping by a titanium sublima-tion pump is possible. In addition, an external turbomolecular pump (with attached abacking roughing pump) can be connected to the UHV chamber through a gate valve.This turbomolecular pump is also used to pump the load-lock system adjacent to themain chamber. The UHV regime can only be reached after baking out the chamber forabout 24 hours (or longer) at temperatures exceeding 160-180◦C. This procedure allows toeliminate residual molecules (predominantly water) adsorbed on the stainless steel walls ofthe chamber, which otherwise would be released at a low rate thus increasing the pressure.A brief introduction to the UHV technology, instrumentation and related protocols canbe found in Refs. [12, 13].

hemispherical

electron energy

analyzer (HSA)

X-ray source

load lock system

ion pump

turbomolecular

pump

+

roughing pumptitanium

sublimation

pump

gate valveMg evaporator

leak

valve

W sample

holder

pressure gauge

UHV chamber

detector

e-

lineO2

Figure 10: Scheme of the UHV chamber with the PES apparatus and ancillary equipment.

15

5.2 X-ray source

A conventional X-ray laboratory source provides characteristic Al Kα radiation. Thesource consists of a cathode filament, which emits electrons upon heating by direct cur-rent (typical emission current: 20-22 mA), and an anode, onto which the electrons areaccelerated by applying a high voltage (typically, 11-12 kV). Water cooling is requiredduring continuous duty operation of the X-ray source, in order to prevent melting of theanode target. Here, the anode is an Al film - some 10 µm thick - supported on a copperrod. During operation, the electrons from the cathode collide with the atoms of the Altarget, causing vacancies in inner electron shells. The subsequent de-excitation by fluo-rescence decay (see §3.1) produces X-ray radiation of characteristic energy.

L

L

L

K

K

K

3

2

1

en

erg

y

α

α

1

2

2p

2p

2s

1s

1/2

3/2

(a) (b)

ħω = 1486.6 eV

FWHM = 0.78 eV

KAl α1,2

Figure 11: Characteristic radiation from an Al anode source: (a) schematic energy level diagramexplaining the production of the individual Kα1 and Kα2 lines; (b) emission spectrum showingthe convolution of the Kα1 and Kα2 lines into a composite Kα1,2 line centered at 1486.6 eV with0.78 eV FWHM. Adapted from Ref. [12].

As illustrated in Fig. 11, the Kα1 and Kα2 lines are generated, corresponding to L3 → Kand L2 → K transitions, respectively, where L3, L2 and K denote the 2p3/2, 2p1/2 and 1slevels. The L2,3 subshell is split due to spin-orbit coupling, such that the relative intensityof the two lines reflects the L3 to L2 population ratio of 2 : 1. As a consequence, the Kα1,2

line is in principle a doublet with an energy splitting of 0.43 eV. However, since each linehas a natural width of 0.47 eV caused by lifetime broadening, the doublet is not resolvedand the resulting composite line has a linewidth of 0.78 eV (FWHM) and is centered at~ω = 1486.6 eV. In addition, a Kα3,4 satellite is also produced, attributed to emissionfrom doubly ionized atoms [12]. This satellite line is centered at about 1496 eV and itsintensity is ∼ 10% of that of the main Kα1,2 emission.

Additional emission lines can arise from contamination (e.g., the O Kα line centeredat ~ω = 524.9 eV if the anode material is partly oxidized) or other modifications ofthe anode (e.g., when the Al film becomes too thin, the Cu Lα line from the copper rodbeneath may be excited, ~ω = 929.7 eV).

5.3 Electron energy analyzer

An electrostatic 180◦ hemispherical analyzer (HSA) is used to analyze in energy the elec-trons emitted from the sample. This electrostatic device consists of two metallic hemi-spheres, concentrically arranged as in Fig.12, and enables to “disperse” the electrons as afunction of their kinetic energy similarly to a prism that disperses light depending on itswavelength. For this purpose, a potential difference ∆V is applied between the inner andouter hemispheres, so that the trajectory of the incoming electrons is bent into a curve6.

