Accepted Manuscript

Title: Energy loss structures in HAXPES spectra of solids

Author: Laszlo Kover

PII: S0368-2048(13)00055-8DOI: http://dx.doi.org/doi:10.1016/j.elspec.2013.04.002Reference: ELSPEC 46119

To appear in: Journal of Electron Spectroscopy and Related Phenomena

Received date: 21-12-2012Revised date: 26-2-2013Accepted date: 2-4-2013

Please cite this article as: L. Kover, Energy loss structures in HAXPES spectraof solids, Journal of Electron Spectroscopy and Related Phenomena (2013),http://dx.doi.org/10.1016/j.elspec.2013.04.002

This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.

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Highlights

Effects of electron scattering on HAXPES spectra of solids are discussed

Parameters and distributions characterizing electron transport in solids are summarized

The methods of describing transport of high energy photoelectrons in solids are reviewed

*Research Highlights

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Energy loss structures in HAXPES spectra of solids

László Kövér

Institute of Nuclear Research of the Hungarian Academy of Sciences (MTA

ATOMKI), 18/c Bem tér, H-4026 Debrecen, Hungary

E-mail: lkover@atomki.mta.hu

(received: )

Abstract

Energy loss processes of high energy electrons induced by hard X-rays are significantly

influencing the shape of the measured electron spectra, therefore the consideration and deeper

understanding of these processes is important for extracting information on electronic

structure or chemical composition of bulk or near surface region of solids using Hard X-ray

Photoelectron Spectroscopy (HAXPES). Beginning with fundamental concepts and

definitions, through discussion of models describing energy loss processes of energetic

electrons in the near surface regions of solids and finally discussing methods of corrections

for these processes turned to be useful when evaluating hard X-ray induced electron spectra,

this review intends to provide a brief summary on this field for users of the HAXPES method.

Introduction

Hard X-ray Photoelectron Spectroscopy (HAXPES) is quickly developing and is applied in a

widening range of fields nowadays. A number of recent reviews [1-4] appeared concerning

the progress of this method and its use in different types of studies and this volume contains

detailed reports on the latest developments of this technique and its applications, including

simulation of HAXPES spectra using the SESSA software package for their quantitative

interpretation [5]. The present paper tries i) to summarize the role and use of electron

scattering and electron energy loss (leading to energy loss structures) in HAXPES spectra,

comparing the parameters and distributions characterizing electron transport (electron

scattering and energy loss processes) in solids in the case of XPS and HAXPES spectra and ii)

to provide a brief overview on the methods useful for describing (or correcting for) effects of

electron transport in solids and when evaluating HAXPES spectra.

Electron transport processes in solids can distort the information carried by the emitted

electrons originating from physical processes taking place in the atomic core or in the

valence/conduction bands in solids. In order to obtain accurate electronic structure

information the distorting effects of electron scattering should be eliminated. On the other

hand, such effects of electron transport reflected in the HAXPES spectra, by themselves can

serve as important source of information on the electronic and physical structure of the solid

material studied. From a different aspect, by the nature and properties of the electron transport

processes involved, these processes can provide valuable and sensitive tools for revealing

materials systems’ structure in a nondestructive way, e. g. through the dependence of the

mean free paths of electrons for inelastic scattering on electron kinetic energy, especially in

the case of layered structures, or through the dependence of the information depth on the

angle of electron emission. For typical HAXPES experiments performed using tunable energy

synchrotron photon beams it is possible even to tune the photon energy to ensure the same

information depths for the photoelectrons and the Auger electrons selected for Auger

parameter measurements and when deriving Chemical Plots.

