electron spectroscopy - theory

7/31/2019 Electron Spectroscopy - Theory

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Forelesningsnotater

(del av fag:DIF4903 Overflatefysikk)

Electron spectroscopy

av

Steinar RaaenInstitutt for fysikk

http://www.phys.ntnu.no/~sraaen/dif4903/elspec.pdf


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CONTENTS

1. Introduction ................................................................................... 11.1. Electron attenuation length .............................................................11.2. Electron spectroscopies ...................................................................21.3. Electron energy spectrometers ........................................................41.4. Photon sources ................................................................................5

2. AES (Auger electron spectroscopy) ............................................. 7

2.1. Introduction .....................................................................................72.2. Quantitative analysis .....................................................................102.3. Depth profiling ..............................................................................142.4. Scanning Auger microscopy .........................................................152.5. Spectator and participator Auger decay ........................................162.6. Auger vs. photon yield .................................................................. 18

3. XPS (X-ray photoelectron spectroscopy) .................................. 193.1. Introduction ...................................................................................193.2. The photoemission process ...........................................................213.3. X-ray satellites and ghost-lines .................................................233.4. Chemical shifts .............................................................................243.5. Metallic screening and Born-Haber cycles ...................................263.6. Surface core level shifts (SCLS) ...................................................273.7. Core levels shifts in alloys ............................................................ 313.8. Plasmon excitations ...................................................................... 333.9. Satellites in core level spectra .......................................................343.10. Line shapes in photoemission ......................................................383.11. Quantitative analysis .....................................................................40

3.12. Inelastic background .....................................................................433.13. Photoelectron diffraction .............................................................. 45

4. UPS (Ultraviolet photoelectron spectroscopy) ......................... 49

4.1. Introduction ...................................................................................494.1. Angle resolved photoemission ...................................................... 494.3. Resonant photoemission ...............................................................554.4. Measuring the work function ........................................................584.5. Exchange splitting .........................................................................60

5. S-XAS (Soft X-ray absorption spectroscopy) ........................... 625.1. Introduction ...................................................................................62

5.2. NEXAFS .......................................................................................635.3. Surface EXAFS .............................................................................68

6. IPES (Inverse photoelectron spectroscopy) .............................. 74

6.1. Introduction ...................................................................................746.2. IPES versus photoemission ...........................................................766.3. Applications of IPES ....................................................................77

Author Index .................................................................................... 81
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Introduction1

1. Introduction

Various types of electron spectroscopy are widely used and includes some of the mostpopular experimental tools in surface science. This is due to the fact that electrons of

kinetic energies from 5 to 2000 eV have a mean free path in a solid, in the range of about 4to 40 . Electrostatic electron energy analyzers are commonly used to detect electrons of agiven kinetic energy. In addition to the pure electron spectroscopies (X-ray PhotoelectronSpectroscopy, Ultraviolet Photoelectron Spectroscopy, Auger Electron Spectroscopy etc.),we will in this discussion also consider related surface sensitive techniques that involves thedetection of photons (Inverse photoemission, Appearance Potential Spectroscopy).

1.1. Electron attenuation length

Electrons that pass through a solid material may loose energy in several ways. The

most important processes in the relevant energy range is: (i) excitation of plasmons (collec-tive mode of conduction electrons), (ii) excitations of valence electrons, and (iii) ionizationof core-levels. These processes severely limit the distance an electron can move without

loosing kinetic energy. In addition to the inelastic processes mentioned above, the distancetravelled by an electron in a solid is also influenced by elastic scattering, since this increasesthe length of path travelled by the electron and thus the probability of suffering inelasticlosses. The distance which characterizes sampling depth is usually referred to as attenua-

Fig.1.1. Electron attenuation length versus kinetic energy (after Zangwill, 1988)


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Introduction2

tion length, which is shorter than the inelastic mean-free- path (which neglects elastic scat-tering). The difference in these two lengths may be as much as 30%.

Figure 1.1 shows electron attenuation length as function of kinetic energy for a varietyof elements, and show that the variation from one element to the other is relatively small.

The highest degree of surface sensitivity is obtained for electrons of kinetic energies near 50eV, where the electron attenuation length is on the order of 4 . The large increase in atten-uation length for kinetic energies below 50 eV is mainly caused by the decrease in the prob-ability of exciting plasmons for lower kinetic energies.

1.2. Electron spectroscopies

In the following we divide various electron spectroscopies according to mode of exci-tation and detection:

(a) electrons in, electron out- AES (Auger electron spectroscopy), involves excitation of a core electron and detec-

tion of an electron that results from the decay of the core-hole. AES is mostly usedfor surface composition analysis. The kinetic energies of the detected electrons areindependent of the energy of the exciting electron.

- EELS (Electron energy loss spectroscopy), kinetic energies of electrons are detectednear the energy of the incident beam of electrons. This technique is used to studymechanisms by which electrons loose energy in a solid. EELS may be surface sen-sitive when the incident beam of electrons is at low kinetic energy.

(b) electrons in, photons out- APS (Appearance potential spectroscopy), involves the identification of the thresh-

old energy for incident electrons to ionize a core level by detecting the onset of softX-ray emission associated with electrons decaying into the core hole. These X-rayshave long mean free paths, so the surface sensitivity is determined by the incidentelectron beam. APS is surface specific due to the fact that it involves the detectionof threshold ionization where electrons that have lost even small energies (e.g. plas-mon excitations) will not have sufficient energy to ionize the core level.

- Inverse photoelectron spectroscopy (IPES) involves detection of photons that are

emitted when an external electron fills an empty energy level. IPES probes unfilledenergy levels, in a similar way as photoemission probes occupied levels.

(c) photons in, electrons out

- XPS (X-ray photoelectron spectroscopy), a core electron is emitted after absorbing aphoton. The kinetic energy of the photoemitted electron is measured.

- UPS (Ultraviolet photoelectron spectroscopy), corresponds to XPS only that avalence electron is photoemitted.

- AES (Auger electron spectroscopy), core excitation by a photon.


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Introduction3

Evac

EF

E2

E1

E3

E

Ground State

Evac

EF

E2

E1

Ekin

h

EB

Evac

EF

E2

E1

hEkin

EB

Auger (CVV)(two hole final state)

Evac

EF

E2

E1

Ekin

E3

Evac

EF

E2

E1

Ekin

Evac

EF

E2

E1

Ekin h

XPS(one hole finalstate)

UPS(one hole final state)

EB=h-Ekin-

Auger(C1C2C2)(two hole final state)

EB=h-Ekin-

Inverse photoemission(one electron final state)

Fig.1.2. Schematic view of several electron spectroscopies

Ekin=(E3-E1)-(Evac-E3) Ekin=(E2-E1)-(Evac-E2) h=Ekin+(Evac-E*)


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Introduction4

1.3. Electron energy spectrometers

Electrons are usually energy analyzed using electrostatic energy analyzers. There areseveral types in use: Retarding field (RFA), single- and double-pass cylindrical mirror

(CMA), cylindrical electrodes, and perhaps most commonly used concentric hemisphericalanalyzers (CHA), where the electrons pass between to concentric spheres. We will in thefollowing brief discussion only limit ourselves to the CHA type of electron energy analyz-ers.An electron energy analyzer is usually operated in two modes:(i) Constant pass energy or fixed analyzer transmission (FAT) where the energy resolution

E is kept constant.(ii) Constant retarding ratio (CRR) where the ratio E/E is kept constant. Here E is the

kinetic energy of the analyzed electrons.The FAT mode is the normal mode of operation for photoelectron spectroscopy, whereas theCRR mode is the normal mode for Auger electron spectroscopy.

The energy resolution of an electron energy analyzer (in the FAT) mode may beimproved by adjusting the voltage across the hemispheres to reduce the energy of the elec-trons that pass through the analyzer. The trade-off is loss of sensitivity. In practice, the passenergy has to be high enough to ensure decent statistics in the data. The sensitivity of theanalyzer may be improved by using an area detector, so that several kinetic energies may bemeasured simultaneously. The sensitivity of the CHA is increased when the radii of thehemispheres increase; therefore a large CHA is desirable to a smaller one.

Sometimes an electrostatic lens is placed in front of the analyzer to improve the sensi-tivity. Electrons that are emitted from the sample specimen is then collected within a smallsolid angle (< 10).

Fig.1.3. Schematic view of a concentric hemispherical analyzer (CHA)


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Introduction5

1.4. Photon sources

The photons that are used for excitation in electron spectroscopies originate fromstandard laboratory sources and from synchrotron radiation sources.

(1) Laboratory sources- Rare gas discharge lamps produce photons in the vacuum-ultraviolet regime. Most

common photon energies: 21.2 eV (HeI), 40.8 eV (HeII). These lamps produce high inten-sity radiation of high energy resolution.

