Photoemission (I)Spectroscopy
Cheiron School 2009
November 8, 2009 Spring-8, Japan

Ku-Ding Tsuei
tsuei@nsrrc.org.tw
National Synchrotron Radiation Research Center

Outline
1. What is photoemission spectroscopy?
2. Fundamental aspects of photoemission.
3. Examples.
4. Increase bulk sensitivity: HAXPES.
5. Challenging future directions.
General reference books:
1. "Photoelectron Spectroscopy" 3rd Ed. by S. Hufner,
Springer-Verlag 2003
2. "Angle-Resolved Photoemission: Theory and Current
Applications", S. D. Kevan, ed., Amsterdam; Elsevier 1992

What is photoemission?

Photon in –> electron out (emission)What are the samples and probed states?
Atoms
Molecules
Nanoprticles
Solidsatomic orbitals (states)
molecular orbitals
core level states (atomic like)valence bands/statescore level states (atomic like)valence bands
core level states (atomic like)What is photoemission spectroscopy?
(photoelectron spectroscopy) (PES)Electron energy analyzer

hv

Monochromatized
photonse-h+sampleInitial state: ground (neutral) state

Final state: hole (excited) state

Conservation of energy

N(Ek)Ek = hv + Ei – Ef (most general expression)
Ek : photoelectron kinetic energy
Ei (N) : total initial state system energy
Ef (N-1): total final state system energy

EkEnergy Distribution Curve (EDC)(Spectrum)

Single particle description of energy levels(Density of States) (most convenient in PE)
Na atom

Na metalE

3p3s

EFFermi level√E (nearly free electron like)
Valence (sp)Band(DOS)

2p3/2
2p1/22s

Core levels

1s
N(E)
(DOS)

Energetics in PES
Ek = hv – EB - φConservation of energy
Ev : vacuum (energy) level
EF : Fermi (energy) level
φ = Ev – EF : work function
E0 : bottom of valence band
V0 = Ev – E0 : inner potential
Ekmax marks EF in spectra
EB measured relative to EF = 0
Hufner, Damascelli

Usually fixed photon energy
scanning not neededAn XPS Energy Distribution Curve (EDC)Å Most spectra expressed
this way
HufnerLight sources and terminology
Ultraviolet Photoemission Spectroscopy (UPS)UV He lamp (21.2 eV, 40.8 eV)
valence band PE, direct electronic state info

X-ray Photoemission Spectroscopy (XPS)(Electron Spectroscopy for Chemical Analysis) (ESCA)
x-ray gun (Al: 1486.6 eV, Mg: 1253.6 eV)core level PE, indirect electronic state info
chemical analysis

Synchrotron radiation:
continuous tunable wavelength
valence band: <100 eV, maybe up to several keV
core level: 80-1000 eV, maybe up to several keV
depending on core level binding energies

Inelastic Electron Mean Free Path (IMFP)
I(d) = Io e-d/λ(E)λ(E): IMFP depending on kinetic energy relative to EF
SR (VUV,SX,HX)
Univeral curve
XPSUPS

Hufner

Minimum due to electron-electron scattering, mainly plasmons

PE is a surface sensitive technique! (requires UHV)High energy photoemission: several keV to increase bulk sensitivity

Core level binding energies arecharacteristic of each orbital ofeach element
Finger prints
Core level BE independent ofphoton energy usedCore level photoemission: chemical analysis of elements
ESCA (XPS)
hv = Mg Kα = 1253.6 eV

Synchrotron hv = 160 eV

Different photon energy Ædifferent relative cross section
for various core levels Æ
Relative intensity changes
with photon energy
PJW, NSRRCsurface component(b)

Cd 3d5/2

Photoemission Intensity (a. u.)

Photoemission Intensity (a. u.)(a)Bulk CdSe

Dm = 42 A

Dm = 32 A

Dm = 18 A
410

409

408

Se 3d

Bulk CdSe

Dm = 42 A

Dm = 32 A

Dm = 18 A
407

406

405

404

403

59

58

Binding Energy (eV)Intensity (a. u.)

Dm = 42 A
Dm = 32 A
Dm = 18 A

86

457

56

55

54

Binding Energy (eV)

Bulk CdSe

10

bulk component

2Binding Energy (eV)0-25352

Surface core level shift(chemical and/orenvironmental)A case study of IMFP
applied to PE of CdSenano particles withtunable SR
How to choose photon
energies for valenceand different core levels
with the max surface
sensitivity?

