xps, optical propertiessusi.theochem.tuwien.ac.at/events/ws2019/blaha_xps...criteria colors harmony...

XPS, Optical properties

Peter BlahaInstitute of Materials Chemistry, TU Wien

(Xavier Rocquefelte)University of Rennes

Photoemission spectroscopy, PES

Energyconservation: ħ + Ekin + Eb

: work function Ekin: kinetic E of e-

Eb: bindingenergy of e-

UPS: UV (He-light, 21.1 und 40.4 eV), for valence-electrons XPS, ESCA: X-rays (Al 1486 eV), for core and valence-electrons Synchrotronradiation: UV or X-rays of “any” wavelength

•Illuminate sample with light of knownenergy, measure kinetic E of emittedelectrons e-

core-e-, Valence-DOS

Work function

potential

bulk

Surface

EF

Work-function

Vacuum

supercell

WF= :VZERO - :FER (check convergence with vacuum)

binding energy of oneparticular state

XPS, core-level shifts

Ionizationpotential of core-e-, IP= Etot(N) – Etot(N-1) gives information on charge state of the atom

core-eigenvalues i are NOT a good approximation: i=dE/dn Slater’s “transition state”: core-eigenvalues i for half occupancy

-SCF-calculation with and without core-hole: Etot(N) – Etot(N-1) supercells to reduce hole-hole interaction

C,N 1s exp.(eV) i -SCF

TiC 281.5 264.7 281.9

Ti4C4 281.5 263.3 281.1

TiN 397.0 377.5 397.1

E

E

n

tangent at N ≠ E

tangent at N-½ ~ secant ~ E

N-1 N-½ N

valence e-: bandstructure via ARPES

Surface stated-bandsp-band

valence PES: usually explained by DOS

a single DOS cannot explain the E-dependency of PES

, ,, Na,l = Partial DOS a,l = atomic cross section

O1s

2s2p

SiO2 valence band XPS

Total DOS gives 5 peaks, but wrong intensities

Cross section modulated PDOS gives better intensities

Renormalized PDOS * gives perfect intensities renormalization according to the inverse

charge fraction of an orbital within the atomic sphere + removal of interstitalDOS: ∑ ,,

PbO2 at 3 different energies

56eV: O-2p PDOS explains the spectrum

1486 eV: all orbitals contribute

7700 eV: O-2p not important

PBO2 at very low BE

56 eV: almost no intensity till -1 eV

7700eV: strong contribution from antibonding Pb-6s

1 – MULTIPLE FACETS OF COLOURED MATTER

2 – ELECTRONIC STRUCTURE OF A SOLID

3 – UNDERSTANDING OF COLORS FROM BANDS

4 – LIGHT‐MATTER INTERACTION

5 – OPTICAL PROPERTIES: WHICH TREATMENT?

6 – ILLUSTRATIONS

Modelling the Optical Properties of Inorganic Materials


DiffusionAbsorption

Coloring and pigments

Sky and clouds Others diffusingSystems …

Intermediate cases

Photons in interactionwith matter

Light‐Matter interaction

Zone ofinterferences

RefractioncolorsRainbow

Diffractioncolors

Interferentialcolor

Waves intransparentmedium

DiffusionAbsorptionLight‐Matter interaction



Intermediate cases



Zone ofinterferences

RefractioncolorsRainbow

Diffractioncolors

Interferentialcolor

Waves intransparentmedium

DiffusionAbsorptionLight‐Matter interaction



Intermediate cases


Eye

Brain Colored shadowCriteria colorsharmony

Colorimetry Color mixing

Light‐Matter interactionRetinal

in interactionwith photons

Nervoussignal


Interaction between the electromagnetic field and matter

Physical color

Diffusion et interferencesDispersion / Reflection et Refraction / Scattering

Transparent matter


Interaction between the electromagnetic field and matter

Physical color Chemical color

Diffusion et interferencesDispersion / Reflection et Refraction / Scattering

AbsorptionEnergy dissipation

Transparent matter Opaque matter


Chemical colors

AbsorptionEnergy dissipation

Opaque Matter

Acceptor electron levels Dissipative absorption

h

VB

CB

Gap

VB

CB

VB

CBUV

IR0

E (eV)