- Soft X-ray sources usually use Al- and Mg-anodes. Photon energies: 1486 eV (AlK) and 1254 eV (Mg K). These sources have line widths of 0.8 and 0.7 eV, respectively.When the radiation is monochromatized a line width as small as 0.2 eV may be obtained onthe expense of sensitivity. Some other anode materials give rise to other photon energies,but are seldom used. In addition to the large line width, satellite lines (K3,4) are present

and have to be considered when analyzing the spectra from non-monochromatized radia-tion.

(2) Synchrotron radiation

There are several synchrotron radiation facilities that are optimized for radiation in

the soft X-ray/vacuum ultraviolet region (h =10-2000 eV). These sources produce tunableradiation of high intensity, and have opened up many new possibilities in electron spectros-copy: (i) resonant photoemission, (ii) soft X-ray absorption, (iii) surface magnetism studies,(iv) photoelectron microscopy, (v) photoelectron diffraction, and others. In particular, corelevel spectroscopy of very high energy resolution have been facilitated by synchrotron radi-ation.

A storage ring is a vacuum vessel that consists of straight sections that are separatedby bending magnets to form a ring. Synchrotron radiation results from electrons that moveat relativistic velocities in this ring, and that emit radiation when they are accelerated in abending magnet or an array of permanent magnets in a straight section (insertion device).

Fig.1.4. Cross-sectional view of a twin-anode X-ray source


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Introduction6

The radiation is collected in a beam line and passed through a monochromator before it maybe used to perform electron spectroscopy. The properties of synchrotron radiation may belisted in the following way:

- High brilliance (#photons/(sec-mm2- mrad2-0.1%BandWidth)). The high bril-liance facilitates a high degree of monochromatation, which enables high energyresolution.

- Tunable photon energy makes it possible to vary the degree of surface sensitivity,which is useful in determining surface composition. Since photo-ionization cross-sections depend on the wavelength, it is possible to enhance or suppress emissionfrom electron states of a given symmetry. Also, various spectroscopies thatinvolves the ramping of the exciting radiation is made possible: e.g. soft X-rayabsorption.

- Polarized radiation. The linear polarized nature of synchrotron radiation makes it

possible to select electronic transitions between states of certain symmetries, andmakes it possible to e.g. determine the direction of a molecular axis for a moleculethat is adsorbed on a single crystalline surface. The radiation immediately belowand above the plane of the orbiting electrons is circularly polarized, and this factmay be utilized in studies of surface magnetism.

- Time structure. Electrons in the storage ring moves in bunches that are separatedin time. The time structure of the synchrotron radiation may be utilized in variousexperiments, e.g. coincident measurements.

Fig.1.5. Overview of a synchrotron radiation facility (MAX-I in Lund)


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AES (Auger electron spectroscopy)7

2. AES (Auger electron spectroscopy)

The Auger effect was discovered by Pierre Auger in 1925. Electron-excited Augerelectron spectroscopy has traditionally been the most widely used of all surface analytical

methods; it has been the standard tool for determine surface cleanliness as a starting pointfor surface science experiments.

2.1. Introduction

Figure 2.1. shows an Auger process the results afterionization of a core-electron in energy level E1. Thedecay of the core-hole may result in the emission of a pho-ton or in the emission of an electron (with a certain proba-bility). The kinetic energy of the emitted electron depends

only on the energy levels of the atom, and thus the distri-bution of kinetic energies provide a fingerprint for eachelement in the periodic table.

Auger spectra are frequently recorded by use of anelectron energy analyzer (e.g. of CMA or CHA type) inconjunction with an electron gun. It is also possible to usea LEED optics as a retarding field analyzer to do Augermeasurements, so that one piece of equipment can be uti-lized for surface structure and surface composition mea-

surements.It is customary to measure the derivative of the sig-nal in Auger applications in order to suppress the largebackground of secondary electrons. This is done by mod-

ulating the voltage on the analyzer and amplifying the signal from the analyzer in a phasesensitive lock-in amplifier. If we denote the number of electrons of kinetic energy E by

Evac

EFermi

E2

E1

Ekin

E3

Fig.2.1. The Auger process

Fig.2.2. Typical Auger spectra from Ag.


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N(E), one usually plots dN(E)/dE as function of E (see Fig.2.2).The kinetic energy Ekin of an Auger electron may be written in terms of the energy

levels (e.g. E1 and E3 in Fig.2.1.) of the atom in question:

where U33 is the hole-hole interaction energy in the two-hole final state, and is small com-pared to differences in energy levels, and are frequently neglected. Differences in thechemical environment of an atom may cause changes in the kinetic energy of a specificAuger peak, which are referred to as chemical shifts. These shifts may originate both aschanges in the electronic levels and in the two-hole interaction energy. Auger emissionfrom carbon (KVV) in different environments are shown in Fig.2.3.

Even though chemical shifts are frequently observed in Auger electron spectra, rela-tive little effort has been used to investigate the nature of these shifts in a systematic fash-ion. X-ray photoelectron spectroscopy has emerged to be the most powerful technique inthis regard.

Standard Auger electron spectra have been published (Handbook of Auger ElectronSpectroscopy, Physical Electronics, Perkin-Elmer) for all elements in the periodic table.These spectra are routinely used to identify the presence of elements on the solid surfaceunder investigation, and the spectra may also be used to estimate the amount of various ele-ments on a surface. This is referred to as quantitative Auger analysis.

Ekin E3 E1 Evac E3( ) U33=

Fig.2.3 Auger spectra (dN/dE) from C in different chemical environments.


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In figure 2.4. is shown a table that show kinetic energies for the major Auger peaks for theelements in the periodic table.

By use of a chart like in Fig.2.4. its is possible to relatively rapidly get a picture of themost abundant elements on a solid surface. Frequently, the main Auger lines are anticipatedbased on knowledge of the sample specimen in question; in addition, at least oxygen andcarbon are expected to be present on a surface that have not been thoroughly cleaned in theultra-high-vacuum chamber.

Fig.2.4. Chart of Auger peaks.


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2.2. Quantitative analysis

Standard Auger spectra for Al and Ni are shown in Fig.2.5.

The standard Auger electron spectra may be used to quantify the amount of variouselements on a surface. In order to determine the relationship between Auger peaks and

Fig.2.5. Standard Auger spectra for Al and Ni (Handbook of Auger Electron Spectroscopy).


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atomic concentration it is necessary to consider the effect of instrumental parameters on themeasured Auger signal. Important instrumental parameters are the primary electron beamcurrent Ip, the primary beam energy Ep, and the modulation energy Em (when consideringderivative spectra). The characteristics of the electron analyzer: resolution and transmission

function also affect the Auger electron spectra. The standard spectra are recorded by use ofan CMA in the constant retarding ratio mode, where E/E is kept constant. The Auger sig-nal may be assumed to be proportional with Ip and Em for low values for Em (less than about2 V). The Auger signal varies with Ep, and since the standard spectra are recorded at 3 keVand 5 keV, it is recommended to use these energies for the primary beam. Relative Augersensitivities for the elements at primary beam energy Ep=3 keV are shown in Fig.2.6.

If the parameters of the actual electron analyzer used to record an Auger spectrum arethe same as the ones used in the standard Auger spectra, atomic concentrations on a surfacemay be estimated by using the standard spectra for the elements on the surface.

A quantitative analysis may be performed by use of elemental standards that aremounted in the measurement chamber. The atomic concentration Cx of a certain element xon the surface of a sample is then given by the peak-to-peak intensities of the Auger signals

Fig.2.6. Relative Auger sensitivities at Ep=3 keV (from Handbook of AugerElectron Spectroscopy)


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from the sample Ix and the elemental standard Ix,std in the following way:

This technique, although in principle very simple, requires several elemental standards andis usually not used in practice.

Usually a better method is to compare the observed Auger peaks to a Ag-standard(which is mounted in the vacuum chamber), and then used the Handbook of Auger Spec-troscopy to estimate relative atomic concentrations. The relative sensitivity Sx between anelement x and Ag may be obtained from:

where IxH

and IAgH

are the peak-to-peak amplitudes from the Handbook of elements x andAg. Kx is the handbook scale factor (KAg=1). A and B are the chemical formula indices ofcompound XAYB, and are used to obtain a lowest order correction for the density of X in theanalysis volume. The atomic concentration of element X is then given by:

where Ix is the peak-to-peak amplitude of the element x from the sample, IAg is the peak-to-peak amplitude from the Ag standard, and Dx is a relative scale factor between the spectrafor the sample and Ag. Dx=1 if the standard Ag spectrum and the sample were measuredusing the same settings for amplifier sensitivity Lx, modulation energy Em and primarybeam current Ip. If these parameters are different, then we get:

When a Ag standard is not used, the atomic concentration Cx may be expressed by thefollowing expression:

where the summation is over one peak per element and dx is the scale factor defined bydx=Lx Em,x Ip,x (dx=1 if amplifier sensitivity, modulation energy, and primary beam currentare kept constant). This last method where no standard samples are mounted in the vacuumchamber is perhaps the most widely used technique to perform quantitative Auger analysis.