6To prevent perturbation of the electron trajectories by stray magnetic fields, the analyzer region isshielded by a µ-metal shield inside the vacuum vessel.

16

electron

optics

detectorV(R ) = - V1 1

V(R ) = - V2 2

∆V = V(R ) - V(R )1 2

Figure 12: Schematic of a concentric hemispherical analyzer. Both hemispheres are at negativepotential, with V (R2) < V (R1) (→ V2 > V1). Adapted from Ref. [14].

An electrostatic lens between the sample and the entrance slit S of the analyzer focusesthe photoelectrons from the sample onto S. At a given ∆V , ideally only the electronswith a well-defined kinetic energy Ep are able to complete their path along the mediantrajectory of radius R0 = (R1+R2)/2 (R1 and R2 radii of the inner and outer hemisphere)and emerge at the exit slit F . Ep is called pass energy and its typical values range between5 and 50 eV for XPS measurements.

An important concept is that of energy resolution of the analyzer. This is a measureof the ability of the analyzer to distinguish and separate (→ resolve) peaks that differ inenergy by only small amounts. As discussed in §2.2, the energy resolution of the analyzercontributes to the overall FWHM of a core level peak (Eq. (10)). For the HSA, the energyresolution can be expressed by the formula [12, 13]:

∆E/Ep =WS +WF

4R0+α2

2(14)

in which ∆E is the FWHM, WS and WF are the widths of the entrance and exit slit,respectively, and α is the angular spread of the electron beam. The analyzer is operatedat constant pass energy to yield a constant absolute resolution ∆E. The lower the passenergy, the better the energy resolution.

In order to enable scans over arbitrary kinetic energy ranges, the electrons are retarded(or accelerated) to the kinetic energy Ep by a potential difference R inside the lens systemsituated between the sample and the entrance slit. A channel-type electron multiplier(channeltron) is located behind the exit slit of the analyzer, where the emerging electronsare counted. Therefore, by scanning R a spectrum of the photoelectron intensity as afunction of the kinetic energy is recorded, the measured kinetic energy being simply R+Ep.

When R = 0, the Fermi levels of sample and analyzer are aligned (in practice, bothobjects are grounded), whereas they are separated by R when the retarding voltage isapplied. However, due to the different values of the work function, the vacuum levelsof sample and analyzer do not coincide even for R = 0. From the energy level diagramillustrated in Fig. 13 it then follows:

Eb = ~ω − (Ep − Φanalyzer −R) = ~ω − Eanalyzerkin, vacuum − Φanalyzer (15)

17

E

E

Sample Analyzer

E

e

vacuum,sample

Evacuum,analyzer

Ekin,Fp

EF,analzyer

EF,sample

-

Core Levels

R

hω

Φ

Φ

w

analyzer

bEkin,F EpR

w

Φanalyzer

(measured)

= + +

(Φ Φ )analyzer+ -

Ekin,vacuum

analyzerEpR= +

Ekin,vacuum

sampleEpR= +

Figure 13: Photoelectron detection by an electron energy analyzer: schematic diagram of relevantenergy levels and voltages.

Eq. (15) shows that the work function of the analyzer, rather than the work function ofthe sample, needs to be taken into account. Φanalyzer enters the equation because in theexperiment the kinetic energy scale is referenced to the vacuum level of the analyzer. Tokeep Φanalyzer constant, all electrodes are covered with a chemically inert material (goldor graphite; in the present case graphite).

5.4 Samples

Three samples will be investigated during the experiment. A tungsten (W) ribbon will bestudied initially. It can be heated up to 2500 K by direct current flow in order to removecontamination from the surface. The W ribbon is mounted on a four-degree-of-freedommanipulator enabling translational motion along three orthogonal directions and rotationaround the axis of the manipulator. In this way, the polar angle θe defined in Fig. 2a canbe changed, thus varying - when needed - the surface sensitivity of the PES measurements.

