core-level spectroscopy: xas, ped, xes - ondrej iprmaca/povrchy2013/t10xrayspec_os2013.pdf ·...

Core-level spectroscopy:

XAS, PED, XES

Ondrej Sipr

X.

NEVF 514 Surface PhysicsWinter Term 2013 - 2014

Troja, 22nd November 2013

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

◮ Most of the absorption goes on account of the photoelectriceffect 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 decreases if x-ray energy increases

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

◮ Electrons from one core level only dominate close to this jump

Angular momentum selectivity

Dipole approximation (recall lecture on photoemission):

Mfi ≈ ǫ · 〈ψf |p|ψi〉 .

Selection rules:

If wave functions |ψi 〉 and |ψf 〉 have certain symmetries, the(dipole) matrix element will be identically zero.

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

ℓf = ℓi ± 1

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






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

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)

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 determined with accuracy ofabout 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

◮ Issues with intensity: small amount of absorbing material,signal may be too noisy, sometimes only XANES signal can beobtained

Outline






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′

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 experimental spectrum.

PRB 60, 14115 (1999)

Use of XANES for finding the adsortion site

Adsorption of Oon Ni(100)

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 not very good,exchange and correlation potential should beenergy-dependent

◮ Core hole: big problem for transitions to semi-localized states

Outline






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

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

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 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.

core-level spectroscopy: xas, ped, xes - ondrej iprmaca/povrchy2013/t10xrayspec_os2013.pdf ·...

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