It is important to be aware that the atomic concentration Cx is a measure of the inten-sity of emission from a given element, and that it does not correspond to the actual numberof atoms in the surface region of a sample. This is so because the structure of the topmostlayer is generally not known. For instance, Auger emission from atoms that are below the

CxIx

Ix std,---------------=

SxA B+

A--------------

IxH

Kx IAgH

------------------------=

CxIx

IAg Sx Dx -------------------------------=

DxLx Em x Ip x,,

LAg EmAg Ip Ag, ,---------------------------------------------------=

CxIx

Sx

dx

----------------= I

S

d

------------------


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outermost layer will be attenuated so that the number of atoms of a said element may beunderestimated. The morphology of a surface/interface has to be determined before theactual number of atoms of each element can be determined.

As an example of quantitative Auger analysis we will consider the spectrum in

Fig.2.7, which is from a stainless steel sample. Auger lines from Cr, Fe and Ni are visible in

the spectrum. For a quantitative analysis we pick out the major peak from each of the threeelements. Since all peaks are in the same spectrum (i.e. recorded using the same parametersof the electron gun and energy analyzer) the factor dx=1. The data has been recorded usinga primary beam energy of 3 keV. By using the lower formula on the previous page, we cansummarize the various parameters in Table.2.1.

The bulk concentration of this stainless steel alloy is reported to be 70.2% Fe, 20.5%Cr, and 9.3% Ni, which are close to what is determined from the Auger analysis from thesurface region of the sample.

Table 8: Auger analysis of a stainless steel sample

Auger peak Peak-to-peak intensity(arbitrary units)

Sensitivity factor(relative Ag)

Atomic concen-tration (%)

Fe (703 eV) 10.1 0.20 70

Cr (529 eV) 4.7 0.29 22

Ni (848 eV) 1.5 0.27 8

Fig.2.7. Auger electron spectrum from a stainless steel sample.


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2.3. Depth profiling

Most of the signal in Auger electron spectroscopy stems from the outermost couple ofatomic layer of a sample. However, by removing layer by layer by use of Ar-ion bombard-

ment, it is possible to investigate the composition of a sample as a function of distance fromsurface. This technique is referred to as depth-profiling measurements. However, whenusing this method one should bear in mind that the composition may be altered by the sput-tering process itself since various species in a sample may be removed at different rates. Inaddition, a possible tendency of surface segregation of one or more species may be present.

In Fig.2.8. is shown depth profiling data from a thin nichrome film on Si. Initially, the oxy-gen signal predominates, eventually, when the outermost layers of the sample has beenremoved, Si is the dominant element.

The depth resolution may be limited by sample inhomogeneities as well as uncer-tainty in the sputtering rate (the rate by which layers are removed from the surface). If forinstance the polycrystalline grains in a film is of size comparable to the film thickness, theobtained depth profile may depend on the area of the sample that was investigated.

Fig.2.8. Depth profiling measurements from a thin nichrome film on silicon (after

Czanderna, 1975)


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2.4. Scanning Auger microscopy

By varying the area of the sample that is being probed by the Auger spectrometer, it ispossible to perform a two-dimensional surface analysis. This is usually done by scanning a

fine-focussed electron beam over the surface. In this way it is possible to monitor a singleAuger peak from a specific element and thus obtaining a map of the atomic concentration ofthis element over the surface. An example of this is shown in Fig.2.9, which shows elementspecific pictures of the surface of an integrated circuit transistor. Bright areas on these

images correspond to a high concentration of the element in question. The recording timefor the images was one minute.

It is possible to perform a three-dimensional imaging of atomic concentration by com-bining scanning Auger and the depth profiling technique. This is shown in Fig.2.10.

Fig.2.9. Scanning Auger images of Si, O, P, and Au on an integrated circuit transistor (after

Czanderna, 1975)

Fig.2.10. Three-dimensional analysis combining scanning Auger and depth profiling (after

Czanderna, 1975)


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2.5. Spectator and participator Auger decay

Traditionally Auger electron spectroscopy has been performed using an incident elec-tron beam to core-excite the atoms. In recent years synchrotron radiation has to an increas-

ing extent been used in the study of decay of core holes. The great advantage by usingphotons instead of electrons is the fact that a pure dipole transition results, which in turnsimplifies the spectra. Let us consider the energy level diagrams shown in Fig.2.11. The

ground state is being perturbed by a photon of energy h that excites an electron into abound state of the system (molecule). The system is therefore not ionized by this excitation.Two different decay channels of the excited system is possible: (1) An electron in a lowerenergy level may decay into the deep core hole, while the initially excited electron remainsin its state. This is called spectator decay. (2) The electron that was initially excited maydecay into the core hole. This is called participator decay. In both cases a second elec-tron is ejected from the system in the Auger process. This electron may then be detected byan electron analyzer. The normal Auger process is obtained by using a higher energy forthe exciting radiation so that the system is core-ionized in the initial excitation.

Ground state Excited stateTwo-holefinal state

Single-holefinal state

h

Fig.2.11. Schematic representation of the decay of a core-excited state in participator and spec-

tator channels

Partic

ipatordecayS

pectato

rd

ecay


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Analysis of different decay channels in this way may lead to new insight of electronicstates in the ground state as well as in excited states of the system. Experimental data thatwere obtained for N2 in the gas phase is shown in Fig.2.12. The top curve (a) shows thenormal Auger decay following core ionization. Curves (b) and (c) show the decay of

the N 1s -> 3p and of the N 1s -> 3s Rydberg state excitation, respectively, and the bottomcurve (d) shows the decay of the N 1s -> 1g(*) excitation.

Fig.2.12. Electron emission spectra generated in the decay of various core excited states

of the N2 molecule (after Eberhardt et al., 1992)


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2.6. Auger vs. photon yield

A core excited atom has a certain probability of decaying by sending out a photon anda certain probability of decaying via electron emission. In the energy range of interest for

surface studies, a core hole has a large probability to decay by an Auger transition. Thedecay of a core hole is only dominated by photon emission when the core hole has a bindingenergy larger than around 10 keV. For the energy levels that are of most interest in surfacestudies, the Auger yield is usually larger than 95%.

The relative amount of Auger decay is shown in Fig.2.13 for core shells K (1s) and L3(2p3/2). The limit that can be reached by an excitation energy of 1.5 keV is marked byarrows.

Fig.2.13. Relative Auger yields as function of Z (after Park, 1985)


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XPS (X-ray photoelectron spectroscopy)19

3. XPS (X-ray photoelectron spectroscopy)

The technique of XPS was developed by Kai Siegbahn (Nobel Prize 1981) andcoworkers in Uppsala. Since the introduction soft X-ray synchrotron radiation sources,

photoelectron spectroscopy (of core levels) has reached a position as one of the major tech-niques for studying solids, surfaces and thin films. The method provides information on theatomic composition of a sample as well on the chemical states of the observed atoms.

3.1. Introduction

XPS is in principle a particularly simple process. Aphoton of energy h penetrates the surface, and isabsorbed by an electron with a binding energy of E1. Thiselectron is then emitted into the vacuum with a kinetic

energy: Ekin = h - EB - (Evac - EFermi). Therefore, in thesimplest approximation, the energy distribution of photo-electrons should correspond to the energy distribution ofelectron states in the solid surface. This picture is compli-cated in practice by the fact that the probabilities of thephoton being absorbed by all the electron states are not thesame. In addition, final state processes (e.g. plasmonexcitations, electron excitations and electron correlationeffects) complicates the simple picture further.

The advantage by using photons in exciting elec-trons lies in the fact that the resulting dipole transitionsare particular simple to interpret, as compared to electronexcited transitions where Coulomb interactions have to beconsidered.

The binding energies in XPS are measured withrespect to the Fermi level of the electron spectrometer. .The fermi level is determined to beat the point where the electron emission goes to zero. This point in the spectrum stays fixedindependent of sample measured, and the X-ray photoelectron spectrum may directly be

Evac

EFermi

E2

E1

Ekin

h

EB

Fig.3.1 Schematic view of XPS

Fig.3.2. Typical X-ray photoelectron spectrum


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recorded as function of binding energy. A typical XP-Spectrum is shown in Fig.3.2 Therelationship between the measured kinetic energy (in the electron energy analyzer) and theelectronic levels of the sample is shown in Fig.3.3. From the figure it is seen that the rele-vant work-function for determining the binding energy of a core level is the work-function

of the spectrometer rather than that of the sample itself. Since this is the case, the Fermilevel of the photoemission spectrum will appear at constant kinetic energy (independent ofthe sample) in the electron spectrometer (or analyzer).