*Manuscript

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Energy loss of high kinetic energy electrons in solids: fundamental concepts and

definitions, electron transport parameters for HAXPES

For illustration of the significance and role of the energy loss structures in HAXPES spectra,

Fig. 1 a. shows the different energy loss structure of the C 1s spectra, excited from graphite

and diamond using 8 keV energy photons [6], in the proximity of the photoelectron peak. In

the case of graphite, the structure in the spectrum at about 5 eV energy loss (see the inset)

appears due to interband transitions, while in the case of diamond in the energy loss region

between the elastic peak and the 5.5 eV energy loss a deep minimum can be observed in the

intensity due to the band gap. At larger energy losses the intensity of the spectra approach the

same intensity level ac. Looking at Fig. 1b., where the plasmon structure in the electron

energy loss functions (obtained from fitting the experimental optical data to Drude – Lindhard

type oscillator functions) is shown for various – amorphous carbon, graphite, glassy carbon,

C60 fullerite and diamond - carbon allotropes [7], it becomes clear that the different energy

loss structures in the experimental C 1s spectra can be qualitatively interpreted on the basis of

the respective energy loss functions and most of the details of the structures can be

understood. Energy losses of photoinduced electrons are mostly attributed to extrinsic

excitations in electron transport processes, i. e. inelastic electron scattering within the solid or

near the surface, however, intrinsic excitation processes, such as the sudden creation of the

atomic core hole(s) during photoionization and Auger transition can also result in collective or

individual electron excitations and as a consequence, to energy loss of the photoinduced

electrons. It is difficult to observe experimentally the contributions of intrinsic excitations to

the energy loss part of the electron spectra, however, the observation of the contributions from

extrinsic excitations is feasible. In Fig. 2. the C 1s photoelectron spectrum, excited by 8 keV

energy photons from a diamond sample covered by a 52 nm thick Al overlayer is shown [8].

Due to multiple Al plasmon creation a series of plasmon loss satellites are present in the

spectrum. The first satellite peaks are more intense, than the (elastic) photopeak showing the

strong effect of extrinsic plasmon excitation in the Al overlayer by the C 1s photoelectrons

during their transport to the surface. Excitation of Al plasmons due to the sudden appearance

of the C 1s core hole upon photoionization is negligible here because of the large thickness of

the Al overlayer, therefore the experiment demonstrates the effects of the electron transport in

the Al film. The solid line shows the result of a model calculation (described in [8]) for

extrinsic plasmon excitation indicating a good agreement with the experimental data.

From these examples we can see that the energy loss function of the material is strongly

influencing the shape of the energy loss part of the HAXPES spectra. The energy loss

function ELF can be derived from the complex dielectric function (ω) of the solid in the

case of q = 0 :

(1)

where q is the momentum and is the energy transferred to the atoms and electrons of the

sample by the interacting electron. The real and imaginary parts of the complex dielectric

function can be expressed in terms of n(ω), the refraction index and k(ω), the absorption

coefficient of the material, both obtainable from optical experiments [9]:

(2)

(3)

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The ELF derived from (ω) is given by

(4)

and for nonzero momentum transfer, e. g. in the case of Penn’s model [10] assuming

quadratic dispersion

(5)

Near the surface of the solid electron energy losses caused by excitations of collective

electron density oscillations in the bulk and at the surface are possible. In the approximation

of Tung et al. [10] bulk excitations occur when the electron is moving inside the solid up to

the solid-vacuum interface while surface excitations of two dimensional electron density

oscillations take place when the electron is moving in the vacuum near the solid-vacuum

interface. For describing the probability that the electron with energy E moving in the bulk

material suffers an energy loss ω (atomic units are used) the Differential Inverse Inelastic

Mean Free Path (DIIMFP) is defined [11,13]

(6)

where due to the energy and momentum conservation (using the classical binary collision

model)

(7)

The mean free path λinel between two inelastic interactions of the electron with energy E

within the bulk solid (inelastic mean free path, IMFP) is obtained as

(8)

Fig. 3. shows the summary of the IMFP values as a function of electron energy (up to 30

keV), calculated for 41 elemental solids [12] using the simple Penn model [10] in the electron

energy range 330-30000 eV and the full Penn model [12] for electron energies below 330 eV,

illustrating the magnitude of the dependence of the IMFPs on the electron energy as well as

on the material of the solids.