Further, the W ribbon will serve as substrate for the growth of a Mg film that willbe deposited in-situ under UHV conditions. The subsequent oxidation of magnesiumwill provide a clear illustration of the concept of chemical shift; moreover, measurementswith different surface sensitivity will provide structural information on the depth of theoxidation process.

Finally, a third sample to be analyzed will be introduced through the custom-madeload-lock system, which allows fast insertion of ex-situ prepared samples without breakingthe vacuum of the main chamber. An UHV compatible sample chosen by the studentswill be inserted into the chamber and characterized by PES. Possible examples: a metalsubstrate covered by an organic sulphur-containing self-assembled monolayer (SAM); acoin; a (cheap!) piece of jewellery; the crown cork of a bottle; a fragment taken from abroken DVD, CD or hard disk; a piece of special glass, etc.

18

5.5 Magnesium evaporator

The evaporator consists of a small high-melting-point crucible containing Mg grains. Thecrucible is heated by passing current through a conducting wire coiled around it. Priorto evaporation, the Mg grains need to be outgassed repeatedly, in order to ensure that aclean Mg film is deposited on the tungsten ribbon during the experiment.

5.6 Gas handling line

A gas line filled with molecular oxygen is connected to the main chamber through a high-precision leak valve. In this way O2 can be admitted into the chamber in a controllablefashion during the experiment.

6 Concepts to be understood before the experiment

• Fundamental principles of PES and AES: the photoemission process, Auger tran-sitions. Core level lines, valence band excitation. Binding energy. Work function.Satellite lines. Spin-orbit splitting. Chemical shifts.

• Surface sensitivity of PES and AES. Importance of the electron detection geometry:normal emission vs. grazing emission.

• Generation of characteristic X-rays by fluorescent decay. Working principle of theAl anode X-ray source.

• Hemispherical electron energy analyzer. Pass energy. Retarding voltage. Instru-mental resolution.

• Ultra-high vacuum. Adsorption of foreign species. Dissociative adsorption.

7 Instruction for the experimental session

The goal of the experiment is to characterize by core level PES the tungsten ribbonmounted inside the chamber, and to study by PES and AES the modifications introducedby the deposition of a Mg film. The effect of the oxidation of the Mg film is also part ofthe investigation. In addition, insight into the performance of the hemispherical analyzerwill be gained, in particular as to the dependence of the core level intensity and energyresolution on the pass energy. In order to stimulate the scientific curiosity of the students,in the final part of the experiment the possibility of studying an additional sample at choiceis offered. In this way, the experiment provides an overview on the main information thatcan be obtained from the two experimental techniques, on some technical aspects and ontypical issues faced in adsorption studies and surface science.Proceed according to the following steps:

A. Performance of the analyzer and characterization of the W sample

1. Get an introduction to the experiment and to the equipments by your advisor.

2. Clean the W ribbon following the advisor’s instructions. After setting the passenergy to Ep = 50 eV, record a survey spectrum7 with 100 eV ≤ Ekin ≤ 1500 eV.In this broad scan you are not interested in the fine details of the core level lines,

7Unless otherwise stated, photoemission spectra will be taken at an electron emission angle of 45◦,which corresponds to an incidence angle of 45◦ of the photon beam relative to the surface normal.

19

so you can use a large energy step (1 eV). Try to assign all maxima to known corelevel and Auger peaks: this may be easier if you plot the spectrum in the bindingenergy scale, using the appropriate computer software.

3. Zoom-in into the W 4f doublet using an energy step of 0.1 eV and record a sequenceof spectra with different values of Ep (e.g., 7.5, 10, 15, 20, and 50 eV). In order to havegood statistics, at each value of the pass energy select appropriately the integrationtime per energy point.

4. Zoom-in into the C 1s and O1s core level regions at Ep=50 eV. Is the surfacecompletely free of contaminants?

5. At Ep = 20 eV record a photoemission spectrum of the W valence band (see Fig. 7).Determine Φanalyzer from the position of the Fermi edge.

