Core-level spectroscopy:

XAS, PED, XES

Ondrej Sipr

VIII.

NEVF 514 Surface PhysicsWinter Term 2018–2019

Troja, 16th November 2018

Outline

X-ray absorption spectroscopy: basic principles

EXAFS: structure determination

XANES: more information than just DOS

Photoelectron diffraction: getting more out of XAS

X-ray emission spectroscopy: Another look at valence states

Outline

X-ray absorption spectroscopy: basic principles

EXAFS: structure determination

XANES: more information than just DOS

Photoelectron diffraction: getting more out of XAS

X-ray emission spectroscopy: Another look at valence states

Outline

X-ray absorption spectroscopy: basic principles

EXAFS: structure determination

XANES: more information than just DOS

Photoelectron diffraction: getting more out of XAS

X-ray emission spectroscopy: Another look at valence states

Outline

X-ray absorption spectroscopy: basic principles

EXAFS: structure determination

XANES: more information than just DOS

Photoelectron diffraction: getting more out of XAS

X-ray emission spectroscopy: Another look at valence states

Outline

X-ray absorption spectroscopy: basic principles

EXAFS: structure determination

XANES: more information than just DOS

Photoelectron diffraction: getting more out of XAS

X-ray emission spectroscopy: Another look at valence states

Outline

X-ray absorption spectroscopy: basic principles

EXAFS: structure determination

XANES: more information than just DOS

Photoelectron diffraction: getting more out of XAS

X-ray emission spectroscopy: Another look at valence states

X-ray absorption spectroscopy howto

◮ X-rays go in, x-rays go out, absorption coefficient is measuredas a function the energy of the incoming x-rays

x-rays inx-rays out

sample

◮ Focusing on energies where most of the absorption (or itsvariation with the energy) goes on account of thephotoelectric effect on core electrons

Absorption via core electron excitation

EF

Core hole is left behind the ejected (photo)electron.

Probing density of unoccupied states

EF

EF

Analogy to photoemission:Larger DOS means larger probability of a transition.

In photoemission, energy of ejected photoelectrons is usually muchlarger than in XAS.

Chemical selectivity

EF

absorption coreedge level

K 1sL1 2sL2 2p1/2L3 2p3/2

◮ Absorption coefficient µ decreases if x-ray energy increases[µ ∼ 1/(~ω)3].

◮ If incoming x-rays energy is large enough to excite anothercore electron, the absorption coefficient increases by a jump.

◮ Close to this jump, photoelectric effects on electrons from onecore level only dominate.

Angular momentum selectivity

X-ray absorption is like angle-integrated photoemission from corestates. Probability of capturing a photon by an electron::

w =2π

~|Mfi |2 δ(Ef − Ei − ~ω) .

Dipole approximation: Mfi ≈ ǫ · 〈ψf |p|ψi 〉 .

Selection rules: If wave functions |ψi 〉 and |ψf 〉 have certainsymmetries, the (dipole) matrix element will be identically zero.

Only transitions between states with their angular momentumquantum numbers differing by one are allowed:

ℓf = ℓi ± 1

K and L1 spectra (1s or 2s core levels) probe p states.L2 and L3 spectra (2p1/2 or 2p3/2 core levels) probe d states.

Energy ranges: EXAFS, XANES

◮ High photoelectron energies (100–500 eV)EXAFS (Extended X-ray Absorption Fine Structure)

◮ Low photoelectron energies (0–50 eV)XANES (X-ray Absorption Near Edge Structure)

◮ Different approximations for theoretical description needed, different

information content

Outline

X-ray absorption spectroscopy: basic principles

EXAFS: structure determination

XANES: more information than just DOS

Photoelectron diffraction: getting more out of XAS

X-ray emission spectroscopy: Another look at valence states

EXAFS intuitively (1)

Electron is ejected off the atom. Electron starts travellinginside the solid.

EXAFS intuitively (2)

◮ Electron is scattered by neighboring atoms.

◮ Quantum mechanics: scattered electron waves interfere(destructively or constructively).

◮ By varying photoelectron energy we vary also wavelengh ofthe photoelectron wave.

⇒ Absorption coefficient oscillates as a function of energy.

These oscillations are very faint (1 %).

