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CHAPTER 14
SOFT X-RAY EMISSION AND RESONANT
INELASTIC X-RAY SCATTERING
SPECTROSCOPY
1
E.J. Nordgren, S.M. Butorin,
2
1
Uppsala University, Department of Physics, Uppsala, Sweden
2
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
14.1 INTRODUCTION
X-ray spectroscopy was a key technique to elucidate the atomic structure of
matter, starting in the early 20th century through the discovery of X-ray
diffraction and the observation that X-rays have characteristic energies for
different elements of the periodic system. Later, soft X-ray emission
spectroscopy offered an experimental basis for the exploration of the
electronic structure of solids. Over the years X-ray spectroscopy has been
widely used both for elemental analysis in various applications, and as a
method for basic research in physics and chemistry.
The introduction of synchrotron radiation, and in particular the subsequent
continued development of this kind of X-ray sources, has paved the way for
new applications of X-ray spectroscopy. Early on the availability of tunable
X-rays from synchrotron radiation storage rings promoted the field of X-ray
absorption spectroscopy to more general applicability. The notion that total
yield methods replicate X-ray absorption quite well meant that one had a new
and simple method at hand for many different kinds of samples. The use of
near edge fine structure in X-ray absorption (NEXAFS or XANES) to reveal
chemical states is widespread [1], and the use of extended features (EXAFS)
provides a standard technique today for determining bond lengths and local
order [2].
X-ray emission spectroscopy (XES) (often called fluorescence for photon-
in photon-out processes), with its low yield being more dependent on intense
sources, had to await the third generation synchrotron source development
before seeing a substantially increased interest and use. This was especially
true for soft X-ray emission where yields typically are in the 1% range [3].
X-ray emission possesses an inherent local character due to the
involvement of core electrons. For valence-core transitions (K
β
,L
β
, etc.) this
L.-C. Duda, and J.-H. Guo
means that direct probing of the valence band at a particular atomic species is
conducted. Furthermore, the transitions are governed by selection rules,
usually electric dipole rules that impose restrictions on the states involved.
This approach provides valuable selectivity with respect to orbital symmetry.
For molecules, it can be used to describe molecular orbitals in terms of atomic
composition (LCAO, linear combinations of molecular orbitals), and for
solids, partial densities of states can be used to describe the electronic
structure of the bands. In either picture, soft X-ray emission offers a means to
determine the weight of the respective components. For an overview of soft
X-ray emission for molecular applications, see, e.g., [4].
In addition to the local character and symmetry-probing capability of X-
ray emission the use of tunable synchrotron radiation provides a further means
of obtaining detailed information about the electronic structure and dynamics
of various systems. The tunability of synchrotron radiation facilitates
excitation at specific chemical sites of a compound, since electron-binding
energies differ between atoms in different chemical environments. The well-
defined polarization of synchrotron radiation can also be used to obtain
information on local order and orientation as well as magnetic state contrast.
Detuning from resonant excitation of X-ray emission provides a means to
obtain timing information in the sub-femtosecond range in an indirect way,
since the detuning leads to an effective shortening of the X-ray scattering
timescale.
Resonant X-ray emission (RXE) is a common term for describing emission
that is excited by monochromatized photons at a specific resonance. The
process is often seen as a two-step process where the first step is the X-ray
absorption and the second step is the emission. The absorption step offers
selectivity with respect to, for example, site, and the emission probes the local
electronic structure at the particular site selected. Usually emission spectra are
recorded at a number of different excitation energies and plotted together with
an X-ray absorption spectrum in which the energy positions of the various
excitations have been indicated.
It is important to note that in many cases resonant X-ray emission cannot
be treated in terms of two consecutive, disconnected steps: excitation and de-
excitation. Instead, one needs to regard the entire process as one scattering
process where the excitation and emission steps are interlinked. This is
because the cross-section for inelastic scattering (which is very small for soft
X-rays in nonresonant cases) can become very large at resonances, and this
has a number of important consequences. Resonant X-ray emission is
therefore often termed resonant inelastic X-ray scattering (RIXS) when the
inelastic scattering process becomes significant.