B. Cleanliness of the Al anode of the X-ray source

6. Using Ep= 50 eV, acquire a PES spectrum for 200 eV ≤ Ekin ≤ 530 eV with theX-ray source operated at reduced anode voltage of 1.4 kV and an emission currentof 6 mA (consult the advisor to change the operation conditions). Now that the AlKα emission is suppressed, what is the origin of the spectral features observed?

C. Deposition of a Mg metal film

7. The advisor will now deposit a Mg film on the W sample: record a survey spectrumfrom 50 to 1500 eV (Ep = 50 eV, ∆Estep = 1 eV). Assign all the features of thisspectrum and assess qualitatively the cleanliness and thickness of the film. Can yousee any signal from the W substrate?

8. Record the Mg KLL Auger spectrum in the kinetic energy range from 1060 eV to1200 eV (Ep = 20 eV, ∆Estep ∼ 0.3 eV) for:(1) nearly normal electron exit (θe = 10◦);(2) nearly grazing electron exit (θe = 80◦).Keeping in mind the different probing depth of the two geometries, can you concludethat the (electronic) structure of the metallic film is uniform across its thickness?

9. Zoom-in into the Mg 1s region (Ep = 10 eV). Write down the kinetic energy of themain line. Record a photoemission spectrum (Ep = 10 eV) from the O 1s region.Any feature?

D. Oxidation of the Mg film at room temperature

10. After the Mg overlayer has been oxidized by dosing ∼45 L O2 at room temperature(PO2 = 2×10−7 mbar), repeat step 9. Any changes? Explain the results in the lightof what you have learnt about the chemical shift.

11. Repeat step 8. Which conclusions can be drawn based on the different surfacesensitivity of the two collection geometries? Is the film uniformly oxidized andstructurally homogeneous across its thickness?

20

E. Elemental analysis of a sample at your choice

12. Help the advisor to insert the ex-situ prepared sample you have chosen into the load-lock chamber. Follow instructions to start pumping. After a good pressure has beenreached, open the gate valve to the main chamber and bring the sample into themeasurement position in front of the X-ray source. Take all XPS spectra you deemare necessary for characterizing the sample in terms of its elemental composition.

8 Writing up your report

Write up a short report of your experiment. After a concise introduction on the PES andAES techniques, discuss the experimental results addressing all issues listed below:

• Assign all spectral features in 7.2. Calibrate the binding energy scale by making useof 7.5. As an alternative method to determine the analyzer work function, searchfor the literature value of the W 4f7/2 binding energy of metallic W (if possible, fora polycrystalline W foil) and use Eq. (3) together with the results of 7.3. Commenton the surface cleanliness (see 7.4).

• Focus your attention on the W 4f doublet (from 7.3). Discuss the spin-orbit splittingand the intensity ratio of the components. Determine the W 4f intensities afterbackground subtraction and plot them as a function of Ep, commenting on theobserved dependence.

• Plot the experimentally obtained FWHMs for the two constituents of the 4f doubletas a function of Ep. How does the trend compare to Eq. (14)? Referring to Eqs. (9and (10), set a lower limit for the core hole lifetime using - for instance - the dataat Ep = 10 eV.

• Rationalize the results of 7.6. Consider X-ray emission from contaminants on the Alanode.

• Assign all spectral features from 7.7. Comment on the thickness of the metallic filmand, using 7.8, make conclusions on its uniformity.

• Explain all details of 7.8 and identify the main Auger transitions (KL2,3L2,3, KL1L1

etc.) by consulting available literature. You can also check the reliability of thework function value determined above by comparing the tabulated and experimentalvalues for the KL2,3L2,3 (1D) line8.

• Consider the progression of plasmon losses in the Auger KLL spectrum: determinethe plasmon energy and compare your estimate with the expected value (see alsoexercise 3 below).

• In the Auger KLL spectrum select a transition of your choice and calculate thehole-hole interaction energy Uh−h from Eq. (13).

• Compare the Mg 1s and O 1s data from 7.9 and 7.10. Describe the effect of theoxidation (structural and chemical evolution).

• Compare and interpret the results of 7.8 and 7.11. Is the Mg film uniformly oxidizedthrough its thickness or can you infer differences between the surface layer(s) andthe region underneath?