EXAFS: basic theory (1)

Absorption coefficient (probability of transition from core level tounoccupied states):

µ(~ω) = −2π2m2

~5k2ℑ∑

LL′

M∗

L τ00LL′ ML′ ,

k =√

2m(~ω − E0)/~2 photoelectron wave vectorML atomic-like transition matrix element

τ00LL′ is the scattering-path operator comprising all the scatteringevents,

τ00LL′ = t0LδLL′ +∑

p

∑

L′′

t0L G0pLL′′

τp0L′′L′

.

t0L single-site scattering matrix

G0pLL′′

free-electron propagator (Green’s function)

EXAFS: basic theory (2)

Retaining only single-scattering approximation and assumingplane-wave character of the photoelectron (justified at largeenergies), one gets for the fine structure

χ(k) ≡ µ− µ0µ0

=∑

p

3(ε · Rp)2

kR2p

ℑ[

fp(k) e2ikRp+2iδ0

ℓ=1

]

.

µ0 absorption coefficient of a free atom (smooth function of k)ε polarization vectorRp distance between the photoabsorbing atom and the atom p

fp(k) backward scattering amplitudeδ0ℓ=1 scattering phaseshift of the central atom (for the K edge)

Polarization (angular) dependence of the spectrum

using drawing of G. Waychunas

χ(k) ≡ µ− µ0µ0

=∑

p

3(ε · Rp)2

kR2p

ℑ[

fp(k) e2ikRp+2iδ0

ℓ=1

]

By varying the direction of the x-rays polarization vector ε(a.k.a. E ), one probes the local environment in different directions.

EXAFS: extracting information about distances (1)

χ(k) =∑

p

3(ε · Rp)2

kR2p

ℑ[

fp(k) e2ikRp+2iδ0

ℓ=1

]

◮ χ(k) is a superposition of oscillatory functions of k ,interatomic distances Rp determine the periodicities of theseoscillatory functions.

◮ This calls for a Fourier transformation — peaks inFourier-transformed χ(R) should correspond to interatomicdistances present in the system.

◮ Life is not that simple: further k-dependence introduced byδ0ℓ=1(k).

◮ (Other complications not mentioned here. . . )

EXAFS: extracting information about distances (2)

◮ In praxis: fitting calculated and experimental signals.

◮ Interatomic distances of nearest neighbors determined withaccuracy of about 0.01 A.

Comparing EXAFS and diffraction

◮ X-ray diffraction is more accurate, it gives a completeinformation (when treated properly).

◮ EXAFS does not require translational periodicity:◮ amorphous systems◮ alloys (solid solutions)◮ adsorbates

◮ Information provided by EXAFS is chemically specific.

Surface EXAFS (SEXAFS)

◮ Element specific: convenient for adsorbates.

◮ Simple (well, doable. . . ) analysis.

◮ Only bond lengths are directly accessible.◮ Using polarized incoming light, some directional knowledge can

be obtained as well.

◮ Surface sensitivity may be achieved◮ by exploiting the chemical selectivity (certain element is only

at the surface),

◮ by choosing a grazing incidence of the incoming x-rays (theyprobe only the surface region),

◮ by recording the spectra in an electron yield mode, i.e., byrecording electrons released as a result of the x-ray absortion(small mean free path means that only few A’s below thesurface are effectively covered).

Outline

X-ray absorption spectroscopy: basic principles

EXAFS: structure determination

XANES: more information than just DOS

Photoelectron diffraction: getting more out of XAS

X-ray emission spectroscopy: Another look at valence states

XANES: basics

EXAFS XANESsingle-scattering multiple-scattering

◮ Low energies: single-scattering approximation not good

◮ More information at much higher cost (bond angles are there)

◮ One has to evaluate the full equation:

µ(~ω) = −2π2m2

~5k2ℑ∑

LL′

M∗

L τ00LL′ ML′

Why single scattering for EXAFS and not XANES?

Scattering amplitudef (k) as a function ofthe photoelectronwavevectork =

√2mE/~ for O,

Fe, and Pb atoms

From M. Newville

Rule of thumb:Scattering amplitude is large for low photoelectron energies,small for high photoelectron energies.

In the EXAFS region the scattering amplitude is small and theprobability of the electron being scattered more than once isnegligible.

Why to care about the XANES anyway?

If theory and interpretation of XANES is complicated, why to careabout it?Why not be satisfied with the EXAFS region?

Issues with intensity:

If the amount of absorbing material is small (as is the case forimpurities, adsorbates, monolayers), the x-ray absorption is verylow and signal may be noisy.

If the x-ray absorption signal is too noisy, only the relatively largeXANES signal can be obtained. EXAFS oscillations are too faint tobe discerned in the noise.

