Photoelectron Spectroscopy for Functional Oxides

International Summer School on Surfaces and Interfaces in Correlated Oxiides, Vancouver, 29 Aug – 01 Sep 2011

FOR

1346

Ralph Claessen (U Würzburg, Germany)

Photoelectron spectroscopy of functional oxides: Heterostructures and buried interfaces

• Photoelectron spectroscopy (PES)

• PES theory in a nutshell

• PES with hard x-rays (HAXPES)

• HAXPES of oxide heterostructures

Heterostructures of functional oxides

strong coupling between charge/orbital/spin/latticedegrees of freedom lead to:

3d transition metal oxides

- metal-insulator transitions- charge and orbital ordering- local magnetism (ferro, antiferro,…)- high-temperature superconductivity- collossal magnetoresistance- …

Epitaxial heterostructures by MBE, PLD

controlled interfaces, additional functionalities:- strain engineering- interfacial 2dim electron gas (2DEG)- electrostatic doping (by polarity or field effect) - artificial multiferroics- spin injection- …

"The interface is the device"(H. Kroemer, Nobel lecture 2000)

Want information on:

• chemical composition

• electronic structure

• vertical depth profile

photoelectron spectroscopy (PES) with soft and hard x-rays

Oxide heterostructures

Photoelectron spectroscopy (PES)


Ekin = hν – EB - Φ0

sample

spectrum

hν

Ekin

measure kinetic energy distribution of photoelectrons


Chemistry (core levels):→ composition→ chemical bonding→ valencies

Electronic structure (valence band):→ density of states → band structure → Fermi surface

→ spectral function A<(k,E)

sample

spectrum

Core level spectroscopy: ESCA

Inte

nsity

[a.u

.]

140012001000800600400Kinetic Energy [eV]

Bi2Sr2CaCu2O8+δ

•Cu 2p•CuO

C 1s

Ca 2p

O 1s

Bi 4f

hν = 1486.6 eV [Al - Kα]

Sr 3d

Inte

nsity

[a.u

.]1500149014801470

Kinetic Energy [eV]

Fermi level

Bi 4d

Inte

nsity

[a.u

.]

1340133013201310Kinetic Energy [eV]

Bi 4f7/2Bi 4f5/2

Bi 5d

Electron Spectroscopy for Chemical Analysis

courtesy of A.F. Santander-Syro

Core level spectroscopy: Chemical shift and valency

1080 1075 1070 1065

binding energy (eV)

Na1s

37%32%23%

10%4%

15%

dopi

ng x

(%

)

462 460 458 456 454

binding energy (eV)

Ti2p3/2(+ Na)

Ti3+Ti2+

Na

Example: alkali metal doping of TiOCl

valence change:Ti3+(3d1) Ti2+(3d2)

PRL 106, 056403 (2011)

TiOCl

O 2p / Cl 3p

Ti 3d

Valence band spectroscopy

k-integrated spectrum

PRB 72, 125127 (2005)

band structure and Fermi surface

Valence band spectroscopy: ARPES

Angle-Resolved PhotoElectron Spectroscopy

courtesy T. Deveraux/A. Damascelli

emis

sion

ang

le (i

.e. m

omen

tum

)

energy

PES instrumentation

• rare gas discharge lamp (<40.2 eV)• x-ray tube (1.256 and 1.486 keV)• synchrotron radiation (10 eV … 10 keV)

• hemispherical anylzer• time of flight (TOF) analyzer)

typically 10-10 mbar

Wikipedia

PES theory in a nutshell:

1) Independent electron approximation

Unperturbed electron system: one-electron states with energy E

Perturbation: classical radiation field with vector potential

Fermi´s Golden Rule for the photoinduced transition rate from initial to final states:

Hence, the total photoelectron current is:

