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1
UPS=Ultraviolet Photoemission Spectroscopy
XPS=X-Ray Photoemission Spectroscopy
AES=Auger Electron Spectroscopy
ARUPS= Angular Resolved UltravioletPhotoemission Spectroscopy
APECS=Auger-Photoelectron Coincidence Spectroscopy
Electron Spectroscopy for Chemical Analysis
(ESCA)
BIS= Bremsstrahlung Isocromat Spectroscopy
…………………………………..1
It is the collective name of a series of techniques of surface analysis
2
Vacuum level
Fermi level
Free electrons
Ene
rgy
kk ,
Filled bands
Core levelsh
Photoelectron
J
k
Photoemission spectrum (XPS;UPS):filled states
Empty states
2
33
4
Fast photoelectrons: no post-collisional interactions
Photoemission cross section: golden rule expression
†
mn
N3
i ii
Interacting system hailtonian H Perturbation: H'=
' [ ( ). . ( )]2
Equivalent alternative formulation, directly from the relativistic
theory,
H' - d xA(x ) · j(x )
mn m n
N
i i i ii
M a a
eH A x p p A x
mc
The photoemission cross section Dσ(w) can be worked out starting from the Fermigolden rule; the photoelectron is in |f>
wD 22| ' |
i Ff
f H i E E
info on ion left behind from energy conservation4
5
2 2 2 2
† †
†
Hamiltonian after photoionization
H=H , photoelectron KE2 2
H describes final state ionized solid (set of ion states f )
H f f , , f ion,f f
cruci photoelectron andal: io
k k k kk k
f ka
k ka a a a
m m
E
n do not interact any more
w
D
D
D
22cross section: | ' |
, solid angle accepted by detector
i Ff
f kf
f H i E E
Basic Theoretical framework
5
†
kn
H'= , k = photoelectron momentumkn k n
M a a
†
n
the contribution H'= , creates photoelectron
with momentum k
kn k nM a a
w
D
D
D
22cross section: | ' |
, solid angle accepted by detector,
sums over ion final states
i Ff
f kf
f
f H i E E
†
kn
H'= , k = photoelectron momentumkn k n
M a a
†' '
hole state in solid
k km k k m km mm m
f H i f a H i M f a a a i M f a i
m
†Recall f fing , f ion,ka
7
D
D D
If detector accepts a small ,
density of final states for photoelectron
kk
k
w
D
D
2 * †
,
22
final hole state. Trick:
|
||
|
km km kn
k i kf
n m
km mf m
m mm
n
M f a
M M
i
f a i
E
M i a f
m
f a
E
i
7
differential cross section:
w
D
D
D
†
22Recall: | ' |
, solid angle accepted by detector,
, f ion, sums over if f on final states
i Ff
f kf
kf
f H i E E
a
8
w
w
D
D
* †
,
22| |
2k km
k km m i k
kn n
fmf
m i kfm nf
M M i a f f a i E E
M f a i E E
† † 1Imn i k m n m
i k
i a E H a i i a a iE H
w w
differential cross section:
* †
,
* †
,
2
2
k km kn n i k mm nf
k km kn n i k mm n
M M i a E H f f a i
M M i a E H a i
w
w
D
D
sum over final ion states using closure:
8A hole Green’s function is involved.
9
spectroscopic notation KLMNO,...
n=1,2,3,4,5,...
guscio N
4s1/2 N1
4p1/2,3/2 N2,N3
4d3/2,5/2 N4,N5
4f5/2,7/2 N6,N7
XPS from Hg vapour using Al Ka h=1486.6 eV. Lines are labelled by final core hole state of Hg+
9
10
The same core lines can be observed by X-Ray emission
Dirac-Fock codes do NOT grant good agreement with experiment
Chemical analysis: tiny amounts suffice to recognize elements (binding energies are well known)
11
12
solid Si 2p XPS core spectrumSi configuration: [Ne]3s23p2
2p is core
12
13
Milano 4 Luglio 2006
Al valence bandAg valence band
Fermid band
s band
13
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UPS (ultraviolet photoemission) produces slow electrons- excape probabilitystrongly depends on energy and on angles
14
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UPS produces slow electrons- excape probability strongly depends on coverage
No Ag
1 monolayerAg
2 monolayerAg
background
Background due to incoherent losses: one can measure it by eels
The universal electron mean free path curve. Electron spectroscopiesare surface sensitive (because of outgoing electrons, much more than for incoming photon mean free path)
16
Laplace equation for moving electron (constant speed v = l/T= w/k)
17
3
3( )
4
Since v exp( . ) exp( .v ) and
exp( .v ) ( .v), one obtains:
v (2 ) ( .v)(2 )
i t
i kr t
r t d k ik r ik t
ik t d e k
d kdr t e k
w
w
w w
w w
Jean Baptiste Joseph Fourier
The produced by the fast electron is given by: 4 ( ) ( vt)
To Fourier transform we need:
D divD e r
D
David Penn, Phys. Rev B35 (1986)
Hence, Poisson--> ikD=4 e2 ( -k.v) w
We can explain qualitatively the universal mean-free-path curve by a simpliefied model
The electron is treated as a classical point charge moving in the solid with a constant velocity
18
2
2
2
2
8 ( v)( , ) is consistent with the above result:
scalar-multiplying by one finds . ( , ) as above.