Actual choices:
Cd 3d5/2 :Se 3d:
Valence band:

480 eV
120 eV
50 eV

Ek ~ 45-74 eV, most surface sensitive
Wu, PRB 2007 NSRRC

Core level photoemission:
chemical shift
higher oxidation state=> higher BEBE

higher emission angle
Æ more surface sensitive(IMFP)Pi, SS 2001 NSRRC

Auger Electron Spectroscopy
Core electron ionized by photons
or high energy electrons
Non-radiative core hole decay
Æ Auger electron emission
Radiative decayÆ Fluorescent x-ray emission

Comparison between PESand AES
PES: constant BE, Ek shift
with changing photon energy
AES: constant Ek, apparent
BE shift with changing
photon energy(synchrotron)

Photoemission Process

Explicitly responsible for IMFP

Implicitly responsible for IMFP

Hufner, Damascelli

Conceptually intuitive,
Simple calculation works

Rigorous,
requires sophisticated calculation

Schematic wave functions of initial and final states(valence band initial states)

Bulk band gapBulk band gap(a) Surface resonance(b) Surface state(c) Bulk Bloch state(d) Surface resonance(e) in-gap evanescent state(f) Bulk Bloch final stateElectron kinetic energy inside and outside of solids
Inner potential: EV – E0

Concept of inner potential is used to deduce 3D band structure from PE dataassuming free electron like final state inside solids

Angle Resolved Photoemission Spectroscopy (ARPES)

θzxxz plane: crystal symmetry planeөElectron emission angle:Photon incident angle: ψ, s- and p-polarization

Conservation of linear momentum parallel to the surface

2mk // =Ek ⋅ sin θ2hk // ( Å -1 ) = 0.5123 Ek ( eV ) ⋅ sin θk||(inside) = k ||(outside)
Conservation of liner momentum
Important for 3D and 2D band mappingk┴ (inside) ≠ k ┴ (outside) because of inner potential
Ultimately to deduce band dispersion E(k┴) or E(k┴,k||)Normal emission: θ = 0, or k|| = 0, most used detection geometryBand Mapping (3D) E(k┴, k||=0)k┴Pilo, Damarscelli

1st B.Z.

Vertical transition (using visible, uv and soft x-rays) at normal emission
For hard x-ray photon momentum cannot be neglected
Using different hv at normal emission to map out E(k┴)

Bulk band structure andFermi surfacesCu

Fermi surfaces:
Electron pockets and hole pockets
Related toHall coefficientElectric conductivity
Magnetic susceptibility

Gap below EF(=0) at L-point(nearly free electron like) sp-band
Small dispersion d-band
more localized state
Large dispersion sp-band
extended state

Dispersion of a band can tell how localized
or extended a state is in a solidL(111)

ΓX
(001)

HufnerQuantum well states: manifestation of particle in a box
in real materials
Ag(111) thin films expitaxiallygrown on Au(111) substrate
Au E Ag vacuum
EFBand gap
below EFLAg QWS canexist within
Au gapz
Quantized discretely along z-direction
Energy levels depend on film thickness L
Nearly free electron like in xy-plane

Bulk projected bands along ΓLof Au and Ag, respectively

Å Ag S.S.
2DInt.
plotsAg QWS

k|| = 0EDCs

Luh et al.
PRL 2008
NSRRC
BL21B1

Clean Au(111)surface state

Deposit 22 ML Ag
at 37 K
disordered form

Anneal to 258 K
Atomically flat
22 ML thin film

Anneal to 180 K
QWS appear
minimal flat
dispersion
Small localized
domains within
xy-planeAnneal to 189 K
Coexistence of
two kinds ofdispersion
Anneal to 258 K
Well developed
dispersion
Large, good
crystalline
domainsin xy-plane

Proposed growth model
Annealing Temp

Same QWS energies ÆSame crystalline film
thickness along z
even though lateralcrystalline domains
grow from small tolarge

One-particle spectral function near EF measured byARPES with many-particle correction (quasi-particle)
Σ" (k , ω )A( k , ω ) = −π [ω − ε k − Σ' (k , ω )]2 + [Σ" ( k , ω )]2
1

εk : single particle energy without many-particle correction
ω= 0 : EF

Self energy correction due to interaction with phonons, plasmonsand electrons, etc.

