XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit...

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XPS lineshapes and fitting Georg Held

Transcript of XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit...

Page 1: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

XPS lineshapes and fitting

Georg Held

Page 2: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

What affects Lineshapes?

• Intrinsic lineshape:– spin-orbit coupling– lifetime

• Final state effects:– Satellites, – Vibrations

• Instrumental broadening:– Analyser,– Source

• Different chemical states.

Page 3: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Lifetime Broadening

• The core hole is filled by a ‘secondary process’ (Auger or X-ray emission).Finite lifetime of core hole τ (10-16 – 10-12 s)

• The outgoing electron ‘knows’ about the lifetime of the core hole.

• Heisenberg’s relation:

τ · ΔE ≈ h/π

(ΔE = 1.3 eV for τ = 10-15 s)

Photoemission

Secondaryprocess

Page 4: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Lifetime - Lineshape

• Decay of core hole is exponential:

|Ψ(t)|2 exp (-t / τ)

• This causes a Lorentzian energy distribution of photoelectrons:

L(E) [(E-E0)2 + Γ2]-1

(FWHM = 2Γ)0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10

BE / eV

FWHM

Γ = 1eV

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2 2.5

time / 10-15 s

τ = 1x10-15s

Page 5: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Lifetime

• Lifetime decreases with increasing BE– FWHM increases with increasing BE– Example C1s and O1s of CO

• Additional lifetime broadening through Coster-Kronig processes:– C.K.: vacancy is filled by an electron from a

higher sub-shell of the same shell.– Super-C.K.: emitted Auger electron is also

from the same shell (e.g. L1L2L3).

– Not possible for lowest sub-shell with lowest BE (always narrowest).

C.K.Auger process

Sam

e Shell

L1

L2

L3

Page 6: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Lifetime

• Example: CO/Pt{531}– O1s: BE=533eV, FWHM=1.2eV– C1s: BE=286eV, FWHM=0.6eV

O1s C1s

Page 7: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Lifetime

• Lifetime decreases with increasing BE– FWHM increases with increasing BE– Example C1s and O1s of CO

• Additional lifetime broadening through Coster-Kronig processes:– C.K.: vacancy is filled by an electron from a

higher sub-shell of the same shell.– Super-C.K.: emitted Auger electron is also

from the same shell (e.g. L1L2L3).

– Not possible for lowest sub-shell with lowest BE (always narrowest).

C.K.Auger process

Sam

e Shell

L1

L2

L3

Page 8: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Lifetime

• Example: Pt4f, Pt4d– Pt4f: lowest BE in N shell; FWHM ≈ 1eV– Pt4d: Super C.K. (through 4f); FWHM≈4eV

Pt4d5/2 Pt4f

Page 9: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Spin-orbit (LS) Coupling

• The spin of the excited (missing) electron combines with the angular momentum of the orbital to a total angular momentum J = L - ½ or L + ½.

• Two peaks observed– only L > 0

– p orbital (L = 1): J = 1/2 or 3/2; p1/2 and p3/2

– d orbital (L = 2): J = 3/2 or 5/2; d3/2 and d5/2

– f orbital (L = 3): J = 5/2 or 7/2; f5/2 and f7/2

• Energy difference (splitting)increases with increasing BE.

• decreases with increasing L• BE(L+½) < BE(L-½) L-½ L+½

Page 10: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Spin-orbit (LS) Coupling

• Multiplicity 2J+1: J, J-1, … , -J+1, -JNumber of quantum states with same J.(e.g. J = 3/2: 3/2, 1/2, -1/2, -3/2).

• Intensity ratio between (L+½) and (L-½)is (2L + 2) / 2L = (L+1) / L.

• (L+½) state is more intenseand narrower (see later)

L-½ L+½

BE

Page 11: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Pt4d Pt4f Pt5p3/2

Pt 4d, 4f and 5p levels

Med L, high BE: large LS splitting (17eV)Super C.K: large FWHM (4eV)

High L, Low BE: small LS splitting (3.3eV)C.K for 4f5/2: larger FWHM (1.3 vs 1.1eV)

Low L, Low BE: large LS splitting (24eV)Super C.K: large FWHM (4eV)

Pt5p3/2

Pt4f

Pt4d

Page 12: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Final State Effects

• Secondary electron energy losses:– electronic transitions with well-defined energy

(satellites)– Plasmons– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Page 13: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Secondary electron energy losses

• ‘Naïve Picture’:– Photoelectron interacts with other

electrons on its way out and loses energy.– Lower kinetic energy: additional intensity at

BE higher than the actual peak.

• Possible excitations:– Excitons (electron hole pair):

between bands: narrow satellite peak (shake up).within the same band (metals): asymmetric broadening of main line

– Electron emission (shake off):broad satellite peak.

