Vij D.R. Handbook of Applied Solid State Spectroscopy

Подождите немного. Документ загружается.

14.3 Resonant Inelastic X-Ray Scattering

Inspecting the denominator of this expression one realizes that the intensity

can increase very much near a core excitation edge. Also, one can notice that

cross terms appear by the squaring, since the summation over the intermediate

state is done for amplitudes rather than intensities. These cross terms

represent interference between different paths of the scattering when

degenerate intermediate states are present.

Dipole transition amplitudes for exciting and de-exciting intermediate core

states govern the intensity. In the time-independent, two-step model the

probability for scattering to a final state is the product of the probability for

exciting the intermediate states and the probability for de-excitation of those

intermediate states to the specific final state. This is an approximation, which

is not valid when the final states can be reached via several excitation paths.

Then, one cannot assume that one particular intermediate state is excited, and

instead the various channels interfere.

The two-step approximation is good, however, when one single

intermediate state dominates. It may be intuitively obvious that not much can

be said about the dynamics when only one path is involved: Only one thing

may (or may not) happen and there are no amplitudes to compare.

There is one conceptually simple but important aspect of the dynamics in

which the scattering process could be considered a three-step, rather than a

two-step process. In this language the intermediate state may undergo a

transition in the time interval between the excitation and the emission of the

soft X-ray photon, e.g., an electron or a phonon could be emitted or absorbed.

The rate for this transition can then be directly compared to the core hole

decay rate, and information about the time-development in the range of the

range.

The cross terms in the time-independent framework describe the

interference between the various excitation-emission paths. This interference

contains information about the dynamics in the scattering process. The

time-independent theory is successful in predicting experimental results, and

the mathematical description is relatively simple (at least in principle). There

seems to be little need for alternative descriptions. On the other hand, it has

been shown that a time-dependent framework equally well reproduces the

data. Mathematically such a treatment becomes more involved than time-

independent theory, but the advantage is that one can relate the observations

to the time development of the wave functions in a direct way. Thus, the time

development is not probed in the same way as in pump-probe experiments.

Instead, the duration time of the scattering process is used to get information

on the time development.

An interesting consequence of the notion that resonant X-ray emission is

essentially a photon-scattering process is that the lifetime broadening of the

intermediate core excited state does not lead to broadening in the scattering

core hole lifetime is achieved, i.e., in the femtosecond and sub-femtosecond

603

spectra. From traditional X-ray spectrometry one is used to observing a

resolution limitation corresponding to the short lifetime, for soft X-rays

typically 0.1–1 eV. In RIXS spectra, however, only the sharpness of the

excitation and the resolution of the recording instrument determine the detail

to which the final states can be studied. This has significant consequences for

the application of resonant X-ray emission spectroscopy.

The independence of the intermediate core state lifetime broadening on the

resolution of the RIXS spectrum is clearly demonstrated in a study of low-

222

mechanism of superconductivity was investigated [9]. The energies of the

lowest excitations in the Cu-based superconductors are basic quantities of

interest to determine the underlying electronic structure and elementary

a topic of debate. The study was carried out at the Cu 3p edge, i.e., M edge

spectrum, as shown in Figure 14.5. Incidentally, the study in question ruled

mechanism.

Figure 14.5 RIXS spectra of Sr

CuO

at the M

and M

edges. The observed features are

about 0.2 eV despite the 1.5 eV lifetime width of the M

2,3

hole state. Lower part shows

calculated spectra.

Strong dependence on excitation energy for valence band soft X-ray

emission in broad band materials was observed for crystalline silicon [10],

and an explanation was later found in the analysis of resonant X-ray emission

spectra of diamond [11]. The observations made for the resonant X-ray

emission of diamond that there is strong excitation energy dependence could

be explained in terms of RIXS with momentum conservation. It was

recognized that momentum conservation leads to restrictions for the

absorption-emission scattering process. The analysis demonstrated that RIXS

14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy

energy excitations in Sr CuO Cl , where the role of d d excitations for the

out the alleged importance of on-site dd excitations for the superconductivity

1.5 eV, it was possible to obtain 0.2 eV resolution in the resonant SXES

excitations, and among other things the local on-site dd excitations have been

RIXS, and although the natural lifetime width of the Cu 3p hole state is

604

14.4 Experimental Techniques

can be used as a photon-based, band-mapping technique, as a complement to

angular-resolved photoemission. This suggests a wide range of applications

and several attempts to apply the method to semi-conducting broad band

materials have been made [12]. For high symmetry points of the Brillouin

zone, band structure information has been extracted to a certain extent. The

feasibility of quantitative photon-based band structure mapping for TiC has

been demonstrated [13].