The differential surface excitation probability (DSEP) s according to the Tung model [13] is

(9)

(10)

(11)

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where Ps means the differential probability of the surface excitation when the incoming or

outgoing electron crosses the surface at an angle α relative to the surface normal, qs the

momentum component transferred along the surface plane. The surface excitation probability

(SEP) s (E, α) is

(12)

i. e. the integral of the DSEP over all possible energy losses. It should be noted that compared

to the Tung’s model more accurate approximations are also available that are describing the

surface excitations inside the solid (as well as in the vacuum side part of the electron

trajectory) very close to the surface, accounting for the decrease in the probability of the bulk

excitations approaching the surface inside of the solid. Such models include the model

developed by Li et al. [14] and the dielectric response model developed by Yubero and

Tougaard [15] (an extensive comparison of the available models is given in the recent paper

of Salvat-Pujol and Werner [15a]).

In addition to inelastic scattering, the electrons can be scattered elastically on the screened

atomic nucleus, and as a consequence, change their momenta. The relation between the total

(σe) and differential (dσe/dΩ) cross section for elastic electron scattering describing these

processes is

(13)

where θ is the scattering angle and Ω is the solid angle. The mean free path between two large

momentum transfers or two large angle elastic scattering events is the transport mean free

path λtr of the electrons

(14)

where N is the atomic density of the solid.

The bulk energy loss functions can be derived from experimental optical data n(ω) and k(ω)

using e. g. the Tung model above. Fig. 4 a. shows the optical bulk energy loss function of Ge,

derived from experimental optical data, in comparison with the loss function obtained from

calculations using the Tung model [9]. Note the structure at about 32 eV energy loss,

appearing as a consequence of excitation of Ge 3d electrons.

The electron transport parameters described above can be determined from electron

backscattering experiments. Neglecting surface excitations and most effects of elastic electron

scattering, Tougaard and Chorkendorff proposed a formula for determining the ELF from a

REELS spectrum [16, 17]

(15)

where jl (E) is the measured REELS spectrum, K (E0, T= E0 – E) the probability for energy

loss T per unit pathlength and unit energy loss for the electron moving in the solid (bulk), L is

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the characteristic length of the pathlength distribution along the trajectory of the electron to

the surface. In the P1 approximation to the Boltzmann transport equation L~ 2λtr and because

of the strongly forward peaked cross section for elastic electron scattering (here λ stands for

λinel)

(16)

Accounting fully for effects of elastic scattering and surface excitations in REELS spectra,

Werner developed a procedure to retrieve the normalized DIIMFP and DSEP (both assumed

to be independent of electron energy) analyzing two REELS spectra for which the relative

contributions from surface and bulk electron scattering are sufficiently different, measured

using i. e. different primary electron energies or surface crossing angles [18]. In this

procedure applying the Monte Carlo method for simulating electron scattering in the solid, the

surface and bulk excitations are assumed to be uncorrelated and the normalized DIIMFP to be

independent of the angle of surface crossing and the electron energy. For illustration of the

application of this method, Fig. 4 b. shows electron energy loss spectra of Fe, measured using

500 eV and 2000 eV primary electron beam energies. The corresponding simulated spectra

(also shown in Fig. 4 b.) were obtained using the DIIMFP and DSEP distributions retrieved

(applying the method of Werner [18]) from the analysis of two experimental REELS spectra

measured using 1200 eV and 4000 eV energy primary beams [19]. It can be seen that the

DIIMFP and DSEP distributions derived from the pair of experimental REELS spectra yield

an accurate simulated REELS spectrum in the case when 2000 eV energy primary beam is

assumed, while for the simulated REELS spectrum assuming 500 eV energy primary beam,

slight deviations occur from the experimental data. The data presented in Fig. 5. support the

validity of the assumptions of the method of Werner [18] mentioned above. Pairs of REELS

spectra of Ag measured using different scattering geometries and primary beam energies 5

keV and 40 keV are compared [20] in the upper panels of Fig. 5. while in the lower part of the

Figure the DIIMFP (Wb) and DSEP (Ws) distributions derived from the corresponding pairs

of REELS spectra (measured in different geometries) [20] applying the method of Werner

[18].