In the same manner as distribution of kinetic energies give fingerprints of the ele-

ments in the periodic table in Auger electron spectroscopy, distribution of binding energiesgive fingerprints of the elements in XPS. A chart showing a summary of core level bindingenergies below 1100 eV is given in Fig.3.4. The lines that are sharpest and thus best suitedfor core level measurements are marked with thick solid lines.

The Handbook of X-ray Photoelectron Spectroscopy (by the Physical Electronicsdivision of Perkin Elmer) is a collection of standard XP-Spectra, and is useful in identifyingthe various elements on the surface of a sample, especially when using standard Al-K(h=1486 eV) or Mg-K (h=1254 eV) X-ray sources. Sensitivity factor for various core

Fig.3.3. Energy level diagram of the XPS experiment (after R.L. Park, 1985)


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levels (at these photon energies) are also tabulated in this handbook, and facilitates quantita-tive analysis of XPS. We will return to this point later, and will focus on the analysis of asingle substrate core level as changes are done to the surface system.

3.2. The photoemission process

The photoemission process involves a transition from an initial state i of wave func-tion i to a final statef of wave function f. This transition is induced by the photon fieldwith the associated vector potential A. The transition probability may be calculated by useof Fermis Golden Rule, which in the dipole approximation gives:

Where r is the dipole operator. In order to discuss the transition matrix element certainassumptions about the wave functions have to be made. The simplest approximation is toassume that the initial and final states may be described in terms of single electron wavefunctions. In addition, the final states involves a free electron of kinetic energy Ekin. Wecan then write the initial state wave function as a product of the orbital i,k from which theelectron was excited and which represents the N-1 remaining electrons (andthe index kindicates that electron k is not included):

Fig.3.4. Summary of core level binding energies below 1100 eV. The thick solid lines mark

the narrowest levels. (After N. Mrtensson, 1992)

w42

h--------- f |r i|

2 Ef E i h( )=

i Rk N 1( ),

i N( ) Ci k, i Rk N 1( ),= (where R means remaining)


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In a similar fashion the final state wave function may be written as:

Therefore the transition matrix element may be written as:

If the N-1 remaining electrons are unaltered by the photoemission process the final factor inthe above expression , and the transition matrix elementreduces to the simple expression that contains two one-electron wave functions:

This is often denoted the frozen orbital approximation. The photoemission experimentthen measures the Hartree-Fock energy of the orbital k: EB,k = - k, which is the Koop-mans binding energy.

However, this approximation is usually not very good since, after the excitation of theelectron from orbital k, the system will readjust the remaining N-1 electrons in such a wayto minimize its energy. This is called relaxation.

To account for relaxation we now assume that the final state of N-1 electrons has mexcited states and corresponding wave function: , and energy Em(N-1). Theexpression for the transition matrix element becomes:

where cm is given by:

Here |cm|2 is the probability that the removal of an electron in orbital k of the N-electron

ground state leaves the system in the excited state m of the N-1 electron system. Forstrongly correlated systems many of the cm are non-zero. In the photoemission spectrumthis means that for m=k one obtains the main photoemission peak, and for the other non-zero cm one gets satellite peaks. If electron-electron correlations are weak, the cm arezero for , and only the main photoemission peak results.

Frequently, in applications of photoelectron spectroscopy we do not have to considercorrelation satellites; however, such satellites play an important role in various areas in solidstate physics. Satellite peaks which stem from relaxation, shake-up (excitation to a boundstate) and shake-off (excitation to the continuum) processes are many-electron or many-body effects, and are in principle complicated to describe in a comprehensive way.

Since the photoemission process is very rapid (on a time scale of 10-16s) the systemhas usually not time to relax into an equilibrium state, and the process has to be described interms of the sudden approximation, i.e. the electron in the final state is in an excitedbound state of the system.

f N( ) Cf Ekinf Rk

N 1( ),,=

f |r i| f Eki n, |r i k,| f Rk N 1( ), i R,

k N 1( ) | =

f Rk N 1( ), i R,

k N 1( ) | 1=

f |r i| f Ekin, |r i k,| =

kf m N 1( ),

f |r i| f Eki n, |r i k,| cmm

=

cm f m,k N 1( ) i R,

k N 1( ) | =

m k and ck2, 1=


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3.3. X-ray satellites and ghost-lines

In XPS applications using standard Al or Mg anodes (non-monochromatized) one hasto account for the presence of X-ray satellites on the low-binding-energy side of each photo-

emission peak. The dominant X-ray satellite is the K3,4 emission which appears to about10 eV lower binding energy than the main peak, and has an intensity of about 8% of themain peak. The X-ray satellite structure for Mg is shown in Fig.3.5.

Other artifacts in XP-Spectra are so-called ghost lines which are present in photoe-mission spectra that are recorded by use of twin-anode X-ray sources. For example, when

using the Al anode, some electrons from the filament may hit the Mg anode, and low inten-sity Mg X-rays may be present along with the more intense Al X-rays. Therefore, some ofthe dominant peaks in the spectrum may also appear with low intensity, shifted by the dif-ference in photon energy between Al and Mg X-rays (1486-1254=232 eV).

Fig.3.5. X-ray satellites associated with the Mg K radiation (after Woodruff and Delchar,1994)


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3.4. Chemical shifts

One of the most important features of XPS is that the core-level positions depend onthe chemical state of the atoms. Changes in the local charge and potential of an atom cause

shifts in the core level binding energies. These shifts are called chemical shifts. By study-ing the chemical shifts one can thus obtain information on how the atoms are chemicallybound in a system. An example of this is shown in Fig.3.6. which show XP-Spectra fromtwo Viton polymers. Viton is a co-polymer of two types of monomers as shown in the fig-ure. In the binding energy range of the carbon 1s peaks near 285 eV binding energy, severalpeaks are resolved in the spectrum. The electronegative fluorine ligands have a pronounced

effect on the binding energies of the carbon core electrons. In the polymer chains there arecarbon atoms with zero to three fluorine ligands. Depending on the number of fluorineneighbors, the C 1s peaks are shifted by different amounts and each peak can thus be identi-

fied with one type of carbon atom in the structural formula. From the measured intensitiesof each peak it is straightforward to derive the relative concentrations of the two monomers.Observed chemical shifts may be used as a fingerprint technique to identify various

chemical states of the atom. It may also, however, be used to investigate electronic struc-ture of a system in a more fundamental way. In returning to the Viton polymers in Fig.3.5,the relative magnitudes of the core level shifts may be understood in terms of screening ofthe emitted photoelectron. Fluorine being an electronegative element, has the tendency toattract additional electronic charge, thereby leaving less charge on the carbon atom in thecase of CFn complexes. When an electron is photo-emitted from the C 1s core level, less

Fig.3.6. XP-Spectra from two Viton polymers (after N. Mrtensson, 1992)


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charge remains to screen the positive hole left on the C site. Therefore, the emitted electronis more attracted to the positive hole, and it emerges with a lower kinetic energy, i.e. with ashift to higher binding energy as compared to emission from pure carbon. The more Fneighbors of the C atom, the less charge on C, and the higher the binding energy of the

photo-emitted electrons. For CH2 more of the charge are localized to the C site, and thebinding energy is lower. In the case of graphite like C the core hole is experiencing an evenbetter screening, and therefore the binding energy is even less (the photoelectron has higherkinetic energy).

A chemical shift results from a change in the initial state (ground state) of the systemand is therefore referred to as an initial state effect. Chemical shifts in a spectrum from a

oxidized Al(111) crystal are shown in Fig.3.7. The peak labeled (f) corresponds to bulkAl2O3, whereas peaks (c) to (e) correspond to sub-oxides. Peaks (a) and (b) are from Alatoms in a metallic environments.

Fig.3.7. Photoemission spectrum from oxidized Al(111) (after Berg et al., 1993)


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3.5. Metallic screening and Born-Haber cycles

Screening is important in considering the photoemission process, and is particularlyeffective in a metal. When a core electron is photoemitted, a charge will flow from the con-

duction band to the ionized atom, to provide charge neutrality in the Wigner-Seitz cell.Therefore the final state corresponds to one where an extra conduction electron has been

added. A simple approximation to this state (with a core hole and an additional conductionelectron) is that of the Z+1 element (where Z is the atomic number). This is the Z+1approximation that have been successfully used in connection with core level spectroscopy

on metals. The final state in the photoemission process is equal (in this approximation) tothe ground state of the Z+1 element. This simplification can be used in connection withBorn-Haber cycles to calculate binding energy differences in photoemission.