– Plasmons (collective excitation of all electrons): series of narrow satellite peaks with the same energy separation.

Photoelectron

‘Shake up’

Photoelectron

‘Shake off’

Page 14: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Secondary electron energy losses

CO on Al

Plasmon

Shake off

Shake off

Page 15: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Secondary electron energy losses Examples

Ni 6 eV satellite disappears when Ni is diluted in Cu

Metallic Cr: asymmetric peak

Organo-metallic compound: symmetric peak

Page 16: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Secondary electron energy losses

Si

Plasmons

Page 17: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Vibronic excitations

• Excitation of molecular vibration in connection with photo-ionisation.– Sometimes resolved as

shoulders (isotopic difference!).– Mostly just seen as additional

asymmetric broadening.

ΔBE for vibronic excitation of C6H6 is √2 x that of C6D6

Page 18: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

What affects Lineshapes?

• Intrinsic lineshape:– spin-orbit coupling– lifetime

• Final state effects:– Satellites, – Vibrations

• Instrumental broadening:– Analyser,– Source

• Different chemical states.

Page 19: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Instrumental Broadening

• Instrumental broadening is caused by:– Finite analyser resolution,– Band width of X-ray source

• Usually modelled by Gaussian line shape (normal distribution)

• The observed spectrum is a convolution of– intrinsic line (Lorentzian shape), – final state effects (e.g. asymmetry, satellites)– instrumental broadening (Gaussian shape)– Additional broadening can be caused by

inhomogeneous distribution of chemical states.

Page 20: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Instrumental Broadening

• Gaussian line shape:

G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10

BE / eV

Page 21: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Voigt Function• Convolution of Gaussian

and Lorentzian.– Often Approximated by

Sums or products of Gaussian and Lorentzian functions.

– GL mix defines how ‘Gaussian’ or ‘Lorentzian’ the function is.

– Asymmetry can be added through exponential decay function (exp(-α·E) ) at the high BE side of the peak.

0

0.2

0.4

0.6

0.8

1

1.2

-3 -2 -1 0 1 2 3

G(x) L(x) G+L G*L

Page 22: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Background• Step-like background shape

at peak position. – Each photoemission line

contributes to secondary electrons at lower kinetic energies.

– In general proportional to peak intensity.

• Long-range structure of background due to inelastic losses.– Very noticeable at low kin.

energies.– Usually not important for short

(high res.) spectra.

Page 23: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Background

• Simple background functions– Linear– Quadratic

B(E) = Eoff + a·E + b·E2

• Shirley (step-like)– Background is proportional to

integral over peak up to the point where background id determined

S(E) = Eoff + a·∫0 to E I(E’)dE’

– Strictly, S(E) is found by iterative approach

– Can be approximated by analytical function.

Page 24: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Background

• Tougard background– Use experimental

(parametrised) electron energy loss spectrum.

– Only important for accurate quantification of element concentration.

– Very similar to Shirley background near peaks

Page 25: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Peak Fitting

• Spectra consist of• Peaks

– Position– Height– Width (FWHM)– (GL mix, Asymmetry)

• Background– Offset– Linear, quadratic coefficients– Shirley parameter

Page 26: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Peak Fitting – General Rules• Determine number of peaks needed from

– chemical formula, – literature, – common sense.

• R-factor / Chi square = quality of fit (should be small).• Optimisation uses search algorithm

– Can be trapped in local minimum.– Use different sets of start parameters.

• As many fit parameters as necessary as few as possible.– Use constraints– Determine peak parameters from related data

Page 27: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

IGOR Practice session - 1

• Create a wave E_axis representing 201energy data points ranging from 90 – 110 eV. (Use the make command of IGOR)

• Create waves Gaus_1 and Lor_1 (201 data points) containing Gaussian and Lorentzian peaks with peak positions at 100 eV and FWHM = 4eV and height 100. Use E_axis for the energy values.

• Add linear backgrounds to both curves (and save in Gaus_2 and Lor_2)

Page 28: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

IGOR Practice session - 1

• make \n=201 E_axisE_axis = 90 + 0.1

• duplicate E_axis Gaus_1Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )duplicate E_axis Lor_1

Page 29: XPS lineshapes and fitting Georg Held. What affects Lineshapes? Intrinsic lineshape: –spin-orbit coupling –lifetime Final state effects: –Satellites,

Literature

• S. Hüfner, ‘Photoelectron Spectroscopy’, Springer.Good general Text book (more UPS than XPS)

• CASA XPS manual (from Internet).Contains a good selection of actual formulae

• Briggs and Seah, ‘Surface Analysis’General text book, more emphasis on quantitative element analysis.