The experimentally derived surface excitation probability can be seen in Fig. 6. for Au

(utilizing the DSEP derived from a pair of REELS spectra and Werner’s method) as a

function of electron energy [21], in comparison with fits to different formulae proposed by

Kwei et al. [22] (solid line) and Chen [23] (dashed line). The results presented in the Figure

demonstrate the strong decrease of the SEP with increasing electron energy and the excellent

agreement between the experimental data and the Kwei formula.

A simplified approximate version [24] of the Werner-method [18] for retrieval of DIIMFP

and DSEP from pairs of measured REELS spectra has been developed recently using the

Tougaard-Chorkendorff type (TC) ELF given by (15) derived from each of the two measured

spectra. Werner showed that the TC ELF is equivalent to the following expression [24]:

(17)

( denotes convolution here) where wb and ws correspond to the DIIMFP and DSEP,

respectively, αi,j partial intensities for electrons suffered energy losses in i bulk and j surface

inelastic scattering events and κ = L/(L+ λinel). From this expression it is clear that the TC ELF

is not a single scattering inelastic cross section, but it contains terms related to single bulk and

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single surface losses, as well as to a single bulk plus a single surface loss. Novák

demonstrated that in the case of Si the deviation of the TC ELF from the single scattering

inelastic cross section was significant for different scattering geometries and primary electron

energies [25]. In addition, the elastic electron scattering statistics plays a significant role in the

shape of the TC ELF through the partial intensities. For retrieving the DIIMFP and DSEP in a

simplified way from a pair of REELS spectra (y1 and y2) obtained using different energy

primary electrons, first the TC ELFs y1* and y2* are to be derived and then the DIIMFP and

DSEP can be determined with a good accuracy [24] from the equation

(18)

where the coefficients u10, u01 and u11 are (for both bulk and surface losses) simple functions

of the first bulk partial intensities α1 and β1 (partial intensity: total number of electrons in an

Auger, XPS or REELS electron spectrum, participating in a given number of inelastic

collisions in the sample before detected) [18, 27] as well as the respective incidence and

emission angles in the case of the two REELS spectra (the respective expressions for these

functions can be found in Ref. [24]). The corresponding partial intensities can be derived by

Monte Carlo simulation of electron scattering in the given solid. However, the recent

extension of the Oswald-Kasper-Gaukler (OKG) model for elastic electron scattering to

describe the inelastic electron scattering as well, makes it possible to derive these partial

intensities using simple analytical formulae without the need for any Monte Carlo simulations

[26]:

(19)

Here Cnb denotes the nth bulk partial intensity, Ωi and Ωo the directions of the incoming and

the outgoing scattered electron beam, respectively, μi/o =cosθi/o where θi/o is the angle of the

incident/scattered electron related to the surface normal. λe is the mean free path between two

elastic electron scattering events and Γne is the (ne – 1)st self-convolution of the corresponding

differential cross section for elastic scattering on the unit sphere (the angular distribution of

electrons following ne elastic collisions). Furthermore, here λt is the total mean free path of the

electrons, λt-1

= λe-1

+ λinel-1

. In the case of Au, the REELS partial intensities (as a function of

electron emission angle) obtained from Monte Carlo simulation and the Oswald-Kasper-

Gaukler (OKG) method are compared in Fig. 7., for different primary beam electron energies

and angles of incidence [26]. A good agreement between the partial intensities derived by the

OKG model and the MC simulation can be observed in the Figure and a criterion is given in

Ref. [26] for estimating the validity of the OKG model for a given material, experimental

geometry and kinetic energy of primary electrons.

The relationship between the energy loss functions (DIIMFP and DSEP) retrieved from the

experimental REELS spectra and the complex dielectric function can be obtained through

fitting of the theoretical expressions for the DIIMFP and DSEP (the Drude-Lorentz expansion

of the dielectric function, obeying the Kramers-Kronig dispersion relation and the screening

sum rule) to the corresponding experimental distributions [27]:

(20)

(21)