)(2

0 νδψψ hEEpeAw ifirki

ffi −−⋅∝ ⋅→

ψ

PES theory: Independent electrons

)2(0),( trkieAtrA πν−⋅=

)()(,

ffi

fiPES EwI −∝∑ → εδε

Time-dependent perturbation theory

)(2


ffi −−⋅∝ ⋅→

final state:inverted LEED state(eigenstate of semi-infinite crystal)

energy conservation


initial state:Bloch wave or core level

)(2


ffi −−⋅∝ ⋅→

final state:inverted LEED state(eigenstate of semi-infinite crystal)


One-step model Three-step model

final state: high-energy Bloch state of infinite crystal,steps 2 and 3 incoherently decoupled

courtesy A. Damascelli

)(2


ffi −−⋅∝ ⋅→

transition matrix element


If the radiadion field is only weakly modulated on atomic length scales, (i.e. >> few Å), the photon momentum can be neglected in the transition matrix element:

Examples:

hν = 20 eV λ ≈ 600 Å

hν = 2000 eV λ ≈ 6 Å

k

πλ 2= k

irefAipAfipeAf rki

⋅∝⋅≈⋅⋅000

Dipole approximation


Dipole approximation and k-selection rule for Bloch states

momentum conservation:

photonif kGkk

++=only"vertical" transitions

ARPES

oxides of the 3d transition metals: M = Ti, V, … ,Ni, Cu

basic building blocks: MO6 octahedra (or other ligand shells)

electronic configuration: O 2s2p6 = [Ne]

TM 3dn

cubic perovskites perovskite-like anatas rutile spinel

O2-

quasi-atomic,strongly localized strong intraatomic Coulomb interaction

and breakdown of independent electron approx.

Transition metal oxides: electronic correlations

TMX+

PES theory in a nutshell:

2) Many-body picture

Ekin

hν

N interacting electrons:

"loss" of kinetic energy due to interaction-related excitation energy stored in the remaining N-1 electron system !

Many-body effects in photoemission

Photoemission process:

sudden removal of an electron from N-particle system

Fermi´s Golden Rule for N-particle states:

with

N-electron ground state of energy EN, 0 ("initial state")

N-electron excited state of energy EN, s, ("final state")

consisting of N-1 electrons in the solid and a free photoelectron of momentum and energy ε

in second quantization with suitable one-electron basis

)(ˆ)( 0,,2

0,, νδε hEEI NsNs

isf −−Ψ∆Ψ∝∑

0,0, Ni =Ψ

sNksf ,1,, −=Ψ

k

ifif

N

iii ccMprA +

==⋅=∆ ∑

1)(ˆ

one-particle matrix element

Reinterpretation of Fermi´s Golden Rule

Electron removal spectrum

Fermi´s Golden Rule for N-particle states:

The ARPES signal is directly proportional to the

single-particle spectral function )()(Im1)( ωωπ

ω fGA ×−=<

)(εI

a little bit of mathand a few plausible assumptions (sudden approximation)

single-particle Green´s function

probability of removing an electron at energy ω from the system

)(ˆ)( 0,,2

0,, νδε hEEI NsNs

isf −−Ψ∆Ψ∝∑

ωµ

U

TiOCl

O 2p / Cl 3p

Ti 3d1

d1 → d0

LHBd1 → d2

UHB

Example: PES of the Mott insulator TiOCl

spectral function A<(ω) (DMFT)

Photoemission probing depth:

soft and hard x-ray PES

Inelastic scattering of the photoelectron

Three-step model


Step 2: photoelectron transport to the surface

inelastic scattering with other electrons (excitation of e-h-pairs, plasmons)

• generation of secondary electrons("inelastic background")

Ekin

intensity intrinsic spectrum

incl. background

Inelastic scattering of the photoelectron

Three-step model

Step 2: photoelectron transport to the surface

inelastic scattering with other electrons (excitation of e-h-pairs, plasmons)

• generation of secondary electrons("inelastic background")

• loss of unscattered photoelectron current⇒ inelastic mean free path λ


"conventional" VUV/XUV-PES:surface sensitive on atomic length scale !

