Vij D.R. Handbook of Applied Solid State Spectroscopy

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14.5 Applications

Figure 14.24 Circular dichroism of the specular reflection at the Fe L-resonances from a thin

difference spectrum (MCD).

14.5.3.5 Nitrides

Group III nitrides are wide band-gap semiconductor materials which are of

considerable technological interest. The range of the band gaps in InN, GaN,

AlN is 1.9–6.2 eV, which corresponds to photon energies covering the entire

visible to ultraviolet parts of the electromagnetic spectrum. Therefore,

knowledge of the electronic structure of valence and conduction bands of

these materials is of great importance. Compared to photoemission

spectroscopy (PES), which is a common method used to study the valence

states of materials, SXES has the advantage of directly probing the bulk

material. SXES is less prone to suffer from surface-related ambiguities in the

interpretation than the highly surface-sensitive PES, especially since cleaning

procedures can be time-consuming and intricate.

Combined SXAS and SXES studies of pure GaN [97] and the alloy system

1–x

N [98] showed early on how valuable information about the

electronic structure can be extracted. Due to the atomic and orbital sensitivity

of either methods the spectra can be interpreted as partial occupied (SXES,

Figure 14.25) or unoccupied (SXAS, Figure 14.26) DOS. By plotting the

onset of the high energy edge of the N K-emission spectrum and the low

energy onset of the N K-absorption spectrum, one can extract information on

the band gap behavior as a function of the relative concentration of Al and Ga

in the Al

1–x

N system, and it was found that the band gap essentially has a

linear dependence with no detectable band bowing. Hybridization effects

allow the determination of binding energies of important shallow core-level

iron film. The top spectra are the raw data and the bottom spectrum is the corresponding

633

states such as Ga 3d-states, which are found some 19 eV below the top of the

valence band maximum of Al

independent of the Al concentration

(Figure 14.27). Similar hybridization features were investigated recently in

1-x

N [99] as well as post-transition metal oxides [100]. Polarization-

dependent SXAS is expected to show a strongly anisotropic behavior of the

bonding in single crystalline nitride films.

x 1–x

N of different Al concentrations x shown on a scale

relative to the valence band maximum. Six different Al concentrations (x = 0 –1) are compared.

Dashed lines indicate the approximate extent of the N 2p-band and emphasize the movement of

the top of the valence band as a function of Al concentration.

Figure 14.26 N K-absorption of Al

1–x

N of different Al concentrations x. Spectra for 6

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

14.25 N K-emission of Al Ga

Figure

different Al concentrations (x = 0 7) are compared (with vertical offset).

–

634

14.5 Applications

Figure 14.27 Blown-up view of the N K-emission of Al

1–x

N of different Al concentrations

x shown on a scale relative to the valence band maximum. The elastic peak contribution and

the Ga 3d-hybridization peak at 19 eV below the VBM are marked.

14.5.3.6 Lanthanides

When the symmetry in a solid is not spherical, the angular momentum of f

However, the crystal field is an order of magnitude smaller than the spin-orbit

splitting and can be treated as a perturbation. In the case of weak

hybridization effects, the interlevel coupling and consequently J-mixing in the

ground state of the system are often disregarded in the interpretation of

experimental data by the application of a pure atomic approximation (mainly

for high-energy spectroscopies) or by using a first-order crystal field theory

where the crystal field interaction is assumed to act only within the separate J

the ground state J-mixing directly from the data. For example, the estimation

of the J-mixing degree in high order crystal field theory by adjusting the

originating from difficulties in calculating the intensities of dipole-forbidden

electron-energy-loss spectra [101, 102] may result in a large uncertainty

manifolds. This is partly due to complications in extracting information about

crystal field parameters from the fit of optical absorption or low energy

Since the nature of the ground state defines various physical properties of a

system, knowing the ground state character is a key issue, especially in

technique can provide information about J-mixing in the ground state through

studies of intra-atomic fof excitations.

electrons is not conserved, and therefore J is not a good quantum number.

