Photoemission (I)Spectroscopy
Cheiron School 2008
October 5, 2008 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.
4.
HAXPES
5. Challenging future directions.
General reference books:
1. "Photoelectron Spectroscopy" 3rd Ed. by S. Hufner,
Springer-Verlag
gg 2003
2. "Angle-Resolved Photoemission: Theory and Current
Applications", S. D. Kevan, ed., Amsterdam; Elsevier 1992

What is photoemission?

Photon in –>> electron out (emission)

Wh t are theWhat
th samples
l andd probedb d states?
t t ?
Atoms
Molecules
Nanoprticlesp
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)hv

Electron energy analyzer

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

Final state: hole (excited) state

Conservation of energy

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

Ek
Energy Distribution Curve (EDC)(Spectrum)

Singleg pparticle description
pof energy
gy levels(Density of States) (most convenient in PE)
Na atom

Na metal
E

3p
3s

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

2p3/2
2p1/2
/
2s

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Lightg sources and terminology
gy
Ultraviolet Photoemission Spectroscopy (UPS)UV He lamp (21
(21.2
2 eV
eV, 4040.8
8 eV)
valence band PE, direct electronic state info

X-ray Photoemission
X
Ph t
i i S
Spectroscopyt(XPS)(Electron Spectroscopy for Chemical Analysis) (ESCA)
x-ray gun (Al:(Al 14861486.66 eV,V M
Mg: 1253
1253.6
6 eV)V)core level PE, indirect electronic state info
chemical analysis

Synchrotron radiation:
continuous
tittunable
bl wavelengthlthvalence band: <100 eV, maybe up to several keV
core level: 80-1000
80 1000 eV
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
XPS
UPS

Hufner

Minimum due to electron-electron scattering, mainly plasmons

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

Core level binding energies arecharacteristic of each orbital ofeachh elementlFinger prints
Core level BE independentpofphoton 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

Photoemmission Intenssity (a. u.)

Photoeemission Intennsity (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)Intensitty (a. u.)

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

8

6

4

57

56

55

54

Binding Energy (eV)

Bulk CdSe

10

bulk component

2

Binding Energy (eV)

0

-2

53

52

Surface core level shift(chemical and/or
environmental)
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
eV, most surface sensitive
Wu, PRB 2007 NSRRC

Core level photoemission:pchemical shift
higher oxidation state=> higher BEBEhigher 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
ad at e decayÆ Fluorescent x-ray emission

Comparison between PES
and AESPES: constant BE
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

Conceptuallypy intuitive,,
Simple calculation works

Rigorous,g,requires sophisticated calculation

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

Bulk band gap(a) Surface resonance(b) Surface state(c) Bulk block state(d) Surface resonance(e) in-gap
in gap evanescent state(f) Bulk block final statePhotoemission cross section
in single particle approximation(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,
h t l tno orbital
bit l symmetryt retainst i (non-resonance(photoemission)
h t
i i )
(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 elementg supposepp
A(0)( ) = Ax,, <eikz | x | ψi((x)) > = 0 if ψi((-x)) = +ψi((x))
e.g.
Important for crystalline samples

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 datag free electron like final state inside solids
assuming

A l R
Angle
Resolvedl d PhPhotoemissiont
i i SSpectroscopyt(ARPES)θzxxz plane: crystal symmetry plane

Electron emission angle: өPhoton incident angle: ψ, s- and p-polarization

C
Conservationti off linear
li
momentumtparallelll l tto th
the surfacef2m
k // =
Ek ⋅ sin θ2hk // ( Å -1 ) = 0.5123 Ek ( eV ) ⋅ sin θk||(inside)(i id ) = k ||(outside)( t id )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)0)k┴Pilo, Damarscelli

1st B.Z.

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

Bulk
B
lk b
band
d structure
t t
and
d
Fermi surfacesCu

Fermi surfaces:
Electron pockets and hole pockets
R l d toRelatedHall coefficientElectric conductivity
M
Magnetic
ti susceptibility
tibilitGap 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 solid

L
(111)

Γ

X
(001)

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

Bulk projected bands along ΓLof Au and Ag, respectively

Å Ag S.S.
2D
Int.
plots

Ag QWSk|| = 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 ÆS
Samecrystalline
t lli filfilm
thickness along z
even though lateralcrystalline domains
grow from small tolargeOne-particle
One
particle spectral function near EF measured by
ARPES 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, plasmons
andd electrons,
l t
etc.
t

Σ( k , ω ) = Σ' ( k , ω ) + iΣ" ( k , ω )Real part: shift observed peak energy from single particle energygyp
part: ppeak FWHM = 2 Σ”
ImaginaryPeak position
Featurelesssingle particle
dispersion
curve

Kink ~25 meV due to electron-phonon scattering

Peak position – single particle curve

Width due toelectron-electron
scattering ~ ω2
Width due toelectron-phonon
scattering
Const bkg width
due to impurities

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

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

2
O2-

Cu2+
Cu+

Cu2+ : 3d9 Æ spin-1/2
Quasi-1D spin-1/2 chain
Coexistence of spin
spin-spiralspiral long range orderwith ferroelectricity Æ multiferroniccbaa = 2b

Ideal spin-1/2
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 by
ARPES with polarization