Photoemission probing depth

λ(Ekin)

hνEkin

probing depth (3λ) up to >10 nm access to bulk, buried nanostructures, and

interfaces

depth profiling of thin films

λ(Ekin) "universal curve"

hard x-ray PES = HAXPESsoft x-ray PES (SX-PES)

0≠µ0=µ0=µ

O2-

TMX+

Transition metal (TM) oxides form lattice of ionic charges

Classification of surfaces (Tasker): - surface charge Q- electrical dipole moment in repeat unit

P. W. Tasker, J. Phys. C 12, 4977 (1979)

Transition metal oxides: Instability of polar surfaces

O2-TMX+

µ

0=Q 0≠Q 0≠Q

O2-

TMX+

type 3 surfaces are energetically unfavorable:


charge field potential

"polarization catastrophe"

will be avoided by atomic/ionic/electronic surface reconstruction

⇒ surface ≠ bulk

-σ+σ-σ+σ

8.2 Å

PRB 76, 075412 (2007)


Example: Fe3O4 (magnetite) different reconstructions of the (111) surface (STM)

VUV-PESsurface-sensitive

Soft X-ray PESprobing depth 2x larger


Example: Fe3O4 (magnetite)

EPL 70, 789 (2005)

∑∑ ↑↓+ +−=

iii

jiji nnUcctH

σσσ

,,

ˆ

kinetic energy,itinerancy

local Coulomb energy,localization

Surface effects in Mott-Hubbard-type oxides

t

Uspectral function (DMFT for n=1)

U/t


spectral function (DMFT for n=1)

U/t

Example: CaVO3

A. Sekiyama et al., PRL 2004

surface

"bulk"

lower Hubbard band

quasiparticle peak


Example: CaVO3

A. Sekiyama et al., PRL 2004

surface

"bulk"

lower Hubbard band

quasiparticle peak

reduced atomic coordination @ surface:

stronger electron localization

smaller effective bandwidthWsurf < Wbulk

surface stronger correlated:U / Wsurf >U / Wbulk

"conventional" VUV/XUV-PES:surface sensitive on atomic length scale !

Photoemission probing depth

λ(Ekin)

hνEkin

probing depth (3λ) up to >10 nm access to bulk, buried nanostructures, and

interfaces

depth profiling of thin films

λ(Ekin) "universal curve"

hard x-ray PES = HAXPESsoft x-ray PES (SX-PES)

hν = 6 keV λ ≈ 2 Å, kphot ≈ 3 Å-1

HAXPES: drawbacks and caveats

Non-negligible photon momentum

hν = 6 keV λ ≈ 2 Å, kphot ≈ 3 Å-1

• suppression of direct (k-conserving) transitions

Debye-Waller factor for direct transitions


ARPES of W(110) @ hν = 870 eV Plucinski et al., PRB 78, 035108 (2008)

( )atomphotdir MTkW 2exp α−=


hν = 6 keV λ ≈ 2 Å, kphot ≈ 3 Å-1


• atomic recoil effect

photon-absorbing atom takes up recoil energyat the expense of

photoelectron energy,

depending on atom mass and lattice stiffness



MkE photkin 222=

Y. Takata et al., PRB 75, 233404 (2007)

hν = 6 keV λ ≈ 2 Å, kphot ≈ 3 Å-1



• quadrupolar contribution to transition matrix element



( ) iprkiAfipeAf rki

⋅⋅+≈⋅⋅ 100

hν = 6 keV λ ≈ 2 Å, kphot ≈ 3 Å-1



• quadrupolar contribution to transition matrix element

• cross section for photoemission

• electron analyzer transmission

need bright x-ray source…



Low photoemission signal

( ) 3−∝ νσ h1−∝ kinEt

HAXPES set-up @ PETRA III (DESY, Hamburg)

X-rays fromPETRA III

"High-resolution hard x-ray photoemission for materials science" (BMBF)

• joint project with C. Felser (U Mainz) and W. Drube (DESY)