A Born-Haber cycle for the core excitation of metallic atom is shown in Fig.3.9. Onthe left hand side of the figure we start with an atom Z in its metallic state. By adding thecohesive energy Ecoh

Z we obtain the atomic state. The Z-atom is then core ionized by theenergy EB

V(gas), which is the atomic core level binding energy (referenced to the vacuumlevel). Then the Z-atom is left in its core-ionized state Z* which is an ion with charge +e(denoted +1-ion). Then we neutralize the ion by adding an electron to a valence orbital,

which lowers the energy by IZ*

(which may be the first ionization potential). We are nowleft with the Z* atom. By subtracting the cohesive energy EcohZ*, we obtain a Z* atom in its

metallic state. The final term EimpZ*(Z) concerns the energy associated with embedding a

Z* atom (in its metallic state) in a Z metal. The binding energy of the core electron in themetallic state is then EB

F(met), which are then given by these other properties:

In the Z+1 approximation we can replace Z* by Z+1, and first ionization and cohesiveenergies can be taken from tabulated values for the Z+1 element. The last term ,

Fig.3.8. Construction of a primitive Wigner-Seitz cell shown in two-dimensions. All space

may be filled by these cells.

EBF met( ) Eco h

Z EBV gas( ) IZ

Ecoh

Z EZ

imp Z( )+ +=

EZ

imp Z( )


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which is the energy of implanting a Z+1 impurity in a Z matrix, is usually small and mayoften be neglected. However, in the case of calculating chemical shifts in alloys and inter-metallic compounds, this terms must be considered.

3.6. Surface core level shifts (SCLS)

Interactions with neighboring atoms are also important for atoms in a metal as regardsbinding energies of core levels in photoelectron spectroscopy. One particular example

regards the atoms at the surface, where surface to bulk core level shifts, denoted surfacecore level shifts (SCLS) are present for most elements. For transition metals the SCLS tendto be to higher binding energies as compared to the bulk emission for the earlier elements(less than half filled d-bands), and to lower binding energies for elements where the d-bandis more than half filled. This is schematically shown in Fig.3.10. Due to the lower coordi-nation at the surface a band narrowing is experienced. This is caused by the lower numberof atoms that hybridize to form a band. Since the d-band occupancy is mostly unchangedfor the surface atoms, and since Fermi levels align, the center of the d-band is shifted up(shifted down) in energy for d-band filling less than half (more than half). The core levels

Fig.3.9. Born-Haber cycle for the core excitation of an electron in a metal. The right hand

side of the figure shows the Z+1 approximation (after Johansson and Mrtensson,

1980)


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31/84


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Ta is one of the earlier 5d transition metals (less than half filled d-band) the SCLS is tohigher binding energy. The magnitude of the SCLS was determined to be about 0.35 eV inthis case. Tantalum has the BCC-structure and the (110)-surface is the closest packed ofthe low index surfaces, therefore the coordination number is larger than e.g. for the (100)-and (111)- surfaces, and consequently the surface-to-bulk core level shift is smaller.

Another example on a SCLS is show in Fig.3.13 for the (100)-surface of Rh, whichhas the FCC-structure. On a FCC-crystal the (111)-surface is the closest packed one, wherethe smallest SCLS is expected. The (110) surface is the most open surface, where thelargest SCLS is expected (since the coordination number and thus the cohesive energy is ata minimum). The SCLS was estimated at 0.62 eV for the Rh(100)-surface. Since Rh isnear the end of the 4d transition metal series, the SCLS is to lower binding energy (aspredicted from the above discussions of surface core level shifts).

2 5 2 4 2 3 2 2 2 1

o x i d e

J = 5 / 2

J = 7 / 2

b u l k

s u r f a c e

h = 1 2 0 e V

T a ( 1 1 0 ) , T a 4 f

IN

T

E

N

S

IT

Y

(a

rb

.units)

B I N D IN G E N E R G Y ( e V )

Fig.3.12. Tantalum 4f photoemission spectrum showing the SCLS (after Strisland et al., 1996)

Fig.3.13. Photoemission from Rh(100) showing the SCLS (after Borg et al., 1994)


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3.7. Core levels shifts in alloys

In the case of metal alloys core level shifts are harder to anticipate, as compared tochemical shifts where charge transfer from on atom to another may be assumed. In an alloy,

core level shifts may be in either direction depending on the nature of hybridization of con-duction electrons of the constituents in the alloy. Let us consider an AuSn alloy where onefrom electronegativity considerations would expect charge to be transferred from Sn to Au.Naively, one would then expect Au core levels to shift to lower binding energy because ofbetter screening of the core hole. This conclusion is however not correct, since hybridiza-tion of Sn and Au states leads to a reduction of d-character of the Au 5d band. Since con-duction electrons of d-character provide better screening than s- and p-electrons, the netresult is that a poorer screening of the core hole achieved, and therefore Au core levels shiftto higher binding energies (Watson and Perlman, Struct.Bonding 24, 83(1975)).

An example of core level shifts in alloys is shown in Fig.3.14, where the metal ceriumhas been deposited on top of palladium, silver and rhodium. In these cases interface alloys

have been shown to form. The core level shifts are quite different in the three cases. For Ceon Pd, the Pd core levels shift about 1 eV to higher binding energies, and for Ce on Ag theAg core level shifts are smaller in the same direction. For Ce on Rh, however, the Rh corelevels shift about 0.3 eV to lower binding energies. These shifts are related to hybridizationbetween 4d conduction states of Rh, Pd and Ag, and 4f and 5d states of Ce. It is evidentfrom the figure that large changes in core level shifts may be observed on systems that areexpected to have similar properties, like e.g. Rh, Pd and Ag that are neighbors in the peri-odic table. The presence of distinct core level shifts in metal overlayer systems may be

Fig.3.14. Shifts in Rh, Pd and Ag 3d core levels as Ce is deposited (after Berg et al, 1994)


34/84


taken as an indication that a surface or interface alloy has formed. However, the absence ofa shift may not necessarily mean that an alloying reaction has not taken place, since the corelevel shift may be close to zero.

In returning to the model of core level binding energies using Born-Haber cycles, we

note that the core level shift in an alloy may be expressed in terms of the implantation terms.For the pure metal Z we had the expression (using the Z+1 approximation):

where the final term is the energy associated with implanting a Z+1 metal in a Z matrix. Allother terms will be the same in an alloy A where Z is one of the constituents. An extraenergy term is required since the energy of implanting Z in the alloy A must be included:

The core level shift is then given by:

These implantation terms correspond to solution energies, which may in principle beobtained from thermochemical data, i.e. heat of formation data. These energies may also becalculated by using a semi-empirical scheme. It is important to note that there is a directconnection between core level shifts in metallic systems and thermochemical data.

EBF

met( ) EcohZ EB

Vgas( ) IZ 1+ Ecoh

Z 1+ E

Z 1+imp Z( )+ +=

EBF

Z A,( ) EimpZ

A( ) EcohZ EB

Vgas( ) IZ 1+ Eco h

Z 1+ E

Z 1+imp A( )+ + +=

E Z A,( ) EBF Z A,( ) EB

F met( ) EZ 1+imp A( ) EimpZ A( ) EZ 1+imp Z( )= =


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3.9. Satellites in core level spectra

Extra features are frequently observed in photoelectron spectra. Such features aredenoted satellite peaks and are most often found on the high binding energy side of a main

photoemission peak. In that case they are called shake-up satellites (if the excitations is intoa bound state) and shake-off satellites (if the excitation is into the continuum). Sometimes,in systems based on rare earths, structures to the low binding energy side of the main peakare observed. These peaks are referred to as shake-down satellites. All these satellites are

final state effects (in contrast to chemical shifts which results from initial state effects).Photoemission spectra from the 2p core of CuO and CuO2 are shown in Fig.3.16. A distinctshake-up satellite structure is seen in the case of CuO. A weak satellite structure is alsoseen in the Cu2O spectrum.

The spectra in Fig.3.16 may be qualitatively understood by considering that the Cu atom inCuO has a valency of +2 and in Cu

2O has a valency of +1:

Where L denotes a ligand orbital and L-1 indicates one less electron. In the case of Cu2Owe can write:

Since the 3d shell is filled, the possibility of a satellite excitation does not exist for Cu2O.Similarly, a shake-up satellite is present in the 2p core level spectrum of Ni from Ni metal.

Fig.3.16. Cu 2p photoelectron spectra from CuO and Cu2O(after Rosencwaig and Wertheim,

1973)

CuO Direct photoemission( ) 2p63d9L 1 2p53d9L e+;

CuO Shake up satellite( ) 2p63d9L 1 2p53d10L 1 e+;

Cu2O Direct photoemission( ) 2p63d

10L

1 2p53d

10L e+;


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The origin of this satellite is somewhat like the one in CuO,; however, the detailed under-standing is quite different. Nickel core level spectra are shown in Fig.3.17. In the case of

metallic Ni we can write for the photoemission process:

where the satellite structure results from d-d correlation in the final state. This satellite isobserved in Ni, but are not observed in the other 3d metals. This is due to the narrowing ofthe conduction band (and thus increased d-d correlation) towards the end of the 3d series. Areduced number of d-electrons leads to poorer screening of the core hole, and therefore thesatellite appears at the high binding energy side of the main peak.