14.4 EXPERIMENTAL TECHNIQUES

In order to study details of valence electronic structure in soft X-ray emission

spectra one needs resolutions substantially better than 1 eV, and for the lower

energy range there is presently no alternative to using gratings as dispersive

elements. Bragg diffraction requires crystal periods of at least half the

wavelength and natural crystals are not available for practical use for softer

X-rays than oxygen K emission at about 500 eV. Artificial Bragg crystals are

available in the form of synthetic multilayer structures, but to date sufficient

resolution has not been obtained due to limited interface quality and number

of periods effectively used in the structures. Energy dispersive detectors offer

an efficient means for elemental analysis, but not for chemical analysis.

Detectors based on superconducting tunnel junctions offer the highest energy

resolution among energy dispersive detectors and they are constantly

improving. However, they are still not a feasible alternative for high

resolution spectroscopic work.

For harder X-rays than about 500 eV, natural Bragg crystals with

sufficiently large period exist. Bragg diffraction occurs at one particular

wavelength at a time for a specific angle of incidence, as opposed to grating

diffraction. For small sources, usually encountered for synchrotron radiation,

this gives grating diffraction an advantage when using spatially sensitive

detectors. For large sources (or virtual sources at off-Rowland geometry), on

the other hand, Bragg diffraction works with area detectors generating a

multichannel spectrum, each part of the source only contributing to one

specific wavelength.

14.4.1 Grating Spectrometers for Soft X-Ray Emission

The advancement in soft X-ray fluorescence spectroscopy is strongly linked

to the development of synchrotron radiation sources, although new grating

instrument concepts have also contributed. The basic optical and electronic

design of the first soft X-ray spectrometer [14] to be used with

monochromatized synchrotron radiation, briefly outlined below, was

605

subsequently adopted by a number of researchers in the field. This instrument

is based on the use of spherical gratings at Rowland mounting. Recently, other

schemes have been developed, e.g., designs that utilize plane gratings with

variable line spacing [15, 16, 17].

A grating for soft X-rays has to work at grazing incidence in order to

achieve total reflection, a necessity due to the low reflectivity at vacuum

wavelengths. The resolving power is determined by the number of grating

grooves that are coherently illuminated, and therefore one has to have a small

source or choose a substantial distance between source and grating,

alternatively to work at every grazing angle in order to attain high resolution.

This leads to a small angle of acceptance and, hence low efficiency of the

instrument. Increasing the groove frequency can obviously also offer higher

resolution, but only to a limit, as grating efficiency becomes strongly grating

period-dependent for high groove frequencies.

The energy resolution of a Rowland instrument, like the present one, is

wavelength-dependent, unlike its wavelength resolution, which is constant.

An instrument configured for high energy resolution at high energies may

therefore become unnecessarily long if low energies also need to be covered.

Therefore, in order to cover a large energy range, 50 – 1000 eV, the present

spherical grating spectrometer uses several individually blazed gratings of

different radii and ruling density in order to optimize the overall performance

of the instrument. The instrument is compact in order to allow it to be

mounted on a UHV chamber that can rotate around the synchrotron radiation

beam. This facilitates the use of the defined polarization properties of

synchrotron radiation. Since it is difficult to measure the polarization state of

the emitted X-rays one instead measures the anisotropy of the emission by

rotation of the spectrometer. Recently, one has designed beamlines that allow

full control of the polarization of the synchrotron radiation. This makes it

possible to perform polarized experiments without rotating the experiment

chamber.

Figure 14.6 shows the optical outline of the instrument. It consists of an

entrance slit, a movable and adjustable shutter for selecting grating and

illumination area, three gratings mounted fixed on a precision slab using

gauge pieces, and an area detector that can be moved in a three-axis

coordinate system (two translations and one rotation). The optical

arrangement follows Rowland geometry, and the concept can be seen as three

different Rowland spectrometers merged into each other such that they have a

common entrance slit. The different Rowland circles run relatively close to

each other so that a detector moving in a three-axis coordinate system can be

positioned and aligned to the focal curve of the grating in use. Gratings with

different ruling density as well as radii are mixed in order to accomplish

optimal performance. Illumination of a defined area of a particular grating is

done by the shutter. In this way no moving parts of crucial nature for the

14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy 606

14.4 Experimental Techniques

alignment of the instrument are necessary. Figure 14.7 shows the

spectrometer in a version that is presently marketed by Gammadata/Scienta

[18].

Figure 14.6 Outline of the compact Rowland multigrating spectrometer. Each grating defines a

Rowland circle that can be reached by the two-dimensional detector. The resolution is about

1000–3000, depending on energy range.

Figure 14.7 Photograph of flange mounted compact soft X-ray emission spectrometer [14].

The detector is based on multichannel plates, coated with CsI for enhanced

of the detector reduces the intensity loss due to escaping secondary electrons.