• photon energy: 2.5…15 keV

• energy resolution: 30 meV

• linearly/circularly polarized x-ray radiation

• commissioned in 2010

• user operation since 2011

other HAXPES instruments worldwide:- Spring-8, Japan (>4)- BESSY, Germany (HIKE)- ESRF, France (ID-9)- Soleil, France (under construction)- Diamond, UK (under construction)

HAXPES of oxide heterostructures:

(1) Fe3O4/GaAs

Fe3O4

GaAs

Epitaxial growth of Fe3O4/GaAsPRB 79, 233101 (2009)

surface Datta-Das spin transistor

semiconductor with large spin diffusion length

semimetallic ferromagnet(100% spin polarization @ EF)

resistively matched to semiconductor

Fe3O4 (magnetite), (RE,Sr)MnO3, CrO2, Heusler compounds, …

Fe3O4

GaAs

Epitaxial growth of Fe3O4/GaAsPRB 79, 233101 (2009)

surface

MBE growth of thin magnetite film:

• epitaxial Fe deposition @ RT

• postoxidation @ 600 - 800K / p(O2) = 10-5 mbar (10-30 min)

Fe valency?

mixed-valent Fe3O4 vs. (Fe2+ )O and (Fe 3+)2O3 ?

chemical depth profile ?

700 705 710 715 720 725 730 735 740 745 750

Fe2O3

Fe3O4

FeO

Fe

charge transfer satellites

binding energy (eV)

Valence signatures in Fe 2p spectrum

Fe3+

Fe2+

Fe0

Fe2+/Fe3+

2p1/2 2p3/2

Fe3O4

GaAs

Depth profiling of Fe3O4/GaAs

Fe 2p spectra

PRB 79, 233101 (2009)

surface

interface

surface


Tuning the information depth by variation of

(1) photon energy, or (2) photoelectron escape angle

energy

mea

n fr

ee p

ath

θ

λeff

λeff = λIMFP cos θ

Fe3O4

GaAs


Fe 2p spectra

PRB 79, 233101 (2009)

surface

film: mixed-valent Fe2+/3+

interface: divalent and metallic Fe (O-deficient)

interface

surface

Fe3O4

GaAs

interface (Fe, FeOx, GaOx, AsOx)


Fe 2p spectra As 2p3/2 spectra

PRB 79, 233101 (2009)

surface

film: mixed-valent Fe2+/3+

interface: divalent and metallic Fe (O-deficient)oxidized Ga,As

Fe3O4

GaAs

interface (Fe, FeOx, GaOx, AsOx)

Validation by electron microscopy

surface

TEM

STEM-EELS

J. Verbeeck, H. Tian, and G. van Tendeloo, U Antwerp

Fe3O4

ZnO

Fe3O4/ZnO: An all-oxide structure

also PLD-grown contacts: R. Gross et al.

APL 98, 012512 2011

HAXPES TEM

film grown by reactive deposition in O2-atmosphere (∼10-6 mbar)


(2) Interface 2DEG in LaAlO3/SrTiO3

•epitaxial growth by PLD

A. Ohtomo et al., Nature 419, 378 (2004) S. Thiel et al., Science 313, 1942 (2006)N. Reyren et al., Science 317, 1196 (2007)

LAO/STO heterostructures in a nutshell

LaAlO3∆=5.6eV

SrTiO3∆=3.2eV

•epitaxial growth by PLD

•both oxides: wide gap insulators

• if LaAlO3 film thicker than 3 unit cells (uc) : → formation of a high-mobility 2DEG

at the interface


2DEGconductivity

sheet carrier density (Hall)


LaAlO3∆=5.6eV

SrTiO3∆=3.2eV


2DEG


properties of the 2DEG:

• tunable conductivity by electric gate field

• superconducting below 200 mK

•magnetoresistance

•coexistence of s.c and magnetism / electronic phase separation

origin of 2DEG, threshold behavior ?