But ( , ) ( , ) ( , ), hence
8 ( v)( , ) .
( , )
We can obtain
e k kD k
i k
k k D k
D k k E k
e k kE k
i k k
ww
w
w w w
ww
w
2
2
the screened potential V, since ( , ) ( , )
8 ( v)screened potential ( , )
( , )
e kV k
k k
E k ikV k
w
w
w
w
w
ikD=4 e2 ( -k.v) w
19
23
2
( v) 1decay rate Im( )
2 ( , )
e kd kd
k k
ww
w
2
2
The potential of the screening charges
acting on the electron*electron charge=electron
8 ( v)scr
self-energy.
But Im(self-energy)=dec
eened potential
ay r
( , )( )
ate
,
e kV k
k k
ww
w
v free path of electrons mean
20
23
2
( v) 1decay rate Im( )
2 ( , )
e kd kd
k k
ww
w
Recall: the Dielectric function
1°-order Perturbation theory in exact many-body system
22
0 02
1 4Im 0 ( ) ( )
,k n n
n
en
k k
w w w w
w
23
2
( v) 1Im( )
2 ( , )
is proportional to the sum of the Fourier components of the disturbance
at the excitation energies o
Thus the decay r
f the sy
ate
stem.
e kd kd
k k
ww
w
21
The electron that emits an excitation is out of the beam and
continues to lose energy untill it is thermalized.
At tens or hundreds of eV all solids are well approximated by
Jellium (gaps are much less) and behave similarly; at low
energy the losses are often small (Landau quasiparticles are
narrow in energy, as we shall see) and this explains
qualitatively the universal curve.The minimum corresponds
to the energy region in which multiple plasmon excitations
occur.
= (about) = (about) Jellium In far ultraviolet
22
Shen (PRB 1990) e Tjernberg (J. Phys. C 1997) note that line shape depends strongly on photon energy, since the O cross section decreases with energy faster.
(compare 777.3 eV and 778.9 eV)
CoO valence band in UPS CoO has an octahedral structure and is an antiferromagnet: strong correlation produces a complex multipletstructure which informs us about the screened interaction.
22
hv=777.3 eV
hv=778.9 eV
23
CoO UPS ultraviolet photoelectron spectroscopy
Still another line shape at 40.8 eV
23
Ag has a surface state at the Fermi energy, s-p states below the Fermi energy and a filled d band 4 eV below.
Exchange splitting in final state ions
2
In the Hartree-Fok picture, NO has a partially filled 2 shell
with spin-orbitals , ; is also paramagnetic.O
NO
N2
N1s
O2
545 540
binding energy
415425
binding energy (eV)
O1s
NO
545540
1.2 eV
0.9 eV 0.9 eV
0.9 eV
26
Ratio 2:1 Ratio 3:1
Core level XPS
27
+
z
π s π sNO : 4 determinants all with Λ=|L |=1.
π s π s
We must account for singlet-triplet splitting.
1 1The singlet is :
2s s
1 1readily seen to be a singlet since 0
2S s s
3 1
2
s
s s
s
+The partially filled shells of NO include O1s denoted by s below
27
28
12
12 ,E J J s s
r D exchange integral
Sz=0 sector: 1 1
2s s
3 1
2s s
( ) | 0s h i s
Since determinants differ by 2 spin-orbitals, only the interaction contributes.