1.65

3.26

Chemical color « Inelastic diffusion »

From insulator to semiconductor to metal systems



p

s

From the atom to the molecule and to the solidEnergy

AtomAtomicOrbitals

p

s

*LCAO : Linear Combination of Atomic Orbitals

MoleculeLCAO*

MolecularOrbitals

From the atom to the molecule and to the solid

AtomAtomicOrbitals

Energy


SolidDispersion

Eg

CB

BV

ConductionBand

ValenceBand

BandGap

Bloch Orbitals= Bands

p

s

*LCAO : Linear Combination of Atomic Orbitals

MoleculeLCAO*

MolecularOrbitals

AtomAtomicOrbitals

Energy

From the atom to the molecule and to the solid


h

BV

CB

UV

IR

E (eV)

0

1

2

3

4

5

6

h

VB

UV

IR

E (eV)

0

1

2

3

4

5

6 Color of a SC* with 1 gap

*SC : Semiconductor


GAP

Abs

orpt

ion

(a.u

.)

Energy (eV)0 1 2 3 4 5 6

Transmittedlight

Color of thecompound

BV

CB

BV

CB

VB VB

Gap

0 1 2 3 4 5 6

hUV

IR

E (eV)

0

1

2

3

4

5

6

hUV

IR

E (eV)

0

1

2

3

4

5

6


Color of a SC* with 1 gap

Abs

orpt

ion

(a.u

.)

Energy (eV)

Transmittedlight

*SC : Semiconductor


BV

CB

BV

CB

BV

CB

VB VB VB

BI

Abs

orpt

ion

(a.u

.)

Energy (eV)0 1 2 3 4 5 6

No transmittedlight

*SC : Semiconductor

hUV

IR

E (eV)

0

1

2

3

4

5

6

hUV

IR

E (eV)

0

1

2

3

4

5

6


Color of a SC* with 1 gap


0 1 2 3 4 5 6BV

CB

VB

TransmittedLight

Energy (eV)

Abs

orpt

ion

(a.u

.)

EnergyColor of a SC* with several gaps

*SC : Semiconductor


*SC : Semi‐conducteur – BI : Bande interdite

0 1 2 3 4 5 6Energy (eV)

Abs

orpt

ion

(a.u

.)Transmitted

Light

BV

CB

VB

EnergyColor of a SC* with several gaps


Powder sample of TiO2 (rutile)

Charge transfercolor

TiO2


‐10

0

10

Energy (eV)

‐5

5

2 O2‐ (2p6)

Ti4+ (3d0)

“t2g”

“eg”

Eg 3 eV

TiO2

O Ti

Powder sample of TiO2 (rutile)



‐10

0

10

Energy (eV)

‐5

5

2 O2‐ (2p6)

Ti4+ (3d0)

“t2g”

“eg”

Eg 3 eV

TiO2

O Ti

Absorption (a.u.)

Energy (eV)0 1 2 3 4 5 6

UV



‐10

0

10

Energy (eV)

‐5

5

2 O2‐ (2p6)

Ti4+ (3d0)

“t2g”

“eg”

h> 3 eV

TiO2

Absorption (a.u.)

Energy (eV)0 1 2 3 4 5 6

UV

O Ti



TiCl3in solution

6 O2‐ (2p6)

Ti3+ (3d1)“t2g”

“eg”

h> 3 eV

h 2,5 eV

Ti[H2O]3+

d‐d transition color


Ti[H2O]3+

6 O2‐ (2p6)

Ti4+ (3d1)“t2g”

“eg”

h> 3 eV

h 2,5 eV

Absorption (a.u.)

Energy (eV)0 1 2 3 4 5 6

UV

Rq. : For dn with n > 1 Interelectronic correlations must be taken into accountTanabe‐Sugano diagrams(spectroscopic terms)

d‐d transition color


Aluminecorindon(Al2O3)

BV

CB

VB

EnergieAbsorption (a.u.)