Shake-down satellites are perhaps a little bit more exotic type of final state effect.They occur in metallic systems based on the early rare earths: La, Ce, Pr and Nd. They areassociated with the hybridization strength between conduction electrons and localized 4felectrons. Since the 4-d hybridization becomes weaker as we go along the rare earth series,

Fig.3.17. Core level photoemission from Ni, showing the 2p core satellite (after Hfner and

Wertheim, 1975)

main peak ( ) 2p63d91 2p53d92 e+

satel li te peak( ) 2p63d91 2p53d83 e+


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39/84


Shake-down satellites may be described in the following atomic picture:

where the number of conduction electrons m accounts for charge neutrality in the Wigner-Seitz cell. The lower binding energy of the shake-down satellite as compared to the mainpeak is caused by the improved screening of the core hole by the additional 4f electron inthe final state of the photoelectron process.

main peak( ) 3d

10

4f

n

ds[ ]

m

3d

9

4f

n

ds[ ]

m 1+

e+shake down satellite( ) 3d104fn ds[ ]m 3d94fn 1+ ds[ ]m e+

Fig.3.19. Shake-down satellites in the Ce(Pd1-xTx)3 system, T= Rh or Ag (after Raaen and

Parks, 1985)


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3.10.Line shapes in photoemission

A photoemission peak from a core level is usually assumed to be a convolution of aDoniach-Sunjic (DS) and a Gaussian function. The DS line shape is essentially an asym-

metric Lorentzian function, and it is a result from lifetime broadening of energy levels. Theasymmetry stems from electron-hole pair excitations at the fermi level. The functional formof the DS-function is:

where is the asymmetry parameter, is the gamma-function, and describes the width ofthe peak at position x0. Note that the expression reduces to a Lorentzian for =0. TheGaussian function results from phonon broadening (atomic vibrations), and the instrumental

resolution function is often assumed to be Gaussian. Finally, a disordered system, i.e. sev-eral non-equivalent atomic sites, may also result in a Gaussian broadening. When severalGaussian peaks are convoluted with each other, a new Gaussian results. The Gauss-functionis given by:

The following convolution:

then produce the function that should be fitted to a core level spectrum. Frequently, thewidth of a photoemission peak is measured in FWHM (full width at half maximum). For aLorentzian the FWHM = 2, and for a Gaussian the .

d x( )

1 ( ) 1 ( )x x0

------------

2-------+atancos

x x0( )2

2

+( )1 ( ) 2

----------------------------------------------------------------------------------------------------------------for 0=

= =2

x x0( )2

2

+-----------------------------

g x( ) 12

----------------- e

x x0( )2

22---------------------

=

F x( ) y( )g x y( )d yd

x

=

FWHM 2 2 2ln =

-2 -1 0 1

= 0.17 eV = 0.20 eV

Gaussian

Doniach-Sunjic(=0.1)

Convolution

Intensity(arb.units)

Binding Energy (eV)

Fig.3.20. Doniach-Sunjic and Gaussian line shapes, and the convolution of the two.


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photoemission intensity from the clean substrate, and a is the overlayer thickness.

This is the exponential curve which is plotted in Fig.3.22.However, in the regime from sub-monolayer to afew monolayers, it is necessary to consider thediscrete structure of the atomic layers. Let usnow consider the system in Fig.3.24, where thefirst atomic overlayer is shown. We denote thecoverage by , so that = 1 corresponds to onemonolayer. The intensity of the photoemissionfrom the substrate material may in this case be

written as:

where b is the thickness of an atomic layer. These expressions correspond to the dashedstraight lines in Fig.3.22, and describes layer by layer growth. Frequently, the simplifiedexponential expression is used when estimating overlayer thicknesses. Furthermore, we

have assumed normal emission in these expressions; if the emission is not normal to the sur-face, the expressions should be modified by lowering the mean free path by the factorcos, where is angle with the surface normal.

If two different photoemission peaks are to be compared we have to know the photo-ionization cross sections for the relevant peaks. The size of the cross sections depend on thephoton energy and are tabulated e.g. for Al and Mg K radiation. In addition, the depen-dence of kinetic energy of the electron analyzer has to be known. For instance, in the caseof a CHA (Concentric Hemispherical Analyzer) which is operated in the FAT (Fixed Ana-lyzer Transmission) mode, the intensity can be written as:

If we denote the photo-ionization cross section (at a given photon energy) by(h), the cor-rected core level intensity becomes:

Sometimes the dependence of the photoemission intensity on kinetic energy is included inthe cross section (in XPS tables for standard Al and Mg anode X-ray sources), which are

Isubstrate1--- I

0e

x xd

a

= I0 e a =

x

0b

Fig.3.24. Schematic model of layer by

layer growth

first atomic layer 0 1<


44/84


then called atomic sensitivity factors (ASF). Then we can write:

The intensities from different core level peaks depend on the topography in the sur-

face region in the sample. When considering a system where one material is deposited ontop of another, it is important to know what the growth mode is. Several possibilities exist:

(1) Layer by layer growth (Frank-Van der Merwe growth).(2) Clustering or islands formation (Volmer-Weber growth).(3) One or two monolayers followed by clustering (Stranski-Krastanov growth).(4) Intermixing and formation of an interface alloy.

By investigating the attenuation of a substrate peak as another material is deposited, it maybe possible to obtain some information as to the growth rate; however, since similar inten-sity profiles from quite different growth modes may be observed, additional information on

the topography near the surface is needed. One important observation in this respect maybe core level shifts in photoemission spectra.

IcorrImeasured

ASF---------------------=

Frank-Van der Merwe growth mode (layerby layer)

Volmer-Weber growth (clustering)

Stranski-Krastanov growth (one or twolayers followed by clustering)

Fig.3.25. Schematic picture of different overlayer growth modes

Interface alloy formation


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3.12.Inelastic background

In order to estimate the intensity of a core level peak (i.e., the area under the peak), the

background of inelastic scattered electrons has to be subtracted. A typical XP-Spectrum is

shown in Fig.3.26. An example of inelastic background is drawn in the figure. This type of

background is referred to as Shirley background, and is based on the assumption that the

intensity of inelastic scattered electrons at a given binding energy is proportional to the inte-

grated intensity of the photoemission peak (minus background) from the low binding

85 80 75 70 65

Pt 4f XPS (Al K)

In

tensity

(arb.units)

Binding Energy (eV)

Fig.3.26. Pt 4f XP-Spectrum showing a linear as well as a Shirley-type of background.

360 340 320 300 280

Pt 4d XPS (Al K)

Intensity

(arb.units)

Binding Energy (eV)

Fig.3.27. Pt 4d XP-Spectrum and linear and Shirley-type background of inelastic scat-

tered electrons.


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energy side of the peak to the given binding energy. This may be expressed as:

where E0 is at the low binding energy side of the photoemission peak. It is customary tostart with a approximate linear or polynomial background, and then iterate numerically toobtain an expression for the IBackground (i.e. the Shirley type background).

In reality, however, electron inelastic loss processes include plasmon and electronicexcitations that may contain detailed structure, which are not accounted for in the simpleprocedure described above. Therefore, the background in a photoemission spectrum maybe hard to estimate. For shallow core levels, where the background is relatively small, itmay suffice for most purposes to subtract a linear background (which may in certain cases

in fact be as good an approximation to the real background as the Shirley-type background).Linear backgrounds of inelastic scattered electrons are also plotted in Figs.3.26 and 3.27.

IBackground E( ) I E( ) IBackground E( ){ } Ed

E0

E


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gies (above ~1000 eV) is small for s=180 (i.e. backscattering is negligible). For lowerelectron energies (about ~100 eV) the backscattering amplitude may be substantial.

In referring to Fig.3.28, case (a) shows an adsorbed diatomic molecule on the surface.An electron is photoemitted from the atom that is indicated by an open circle, and is scat-tered in the forward direction by the outermost atom of the molecule. For high enough elec-

tron energies the probability of backscattering will be weak and the results is thereforeinterference between two electron beams from the surface. This interference dependsstrongly on the angle of emission from the surface. Since interference occurs if the phaseshift of the two beams is near zero, it follows that emission along the direction of the molec-ular axis of the adsorbed molecule will be strongest. This is shown in Fig.3.31 which showsa study of CO adsorption onto a Ni(110) surface. Electrons are excited from the C 1s levelat about 284 eV binding energy, and collected in the azimuth direction, Fig.3.30.