This is particularly important when multichannel plates are used for detection

at the grazing angle of incidence since the interstitial surfaces rather than the

channels will provide the effective photoemissive surface. It is estimated that

50 micron for a 20 mm long detector. A negative-potential electrode at the input

efficiency and resistive anode readout. The spatial resolution is 1/400, i.e.,

607

the overall efficiency of the detector is up to about 20% depending on photon

energy.

The requirements on synchrotron radiation beamlines suitable for high

resolution soft X-ray emission spectroscopy are high due to the low yield (low

fluorescence yield and limited instrument sensitivity). It is especially

important to be able to focus the excitation beam onto the sample. This is

nowadays quite feasible down to about 10 microns, and improved focusing

schemes suggest that it will be feasible to work with even smaller beam spots

on a routine basis in the near future at the fluxes required for soft X-ray

less and the sensitivity of spectrometers of the order of 10

–6

we require an

available incident flux on the sample of more than 10

photons per second to

get 100 cps count rate. “Available flux” means the flux on the sample that is

seen by the instrument. These requirements are fulfilled or nearly fulfilled

today at third generation synchrotron radiation sources, and one is witnessing

a continuous improvement. The upcoming linear accelerator-based photon

sources, notably the SASE-type free electron lasers are likely to provide new

and interesting scientific opportunities for soft X-ray emission spectroscopy,

not only because of the very much increased intensities but also because of

the ultrafast time structure and coherence properties.

14.4.2 Samples at Ambient Conditions

As already mentioned, soft X-ray fluorescence spectroscopy is essentially

bulk-sensitive owing to the finite photon attenuation length. The penetration

depth offers some special experimental opportunities not present in electron-

based spectroscopy since electron escape depths are typically two orders of

magnitude less than photon attenuation lengths. Apart from the obvious

advantage of relaxed requirements for ultrahigh vacuum and cleanliness, there

is the feasibility for studying buried structures since windows withstanding

atmospheric pressure can be used to separate the sample from the vacuum

system. This offers the possibility of studying many systems in situ,suchasa

solid exposed to an ambient gas or a liquid, or the gas or liquid itself.

New systems for soft X-ray emission studies of various systems of in situ

character, such as liquids, solids exposed to liquids or gases, and ultrathin

liquid layers on solids are under development in various laboratories. One

system built at Uppsala [18] consists of a dedicated manipulator that can host

one of two different sample heads. The manipulator provides movements and

rotation of the sample head, as well as electrical connections and transfer lines

for gases and liquids from the outside. The heads are of two different types.

14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy

emission work. Since fluorescence yields are typically of the order of 1% or

608

14.5 Applications

One is provided with a thin window that can be removed and transferred to a

preparation chamber under vacuum. This allows freshly deposited thin films

to be exposed to a gas or a liquid in the sample head. The other head has a

fixed window mounted at 0.1 mm distance from a removable substrate. The

substrate, which constitutes a quartz microbalance crystal (QCM), can be

removed under vacuum and transferred to a preparation chamber for sample

deposition. Mounted in position with a particular sample film, humidified air

(or any other gas or gas mixture) is flowed past the sample, and measurements

are performed in situ. In this way atmospheric corrosion can be studied under

realistic conditions.

The sample system lends itself to other kinds of studies, like liquids and

liquid mixtures and solutions, properties of materials in the presence of gases,

like hydrogen uptake, and valence electronic structure modification of battery

yttrium exposed to hydrogen at different pressures, soft X-ray absorption and

emission spectra revealed upon increasing H

pressure that a transition from

metallic state to insulator took place. This could be seen as a gap opening up

to about 2.5 eV in the compound soft X-ray emission/absorption spectrum.

The observation was in line with the fact that yttrium becomes transparent at

hydrogen exposure. The results indicate that H and Y states hybridize

strongly, causing breakdown of the rigid band model and redistribution of

electron states [20].

14.5 APPLICATIONS

14.5.1 Surfaces, Interfaces, and Thin Films

Soft X-ray fluorescence spectroscopy applied in different ways can be used to

obtain information about bulk properties as well as to study more surface-

related phenomena, depending on which type of excitation and geometry is

used. X-rays are absorbed in the sample and produce an exponential depth

distribution where the attenuation length depends solely on the material and

the X-ray energy. The attenuation length can be calculated from tabulated

values [5]. Depending on the energies of the exciting photon beam and the

fluorescence, the probe depth can vary from several nanometers at low X-ray

energies to hundreds of nanometers at higher energies. The angular variations

are strictly geometrical for near normal angles but since the refractive index

of materials for X-ray wavelengths is smaller than unity total external

reflection conditions can be reached where the incident radiation penetrates

only several nanometers into the sample. This is the basis for many analytical

electrodes upon cycling of Li ion batteries. In an in situ study of a thin film of

609

techniques where for example trace element analysis on surfaces is performed

with X-ray fluorescence.