XANES without calculations: fingerprinting

◮ Tetrahedral coordination: dipole transitions at the pre-edgeregion are allowed ⇒ intensive pre-peak

◮ 3d states of the photoabsorber hybridize with ligand states toform states of p symmetry

◮ Octahedral coordination: only quadrupole transitions to 3dstates are possible ⇒ weak pre-peak

XANES: comparing with ab-initio calculations (1)

Determining local structure aroundAg in Ag-B-O glasses.

Try and error method.

PRB 69, 134201 (2004)

XANES: comparing with ab-initio calculations (2)

V K -edge of V2O5

Understanding the origin of apronounced pre-peak which appears inthe polarized (a.k.a. angle-dependent)experimental spectrum.

PRB 60, 14115 (1999)

Using XANES simulation to find the adsortion site

Adsorption of Oon Ni(100)

Polarized spectra

calculated by

assuming that the O

atom is sitting in

various adsorption

sites.

J. Phys. C:Solid State Phys.

19 3273 (1986)

XANES theory: issues

◮ Accurate calculation of electronic structure needed (it shouldbe trivial but it is not, among others because for states lyingmore than ∼5 eV above EF the numerics may get heavy).

◮ Dealing with excited states: LDA functionals are not verygood for unoccupied states, exchange and correlationpotential should be energy-dependent (“self-energy”).

◮ Core hole left behing by the excited photoelectron: bigproblem especially for transitions to semi-localized states.

Inverse photoemission

Bremsstrahlung isochromat spectroscopy (BIS).

EF

Electrons arrive from external source,they are decelerated in the vicinity ofions, bremsstrahlung is emitted.

By measuring intensity of thebremsstrahlung of the same energywhile the energy of the incomingelectrons is varied, the unoccupiedband is scanned.

Transition probability (i.e., BISintensity) is proportional tounoccupied DOS.

Limited angular momentum selectivity.

BIS: Example

Different bremsstrahlung energyresults in different weights of s-,p- and d -DOS in the spectrum

The 1487 eV isochromat and5415 eV isochromat probe thesame DOS but the matrixelements are different.

PRB 44, 4832 (1991)

Outline

X-ray absorption spectroscopy: basic principles

EXAFS: structure determination

XANES: more information than just DOS

Photoelectron diffraction: getting more out of XAS

X-ray emission spectroscopy: Another look at valence states

Photoelectron diffraction basics (1)

EF

◮ Recording the outgoing photoelectron — additionalinformation is thus available

◮ XAS is angle-integrated PED

◮ Similar calculational procedures and approximation used forPED and for XAS

Photoelectron diffraction basics (2)

electron energyanalyzer

double scatteredwave

substrat

emitter(adsorbate)

single scattered wave

hν

direct wave

(Philip Hofmann)

http://users-phys.au.dk/philip/pictures/physicsfigures/node19.htm

PED: Diffraction but from a local viewpoint

◮ Element specific

◮ Comparing with theory — fitting the parameters

◮ Analysis can be done introducing the same approximations asin EXAFS

◮ More data to analyze:

◮ energy scan◮ angular scan

PED example: N on Cu(100)

JPCM 13 L601 (2001)

PED example: alanin on Cu(110)

Appl Phys A 92 439 (2008)

Outline

X-ray absorption spectroscopy: basic principles

EXAFS: structure determination

XANES: more information than just DOS

Photoelectron diffraction: getting more out of XAS

X-ray emission spectroscopy: Another look at valence states

X-ray emission spectroscopy (XES)

EF

EF

1. Create a hole in the core

2. Measure the intensity of the x-rays which are emitted whenelectrons from valence band fill this hole

XES – XAS complementarity

◮ XAS probes density of unoccupied states

◮ XES probes density of occupied states

Information from XES

◮ Unlike photoemission, no information about k-vector

◮ Only DOS is accessible

◮ However, we know which DOS we are probing:◮ Chemically specific◮ Angular-momentum-specific

◮ Calculations: similar formula as in XAS◮ Final state has no core hole but a valence band hole.

The valence-band hole usually well screened → usingground-state potential is (usually) adequate.

◮ As DOS is linked to local structure, also XES can be used for(indirect) structural analysis

XES example: CO adsorption on Ni(100)

Surf. Sci. Rep.

55, 49 (2004)

Conclusion

Spectroscopy is a powerful tool but it has to be handled with care.