Applications of soft X-ray emission spectroscopy are found in many areas
of solid state physics and materials science, and the number of applications is
constantly growing. Many synchrotron radiation laboratories in the world
14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy 596
14.2 Properties of X-Ray Spectra
provide soft X-ray fluorescence beam lines, and there are a number of
laboratories that pursue soft X-ray emission using other means of excitation,
notably electron beams. The use of RIXS to study low energy excitations in
strongly correlated materials, compounds of transition metals and rare earths,
has become a widespread technique. The feasibility of investigating buried
structures owing to the finite penetration of soft X-rays compared to electrons
makes soft X-ray emission a powerful tool, also, for various in situ studies of
processes where the sample needs to be separated from the vacuum system by
a thin window. For instance, molecular properties of liquids and in situ studies
of chemical reactions are examples where the direct probing of the valence
band as offered by soft X-ray emission allows interesting studies to be made.
14.2 PROPERTIES OF X-RAY SPECTRA
Spectroscopy is one of the most powerful methods for studying matter at the
atomic level as it directly probes the atomic energy levels and the probability
for transitions between these levels. Valence band X-ray spectroscopy, and
soft X-ray spectroscopy in particular, involves both inner electron shells and
the outermost shell that hosts the weakly bound electrons, i.e., the electrons
that take direct part in chemical bonding between atoms and in transport
phenomena. Therefore, X-ray spectra can directly probe the chemically active
part of the electronic structure and provide partial density of states
distributions or molecular orbital compositions. The use of tunable excitation
as provided by synchrotron radiation yields a trivial but important feature,
namely the ability to separate the parts of spectra that originate in multiple
excitations (so called “satellites”). By tuning the excitation energy to just
above the threshold of the core-state in question, one quenches multiple
excitations by energy discrimination. This ability is important since spectral
features due to satellite transitions do not reflect density of states in the simple
manner that the main (diagram) spectra do.
Owing to the finite attenuation length of soft X-rays [5] probe depths of up
to several hundred nanometers can be attained. The bulk-probing capability of
X-ray spectroscopy is often a useful asset in materials research, since the
decisive structure for a certain property often lies buried at an interface or
below a capping layer. An example demonstrating the depth-probing
capability is shown in Figure 14.1. An ultrathin layer of silicon was buried at
10 nm depth in a gallium arsenide matrix, and it was investigated by means of
Si L-emission excited by synchrotron radiation. Three different samples were
studied, 1 monolayer (respectively 3 monolayers) of Si buried in GaAs, and,
as a reference, bulk Si. One observes clear differences between the spectra.
For the 1-monolayer (ML) case all Si atoms neighbor Ga or As atoms and
597
their states are found to mix strongly into the Si states, while for the 3-ML Si
layer, where 1/3 of the Si atoms have only Si atoms as nearest neighbor, this
effect is fairly small. This example demonstrates the feasibility to study
electronic structure and chemical bonding in buried structures, even for very
dilute samples [6].
Whereas X-ray spectroscopy can be used to probe bulk properties and
buried structures, photoemission spectroscopy is extremely surface-sensitive.
X-ray spectroscopy has a complementary relation to photoemission and Auger
electron emission spectroscopy, both in terms of probing capabilities and the
underlying atomic processes. The states involved in the different
spectroscopic methods are related, as illustrated in Figure 14.2.
Figure 14.1 Si L-emission spectra of 1- and 3-ML Si buried at 10 nm in GaAs, compared with
bulk Si L-emission. 120 eV photons were used for the excitation.
Figure 14.2 Schematic representation of UV and X-ray photoemission, and X-ray and Auger
emission spectroscopy.