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Here ħω = T is the energy loss, ħq the momentum transfer, fi the oscillator strength, γi the

damping coefficient, ωi the energy of the ith oscillator, ω(q) = ωi + αq2/2 (if the quadratic

dispersion is used). The values of the Drude-Lorentz parameters obtained as a result of

minimizing the deviations between the experimental and model data can be used for

parametrization of the dielectric function. It should be emphasized that from the measurement

and analysis of the high energy backscattered (REELS and EPES) electron spectra the

dielectric function of the given material is obtained and therefore all important parameters and

probability distributions describing the electron transport processes reflected in HAXPES

spectra, can be derived. It should be noted here that in addition to obtaining the IMFPs on the

basis of eqn (8) above, the EPES method [28], based on accurate measurements of elastic

peak intensities in the backscattered electron spectra and on Monte Carlo simulation of

electron scattering in solids, is widely used for determining experimental IMFP data.

In quantitative analytical applications of HAXPES an important electron transport parameter

is the Effective Attenuation Length (EAL) [28] of the photoinduced electrons in solids,

usually determined experimentally from HAXPES spectra of overlayer-substrate systems.

Although this parameter depends on the experimental geometry, the overlayer thickness and

the initial angular distribution of the photo- or Auger electrons, this dependence in most cases

can be assumed to be weak in a wide range of emission angle or overlayer thickness and the

EAL (a parameter correcting the expressions for XPS and AES intensities - derived neglecting

elastic electron scattering [29]) accounts for effects of elastic electron scattering in the

material. Fig. 8. shows the EAL/IMFP ratio for Au, as a function of energy of photoelectrons,

up to 15 keV, comparing the measured data [30] to those derived from empirical formulae [4].

It can be seen from the Figure that the EAL approaches the IMFP as the electron energy is

increasing in the high energy range, indicating the weakening role of elastic scattering at these

energies. The agreement is quite reasonable between the experimental data and the data

estimated using the formulae proposed by Seah and Gilmore [31] (filled circles), Powell and

Jablonski [32] (filled squares), Kövér [4] (filled triangles, estimating the single scattering

albedo λinel/(λinel + λtr) - indicated in the equation of the Figure as ω – and using the formula

of Powell and Jablonski [29]) and Rubio-Zuazo and Castro [30] (filled, inverted triangles).

Using a grazing incidence photon beam for excitation, especially highly collimated

synchrotron radiation, HAXPES can ensure a high surface sensitivity in spite of the strongly

increased IMFP of the emitted electrons. Fig. 9. shows calculated attenuation lengths for 10

keV energy photons in Au, as a function of grazing angles of incidence [33]. Below the

critical angle for total external reflection the attenuation length of the photons determines the

information depth for HAXPES.

Modeling energy loss structures in HAXPES spectra and removal of effects of electron

scattering from HAXPES spectra

Using the electron transport parameters calculated or derived from electron backscattering

experiments as mentioned in the previous section, the lineshape of the HAXPES spectra,

including the energy loss structures can be modeled and the spectral contributions attributable

to the effects of electron transport can be identified, separated and removed from the spectra.

Interference between intrinsic and extrinsic excitations is significantly decreasing with

increasing electron energy [34, 35] and although the contribution from the interference terms

does not disappear completely [35], in the first approximation it is usually neglected. The

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application of the dielectric response model (that accounts for extrinsic, intrinsic, surface

excitations and interference effects and neglects effects of elastic electron scattering) for

modeling the intensities and lineshapes of XPS spectra is described in the recent review of

Tougaard [36]. This model needs the dielectric function of the material (obtainable from

optical data or from analysis of REELS spectra) as input and the software based on the

dielectric model is available [37]. In his two step QUASES model and software package [38]

for describing XPS lineshapes quantitatively Tougaard assumed that only bulk extrinsic

excitations take place during the transport of the photoelectrons up to the surface, neglecting

surface excitations. For analysis of XPS spectra the two- and three parameters universal cross

sections λinK(E,T) or the ELF derived from the REELS spectra using the Tougaard-

Chorkedorff formula (15) are proposed to be used in the QUASES model [36]. An alternative

method for modeling the shapes of electron spectra is the Partial Intensity Analysis (PIA)

method based on the assumption of the independence of the different type (bulk, intrinsic and

surface) excitations [27]. The details of the PIA method and the software package SESSA

[39] developed on the basis of PIA, is discussed in another paper of this volume [5].

