Slide 1

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 2

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 3

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 4

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 5

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 6

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 7

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 8

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 9

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 10

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 11

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 12

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 13

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 14

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 15

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 16

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 17

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 18

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 19

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 20

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 21

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 22

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 23

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 24

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 25

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 26

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 27

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 28

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.


Slide 29

XPS lineshapes and fitting
Georg Held

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

Lifetime Broadening
Photoemission

• 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:

hν

τ · ΔE ≈ h/π
(ΔE = 1.3 eV for τ = 10-15 s)

Secondary
process

Lifetime - Lineshape
• Decay of core hole is
exponential:

1.2

τ = 1x10-15s

1
0.8
0.6

|Ψ(t)|2

 exp (-t / τ)

0.4
0.2
0
0

• This causes a Lorentzian
energy distribution of
photoelectrons:
L(E)  [(E-E0)2 + Γ2]-1

0.5

1

1.5

2

2.5

8

10

t im e / 10- 15 s

1.2

Γ = 1eV

1
0.8

FWHM

0.6
0.4
0.2

(FWHM = 2Γ)

0
0

2

4

6
BE / e V

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

O1s

C1s

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

– 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).

L3
L2

L1
C.K.
Auger process

Same Shell

• Additional lifetime broadening through
Coster-Kronig processes:

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

Pt4d5/2

Pt4f

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;
d orbital (L = 2): J = 3/2 or 5/2;
f orbital (L = 3): J = 5/2 or 7/2;

• Energy difference (splitting)
increases with increasing BE.
• decreases with increasing L
• BE(L+½) < BE(L-½)

p1/2 and p3/2
d3/2 and d5/2
f5/2 and f7/2

L-½

L+½

Spin-orbit (LS) Coupling
• Multiplicity 2J+1: J, J-1, … , -J+1, -J
Number 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 intense
and narrower (see later)

L-½

L+½
BE

Pt 4d, 4f and 5p levels
Pt4f
Pt5p3/2

Pt4d

Pt4d
Med L, high BE:
large LS splitting (17eV)
Super C.K:
large FWHM (4eV)

Pt4f
High L, Low BE:
small LS splitting (3.3eV)
C.K for 4f5/2:
larger FWHM (1.3 vs 1.1eV)

Pt5p3/2
Low L, Low BE:
large LS splitting (24eV)
Super C.K:
large FWHM (4eV)

Final State Effects
• Secondary electron energy losses:
– electronic transitions with well-defined energy
(satellites)
– Plasmons
– Intra-band transitions (continuous energy)

• Vibrational (‘vibronic’) excitations.

Secondary electron energy losses
• ‘Naïve Picture’:

‘Shake up’

– 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 off’

Photoelectron

Secondary electron energy losses

CO on Al
Shake off

Plasmon
Shake off

Secondary electron energy losses
Examples
Ni 6 eV satellite disappears
when Ni is diluted in Cu
Metallic Cr:
asymmetric
peak

Organometallic
compound:
symmetric
peak

Secondary electron energy losses

Si

Plasmons

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

What affects Lineshapes?
• Intrinsic lineshape:
– spin-orbit coupling
– lifetime

• Final state effects:
– Satellites,
– Vibrations

• Instrumental broadening:
– Analyser,
– Source

• Different chemical states.

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.

Instrumental Broadening
• Gaussian line shape:
G(E) = exp( -(E – E0)2 / 2σ2)

FWHM = √(8 ln2) · σ

1.2
1
0.8
0.6
0.4
0.2
0
0

2

4

6
BE / e V

8

10

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.

G (x )

L(x )

G+L

G *L

1.2

1

0.8

0.6

0.4

0.2

0
-3

-2

-1

0

1

2

3

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.

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.

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

Peak Fitting
• Spectra consist of
• Peaks
–
–
–
–

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

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

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

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)

IGOR Practice session - 1
• make \n=201 E_axis
E_axis = 90 + 0.1
• duplicate E_axis Gaus_1
Gaus_1 = 100 * exp( -(E_axis – 100)^2 *4*ln(2)/ 4^2 )
duplicate E_axis Lor_1

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.