14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy 598
14.2 Properties of X-Ray Spectra
X-ray photoemission, UV photoemission, X-ray emission, and Auger
emission are represented as diagrams in the figure. X-ray emission
spectroscopy (XPS) measures the binding energy of inner electrons,
identifying the emitting atomic element and yielding information about its
chemical environment. UV photoemission spectroscopy (UPS) measures the
valence band electronic structure (molecular orbitals or density of states
distribution), and, in particular, when pursued in angular resolved mode
(ARUPS or ARPES), it measures the band dispersion in periodic solids. Both
XPS and UPS end up in final states that are ionized, and the XPS final state
decays by either Auger electron emission or X-ray emission. As mentioned
earlier, for soft X-rays the Auger yield dominates by typically a factor of 100
over X-ray emission. Auger electron spectroscopy (AES) leads to doubly
ionized states, whereas in the XES case the transition takes place in the singly
ionized system. In XES one measures transitions between a core hole state
and a valence hole state, i.e., the two different types of states that are probed
by XPS (respectively UPS). One must not take this comparison too far,
though, since the XPS and UPS processes are prompt, whereas XES is a de-
excitation process following possible relaxation of the core hole. Therefore,
spectral shapes may deviate from those that could be inferred from results of
XPS and UPS measurements, respectively, depending on the lifetime of the
core state.
A different situation is encountered when the initial photon is absorbed
(RXES), and resonant Auger emission spectroscopy (RAES).Again,the
possibility for relaxation of the core excited state may affect the emission
spectrum, although, as we will see, one may control this time lag by detuning
the excitation energy in certain cases. Additionally, the UV photon absorption
process is associated with a parity change (one-photon transition), whereas the
X-ray emission decay of the XAS state implies a second parity change. Thus,
UV absorption (one-photon process) probes a different set of states than
resonant X-ray emission (two-photon process). Important examples of this are
the dd and ff excitations that are of importance for strongly correlated
systems, excitations that RXES (or RIXS) is able to probe but the UV
absorption technique is not able to examine. It is important to note that, in the
case of resonant X-ray emission, the transitions take place in the neutral
system, as opposed to traditional X-ray emission and photoemission or Auger
emission.
X-ray absorption (XAS), UV absorption (UAS), resonant X-ray emission
into a discrete state instead of leading to ionization. Figure 14.3 illustrates
599
Figure 14.3 Schematic representation of UV and X-ray absorption spectroscopy and resonant
X-ray emission and resonant Auger emission spectroscopy. The final result of the RXES
process is an excitation of a valence electron to an unoccupied state.
The inner electron binding energies are varying slightly depending on the
chemical environment of the atom, a property that is the basis for the ESCA
photoelectron spectroscopy method. In traditional (i.e., nonselective
excitation) soft X-ray emission atoms in nonequivalent sites (chemically
shifted) give rise to largely overlapping spectra, since generally valence band-
widths are larger than chemical shifts of the core states. Using monochromatic
synchrotron radiation for the excitation solves this problem. Tunable
synchrotron radiation allows selective excitation and one can single out a
specific atomic species at a particular site of a multi-element system for study
in X-ray emission. Therefore, the use of tunable synchrotron radiation for
excitation of X-ray emission takes the inherent element selectivity of normal
X-ray emission one step further, to chemical site selectivity.
One can achieve further selectivity by using the well-defined polarization
of synchrotron radiation in a way that creates contrast with respect to
alignment and local order of the sample. Note that the sample need not
possess global order since the quasi-alignment imposed by the propensity of
excitation of certain suitably aligned states is very long-lived in relation to
core-state lifetimes, and this applies even for gaseous samples (rotational
periods are in the picosecond range and core-state lifetimes are of
femtosecond order). It means, e.g., that a polycrystalline sample can be
preferentially excited to states that happen to be aligned in a suitable way. By
detecting emission at various directions with respect to the incident
polarization, the anisotropy of the emission can be used to reveal information
about the local order and state symmetries. In order to carry out experiments
like the ones described above one needs to have means to rotate the
spectrometer in the vertical plane, in addition to being able to independently
rotate the sample to achieve the desired excitation. This is a challenging task
14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy 600
14.2 Properties of X-Ray Spectra
for traditional designs of grating spectrometers, but with compact design it is
quite feasible. Recent developments in design of insertion devices for
synchrotron sources provide polarization state control of the emitted radiation.
