The Three Principle Soft X-ray Spectroscopies

X-ray Absorption Fine Structure (XAFS)

X-ray Fluorescence Spectroscopy (XRF)

X-ray Photoemission Spectroscopy (XPS)

Photoemission spectroscopy: experimental system

Terminology of Photoemission Spectroscopy

XPS: x-ray photoelectron spectroscopy. Used to determine binding energies of core-levels. These binding energies shift with chemical state (chemical-shift).

UPS: ultra-violet photoelectron spectroscopy. Used to measure binding energies of valence orbitals.

ARPES: angle-resolved photoemission spectroscopy. Measures the intensity of valence band features as a function of emissionangle, which can be used to determine band-structure.

XPD: x-ray photoelectron diffraction. Measures the intensity of core-level features as a function of emission angle, which can be used to determine surface structure.

Basic model of photoemission physics

Energy conservation: measure binding energies

A typical X-ray Photoelectron Spectrum

0

50000

100000

150000

200000

250000

300000

350000

020040060080010001200

Ga

2pG

a 2p

3

Si 2

p

Ga

3d

Ga

3p

Si 2

s

Ga (LMM)Auger

Valence Band

Core-level electrons

Secondary electrons

The inelastic mean-free-path for an electron: Physical origin of surface sensitivity in electron spectroscopy

Primary electrons(elastic)

Secondary electrons(inelastic)

MFPλ

The minimum in the mean-free-path is as small as a single atomic layer.

Variable surface sensitivity by tunable photon energy: Case of pyrite (FeS2)

[100]side view, (100) surface plane

hν (eV)

170.00 165.00 160.00Binding Energy (eV)

Phot

oemi

ssio

nIn t

ensit

y (ar

bun

i ts) S 2p

720

510

380

310

280

250

210

bulk

surface I

surface II

X-ray Photoelectron Diffraction (XPD)

• A powerful tool for determining the atomic structure of surfaces• Precision of bond-length measurement is about 0.02 Angstrom• Source of electrons is known: determined by XPS binding energy• Theory is a multiple-scattering theory; certain experimental conditions permit a single-scattering interpretation• Has been used as a form of quantum holography: direct data inversion

Experimental XPD Patterns

X-ray Beamhνν=60-600 eV

Polar Angle θθ

Azimuth Angle φφ

Electron Analyzer

Diffraction Pattern

θ

φ

Linearly polarized light

Sample surface

XPD of Mn/Ni, ESCA (MgKαα, hνν=1253.6 eV)

Ni Auger, Ni substate Mn 2p, 3 ML MnNi

Mn 2p, 2 ML MnNi Mn 2p, 1 ML MnNi

Mn 2p, 4 ML MnNi

Map of the rowsABOVE the emitter

[110]

[111][112][114][001][103][101][211]

An XPD Diffraction “Volume”Cu(100)

77.3 eV 99.5 eV 124.4 eV

152.1 eV 182.6 eV 215.8 eV

251.8 eV 290.6 eV 332.1 eV

φ

Ele

ctro

n M

omen

tum

θ

φ

Ele

ctro

ns

Photons

Sample

XPD for surface structure determination: The case of Si(100)c4x2

-101.5 -101.0 -100.5 -100.0 -99.5 -99.0

Binding Energy [eV]

5

12

B4

3

θ=60°φ=15°

hν = 144 eV

S1-XPD (left) and MS simulations (right) at hv=140 and 160 eV. Dimer atoms only (Atom 1)

Si(100)c4x2: Dimers and Substrate

Fig.5 S4-XPD (left) and MS simulations (right) at hv=145 and 160 eV. Emitters are those silicon atoms in the second layer substrate labeled as ATOM 4.

Fig.4 S1-XPD (left) and MS simulations (right) at hv=140 and 160 eV. Emitters aredimer atoms at upper positions labeled as ATOM 1. In this figure, we only show the comparison at two energies.

Photoelectron Holography: Analogy to Optical Holography

Objects

Laser Beam

Reference Wave

Object Waves

Detector

Optical Holography

Photo-electron Holography

Method of Photoelectron Holography Inversions

•Barton Algorithm

•Synchrotron Data

•Improvements

A k k k i ikr dk dk dkx yk k k

x y

x y

( ) ( , , ) exp( ), ,

r k.r= −∫∫∫ χ

Energy

Dependent

Photo-e

Diffraction

k

kx

ky

A k i ik r Eoutout

out

k

( ) ( , , )exp( . ) sin( )cos( )cos( ), ,

r k.r= −∑χ θ ϕ θθ

θθθ ϕ

1

•Geometric corrections(Data, angular integration)

•Refraction effects(Low energy)

χ θ ϕχ θ ϕ

θ ϕ α θ ϕ θ ϕ( , , )

( , , )( , , )exp( ( , , )) ( , , )

kk

f k i k S k→

•Scattering factor, phase (SWIFT)

• s/d ratio (shift)• Polarization (asymmetry)

XPH example: Mn on Ni(100)

6.6 Å-1

4.0 Å-1φ θ

k

167 eV

60 eV

Kin

etic

Ene

rgy

Wav

eV

ecto

r

Direct inversion of XPD volumes, using a model called “photelectron holography.” The case of Mn atoms on a Ni(100) substrate is shown.

MODEL EXPERIMENTAL HOLOGRAM

Energy bands and Fermi Surfaces in solids

From Eli Rotenberg, Berkeley-Stanford Summer School 2001

Angle-Resolved Photoemission Spectroscopy (ARPES):A way to directly measure band-structure

• Conservation of energy: determine energy position of bands• Conservation of parallel momentum: determine momentum position• Symmetry selection rules: determine parity of band

From Eli Rotenberg, Berkeley-Stanford Summer School 2001

Measurement of energy bands by scanned-angle ARPES

From Eli Rotenberg, Berkeley-Stanford Summer School 2001

Example: Cu(100)

From Eli Rotenberg, Berkeley-Stanford Summer School 2001

ARPES of a single crystal of PbS (galena)

Resonant PhotoemissionValence Band

Int

ensi

ty

-30 -20 -10 0

Binding Energy

hν=250 eV

Poly(αα-methylstyrene) Resonant Photoemission

bb

dd

a - Valence Band Photoemissionb - Auger Emissionc - C 1s photoemission

(2nd harmonic radiation)d - Resonant Photoemission

LUMO / HOMOtransition

Mechanism of resonant photoemission

LUMO

Energy Levels

HOMO

C 1s

Eg

Con

duct

ion

Ban

dV

alen

ce B

and

Cor

eLe

vel

­ 4 eV

Absorption Profile

Tot

al y

ield

300295290285

Photon Energy

C 1s edge

Valence Band

Int

ensi

ty

-30 -20 -10 0

Binding Energy

hν=250 eV

XAS

XPS

Two paths to the same final state

Transitions in Resonant Photoemission

hνν

IpUnoccupied state

Valenceband

C 1s

IpUnoccupied state

Valenceband

C 1s

hννIp

Valenceband

C 1s

Unoccupied stateBand gap (Eg)

Final state energy

Two (or more) paths to the same final state

X-ray Absorption Spectroscopy

Note the increases in absorption at characteristic energies.

2s,2p

1s

3p2p (2s)

1s