635

materials science. It turns out that for rare earth compounds the RIXS

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

transitions. In turn, the possible influence of the weak metal-ligand

hybridization is difficult to analyze quantitatively in the absence of so-called

charge transfer satellites in high energy spectroscopic data.

In this situation, the use of alternative spectroscopic means to obtain

showed that this mixing could be studied by taking advantage of dichroic

properties of rare earth 3d X-ray absorption. However, the method is limited

to magnetically ordered systems. Here, we discuss the potential of resonant X-

ray scattering spectroscopy in studying of the ground-state J-mixing when

applied to compounds without distinct, long-range, magnetic order and

significant metal-ligand hybridization.

Similar to optical absorption and electron-energy-loss spectroscopy with

respect to probing the optical scale excitations, RIXS at the same time

provides an additional level of the transition selectivity due to the element

specificity and dipole selection rules. In contrast to systems with strong metal-

ligand hybridization where the charge-transfer process leads to appearance of

intense lines in RIXS spectra as a result of interionic excitations, J-mixing in

systems with weak hybridization effects is expected to manifest itself in an

intensity gain of some intra-ionic (fof) transitions which are disallowed for

the pure Hund rule ground state. In other words, transitions with 'J other than

0, r1, and r2 are probed in the resonant excitation-deexcitation process.

Although J is not a good quantum number in the J-mixing case, we use this

terminology for simplicity.

A discussion about the RIXS potential to probe the ground state J-mixing

is based on the analysis of data obtained at the Dy 4d threshold of DyF

room temperature. Measurements at the 4d threshold of rare earths provide

naturally higher resolution than those at the 3d threshold, thus allowing one to

study elementary excitations in greater detail (see, e.g., [104]). Experimental

spectra of DyF

are displayed in Figures 14.28 and 14.29 on, respectively,

photon-energy and energy-loss scales. Two distinct groups of pronounced

inelastic-scattering peaks are observed in these spectra. The first group is dis-

tinguished by small energy losses on the tail of the elastic line, whereas the

second is characterized by energy losses of more than 2.5 eV. When the

excitation approaches the energy of the main broad maximum of the Dy 4d

absorption edge, the first group still possesses significant intensity while the

structures of the second group become relatively faint. Regarding the energy

scale on which the spectral variations occur, the observed transitions can be

attributed to intra-ionic fof excitations. The energy gap between two groups

of inelastic X-ray scattering structures reflects the separation between sextets

and quartets of trivalent Dy [106, 107], which can be reached due to the

excitation-deexcitation process.

636

ground state J-mixing information is essential. Recently, Finazzi et al. [103]

14.5 Applications

Indeed, the overall spectral shapes and their behavior with varying

excitation energies are reasonably well-reproduced by atomic multiplet

calculations for the Dy

ion [108]. The results of calculations show that the

dominant elastic peak in all of the RIXS spectra of DyF

is to a large extent a

consequence of strong interference effects in the intermediate state of the

coherent second-order optical process. The states constituting the main 4d

absorption edge have a lifetime broadening of about 2 eV largely because of

Figure 14.28 The total electron yield spectrum at the Dy 4d edge and resonant X-ray scattering

spectra of DyF

normalized to the incident photon flux [105]. The letters correspond to the

excitation energies indicated in the absorption spectrum.

Normalized intensity

165

160

155

150

145

Photon energy [eV]

DyF

x0.8

x0.6

x0.7

x0.8

the 4d-4f4f Coster-Koenig decay.

637

However, a close inspection of experimental RIXS spectra shows that

the pure atomic approximation. Thus, the feature with the energy loss of about

1.17 eV is observed in spectra h, k,andl, presented in detail in Figure 14.29.