• Briefly describe the results of the elemental analysis of 7.12.

8Note that tabulated values are often given with the kinetic energy measured relative to the Fermi level.

21

9 Exercises

One of these exercises, at your choice, will be asked during the final colloquium:

1. Determine after which time interval an originally clean metal surface (e.g., Mg) will becovered with one monolayer of O atoms at a pressure of 2 × 10−7 mbar (= 2 × 10−5 Pa)of molecular oxygen O2.

[Hint: make use of the Hertz-Knudsen equation (see §4.3) to determine the impingement rate

of O2 onto the surface; assume s = 1 for the sticking coefficient; give an estimate of the surface

density of Mg atoms, e.g. on a Mg(0001) surface for which the size and area of the primitive cell

are known; remember that the adsorption of O2 is dissociative.]

2. Assume a hemisherical analyzer with radii R1 (inner) and R2 (outer). What is thepotential difference ∆V that has to be applied to the hemispheres in order to bend thetrajectory of electrons of kinetic energy Ep into a circular orbit of radius R0 = (R1+R2)/2?Numerical values: R1 = 9.5 cm, R2 = 10.5 and Ep = 5 eV.

[Hint: the centripetal force bending the electron’s trajectory must equate the force exerted by

the electric field; make use of the Gauss’s law.]

3. Determine the bulk plasmon energy (in eV) of magnesium metal in the jellium model,using the formula: ~ωp = [n~2e2/meε0]

1/2, with me electron mass and n number densityof free electrons for Mg metal)

[Hint: n can be determined from the mass density and the atomic weight of Mg, assuming that

two conduction electrons per atom are made available.]

10 Useful tables

• Electron binding energies for all elements:http://xdb.lbl.gov/Section1/Table 1-1.pdf

• Energies of the X-ray emission lines for all elements:http://xdb.lbl.gov/Section1/Table 1-2.pdf

• Subshell photoionization cross-sections:http://xdb.lbl.gov/Section1/Sec 1-5.pdf

• Energies of the main Auger lineshttp://xdb.lbl.gov/Section1/Sec 1-4.html

22

References

[1] H.P. Bonzel and Ch. Kleint, On the History of Photoemission, Progress in SurfaceScience 49, 107 (1995); doi:10.1016/0079-6816(95)00035-W.

[2] S. Hufner, Photelectron Spectroscopy — Principles and Applications, Springer-Verlag,Berlin, 2003.

[3] For a thorough discussion of these effects see for example:C.S. Fadley, Basic Concepts of X-ray Photoelectron Spectroscopy (chapter 1), in:Electron Spectroscopy: Theory, Techniques, and Applications (Vol. 2), edited by:C.R. Brundle and A.D. Baker, Academic Press, London, 1978.

[4] B.D. Ratner and D.G. Castner, Electron Spectroscopy for Chemical Analysis (chapter4), in: Surface Analysis — The Principal Techniques, edited by J.C. Vickerman, J.Wiley & Sons Ltd., 1997.

[5] D. Briggs, XPS: Basic Principles, Spectral Features and Qualitative Analysis (chapter2), in: SURFACE ANALYSIS by Auger and X-ray Photoelectron Spectroscopy, editedby D. Briggs and J.T. Grant, IM Publications and SurfaceSpectra Limited, 2003.

[6] M.C. Biesinger et al., Resolving Surface Chemical States in XPS Analysis of First RowTransition Metals, Oxides and Hydroxides: Sc, Ti, V, Cu and Zn, Applied SurfaceScience 257, 887 (2010); doi:10.1016/j.apsusc.2010.07.086.

[7] J.C. Fuggle and S.F. Alvarado, Core Level Lifetimes as determined by X-rayPhotoelectron Spectroscopy Measurements, Physical Review A 22, 1615 (1980);doi:10.1103/PhysRevA.22.1615.

[8] J.J. Sakurai, Modern Quantum Mechanics, Addison-Wesley Publishing Company,Reading - Massachusetts, 1995. See pp. 341-345.