For homogeneous solids, within the QUASES model (neglecting effects of surface excitations

and elastic electron scattering) the inherent shape (the “source function”) F(E) of the

photoelectron line is obtained as [40]

(22)

where J(E) is the measured spectrum, λi the IMFP, K(E’ – E) is the cross section for inelastic

electron scattering. Knowing K(E’ – E), F(E) can be retrieved from the measured XPS

spectrum. For homogeneous solids and isotropic emitters the PIA method leads to a similar

expression [41]:

(23)

where f0 (E) denotes the source function, Y(E) the measured photoelectron spectrum, w(T) the

energy loss distribution in a single inelastic collision and the q1 coefficient is coming from the

relation Ck = q1Ck-1 for the partial intensities Ck. Fig 10. shows Cu KLL Auger and 2s, 2p

photoelectron spectra excited from a thin Cu layer of ca 40 nm thickness using Cu X-rays (Cu

Kα and bremsstrahlung), following analyses of the spectra by the PIA and QUASES methods

[42]. It can be seen from the Figure that the source functions obtained using the QUASES (2

parameters universal cross section for inelastic scattering) and PIA methods agree well in

general, indicating that in these high energy electron spectra the extrinsic bulk excitations are

dominating [42]. The 2s photoelectron spectrum excited from Ge by 6 keV energy photons is

shown in Fig. 11. together with the lineshapes obtained following the removal of

contributions from bulk, surface and intrinsic excitations using the Partial Intensity Analysis

(PIA) method [43]. The contribution from intrinsic excitations is indicated (by dashed lines)

separately, showing that it is not negligible, contrary to the contribution from surface

excitations.

The influence of the initial (following photoionization) angular distribution of the

photoelectrons and the polarization of the photon beam used for excitation on the lineshape of

the HAXPES spectra can be significant [44]. In addition, especially for higher photoelectron

energies the non-dipole terms in the description of the atomic subshell photoionization cross

sections should also be considered. For example, for linearly polarized photons, the

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differential cross section for photoionization of the ith atomic subshell, dσi/dΩ is given as

[45]:

(24)

where σi is the total subshell photoionization cross section, Ω the solid angle, β the asymmetry

parameter of the angular distribution of the photoelectrons in the dipole approximation and θ

the polar angle between the direction of the momentum of the photoelectron and the

polarization vector of the polarized photon beam. Considering the first non-dipole term, the

differential subshell photoionization cross section given in eq. (24) changes to [45]

(25)

where Φ is the angle between the direction of the photon propagation and the projection of the

momentum of the photoelectron in the plane perpendicular to the polarization vector of the

photon beam, δ and γ are further asymmetry parameters describing non-dipole effects. Note

that in this case the differential cross section depends on both the polar and azimuthal angles.

During Monte Carlo simulation of the photoelectron lineshapes, for linearly polarized

photons in the above non-dipole approximation [44], the photoemission polar angle is

sampled using the probability density function g(θ)

(26)

and the azimuthal angle is sampled using the conditional probability density function f(Φ θ)

[44]

(27)

with

(28)

Fig. 12. shows the effects of photon beam polarization on the HAXPES lineshape in the case

of 1s photoelectron spectra excited from Si by 5 keV energy photons [44]. The data presented

in the Figure were obtained from Monte Carlo simulation of the photoelectron spectra using

dipole approximation (DA) for photoionization and accounting for non-dipole terms as well

(NDA). This clearly shows that the polarization of the photon beam and non-dipole effects

can cause significant modifications in the energy loss part of the spectra.