While atomic multiplet theory predicts the nonzero intensities for resonant

inelastic X-ray scattering transitions to the

13/2

and

11/2

,and

11/2

sextets

of the 4f

configuration (the Hund rule’s ground state is

15/2

), the energy of

the extra-feature in experimental spectra h, k,andl is close to those of

9/2

and

7/2

manifolds of Dy

in LaF

[109]. This is an indication of J-mixing

and the presence of J = 13/2 and J = 11/2 components in the ground state of

DyF

. Indications of other extra-structures missing from atomic multiplet

calculations can be seen in the energy loss range between 1.2 and 2.0 eV, as

in spectra l and m.

Figure 14.29

RIXS spectrum of DyF

excited at various energies across the 4d edge, and

plotted on an energy loss scale.

To simulate the effect of J-mixing, we calculated transition intensities

within the pure atomic approximation by choosing

13/2

and

11/2

as initial

states for the scattering process. The excitation energy was taken to be the

same as that for experimental spectrum l (since the intensity of extra-

structures is higher for excitation energies at the main absorption edge) and

the core hole lifetime broadening was set to 2.0 eV. According to these

calculations, the spectral weight at an energy loss of about 1.17 eV (transitions

Intensity (arb. units)

-6 -4 -2 0

Energy (eV)

DyF

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

there are some spectral structures that are not revealed in calculations within

638

14.5 Applications

9/2

and

7/2

) should constitute 56% and 217% of that at 1.0 eV

(transitions to

11/2

) for

13/2

and

11/2

as initial states, respectively.

Although accounting for weak but finite Dy 4f-F 2p hybridization may give

rise to some changes in calculated relative intensities in both cases, it is clear

that an admixture of the J = 11/2 component in the ground state results in a

stronger effect than for the J = 13/2 component. Since the degree of J-mixing

in DyF

is relatively low, the J = 11/2 contribution to the ground states is

expected to be comparable with the J = 13/2 contribution in order to explain

the noticeable weight of “forbidden” transitions in the inelastic scattering

component has been found to be comparable to the J = 13/2 component in the

ground state of Dy

-doped yttrium scandium gallium garnet [102] as a result

of the crystal field interaction.

To estimate the effect of this interaction on the shape of RIXS spectra,

model crystal field multiplet calculations for the Dy

ion in the crystal field

of O

symmetry with a strength of 35 meV were made. Figure 14.30 shows

the 1.0–2.2 eV energy-loss region of the spectra calculated using a pure

atomic approximation and crystal field multiplet theory. It is clear that

switching on the crystal field gives rise to additional transitions. The

calculated intensities are too low to fully account for the observed spectral

weight in experimental data at the corresponding energy loss. This suggests

that interatomic coupling is also important for the description of the inelastic-

scattering profile in the energy loss range between 1.0 and 2.0 eV and that the

appearance of additional structures is rather a combined effect of the crystal

field interaction and Dy 4f-F 2p hybridization. However, calculations taking

into account both the crystal field and F 2p

o

Dy 4f charge transfer excitations

are complicated by a huge number of multiplets and require very large

computational resources.

The existence of J-mixing in the intermediate state raises a question about

how strongly the inelastic scattering intensity at energy losses between 1.0 eV

and 2.0 eV is related to J-mixing in the ground state of DyF

. To estimate this,

crystal field multiplet calculations with the crystal field interaction switched

off in the intermediate state have been performed. Thus, any J-mixing in the

core excited state was disallowed. A comparison of the results of calculations

with, respectively without, crystal field interaction in the intermediate state

(Figure 14.30) does not reveal any significant changes in the inelastic

scattering intensities of “forbidden” structures on switching off J-mixing in

the core excited state. One of the main reasons for that is a large core hole

lifetime broadening. As a whole, the calculations indicate that the spectral

weight in the energy loss region between 1.0 and 2.0 eV is largely determined

by J-mixing in the ground state of DyF

639

spectra in Figure 14.29. This is not unusual. For example, the J = 11/2

Figure 14.30 A 1.0–2.2 eV energy-loss region of inelastic X-ray scattering spectra of the Dy

system calculated using a pure atomic approach (intermediate coupling) and crystal field

multiplet theory (O

symmetry). In the calculations Slater integrals were scaled down to 80%,

75%, and 66%, respectively, from the Hartree-Fock values. Excitation energy was set to the

main absorption maximum (spectrum l in Fig. 14.28) and the core hole lifetime broadening was

taken to be 2.0 eV.