Energy (eV)0 1 2 3 4 9

UV

10 11 12


Aluminecorindon(Al2O3)

Syntheticrubis

(Al2O3:1%Cr3+)

+ 1% Cr3+

Absorption (a.u.)

Energy (eV)0 1 2 3 4 9

UV

10 11

Absorption (a.u.)

Energy (eV)0 1 2 3 4


Impurity (d‐d) color

Rubis (Al2O3:1%Cr3+)

Cr3+ : electronic conf. d3 Interelectronic correlations must be taken into accountTanabe‐Sugano diagrams(spectroscopic terms)


Multiplicity of spin

Cr3+ : elect. conf. d3

2S+1X

Energy

4F0

4P

2G

2F

No CF*


Free ion: we define the spectroscopic terms :

4Fml +2 +1 0 ‐1 ‐2

L = +3

S = 3/2

*CF : Cristal Field



Energy

4F0

4P

2G

2F

2E2T1

2T2

4A2 (t23e0)

4T2 (t22e1)

4T1 (t21e2)

2A1

No CF* With CF*


Degeneracy lifting due to the octahedralcrystal field effect created by the ligands

Cr3+ : conf. eq d3

t23

e0

t22

e1

t21

e2

Excited States

Fundamental state


*CF : Cristal Field


Energy

4F0

4P

2G

2F

2E2T1

2T2

2A1

No CF* With CF**CC : Champ Cristallin


Energy (eV)0 1 2 3 4 5

Red color+

Slightly blue

Abs. (a.u.)

4A2 (t23e0)

4T2 (t22e1)

4T1 (t21e2)


Cr3+ : electronic conf. d3 Interelectronic correlations must be taken into accountTanabe‐Sugano diagrams(spectroscopic terms)


nvac. = 1

v = c/n

c

Example of a prism

Physical color « Elastic diffusion »

n : index of refraction

Propagation speed is changed


Example of a prism

Oscillating field

Without applied field

Electronic density

re .Dipole moment

nvac. = 1

v = c/n

c

Physical color « Elastic diffusion »

Elastic diffusion mechanismat the electronic level

Succession of absorption and emission

: Inductive dipole moment Receiver‐transmitter antenna

Oscillating Electric Field polarize


0 5 10 15 200.0

0.5

1.0

1.5

2.0

Energy (eV)0 5 10 15 20

0.0

0.5

1.0

1.5

Energy (eV)

n k

Diffusion Absorption

Kramers‐Kronig

Complex index of refraction: N = n + i k


0 5 10 15 200.0

1.0

2.0

3.0

4.0

Energy (eV)0 5 10 15 20

0.0

1.0

2.0

1.5

4.0

Energy (eV)

1 2Complex dielectric function: = 1 + i 2

1 = n2 – k2

2 = 2nk

0 5 10 15 200.0

0.5

1.0

1.5

2.0

Energy (eV)0 5 10 15 20

0.0

0.5

1.0

1.5

Energy (eV)

n k

Diffusion Absorption

Kramers‐Kronig

Complex index of refraction: N = n + i k


0 5 10 15 200.0

1.0

2.0

3.0

4.0

Energy (eV)

0 5 10 15 200.0

0.5

1.0

1.5

2.0

Energy (eV)

n

1

Diffusion in the case of a prism

n(blue) > n(red)

0 5

1.5

2.0


0 5 10 15 200.0

0.5

1.0

1.5

2.0

Energy (eV)

nk

Index of vacuum

Vacuum

0 5 10 15 200.0

0.5

1.0

1.5

2.0

Energy (eV)

nk

0 5 10 15 200.0

0.5

1.0

1.5

2.0

Energy (eV)

nk

0 5 10 15 200.0

0.5

1.0

1.5

2.0

Energy (eV)

nk

Insulator Semi‐conductor Metal

Electron more and more free

Absorption band is displaced towards low energies

Directly related to the oscillator strength



Band structure

VB

CB

Eg

1

The different steps to calculate the optical properties:

Imaginary part of the dielectric function: 2

Dipolartransitions

2

Band structure

VB

CB

Eg

1



Real part of the dielectric

function : 1

Kramers-Kronigtransformation3


Dipolartransitions

2

Band structure

VB

CB

Eg

1



4

1 = n2 – k2

2 = 2nk

Determination ofn = f(E) & k = f(E)

Real part of the dielectric

function : 1

Kramers-Krönigtransformation3


Dipolartransitions

2

Band structure

VB

CB

Eg

1



0 5 10

BiVO4-mono atom 0 size 0.70

Γ A Z M L V Γ

E F

Ener

gy (

eV)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

-1.0

-2.0

-3.0

-4.0

-5.0

-6.0

Ener

gy (e

V)

0 2 4 6 8 10 12 140

5

10

Energy (eV)

2

Band structure DOS

Gap 2.3 eV

Band structure calculation1 Determination of 22

Gap 2.3 eV

Optical properties of m-BiVO4 and z-BiVO4 phases

Example of BiVO4


Determination of 13 4 Determination ofn = f(E) & k = f(E)

0

1

2

3

4

0

1

2

3

kn

Energy (eV)0 2 4 6 8 10 12 14

0

5

10

21

-5

0

5

10

Energy (eV)0 2 4 6 8 10 12 14

Example of BiVO4


Journées communications – 15/01/09

5 – OPTICAL PROPERTIES SIMULATION IN WIEN2k

Interband contributions(based on IPA*)

Intraband contributions(using a Drude‐like term)

EF EF

In WIEN2k, two types of contributions to the dielectric function( = 1 + i.2) could be estimated:

h h

Dielectric tensor / Optical conductivity / Refractive index / Reflectivity / Absorption coefficient / Loss function (EELS)

*IPA: Independant Particle Approximation



Interband contributions(based on IPA*)

EF

In WIEN2k, two types of contributions to the dielectric function( = 1 + i.2) could be estimated:

h h

*IPA: Independant Particle Approximation

Sum over all valence and conduction bands

Im(ij())


5 – INTERPRETATION: Intraband transitions (for metals)

Plasma frequency: (longitudinal oscillations of the electron gas)

Intraband contributions(using a Drude‐like term)

EF


5 – OPTICAL PROPERTIES SIMULATION IN WIEN2kOptical functions:



Symmetry of the dielectric tensor

cubic

monoclinic (, = 90°) orthorhombic

tetragonal, hexagonal

triclinic



Convergence with k‐mesh (expl.: Al)

‐30

‐20

‐10

0

10

Energy (eV)

EF

3p Ti

2s O

2p O

3d Ti

Example of the rutile phase

Atomicstructure

Electronicstructure

Dielectricfunction


6 – ILLUSTRATIONS: TiO2 series

‐30

‐20

‐10

0

10

Energy (eV)

EF

3p Ti

2s O

2p O

3d Ti

0 5 10 15 20 25 300

2

4

6

8

10

12

14

Energie (eV)

2EELS experiments



Atomicstructure

Electronicstructure

Dielectricfunction


‐30

‐20

‐10

0

10

Energy (eV)

EF

3p Ti

2s O

2p O

3d Ti

0 5 10 15 20 25 300

2

4

6

8

10

12

14

Energie (eV)

2EELS experimentsDFT simulation



Atomicstructure

Electronicstructure

Dielectricfunction

GGA (PBE)+ gap correction of 0.6 eV



6 – OPTICS IN WIEN2k

x joint Im ij() ,(case.joint) (JDOS*symmat)

x kram Re ij(), other optical funct.,broadening, scissor operator

opticplot

5

6

7

and high Emax


6 – SOME ADDITIONAL DETAILS



TiO2-RUT.inop2000 1 number of k‐points, first k‐point ‐5.0 5.0 Emin, Emax in Ry for matrix elements2 number of choices (columns in *outmat)1 Re xx3 Re zzOFF write unsymmetrized matrix elements to file?