The Ni substrate is cooled to low temperatures.For low coverages of CO (see the bottom spec-

trum, 1 L = 10-6

storr) a strong intensity increasefor normal emission is observed. This indicatesthat the axis of the molecule is perpendicular tothe surface. For high coverages (the top spec-trum) two peaks at about angles +20 and -20appears. These peaks indicate that the CO mole-cules are now tilted with respect to the surfacenormal. For low and intermediate coveragesanother set of peaks are observed near an angle of

Fig.3.29. Normalized modulus of the elastic scattering factor for a Ni atom at various

electron energies (after Fadley, 1987)

Fig.3.30. Schematic view of the (110)

surface and the azi-

muthal direction.


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50, and these peaks shows that there are two different orientations for the CO molecules atlow coverages.

Two effects contribute to the formation of a peak in the forward scattering direction:First, as the angle is tilted away from the forward direction, the amplitude of the scatteringfactor decreases. Second, since the phase shift also becomes non-zero (i.e. a path lengthdifference occurs), the interference becomes more and more destructive. This is a particu-larly simple case of photoelectron diffraction data interpretation, which is not restricted to

adsorbed molecules, but is also applicable where the scatterer atoms is located above thephotoelectron emitting atoms. However, quantitative interpretation may be difficult due tothe fact that in general the sum of electron emissions from up to several different atomiclayers must be considered.

Another simple use of photoelectron diffraction may be in studies of growth modes.If we assume epitaxial growth, and that a single layer of atoms A form on top of a substrateof atoms B, it is evident that no forward scattering should be observed from electron emittedfrom the atoms of type A. However, if two or more layers of atom A are present, oneshould observe diffraction effects from the A atoms that are in the second or third layers.

Fig.3.31. Photoelectron diffraction measurements from CO on Ni(110) (after Wesner et al.,

1988)


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Therefore, photoelectron diffraction may be sensitive tool to separate e.g. Frank-Van derMerwe (layer by layer) and Volmer-Weber (clustering) growth modes.

The geometry shown in Fig.3.29 (b) may be used when studying an adsorbate atomthat is not too far above the top layer of substrate atoms. In order the achieve a large scatter-

ing factor, grazing angles have to be used (i.e. the scattering has to be in the forward direc-tion).

In order to enlarge the amplitude of the scattering factor it is possible to reduce theenergy of the emitted electron (by reducing the photon energy). For lower electron energies(< 200 eV) the scattering factor is substantially in the non-forward scattering directions, andthe geometry in Fig.3.29 (c) may be utilized. An example of such an experiment is shownin Fig.3.32 where Te and Na adatoms on Ni(100) have been studied. The electrons are

emitted from the Te 4d and Na 2p levels, respectively. The polar emission angle withrespect to the surface normal is 30. The outer points are raw data, and the inner curves areenhanced plots that are obtained by subtracting the minimum value from all points. In thisexperiment the photon source and electron analyzer are fixed in position, and the sample isrotated around the surface normal to vary the azimuthal angle. The angular anisotropy inthese plots result entirely from photoelectron diffraction effects.

Fig.3.32. Photoelectron diffraction measurements on the Te/Ni(100) and Na/Ni(100) systems

in the backscattering mode (after Woodruff et al., 1978)


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UPS (Ultraviolet photoelectron spectroscopy)49

4. UPS (Ultraviolet photoelectron spectroscopy)

Traditionally, the division between UPS and XPS was quite clear, since the ultravioletrare gas discharge lamps and the Al and Mg anode X-ray sources give rise to photon ener-

gies about 20-40 and 1254-1586 eV, respectively. The ultraviolet sources were used forvalence band photoemission and the X-ray sources were used for core level photoemission.In the last couple of decades, synchrotron radiation, which produce tunable photon energiesthat span the region in between the two types of standard laboratory sources, has reducedthe distinction between UPS and XPS. Here we will use the term UPS for valence bandphotoemission in the photon energy region below about 200 eV.

4.1. Introduction

UPS has several advantages as compared to XPS

when it comes to photoemission from valence states usingstandard laboratory sources. First, the energy resolution ishigh due to the small intrinsic width of the rare gas dis-charge lines. The intensity of the radiation is relativelylarge, and photo-ionization cross sections are generally rela-tively large for valence electrons. However, the UPS tech-nique has greatly benefited from synchrotron radiation, andtoday, a large portion of UPS measurements are performedat synchrotron radiation sources.

It is fair to say that UPS is the most powerfulexperimental tool in determining electronic band structure.This done by measuring the angle of emitted photoelectronsas well as their kinetic energies. Another powerful tech-nique is resonant photoemission in which the photon energydependence of photo-ionization cross sections is utilized toenhance and suppress emission from electronic states of dif-ferent character. In addition, UPS offers simple way ofdetermining the work function of a solid. Also, UPS isextremely sensitive to e.g. oxygen and carbon contamination

on a solid surface, in is therefore sometimes very useful inverifying sample cleanliness.

4.1. Angle resolved photoemission

A movable electron energy analyzer is usually used when recording angle resolvedspectra. Such an analyzer accept only electron in a small solid angle in order to measure theemission angle of the electrons. The whole electron energy analyzer is sitting inside thevacuum chamber and can move in the polar and azimuthal directions. The sensitivity is

Evac

EF

E2

E1

h Ekin

EB

UPS

EB=h - Ekin - (Evac-EF)

Fig.4.1. The UPS process


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small as compared to an XPS analyzer, but is usually sufficient for valence band photoemis-

sion. The geometry in an angular resolved photoelectron spectroscopy experiment is shownschematically in Fig.4.2.

The photoemission process must conserve energy and momentum. An electron in avalence band of a solid which is an infinite periodic lattice of atoms, does not belong to asingle atom. However, the reduced momentum or wavevector k is well defined. The samestate of the electron is reproduced by adding a reciprocal lattice vector G. This means thatthe energy and momentum can be conserved in the photoemission process in that the solidtakes up a recoil momentum of exactly one reciprocal lattice vector G. Due to the brokensymmetry at the surface the perpendicular component of the wavevector of the electron is

not conserved (a potential step exists at the surface). The conservation laws then becomes(as illustrated in Fig.4.3):

where Gs is a surface reciprocal lattice vector, f and i denotes final and initial states, respec-tively, and k|| is the component of the wavevector parallel to the surface. It follows from

h

Fig.4.2. Schematic view of angle resolved photoelectron spectroscopy

e -

Ef Ei h=

k f( )|| k i( ) Gs+||=

Electron

ener

gy

Wavevector

E

k

vacuum level

Ei

Ef

Fig.4.3. Schematic view of the photoemission process showing the transition between an initial

and final state (in the reduced zone scheme)

h

Ekin


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Fig.4.2 that we may write:

The final equality holds in the reduced zone scheme, which are shown in Fig.4.4 which

shows dispersion of a free electron, and an electron in a periodic potential for both extendedand reduced zone schemes. The photoemission process may thus be represented by a verti-cal arrow in the reduced zone scheme plot of the dispersion relation of the photoelectron.The perpendicular component of the wavevector in the initial state remains unknown,and its determination requires knowledge of the final state Ef(k). For photon energiesabove about 30 eV the photoelectron may be assumed to be free-electron-like to a goodapproximation. A free electron in an inner constant potential V0 may be written:

From the previous equations it then follows for the wavevectors:

The inner potential V0 is given as a sum of the work function w and the fermi energy EF:V0=w+EF. These equations may be combined to give Fig.4.5, which can be used to deter-

k f( )||2m

h2-------- Ekin sin k i( )||= =

k i( )

Fig.4.4. (a) Dispersion of a free electron and a photon. Dispersion of electron in a weak

periodic potential: (b) extended zone and (c) reduced zone scheme (after Plummer

and Eberhardt, 1982)

Ekinh2

2m-------- k2 V0=

k i( )2m

h2

-------- Eki n V0+2cos[ ]

1 2=

k i( )||2m

h2-------- Ekin sin=


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may be along the rod extending into the three-dimensional zone.

.

Fig.4.6. Surface and bulk Brillouin zones for a FCC-crystal and the (100) surface (after

Plummer and Eberhardt, 1982)

kx

Fig.4.7. Angle-resolved photoemission spectra and electronic band structure for GaAs(110)

assuming free-electron like final states (after Chiang et al., 1980)


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On the left hand side of Fig.4.7. are shown angle-resolved photoelectron spectra fromGaAs(110), and on the right hand side is shown the experimentally determined electronicband structure, assuming a free-electron like final state model.

At lower photon energies the parabolic band (free-electron like) becomes too crude an

approximation for the final state since the outgoing photoelectron feels the crystal potentialstrongly. Semi-empirical corrections have then to be applied to the bands, e.g. opening ofgaps. The critical points of final state bands can be determined directly from experiment.By varying the photon energy, transitions can be turned on across a band gap (see Fig.4.8).

