presentazione standard di powerpointpeople.roma2.infn.it/~cini/ts2017/ts2017-13a.pdf · hence,...

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

14

UPS (ultraviolet photoemission) produces slow electrons- excape probabilitystrongly depends on energy and on angles

14

15

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