LaAlO3∆=5.6eV

SrTiO3∆=3.2eV

Polar catastrophe

polar catastrophe

Nakagawa et al., Nature Mat. 5, 204 (2006)

AlO2

LaO

LaO

LaO

AlO2

AlO2

TiO2

SrOTiO2

SrO

-1+1-1+1-1+1

0000

charge:

electrostatic energy increases linearly with thickness of polar film

electronic or ionic

0.5e- per layer unit cell n2D = 3.5×1014 cm-2

partial Ti 3d occupation Ti3.5 (d0.5) = Ti3+/Ti4+

charge reconstruction

AlO2

LaO

LaO

LaO

AlO2

AlO2

TiO2

SrOTiO2

SrO

-1/2+1-1+1-1+1

-1/2000

∆q = -1/2

and how to avoid it

HAXPES of LAO/STO heterostructures

PRL 102, 176805 (2009)

undoped SrTiO3: |3d0> Ti4+

doped LAO/STO interface: |3d0> + |3d1> Ti3+/Ti4+

Ti 2p spectrum

Ti4+

2p1/2 2p3/2

2DEG

SrTiO3

LaAlO3

Ti3+

Dependence on LAO overlayer thickness

interface charge density increases with LAO overlayer thickness

non-zero Ti d1 signal already for 2uc sample (?)

PRL 102, 176805 (2009)

Ti4+

Ti3+

Ti3+

Depth profiling by angle-resolved HAXPES

θ

d

e-

e-

PRL 102, 176805 (2009)

2DEG thickness

sheet carrier density

Quantitative analysis: 2DEG thickness

*lattice constant of STO unit cell (uc) = 3.8 Åθ

d

e-

e-

PRL 102, 176805 (2009)

Sample 2 uc 4 uc 5 uc 6 uc

d (uc*) 3 ± 1 1 ± 0.5 6 ± 2 8 ± 2

interface thickness < 3 nm

consistent with

- CT-AFM Basletic et al. (2008)

- TEM-EELS Nakagawa et al. (2006)

- density functional theory Pentcheva et al. (2009)

- 2D superconductivity Reyren et al. (2007)

- ellipsometry Dubroka et al. (2010)

Quantitative analysis: sheet carrier density

Sample 2 uc 4 uc 5 uc 6 uc

n2D (1013 cm-2) 2.1 3.9 8.1 11.1

n2D << electronic reconstruction value

n2D >> Hall effect data

el. reconstruction

35

PRL 102, 176805 (2009)

RIXS on LAO/STO

RIXS eg-excitation as fct. of # LAO-overlayers

PRB 82, 241405(R) (2010)

t2g

Ti 2p

Ti 3deg

Ti3+ (3d1)

photon in photon

out

Sheet carrier density: HAXPES, RIXS & Hall effect

• n2D much smaller than expected for purely electronic reconstruction (35 x 1013 cm-2)

• n2D higher than Hall effect data

• photo-generated carriers cannot fully account for observed excess

• remaining excess due to additional localized Ti 3d electrons? (cf. DFT - Popovic et al., PRL 2008)

PRB 82, 241405(R) (2010)

~3 eV

LAO/STO: Valence band spectroscopy with HAXPES

2DEG

SrTiO3

LaAlO3

2DEG

SrTiO3

LaAlO3

Ti 3d electrons should be here, but HAXPES cross-section too small !(theor. estimate: 10-4 of O2p emission)

O2p-derived vb states

Band situation from density-functional theory

surf

ace2D

EGSTO LAO

CBM

VBM

E

core levels

EF

Yu Lin et al., arXiv 0904.1636 (2009)Pentcheva and Pickett, PRL 102, 107602 (2009)

holes@ LAO VBM

electrons@ STO CBM


e-e- surf

ace2D

EGSTO LAO

CBM

VBM

E

core levels

EF


interface

holes@ LAO VBM

electrons@ STO CBM


e-

E

EF

e- surf

ace2D

EGSTO LAO

CBM

VBM

E

core levels


Results from HAXPES

Al 1s core levelvalence band

~3 eV

VBM: ~ 3 eV below EF same width for all samples!