O
O

y

Cu O

x

Basic building unit: CuO4 planar plaquette

O

dxy

Highest energy state:
Cu 3dxy and O 2p antibonding (AB) state
Still keeps dxy symmetry

dxy

yy’
x’

A ’
Ax’

y

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

Ax

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

Focus on B.E. = 0.7 eV peak at Y’hν = 22 eV

h 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′)
(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'
Y

(1.1)

(1.1)

(1.1)

Binding Energy (eV)(X)

(0 55)(0.55)Y (Γ′)

3.0(0)

Intenssity (arb. unit)

1

Intenssity (arb. unit)

(X)

(0)

Γ

Γ
(0)

Inten
nsity (arb.unit)

(0)

x

y

3.0

2.0

1.0

0.0

Binding Energy (eV)

x

y’
x’

Ax

Ax

Ax’
Ax

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
S ARPESSX
S has
as beebeen trieded foro increasingc eas g bu
bulk sesensitivity,sy, moreoefree 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
U9
undulator

CGM

Scienta
SES 200
analyzer

Hemisphericalpelectron energy
gy analyzeryR1 : radius of inner spherep
R2 : 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 mean
radiusResonance photoemission(near-edge absorption followed by Auger likeelectron emission)e.g. Ce3+ (4f1)
4f mixed with other DOS

e-

e-

4f

intermediate
state
EF

4f

Intensity enhanced by absorption
Predominantly 4f DOS

4f

4f

4f

4f
Absorption +

3d/4d

3d/4d
Direct PE

3d/4d
Resonance PE

EF
Auger likeemission

Comments on photoelectron IMFP
ValenceVlbband
d PE using
i VUV andd SX hhas IMFP near minimum,i ivery 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
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
DOS.

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

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

HAXPES example:
p Hard x-ray
y photoemissionpon
Si-high k insulator buried interface
Kobayashi APL 2003 SPring-8
Kobayashi,

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

NSRRC HAXPES projectp j
at SPring-8

Why Hard X-rays?
Electron IMFP (probing depth) and Cross section
2IInelastic Mean Freee Path (A)

Au
SiO2

HAXPES

100
7
6
5
4

XPS

3
2

10

UPS

7
6
5
5 6 7

2

10

2

3

4 5 6 73

10
Kinetic Energy (eV)23

4 5 6 7

4

10

SP8

Higher Ek for deeper probing depth or more bulk sensitivity, for strongly
correlated systems and interface properties
Photoemission signal (σ⋅λ)(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
rate, photon hungry experiment!

Design considerations of a hard X-ray beamline for HAXPES
1. Scan of photon energy is not considered.
2 Focusing
2.
Foc sing on photon energies to hahave
e reasonabl
reasonably large IMFP ofphotoelectrons while reasonably good signal rates.
3. Range of photon energy thus the kinetic energy of photoelectrons
should match the range of available electron energy analyzers (Scienta
or MBS).
4. Minimizing photon flux loss by minimal numbers of reflection and diffraction
and putting the whole beamline under vacuum
vacuum, with few Be windows.
windows
5. Beam spot size at the sample position should match the electron opticsof the analyzer.
6. Using the existing hutches of BL12XU at SPring-8,
SPring 8, must install the first
optical element after front end to intercept the strong white beam fromundulator.
7. Sharing
g beamtime and even flux with the main line pparticularlyy at 10 keV,,which is used heavily.
8. Cost.

Photon energy range 6-12 keV.

Summary of final beamline design
1. Single bounce diamond monochromator (DM) instead of double bounce DCM
A. Diamond is the only choice.
B. High thermal conductivity, low thermal expansion coefficient, can use amuch simpler water cooling system than complicated and expensive
cryogenic LN2 cooling system widely used at SPring-8 (BL12XU main line).
C. Low absorption
por highg transmission of diamond enables us to share beamwith the main line.
D. Two modes are implemented:
a. A thin diamond (100) with (111) diffraction in transmission Laue mode,fine with higher photon energy;
near normal incidence, 80% transmission at 10 keV for the main line.
b. A thicker diamond (111) with (111) diffraction in reflection Bragg mode,must be used at lower photon energy; 90% transmission at 18 keV inthird harmonic for the main line.
E. Drawback: BL after DM and end station must be rotated to match diamondscattering
tt i angle
l 2theta
2th t withith different
difft photonh t energies.
i
2. Single pair of Si channel-cut as high resolution monochromator (HRM).
Drawback: BL and end station must change height with photon energy.
3 KB mirror system focus beam down to 20x20 um^2 to match electron energy
3.
analyzer optics 30x30 um^2.

Optical design concept

DM h
DM:
horizontalit l didispersioniHRM: vertical dispersion

6-12 keV usinggdiamond (111) reflection
Designed for HAXPES

Layout of the side beamline of BL12XU

Diamond monochromator: installed Aug
Aug. 3
3, 2007

Exp hutch: Rotational platform: installed Jan. 27, 2008
High Resolution Monochromator: installed Feb. 14, 2008

KB mirror chamber: installed Mar. 27, 2008

First diffracted beam at 8 keV into experimental hutch: Feb. 19, 2008 04:40

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.

Challenging future directions of
Photoemission Spectroscopy
1. ARPES at submicron to tens of nanometer scale,using Schwatzchild optics or zone plates
plates.
Need brighter light sources.
2. Time-resolved PES. Need efficient detection andbrighter sources.

Thanks for your attention