In the case of studying an adsorbed overlayer of material different than the

substrate’s, like an absorbed layer of atoms or molecules, SXES can be used

even for submonolayer thicknesses. This is due to the fact that different

atomic species have well-separated X-ray energies. The introduction of SXES

as a tool for the study of surface adsorbates about a decade ago has already

contributed to considerable progress in terms of understanding the chemical

bonding of atoms and molecules on surfaces. The element selectivity of SXES

allows one to separate the spectral features pertaining to the adsorbate from

those of the substrate. In photoemission studies of atoms and molecules

adsorbed on transition metal surfaces, the valence band spectrum is often

quite dominated by the 3d density of states (DOS) of the metal. Figure 14.8

demonstrates this by showing photoemission spectra (UPS) of a Cu(100)

surface with and without a nitrogen overlayer, compared with an SXES

spectrum. In the UPS spectrum one observes some modification on each side

of the Cu 3d peak going to the adsorbate system. In the SXES spectrum, on

the other hand, the corresponding parts of the valence band appear as two

intense bands reflecting the N 2p distribution and the hybridization with the

Cu 3d electrons, respectively [21]. For a comprehensive review on the subject

of SXES studies of surface adsorbates we refer to a recent publication [22].

14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy

Figure 14.8 UV photoemission spectra of clean Cu respectively a c(2 2)N/Cu overlayer

system, together with a nitrogen K emission spectrum of the overlayer system.

610

14.5 Applications

In thin film applications, and particularly for in situ characterization,

electron beam-excited SXES has shown interesting potential [23, 24, 25]. An

approach to enhance the surface sensitivity of SXES has been to employ

grazing exit geometry to achieve a higher ratio of surface-to-bulk signal in

thin film growth applications. This can also increase the intensity due to

obvious geometrical effects of probing a larger surface area, thus the changes

in the film composition due to changes in the deposition process can be

detected more quickly with soft X-ray fluorescence spectroscopy.

The angular dependence of the emitted radiation is very large at small

angles as illustrated by Figure 14.9. The angular dependence of the emission

from three different layers in an iron (50 Å), copper (100 Å), and vanadium

(100 Å) multilayer structure has been measured. In the left panel two spectra

are shown, one recorded at grazing exit (2.5°) and one at a larger angle (20°).

There is a clear difference between them, in particular regarding the

intensities of the emission lines originating from different elements. The

identification of different emission lines is made, and some of the transitions

are recorded simultaneously in different order of diffraction. At grazing exit

almost all the intensity originates from the top iron layer, whereas at larger

exit angle, intensity from all three layers can be observed. The X-ray emission

peak of the silicon substrate falls outside the present window of the

spectrometer and is therefore not seen in the spectrum. The Cu L emission

that is dominant in the top spectrum has decreased more than an order of

magnitude by the change in exit angle.

Figure 14.9 Illustration of depth changes with the exit angle. Left: SXES spectrum of a

Fe 50 Å/Cu 100 Å/V 100 Å/Si sample at emission angles 20° and 2.5°. The labels represent

identified X-ray transitions. Right: Angular variation of the Fe, Cu, and V L

core-core

transitions. The solid lines represent simulated intensities. The intensities are normalized to the

intensity at exit angle of 20°.

Intensity (arb. units)

3x10

5 6

Emission energy (eV)

= 2.5°

Fe-L

Cu-L

V-L

O-K

V-L

Cu-L

Fe-L

Cu-L

= 20°

Intensity (arb. units)

(degrees)

Fe L

Cu L

V L

Fe 50Å / Cu 100Å / V 100 Å / Si

611

14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy

Intensity plots of the L

inner transitions of the metals as a function of the

emission angle are presented in Figure 14.9 (right panel). There are benefits

of using the core-core transitions as compared to using the valence transitions

in a study comparing experiments and calculations, since the scattering factors

are better determined for the former. The solid lines are simulated profiles

using tabulated optical constants and known layer thicknesses. The effect

observed originates from the difference in refractive index in the material and

in vacuum. At sufficiently low emission angles, below the total reflection

angle, the emission originates from a depth determined by the range of the

evanescent field, in this case about 5 (UPS) nm [26, 27, 28].

The determination of the chemistry and microscopic structure of carbon

nitride films is of considerable interest because of the scientific and

technological importance of such materials [29, 30, 31, 32, 33]. In resonant

soft X-ray fluorescence spectroscopy, core holes can be created in selected

atoms by tuning the excitation energy to a specific 1s to

 RU s to σ*

transition [34]. Nitrogen K emission spectra are shown in Figure 14.10. The

different excitation energies and calculated spectra (solid lines) from nitrile structures (N1),

pyridine-like N (N2), and graphite-like N (N3).

excitation levels correspond to those absorption resonances. The fact that N

Figure 14.10 Experimental N K emission spectra from the same sample, achieved using

612