Configuration Interaction
1
does not depend on . Compute splitting ini
i i j ij
H h Sr
1 1 1
3 3 3
E H s H s s H s
E H s H s s H s
12
1 1[ ( (1) (1) (2) (2) (1) (1) (2) (2)) ( (1) (1) (2) (2) (1) (1) (2) (2))
2 a a a a J s s s s
r
28
29
0.88 eV for N
0.68 eV for O
triplet is lower (lower binding energy) by:
12
1( (1) (2) | | (1) (2)) J s s
r
12 12
1 1 1[( (1) (2) | | (1) (2)) ( (1) (2) | | (1) (2))], that is,
2J s s s s
r r
Taking the spin scalar products, two terms vanish, and writing the two—electron integrals
29
Ratio 3:1 (triplet versus singlet)
In a similar way, the 1s spectrum of O2 (binding energy ∼ 547 eV ) has two components separated by 1.1 eV with an intensity ratio 2:1 (quartet to doublet ratio).
30
Intial state effects
final state effects
electrostatic potential surrounding the atom
before ionization (several eV of either sign )
Polarization around hole (several eV, to lower BE)
One can tell valence and ionicity from shifts
Chemical shifts
BE eV535 540
O1s
295 29o
C1s
Binding Energy eV
Acetone
31The C bound to O is more electropositive and has larger Binding Energy
Pauling electronegativity scale
Binding energy
eV
Intial state effects, mainly
300
295
Pauling charge
0 10 20
CH4
CF4
CHF3
CO2
CO
CH3OH
CS2
34
the missing line1
2
4 pExtreme initial state effects:
According to Dirac-Fock, a 4p1/2 line should exist between 4s and 4p3/2, but none is seen
4s 3
2
4 p
1
2
4 ?p
35
11.1 eV away from DSCF
virtual processes:
4p1/2 hole2(4d) holes + electron
and Back
Xe+Xe++ +e resonance
9.4 eV away from DSCF
A large self-energy merges 4p ½ with Auger continuum. Many body theory beyond HF is not a matter of refining the position of peaks!
Core level XPS spectra: large
relativistic effects for large Z
Core level XPS spectra- chemical shift
38
Hole Screening satellites Energy shiftsto lower binding
The ion is left excited because of correlation, coupling to phonons, plasmons, etc.
Low –energy satellites arise from excited final states
Screening wins at threshold (final-state shift)
Useful approximate scheme:final-state Hamiltonian is different because of the potential of the hole.
Final-state effects in photoemission spectroscopy
By energy conservation: h = final ion energy + photoelectron energy
Postcollisional interactions seldom involved for fast photoelectrons
excited ion slower photoelectron, but hole screening fasterphotoelectron.
39
Shake-up satellites simple approximations)
We can treat Hfin in Hartree-Fock approximation if we allow for a different final-state Hamiltonian while initial state |i> is the ground state without the hole. Then we can treat the initial state Hiniz in Hartree-Fock as well.
Simplest: Equivalent cores approximation
States of Atom Z with core hole = states of atom Z+1
More accurate: DHF approximation
Method to obtain the answer from the difference of eigenvalues of two HF calculations
iniz iniz
,
makes a hole in frozen initial state spin-orbita
without core hole, det of initial state spin-orbitals
, spin-orbitals with core hole potential.
Core Photoemission line
l
Fok fin
c
H i E i
H
a
i
†
fin
core holeGF
1Im core DOS
shape:
, has core hole and frozen orbitals :
it is no eigenstate of H
c
fi
c c c
n
c
a i i
G
G i a
f
H a i
w
w w w
In both cases the initial and final holes feel different potentials
41
2| |if
w w
ion eigenstates
ifFrozen determinant (N-1 spin-orbitals, obtained by removing core state spin-orbital from neutral HF determinant)
eigenstates of Hfin; in HF, they are determinants of N-1 relaxed spin-orbitals computed with core-hole.
Overlap of determinants=determinant of overlaps: all N-1 body states contribute
Ground-stateground state = threshold, other peaks = satellites
†
fin
1Im c c cG i a H a i w w w
42Satellites perfectly balance the relaxation shift
Shake-up
satellites
Discrete excited states
Shake-off
satellites
Continuum excited states
Sum rules
w w w w
2 2
, , 1d d i f i f
ww w w w w
2 2
, ,
, , ,fin fin
d d i f i f
i f H if i f H i f
From Siegbahn’s lectures. In solids, vibrations but also plasmons
Besides electronic states, one observes phonons and plasmons:
electron optics allow resolution 0.001:
sees rotovibrational structure
E
E
UPS
D
http://www.casaxps.com/help_manual/manual_updates/xps_spectra.pdf
http://www.fisica.unige.it/~rocca/Didattica/Fisica%20dello%20Stato%20Solido%20(Scienza%20ed%20Ingegneria%20dei%20Materiali)/7%20plasmons%20and%20surface%20plasmons.pdf