14.5.3.6 Actinides

The case of uranium is quite illustrative for what the RIXS technique can do.

RIXS measurements at the U 5d threshold provide an opportunity to study in

detail elementary excitations in U compounds due to the higher resolution of

such experiments in comparison with those at the U 3d and 4d thresholds. It

turns out that the technique, in contrast to X-ray absorption spectroscopy, is

very sensitive to the valency and the chemical state of uranium. Figure 14.31

shows X-ray absorption spectra of a number of U compounds recorded across

broadening is quite large, thus reducing the usability of XAS.

As a result, the U 5d absorption spectra in the figure do not exhibit sharp

features. The substantial smearing of spectral structures hampers the analysis

of the chemical state and the chemical environment of uranium in various

compounds. In particular, it is difficult to distinguish between uranium

species with different oxidation states, especially in the case when one of the

species has a much lower concentration than other.

640

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

Intensity (arb. units)

-2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0

Energy (eV)

crystal field (35 meV)

no crystal field in the

intermediate state

atomic

the U 5d edge in the total electron yield mode. The 5d core hole lifetime

14.5 Applications

Figure 14.31 Total electron-yield spectra of UF

, UO

, U

, and UO

near the U 5d

absorption edges.

In this situation, the principally unlimited resolution (defined by the

excitation sharpness and the response function of the instrument) of the RIXS

technique and its ability to enhance transitions to specific excited states are

especially useful. The RIXS profile strongly depends on the choice of the

excitation energy. The spectral weight corresponding to electronic transitions

within the 5f shell is enhanced at excitation energies close to 100 eV, while at

higher energies of the incident photon beam set to the main 5d absorption

edge, interionic excitations of charge-transfer character, such as ligand 2poU

5f charge-transfer, dominate the RIXS spectra. This has been established by

measurements on a set of model U compounds and by model calculations.

The spectral pattern of intra-ionic fof excitations is mainly determined by the

formal valency of U; in turn, the charge-transfer transitions strongly depend

on the chemical environment of U ions.

An example of probing the fof excitations in U systems is illustrated in

Figure 14.32 where the RIXS spectra of solid UF

, recorded for various

incident photon energies in the pre-5d threshold region, are displayed. The

assignment of sharp inelastic scattering structures to the fof transitions is

supported by atomic multiplet calculations for the U

ion. The spectra were

calculated using a model where the varying lifetime of core excited states due

to the autoionization via the 5d-5f5f super Coster-Koenig decay was taken

Intensity (arb. units)

13012011010090

Photon ener

(eV)

U 5d

absorption

641

into account. The autoionization into the continuum of g symmetry only was

considered since it is the most dominant path. Matrix elements were obtained

from Cowan’s programs [110] so that Slater integrals were scaled down to

75%, 75%, 66%, and 80%, respectively, from the Hartree-Fock values. The

reduction factors for Slater integrals represent the effect of the intra-atomic

configuration interaction; the same factors were used in a number of

publications to successfully reproduce 4d X-ray absorption and 4d

photoemission spectra of various rare earth systems [111, 112, 113]. The

density of states of the continuum was assumed to be constant and the kinetic

energy of the continuum electron was set to the value that made the average

energies of 5d

and 5d

Hg equal.

Figure 14.32 Resonant X-ray scattering spectra of UF

[114] recorded at different excitation

energies close to the U 5d threshold (lines with markers) together with the results of atomic

multiplet calculations (sticks with thin lines) for the U(IV) ion. Excitation energies are

indicated by arrows on the total electron yield spectrum at the U 5d absorption edge shown in

the top panel

642

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

Intensity (arb. units)

-5 -4 -3 -2 -1 0 1 2

Energy (eV)

x 1/3

Intensity (arb. units)

10510095

Photon energy (eV)

U 5d

XAS