Additional clues for critical points is extremal behavior of transition intensities, an extremalbehavior of initial energy, and disappearance of a energy splitting.

Ef

Ei

h

k

Fig.4.8. Transition between Ei

and Ef can be turned

on when the photon

energy h is largeenough


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4.3. Resonant photoemission

The photo-ionization cross section varies with photon energy. A particularly interest-ing effect as regarding variation in the cross sections is a quantum interference effect that

occurs in the solid state for transition metals and in the lanthanides and actinides. The reso-nances of the cerium 4f level and the uranium 5f level as a function of photon energies areshown in Fig.4.9.

These resonances may be explained in terms of the following atomic picture (for arare earth (n=1 for Ce): The first process is direct photoemission of an electron from a 4f

orbital. The first step of the second process requires the photon energy to be tuned to the4d4f excitation threshold. The middle state is an intermediate state that will decaythrough a super-Coster-Kronig process, and subsequently a final state results, that is identi-cal to the final state in the direct photoemission process. The resonance in the 4f cross-sec-tion occurs because of quantum interference between the two transition channels. This isfrequently referred to as a Fano-resonance. The intermediate state decays via an Auger

Fig.4.9. Emission from Ce 4f and U 5f levels as functions of photon energy (after Parks et al.,

1984)

4d10

4fn

ds[ ]m

4d10

4fn 1

ds[ ]m 1+

e+ direct photoemiss ion( )

4d10

4fn

ds[ ]m

4d9

4fn 1+

ds[ ]m

4d10

4fn 1

ds[ ]m 1+

e+ super Coster Kronig( )


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transition, in which one 4f electron ends up in the 4d core level, and another 4f electron isemitted into the vacuum.

The Fano-resonance energy for the lanthanides are in the photon energy region aboveabout 120 eV, where emission from transition metal conduction states are suppressed in the

vicinity of their Cooper-minima. Therefore, great use may be made by the Fano-resonancewhen studying rare earth intermetallic compounds and alloys where 4f and d states need tobe separated. In Fig.4.10 is shown a study of surface alloy formation between Ce and Cuwhere the Ce 4f emission has been separated from Cu 3d emission. Spectrum (A) is from

the pure Cu substrate, spectrum (B) is taken at the off-resonance energy of the Ce 4f statesat 112 eV, spectrum (C) is taken at the on-resonance energy of 122 eV, and spectrum (D)shows the difference curve (C)-(B), and shows the photoemission signal of 4f symmetry.

In systems with more than one 4f electron, the resonance spectra are not as simple asin the case of Ce, since f-f correlation effects result in splitting of the peaks in the constantinitial state (CIS) spectra. This is shown for two uranium compounds in Fig.4.9.

Similar resonance effects as in the lanthanides and actinides are also present in transi-tion metals, although to lesser extent. Valence band photoemission intensity from Ta asfunction of the photon energy, in the vicinity of the 5p5d excitation threshold, is shown in

Fig.4.10. Valence band photoelectron spectra from the Ce on Cu overlayer system, demon-

strating 4f resonance in Ce (after Braaten et al., 1989)


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Fig.4.11. The left hand side of the figure shows a Ta 5d photoelectron spectrum, and indi-

cates how the 5d band is divided for the intensity analysis which is shown in the right hand

side of the figure. The resonance process may in the case of a 5d transition metal beregarded in an atomic picture as quantum interference between two channels of identicalfinal states:

It should be noted that this is a solid state effect which is not present in the atomic case.

Fig.4.11. Valence band photoemission from Ta in vicinity of the 5p5d excitation threshold(after Raaen, 1990)

direct photoemission( ) 5p65dn h+ 5p65dn 1 e+

super Coster Kronig( ) 5p65dn h+ 5p55dn 1+ 5p65dn 1 e+


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4.4. Measuring the work function

The work function of a sample is simply given by subtracting the total width from thephoton energy: w = h-E. This is illustrated in Fig.4.11 where Sc has been deposited

onto a Al substrate. In referring to Fig.3.3 we note that the fermi level position in the pho-

toelectron spectrum is determined by the fermi level of the electron spectrometer. By bias-ing the sample at a small negative voltage, the energy levels of the sample will be lifted bythe biasing voltage as compared to the electron spectrometer. A change in the sample workfunction will therefore show up as a change in the low kinetic energy cut-off of the photo-electron spectrum. This is shown schematically in Fig.4.13.

When Sc (which is low work function element) is deposited onto Al the work functionof the system decreases (as shown in Fig.4.12), i.e. the low kinetic energy cut-off moves tohigher binding energy and the photoelectron spectrum becomes wider.

-20 -15 -10 -5 0

~8 Sc

~1 Sc

clean Al

UPS h = 21.2 eVSc on Al(111)

Inten

sity

(arb.units)

Binding Energy (eV)

Fig.4.11. UP Spectra from Sc deposition on Al, showing how a change in the work function may

be determined by monitoring the low kinetic energy cut-off (after Strisland, 1996)

EF

Evacuum

E Al Sc on Al

Fig.4.12. Showing schematically the change in work function when Sc is deposited on Al


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Evac

EFermi

E2

E1

Evac

EFermi

Sample Spectrometer

-eV

sample

spectrometer

Fig.4.13. Schematic energy level diagram showing how a negative voltage -V on the sample

lifts the energy levels so that the low kinetic energy cutoff may be measured by the

electron spectrometer, in order to determine the sample work function

Ekin h


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4.5. Exchange splitting

In a ferromagnetic sample the minority spin electrons (spin down) are sepa-rated from the majority spin electrons (spin up) by the ferromagnetic exchange split-

ting. Therefore electrons of different spins are separated from each other withoutactually measuring the spins of the photoelectrons. Valence band photoemissionspectra from Ni near the Curie temperature and below, are shown in Fig.4.14. It is

clearly seen that the splitting in the spectrum disappears abruptly at the Curie tem-perature, as would be expected from a ferromagnetic system.

The ferromagnetic exchange splitting depends on the symmetry of the elec-tronic states. This is shown in Fig.4.15 which shows two valence band spectra from

Fig.4.14. Valence band photoemission spectra from Ni showing ferromagnetic exchange

splitting of the minority and majority spin electrons (after Maetz et al., 1982)


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S-XAS (Soft X-ray absorption spectroscopy)62

5. S-XAS (Soft X-ray absorption spectroscopy)

Soft X-ray absorption is generally not as surface sensitive as several other electronspectroscopies. This is because the electrons that are detected are secondary electrons

which originates in typically the top ~50 of the surface layer. Since the X-rays penetratesdeep into the solid, the surface sensitivity is governed by the electron mean free path. Still,however, S-XAS has turned out to be an important tool in surface science investigations.

5.1. Introduction

The X-ray absorption process is shown schemati-cally in Fig.5.1. A photon is absorbed by an electron in acore level which is excited into an unoccupied state abovethe Fermi level. The final state in the absorption process

is therefore a neutral excited state.In order to observe the absorption process one has

to detect the electrons that are emitted from the solid whenthe excited state decays. The electron energy analyzermay collect a certain Auger decay at a given kineticenergy (surface sensitive) or the analyzer may be set tomeasure the intensity in the low kinetic energy tail of sec-ondary electrons (less surface sensitive).

The key assumption when doing soft X-ray absorp-

tion, is that the yield of electrons from the decay of theexcited state is proportional to the probability of excitingan electron from a core level to a given electron energylevel above the Fermi level. This assumption is mostly agood approximation, and the electron yield is then takenas a direct measure of the Soft X-ray absorption probabil-ity.

Several different methods are used when measuringthe electrons from the decay of the final state: (i) total yield, which means that no energyanalyzer is used, and that electrons of all kinetic energies are collected. They may be col-

lected by using a channeltron electron multiplier which is placed next to the sample, or bymonitoring changes in the sample to ground current. (ii) Partial yield where an electronenergy analyzer selects a narrow range of kinetic energies to be collected. (iii) Auger yield,where a single Auger line is measured. This is the surface sensitive mode of soft X-rayabsorption, where the probing depth is given by the kinetic energy of the Auger line.

Soft X-ray absorption requires the photon energy to be varied and thus requires theuse of synchrotron radiation. However, the detection system is simple, and the experimentis relatively simple to perform.

Evac

EF

E2

E1

S-XAS

Fig.5.1. Schematic figure of the

Soft X-ray Absorption

process

h


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S-XAS (Soft X-ray absorption spectroscopy)63

5.2. NEXAFS

The acronym NEXAFS (near-edge X-ray absorption fine structure) is used in connec-tion with studies of adsorbed molecules on crystal surfaces, where the polarized nature of

the synchrotron radiation is utilized, and is a very sensitive experimental tool in determiningmolecular orientations on crystal surfaces. Typical NEXAFS spectra are shown in Fig.5.2.NEXAFS really means XAS (X-ray

electron spectroscopy - theory

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