Choices:1......Re <x><x>2......Re <y><y>3......Re <z><z>4......Re <x><y>5......Re <x><z>6......Re <y><z>7......Im <x><y>8......Im <x><z>



TiO2-RUT.injoint1 261 LOWER AND UPPER BANDINDEX0.0000 0.00100 10.0000 EMIN DE EMAX FOR ENERGYGRID IN rydeV output units eV / ryd / cm‐14 SWITCH 2 NUMBER OF COLUMNS0.1 0.1 0.3 BROADENING (FOR DRUDE MODEL ‐ switch 6,7 ‐ONLY)

SWITCH:

0...JOINTDOS FOR EACH BAND COMBINATION 1...JOINTDOS AS SUM OVER ALL BAND COMBINATIONS2...DOS FOR EACH BAND 3...DOS AS SUM OVER ALL BANDS4...Im(EPSILON) 5...Im(EPSILON) for each band combination6...INTRABAND contributions7...INTRABAND contributions including band analysis

TiO2-RUT.inkram0.1 Gamma: broadening of interband spectrum0.6 energy shift (scissors operator)0 add intraband contributions? yes/no: 1/012.60 plasma frequencies (from joint, opt 6)0.20 Gammas for Drude terms



Files generated by:x optic TiO2-RUT.symmat

TiO2-RUT.mommat

x joint TiO2-RUT.joint

x kram TiO2-RUT.epsilon

TiO2-RUT.sigmak

TiO2-RUT.refraction

TiO2-RUT.absorption

TiO2-RUT.eloss

I(є2) V

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

1500 2000 2500 3000 3500 4000 4500

CdTe

CdSe

CdS

ZnTe

ZnSe

ZnS

ZnO

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3.0

52 54 56 58 60 62 64 66 68

Blende structure Wurtzite structure

CdTe

CdSe

CdS

ZnTe

ZnSe

ZnS

ZnO

I(є2)

Refractive index (n)

0 5 10 15 20 250

10

20

30

40

50

2

Energy (eV)

EELS exp.DFT calc.(gap correction)

ZnO Blende ZnS

ZnSe

ZnTe

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.51.61.82.02.22.42.62.83.03.23.43.63.84.04.24.4

Ref

ract

ive

inde

x

Photon Energy (eV)

Ref

ract

ive

inde

x (n

)

Energy (eV)

nCdO 1.95

ZnOZnS

ZnSeZnTe

ZnS

6 –ILLUSTRATIONS: MQ series (M = Zn, Cd & Q = O, S, Se, Te)




7 – Limitations:

The band gap problem Necessity to go beyond DFT

Energy Energy

Electro‐affinity: N+1(N+1) = ‐AIonization energy: N(N) = ‐I

Eg = N+1(N+1) – N(N) = I – A

Energy

Eg = N+1(N) – N(N)

Eg = N+1(2N) – N(2N) + N+1(2N+1) – N+1(2N)

NN‐1

N+1

NN‐1

N+1

NN‐1

N+1

Eg = g + xc

g

with xc: Scissor Operator/mBJ/hybrid/GW…


Fundamental gap: electronic gap optical gapDeduced from the band structure Dipolar transitions

E

O(2p) Ti(3d)

DO

S

g(1)

2

0 2 4 6 8 10 12 140

2

4

6

8

10

12


If excitonic effects: we should go beyond(TDDFT / BSE)

Fundamental gap: electronic gap optical gapDeduced from the band structure Dipolar transitions

E

O(2p) Ti(3d)

DO

S

g(1)

2

0 2 4 6 8 10 12 140

2

4

6

8

10

12

Energy Energy

NN‐1

N+1

NN‐1

N+1Opticalexcitation

7 – Some limitations of DFT simulation of optical properties

‐ Kohn‐Sham eigenstates interpreted as excited states

‐ Independent‐particle approximation (no e‐—h+ interaction)

‐ LDA/GGA are not exact

Use of Bethe‐Salpeter Equation (BSE) – Time‐dependent DFT

Use of hybrid DFT, effective potentialsUse of DFT+U, LDA+DMFT, GW…

xps, optical propertiessusi.theochem.tuwien.ac.at/events/ws2019/blaha_xps...criteria colors harmony...

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