When the initial angular distribution is nearly isotropic for photoelectrons emitted from a

homogeneous semi-infinite sample (e.g., close to the magic scattering angle in XPS) the nth

reduced partial intensity (cn = Cn/C0 [27]) can be expressed as cn = κn [46] reflecting an

exponential path length distribution of the measured photoelectrons in the solid. κ is given by

[27,46]:

(29)

here μ = cos θ where θ is the polar angle of the detected electron relative to the surface

normal and ω = λinel/(λinel + λtr) the single scattering albedo. For such a case, simple

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approaches, like the Extended Hüfner model [9] – without Monte Carlo simulation – should

yield similar result as the PIA method [43]. Results of satisfactory accuracy are expected to be

obtained (without Monte Carlo simulation of electron scattering) by using the simplified

Werner method [24] (17, 18) and the OKG method [26] (19) to retrieve the DIIMFP and

DSEP from an analysis of a pair of REELS spectra and then applying the PIA formalism with

HAXPES partial intensities calculated e. g. using eq. (29) and assuming their exponential

dependence on n.

Surface excitations and intrinsic excitations due to the sudden appearance of the core hole can

cause energy losses of photoelectrons, reducing the intensity of the elastic HAXPES peak.

Pauly and Tougaard using the dielectric response model recently calculated the coefficient

accounting for this peak intensity reduction [47]. The coefficient is defined as the change of

the photoelectron emission probability due to the presence of the surface and the core hole,

compared to the case when the core hole is neglected and the electron travels the same

distance in an infinite medium. The result of their calculations for the combined effects of

surface and core hole (intrinsic) excitations shows that the reduction of the photopeak

intensities can be significant (35-53 %) and it is larger for oxides than for metals and

semiconductors [47].

Finally an example is given for the bulk sensitivity of HAXPES and for the importance of fine

details in the spectra that calls for high accuracy of the corrections for obtaining accurate

electronic structure information from the spectra. Fig. 13. shows Ti 2p photoelectron spectra

excited from an epitaxial anatase Co:TiO2 film, comparing HAXPES (with a photon energy of

7940 eV) and Soft X-ray PES (SX-PES, using a photon energy of 1200 eV) spectra [48]. Only

the HAXPES spectrum shows clearly the presence of metallic Ti3+

states in the bulk. The

hysteresis curve (inset) confirms the room-temperature ferromagnetism in the thin film [48].

In summary, energy loss structures in HAXPES spectra contain very useful information on

electronic structure and/or chemical composition of bulk, near surface or interface regions of

solids and the available methods and models, developed for the interpretation of these spectra

and based on the present level of understanding of electron scattering processes in solids

provide efficient tools for extracting this information.

References

[1] C.S. Fadley, Nucl. Instrum. Methods Phys. Res. A547 (2005) 24.

[2] K. Kobayashi, Nucl. Instrum. Methods Phys. Res. A601 (2008) 32.

[3] (a) C.S. Fadley, Nucl. Instrum. Methods Phys. Res. A 601 (2009) 8.;

(b) C.S. Fadley, J. Electron Spectrosc. Relat. Phenom. 178-179 (2010) 2.

[4] L. Kövér, J. Electron Spectrosc. Relat. Phenom. 178-179 (2010) 241.

[5] W. S. M. Werner, W. Smekal, T. Hisch and J. Himmelsbach, this volume.

[6] C. Kunz, B. C. C. Cowie, W. Drube, T.-L. Lee, S. Thiess, C. Wild and J. Zegenhagen, J.

Electron Spectrosc. and Relat. Phenom. 173 (2009) 29.

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[8] W. Drube, C. Kunz, K. Kobayashi, E. Ikenaga, J. Kim, M. Kobata, S. Ueda and T.

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[9] M. Novák, L. Kövér, S. Egri, I. Cserny, J. Tóth, D. Varga and W. Drube, J. Electron

Spectros. Relat. Phenom. 163 (2007) 7.

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[48] T. Ohtsuki, A. Chainani, R. Eguchi, M. Matsunami, Y, Takata, M. Taguchi, Y. Nishino,

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Rev. Lett. 106 (2011) 047602.

Figure captions

Fig. 1a. C 1s HAXPES spectra excited from graphite and diamond using 8 keV energy

photons [6]. The structure in the graphite spectrum at about 5 eV energy loss (see the inset)

appears due to interband transitions, while the deep minimum in the spectrum of between the

elastic peak and the 5.5 eV energy loss is due to the band gap.

Fig. 1b. The electron energy loss functions of carbon allotropes: amorphous carbon (dot),

graphite (dash), glassy carbon (dash dot), C60 fullerite (dash dot dot) and diamond (solid).

