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
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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)
Photoelectron spectroscopy (PES)
Ekin = hν – EB - Φ0
sample
spectrum
hν
Ekin
measure kinetic energy distribution of photoelectrons
Photoelectron spectroscopy (PES)
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
0 νδψψ hEEpeAw ifirki
ffi −−⋅∝ ⋅→
final state:inverted LEED state(eigenstate of semi-infinite crystal)
energy conservation
PES theory: Independent electrons
initial state:Bloch wave or core level
)(2
0 νδψψ hEEpeAw ifirki
ffi −−⋅∝ ⋅→
final state:inverted LEED state(eigenstate of semi-infinite crystal)
PES theory: Independent electrons
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
0 νδψψ hEEpeAw ifirki
ffi −−⋅∝ ⋅→
transition matrix element
PES theory: Independent electrons
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
PES theory: Independent electrons
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)
"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
courtesy A. Damascelli
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
courtesy A. Damascelli
"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:
Transition metal oxides: Instability of polar surfaces
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)
Transition metal oxides: Instability of polar surfaces
Example: Fe3O4 (magnetite) different reconstructions of the (111) surface (STM)
VUV-PESsurface-sensitive
Soft X-ray PESprobing depth 2x larger
Transition metal oxides: Instability of polar surfaces
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
Surface effects in Mott-Hubbard-type oxides
spectral function (DMFT for n=1)
U/t
Example: CaVO3
A. Sekiyama et al., PRL 2004
surface
"bulk"
lower Hubbard band
quasiparticle peak
Surface effects in Mott-Hubbard-type oxides
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
HAXPES: drawbacks and caveats
ARPES of W(110) @ hν = 870 eV Plucinski et al., PRB 78, 035108 (2008)
( )atomphotdir MTkW 2exp α−=
Non-negligible photon momentum
hν = 6 keV λ ≈ 2 Å, kphot ≈ 3 Å-1
• suppression of direct (k-conserving) transitions
• atomic recoil effect
photon-absorbing atom takes up recoil energyat the expense of
photoelectron energy,
depending on atom mass and lattice stiffness
HAXPES: drawbacks and caveats
Non-negligible photon momentum
MkE photkin 222=
Y. Takata et al., PRB 75, 233404 (2007)
hν = 6 keV λ ≈ 2 Å, kphot ≈ 3 Å-1
• suppression of direct (k-conserving) transitions
• atomic recoil effect
• quadrupolar contribution to transition matrix element
HAXPES: drawbacks and caveats
Non-negligible photon momentum
( ) iprkiAfipeAf rki
⋅⋅+≈⋅⋅ 100
hν = 6 keV λ ≈ 2 Å, kphot ≈ 3 Å-1
• suppression of direct (k-conserving) transitions
• atomic recoil effect
• quadrupolar contribution to transition matrix element
• cross section for photoemission
• electron analyzer transmission
need bright x-ray source…
HAXPES: drawbacks and caveats
Non-negligible photon momentum
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)
• creation of 2D metal states in a correlated electron system by interface engeering
• purely electrostatic doping
• no disorder by chemical dopants
LaVO3Mott ins.∆≈1 eV
SrTiO3band ins.∆=3.2eV
"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)