Σ( k , ω ) = Σ' ( k , ω ) + iΣ" ( k , ω )Real part: shift observed peak energy from single particle energy
Imaginary part: peak FWHM = 2 Σ”

Peak position
Featurelesssingle particledispersioncurve

Kink ~25 meV due to electron-phonon scattering

Peak position – single particle curve

Width due toelectron-electronscattering ~ ω2
Width due toelectron-phononscattering
Const bkg width
due to impurities

Total W=We-e+We-ph+Wim

Photoemission cross section in single particle
approximation (1st step in 3-step model, inside bulk)(2dσ∝ ∑ Ψ f A ⋅ p Ψ i ⋅ δ E f − E i − hνdΩ)M fi = Ψ f A( r ) ⋅ p Ψi ≅ A(0) ⋅ Ψ f p Ψi ∝ A(0) ⋅ Ψ f r Ψidipole approximation
A : polarization vector
Ψi : initial state (orbital) wave function (1s, 2p, valence states etc.)
contain orbital symmetry information
Ψf : final state (orbital) wave function ~ exp(ik.r) for high kinetic energy
photoelectrons, no orbital symmetry retains (non-resonance photoemission)(orbital symmetry in final state is important in near edge absorption
measurements (XAS) and in intermediate state in resonance photoemission)
Dipole transition rule: Δl = +1
Symmetry selection rule for initial (valence) state governed by matrix element
e.g. suppose A(0) = Ax, <eikz | x | ψi(x) > = 0 if ψi(-x) = +ψi(x)Important for crystalline samples

Symmetry of states in ARPES determined by selection rule
example: LiCu2O2
Li+Cu2+O2-2 chains along b-axis built byedge sharing Cu2+O2-4 plaquettes

O2Cu2+Cu+Cu2+ : 3d9 Æ spin-1/2
Quasi-1D spin-1/2 chain
Coexistence of spin-spiral long range orderwith ferroelectricity Æ multiferronic

cbaa = 2b

Ideal spin-1/2 1D chain system will havespin-charge separation of photo-hole decay
Does it happen on LiCu2O2?
Must be checked by ARPES(not discussed further)Will focus on symmetry of states determined byARPES with polarization

OOyCu Ox

Basic building unit: CuO4 planar plaquette

Odxy

Highest energy state:
Cu 3dxy and O 2p antibonding (AB) state
Still keeps dxy symmetrydxyy’x’Ax’

yNormal emission |f> = exp(ikz) even to all symmetry op[i> even to y’z-plane, Ax’ odd to y’z-plane<f| Ax’ |i> = <+| - | +> = 0, forbidden
Off-normal emission [f> = exp(ikz+kx’) even to x’z-plane|i> even to x’z-plane, Ax’ even to x’z-plane<f| Ax’ |i> = <+| + | +> != 0, allowed

xNormal emission [f> = exp(ikz) even to all symmetry op[i> odd to xz-plane, Ax even to xz-plane<f| Ax |i> = <+| + |-> = 0, forbidden

Ax

Off-normal emission |f> = exp(ikz+ikx) even to xz-plane|i> odd to xz-plane, Ax even to xz-plane<f| Ax |i> = <+| + |-> = 0, forbidden

Focus on B.E. = 0.7 eV peak at Y’hν = 22 eVh ν = 47 eVh ν = 47 eVh ν = 73 eV

Γ

Γ

(X)

(0.55)

2.0

1.0

0.0

y(0.55)Y(Γ′)

Y (Γ′)

3.0

2.0

1.0

0.0

x

y(1.5)

3.0

2.0

1.0

0.0

Binding Energy (eV)Binding Energy (eV)Y'(1.1)

(1.1)

(1.1)

Binding Energy (eV)(X)

(0.55)Y (Γ′)

3.0(0)

Intensity (arb. unit)

1

Intensity (arb. unit)

(X)

(0)

ΓΓ

(0)

Intensity (arb.unit)

(0)

xy3.0

2.0

1.0

0.0Binding Energy (eV)xy’x’Ax’
Ax

AxAx

The highest energy peak at 0.7 eV has dxy symmetry!

ARPES for valence band PE uses primarily VUV light because
1. Better absolute photon energy resolution for most BLs designed
as const ΔE/E.
2. Better photoionization cross section at low photon energy.
3. Better momentum resolution for a given angular resolution.
Δk|| = 0.5123 √(Ek) cos(θ) Δθ
SX ARPES has been tried for increasing bulk sensitivity, more
free electron like final states and reduced matrix element effects.
The increasing bulk sensitivity will be discussed.