Calculated data from fitting the experimental (optical) data to Drude-Lindhard type oscillator

functions [7].

Fig. 2. The C 1s photoelectron spectrum of a diamond sample with a 52 nm thick Al

overlayer, excited by 8 keV energy photons [8]. The solid line shows the result of a model

calculation described in [8].

Fig. 3. Electron inelastic mean free paths (IMFPs) calculated for various elemental solids

using Penn’s algorithm [10], as a function of electron energy up to 30 keV [12].

Fig. 4 a. Optical bulk energy loss function of Ge, derived from experimental optical data, in

comparison with the loss function obtained from model calculations [9].

Fig. 4 b. Electron energy loss spectra of Fe, measured using 500 eV and 2000 eV primary

electron beam energies and simulated spectra obtained using the DIIMFP and DSEP

distributions retrieved (applying the method of Werner [18]) from the analysis of two

experimental REELS spectra measured using 1200 eV and 4000 eV energy primary beams

[19].

Fig. 5. Upper panels: pairs of REELS spectra of Ag measured using different scattering

geometries and primary beam energies of 5 keV and 40 keV [20]. Lower panels: DIIMFP

(Wb) and DSEP (Ws) derived from the corresponding pairs of REELS spectra (measured in

different geometries) using the bivariate method of Werner [18].

Fig. 6. Experimentally derived surface excitation probability for Au as a function of electron

energy, compared with fits to different formulae [21].

Fig. 7. Comparison of the REELS partial intensities as a function of electron emission angle

obtained by Monte Carlo simulation and the Oswald-Kasper-Gaukler (OKG) method, for

different primary beam electron energies and angles of incidence, in the case of Au [26].

Fig. 8. Ratio of the Effective Attenuation Length (EAL) to the IMFP for Au as a function of

photoelectron energy. Measured EAL/IMFP values [30] are compared to data derived from

empirical formulae [4, 30-32], see the text for more details. Here the single scattering albedo

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is ω = λinel/(λinel + λtr), ρ denotes the density of the material in g/cm3 and E the energy of the

electron (keV).

Fig. 9. Calculated attenuation lengths for 10 keV energy photons in Au, as a function of

grazing angles of incidence [33]. In the lower panel the mean depth of emission for the

induced photoelectrons is also indicated. This information is important for the Total

Reflection XPS (TRXPS).

Fig. 10. Cu KLL Auger and 2s, 2p photoelectron spectra excited from a thin Cu layer of ca

40 nm thickness using Cu X-rays (Cu Kα and bremsstrahlung), following analyses of the

spectra by the PIA (accounting for bulk, surface and intrinsic excitations) and QUASES

methods [42].

Fig. 11. 2s photoelectron spectrum excited from Ge by 6 keV energy photons and the resulted

lineshapes following the removal of contributions from bulk, surface and intrinsic excitations

using the Partial Intensity Analysis (PIA) method [43]. The contribution from intrinsic

excitations is indicated (by dashed line) separately.

Fig. 12. Effects of photon beam polarization in the case of 1s photoelectron spectra excited

from Si by 5 keV energy photons [44]. Data obtained from Monte Carlo simulation of the

photoelectron spectra using i) dipole approximation (DA) for photoionization and ii)

accounting for nondipole terms (NDA).

Fig. 13. Demonstration of the bulk sensitivity of HAXPES in the case of Ti 2p photoelectron

spectra excited from an epitaxial anatase Co:TiO2 film, comparing HAXPES (with a photon

energy of 7940 eV) and Soft X-ray PES (SX-PES, with a photon energy of 1200 eV) spectra.

The hysteresis curve (inset) confirms room-temperature ferromagnetism in the thin film

[48].

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Fig.1a.

Fig. 1b.

Figure

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Fig. 2.

Fig. 3.

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Fig. 4 a.

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Fig. 4 b.

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Fig. 5.

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Fig. 6.

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Fig. 7.

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Fig. 8.

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Fig- 9.

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Fig. 10.

Fig. 11.

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Fig. 12.

.

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Fig. 13.