Beamlines of this kind dispense with the need to rotate the spectrometer in
order to measure the anisotropy of the emission.
The site and polarization selectivity of resonant soft X-ray emission
spectroscopy is clearly demonstrated by an investigation of the oxygen K-
emission spectra of polycrystalline La
2–x
Sr
x
CuO
4
(x = 0.07) recorded at
different excitation energies across the oxygen 1s absorption edge. Significant
variations in the spectral shape are observed. When the excitation energy is
spectrum, the emission spectrum is wide and exhibits a double-structure
profile with the main maximum at ~ 526.4 eV and an intense shoulder on the
low-energy side. For 532.8 eV-photon excitation, the spectrum becomes a
narrow and nearly symmetric line with a maximum at ~525.5 eV.
The origin of these changes is a large difference in the occupied oxygen
2p density of states (DOS) between in-plane oxygen O(1) and apical oxygen
changes in the local electronic structure at the inequivalent O sites can be
probed separately by tuning the excitation energy to the respective resonance.
The present resonant X-ray emission data support predominant creation of
electronic holes by Sr doping on O(1) atoms. Furthermore, by making use of
polarized excitation and detection of emission anisotropy, further information
can be obtained, as it allows distinguishing between the O 2p-orbital
Traditional X-ray emission is governed by Fermi’s golden rule, i.e., the
transition probability is determined by the square of the matrix element over
the dipole operator between the core state and the final valence state. The core
ionized state has no memory of the excitation and only the population of the
core state matters with regard to the excitation. Since the matrix element is
nonzero only if parity is changed by unity in the transition, owing to the
dipole selection rules, the X-ray intensity distribution will provide a partial
density of state distribution pertaining to the symmetry of the intermediate
hole state, i.e., p partial DOS for s holes, s and d DOS for p holes, and so
forth. Similarly, for a molecular system the X-ray intensity will measure the
weight of local, symmetry-allowed atomic orbitals in a MO-LCAO expansion.
emission of superconducting cuprates [7]. Figure 14.4 displays the oxygen K-
the inequivalent oxygen sites across the K edge. This demonstrates that the
set to a doping-induced pre-edge peak at 528.5 eV in the X-ray absorption
O(2) atoms together with variations in X-ray absorption cross-section for
components.
601
Figure 14.4 By tuning the excitation to certain features in the XAS spectrum one can separate
the contributions from different oxygen sites in the X-ray emission. Also, by detecting
anisotropy one can determine the orbital components of the doping-induced oxygen 2p states.
14.3 RESONANT INELASTIC X-RAY SCATTERING
When excitation of X-ray emission is resonant we can no longer assume that
the intermediate core excited state does not carry any memory of the
excitation. On the contrary, the memory of the excitation can be very strong,
and the entire process has to be treated in the more general framework of
inelastic scattering. In this view the incident photon is inelastically scattered
cross-section for such processes at soft X-ray energies can be very much
enhanced near core-state edges, as seen in the Kramers-Heisenberg formula
governing this kind of process [8]:
()
()
2
mf
inc n g
n
f| |n n| |g
()~
2
IE
i
EEE
∑
∑
Γ
−−+
DD
I(E
m
) is the resonantly scattered intensity distribution. The ground state is
represented by g, the intermediate core state by n, and the final state by f. D is
the dipole operator. E
inc
is the incident photon energy, and E
n
and E
g
are the
energies of the intermediate and ground state, respectively. Γ stands for the
lifetime width of the intermediate core excited state.
14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy
leaving behind a low energy valence excitation. The normally very small
602