band theory versus experiment

EF

e- surf

ace2D

EGSTO LAO

CBM

VBM

E

core levels

also observed by Segal et al., PRB 80, 241107(R) (2009)

STO LAO

• VBMLAO above VBMSTO

• type II interface(valence band offset: 0.35 ± 0.1eV)

• confirmed by core level analysis

Valence band offsets

valence band analysisCB

VB

type I type II

STO LAO STO LAO

band alignment

0.35eV

Band alignment: A possible scenario

DFT band theory:

Photoemission:

STO LAOlocalized hole states induced by surface O-vacancies

interface states (itinerant and localized)


(3) LaVO3/SrTiO3 – electrostatic doping of a Mott a insulator

Electrostatic doping of a Mott insulator

LaAlO3band ins.∆=5.6eV

SrTiO3band ins.∆=3.2eV

q2DEG

LAO/STO

(AlO2)-

(LaO)+

(TiO2)0

(SrO)0

……

polar

non-polar

Idea:replace Al3+ by trivalent transition metal

LaVO3

LVO/STO

LaVO3Mott ins.∆≈1 eV


???

Ohtomo/Hwang, Nature 427, 423 (2004) Hotta et al., PRL 99, 236805 (2007)

LaVO3: - valence configuration V3+ (d2)

- polar oxide

- Mott insulator (∆LVO << ∆STO)

electronic reconstruction and formation of interface 2DEG ?

extra carriers on which side of interface(LVO or STO) ?




???

LVO/STO

band-filling controlled Mott transition without chemical doping ?

LVO/STO: Sample growth and characterization

pulsed laser deposition

RHEED oscillations

RHEED pattern AFM image

STEM image

interface

LVO/STO: metal-insulator transition in transport

metal-insulator transition for n-type interface

p-type interface insulating

critical thickness: ∼ 9 uc LVO (Hotta et al.: 5 uc)

high carrier mobility

HAXPES of LVO/STO: V 2p depth profiles

6 uc LVO

STO

homogeneous "V3+" profile

extra electronic charge on V near interface

10 uc LVO

STO

insulating conducting

HAXPES of LVO/STO: Ti 2p

10 uc LVO

STO

no Ti3+ (d1) signal

possibly some bandbendingon STO side of interface

extra electronic charge on V near interface

LVO/STO: electronic reconstruction picture


LaVO3/SrTiO3:

• creation of 2D metal states in a correlated electron system by interface engeering

• purely electrostatic doping

• no disorder by chemical dopants



"q2DEG"

Summary

Photoelectron spectroscopy of functional oxides:Heterostructures and buried interfaces

• Photoelectron spectroscopy (PES)yields (destruction-free) information on- chemical composition, valencies, local chemistry - electronic structure (band structure, spectral function)

• PES with hard x-rays (HAXPES)- enhanced probing depth giving access to bulk and buried interfaces- needs high x-ray intensity ( synchrotron radiation)- caveat: high photon momentum (ARPES difficult, recoil effects)

• Future directions:- magnetic information with polarized x-rays (XMCD, XMLD) and/or spin detection- soft x-ray ARPES: band mapping of buried interfaces

Photoemission:

• S. Hüfner, Photoelectron Spectroscopy – Principles and Applications, 3rd ed. (Berlin, Springer, 2003)

• A. Damascelli, Angle-resolved photoemission studies of the cuprate superconductors,Rev. Mod. Phys. 75, 473 (2003)

HAXPES:

• K. Kobayashi: Hard x-ray photoemission spectroscopy, Nucl. Instr. Meth. Phys. Res. A 601, 32 (2009)

• László Kövér: X-ray photoelectron spectroscopy using hard X-rays,J. Electron Spectrosc. Rel. Phen. 178-179, 241 (2010)

HAXPES of oxide heterostructures

• R. Claessen et al.: Hard x-ray photoelectron specroscopy of oxide hybrid and heterostructures: a new method for the study of buried interfaces,New J. Phys. 11, 125007 (2009)

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