NSRRC U9 BL21B1 BL andhigh resolution photoemission end station

U9undulator

CGM

Scienta
SES 200analyzer

Hemispherical electron energy analyzer
R1 : radius of inner sphereR2 : radius of outer sphere
Ro=(R1+R2)/2 : mean radius
and along electron path
V1: inner potential
V2: outer potential
Ep: pass energy = electron
kinetic energy along meanradius

Resonance photoemission(near-edge absorption followed by Auger likeelectron emission)e.g. Ce3+ (4f1)4f mixed with other DOS

e-e4f

intermediatestateEF

4f

Intensity enhanced by absorption
Predominantly 4f DOS

4f

4f

4f

4f
Absorption +3d/4d

3d/4d
Direct PE

3d/4d
Resonance PEEFAuger likeemission

Comments on photoelectron IMFP
Valence band PE using VUV and SX has IMFP near minimum,very surface sensitive. It is great to probe surface electronic structuresuch as surface states and surface resonances.
Many strongly correlated systems have electronic structure sensitive tocoordination, thus surface contains different electronic structure fromthat of deeper bulk. Great surface sensitivity posts a serious problem toprobe true bulk properties.
Need larger IMFP by using higher energy photons to enhance bulk sensitivity.

2000

surfacesurfaceBy using Ce 3d Æ 4f Res. PE near 880 eV surface 4f component becomes
greatly reduced compared to 4d Æ 4f Res. PE near 120 eV, the resulting spectra
are closer to true bulk 4f DOS.

Drive to go to even higher photon energies into
hard x-ray regime

HArd X-ray PhotoEmission Spectroscopy(HAXPES)HAXPES not only reach even closer to true bulk properties ofstrongly correlated systems, but also becomes capable of probinginterface electronic structure, Very difficult using conventional VUV/SX.

HAXPES example: Hard x-ray photoemission on
Si-high k insulator buried interface
Kobayashi, APL 2003 SPring-8

Annealed sample
HfSix formation
hv = 6 keV, ΔE ~ 0.24 eV
Take-off angle dependence => non-destructive depth profileCan probe buried interface at 35 nm ! (achievable only by hard x-ray PE)

NSRRC HAXPES projectat SPring-8Why Hard X-rays?
Electron IMFP (probing depth) and Cross section
2Inelastic Mean Free Path (A)Au
SiO2HAXPES

100
7654XPS3210UPS

7655 6 7210234 5 6 7310Kinetic Energy (eV)234 5 6 7410SP8Higher Ek for deeper probing depth or more bulk sensitivity, for strongly
correlated systems and interface properties
Photoemission signal (σ⋅λ) decreases rapidly > 1 keV
Need photon source of higher flux/brightness (modern SR),efficient BL design and good electron analyzers

HAXPES is a low count rate, photon hungry experiment!

Optical design concept

Diamond (111) reflection
6-12 keV

DM: horizontal dispersion

HRM: vertical dispersion

6-12 keV using
diamond (111) reflection
Designed for HAXPES

Layout of the side beamline of BL12XU

Diamond monochromator: installed Aug. 3, 2007

Diamond glows even under weakradiation at a fully opened gap 50 mm.
Its shape is like a trapezoid.

Strong radiation at a small gap 10 mm~ 6 keV makes the diamond glow
like a bright mercury-vapor lamp.
Strong scattered radiation causes
snow like noise on camera.

February, 2008

Commission of SPring-8 BL12XU SL HAXPES end station – Apr. Jul. 2009
MBS energy analyzer End station
Horizontal
setup

Verticalsetup

High Res.
Mono.
KB focus
mirrors
Rotational
platform

KB Focus at sample
Aft HRM Si(333)7.6 keV
38x38 microns

In collaboration withCologne U of Germany

Low resolution w/o HRM
8 keV

Medium resolution
Si(333) HRM, 7.6 keVChallenging future directions ofPhotoemission Spectroscopy
1. ARPES at submicron to tens of nanometer scale,using Schwatzchild optics or zone plates.
Need brighter light sources.
2. Time-resolved PES.
Pump-probe: dynamics.
Need efficient detection and brighter sources.
lasers or laser+SR.

Thanks for your attention