[9] C.C. Chang, Auger Electron Spectroscopy, Surface Science 25, 53 (1971);doi:10.1016/0039-6028(71)90210-X.

[10] H. Luth, Solid Surfaces, Interfaces and Thin Films, Springer-Verlag, Berlin, 2001.

[11] J.T. Grant, AES: Basic Principles, Spectral Features and Qualitative Analysis (chap-ter 3), in: SURFACE ANALYSIS by Auger and X-ray Photoelectron Spectroscopy,edited by D. Briggs and J.T. Grant, IM Publications and SurfaceSpectra Limited,2003.

[12] I.W. Drummond, XPS: Instrumentation and Performance (chapter 5), in: SURFACEANALYSIS by Auger and X-ray Photoelectron Spectroscopy, edited by D. Briggs andJ.T. Grant, IM Publications and SurfaceSpectra Limited, 2003.

[13] J.C. Riviere, Instrumentation (chapter 1), in: PRACTICAL SURFACE ANALYSIS,Vol. 1: Auger and X-ray Photoelectron Spectroscopy, edited by D. Briggs and M.P.Seah, J. Wiley & Sons Ltd., 1990.

[14] P. Willmott, An Introduction to Synchrotron Radiation — Techniques and Applica-tions, J. Wiley & Sons Ltd., 2011.

23

Appendix A: Theory of core level photoemission

The interaction of electromagnetic radiation with an electron system is described by theHamiltonian:

H =1

2m

(~p+

e

c~A)2

+ eΦ + V = Ho +H ′ (A.1)

with

Ho =~p2

2m+ V (A.2)

being the unperturbed Hamiltonian of the electron (e.g., in a solid in the absence of theelectromagnetic field), and

H ′ =e

2mc(~p · ~A+ ~A · ~p) + eΦ +

e2

2mc2~A2 (A.3)

the perturbation due to the photon field with vector potential ~A. By assuming source freespace, adopting appropriate gauge transformations (Coulomb gauge: Φ=0, div ~A=0) andneglecting higher orders of ~A (i.e., the term ~A · ~A, which represents two photon processes)one obtains:

H ′ =e

mc~A · ~p (A.4)

Here, the vector potential ~A of the electromagnetic radiation defines the direction ofpolarization, while ~p is the momentum operator. Assuming a small perturbation H ′, inthe first order perturbation theory the Fermi’s Golden Rule provides the transition ratePi→f (transition probability per unit time) for the excitation from the initial N -electronstate Ψi of energy Ei to the final N -electron state Ψf of energy Ef :

Pi→f =2π

~|〈Ψf |H ′ |Ψi〉|2 δ(Ef − Ei − ~ω) (A.5)

The angle-integrated cross-section will be therefore:

dσ

dEf∼∑|Mi→f |2 δ(Ef − Ei − ~ω) (A.6)

where the transition matrix element is Mi→f = 〈Ψf | ~A · ~p |Ψi〉, and the sum is performedover all initial and final states that are allowed by energy conservation (= for which theargument of the delta function is zero).If one separates the wavefunction of the photoelectron from that of the other N − 1“passive” electrons, the previous equation can be expressed as [2]:

dσ

dEf∝∑f,i,k

|〈φf,Ekin| ~A · ~p |φi,k〉|2

∑s

|cs|2 δ(Ef,kin + Es(N − 1)− E0(N)− ~ω) (A.7)

where the cs coefficients denote N − 1 overlap integrals and the∑

s is calculated bysumming over all possible excited final states of energy Es(N − 1); E0(N) is the energyof the initial N -electron state (ground state energy) and Ef,kin represents the kineticenergy of the photoelectron, which has been excited from the inner orbital φi,k to thefinal state of wavefunction φf,Ekin

. Eq. (A.7) thus contains the main ingredients of a corelevel photoemission spectrum that have been discussed in section 2, namely a “main line”accompanied by a number of satellites which reflect the excitation spectrum of the electronsystem with the core hole.

24