Optical propertiesand

Interaction of radiation with matterS.Nannarone

TASC INFM-CNR & University of Modena

Outline

•Elements of Classical description of E.M. field propagation in absorbing/ polarizable media Dielectric function

•Quantum mechanics microscopic treatment of absorption and emission and connection with dielectric function

Physics related to a wide class of Photon-in Photon-out experiments including Absorption, Reflectivity, Diffuse scattering, Luminescence and Fluorescence or radiation-matter interaction

[some experimental arrangements and results, mainly in connection with the BEAR beamline at Elettra

http://new.tasc.infm.it/research/bear/]

Systems

•bulk materials the whole space is occupied by matter

•Surfaces matter occupies a semi-space, properties of the vacuum matter interface on top of a semi-infinite bulk

•Interfaces transition region between two different semi-infinite materials

•Electronic properties full and empty states, valence and core states, localized and delocalized

states

•Local atomic geometry /Morphology electronic states – atomic geometry different faces of the same

coin

Information [see mainly following lectures]

Energy range Visible, Vacuum Ultraviolet, Soft X-rays)

Synchrotron and laboratory sources/LAB

This can be done by Laboratory sources

They cover in principle the whole energy range nowadays covered by synchrotrons (J.A.R.Samson Techniques of vacuum ultraviolet spectroscopy)

•Incandescent sources

•Gas discharge

•X-ray e- bombardment line emission

•Bremsstrahlung continuous emission sources

•Higher harmonic source

Conceptually Shining light on a system, detecting the products and measuring effects of this interaction

Synchrotron and laboratory sources / Synchrotron

Some well known features

•Collimation

•Intrinsic linear and circular polarization

•Time structure (typically 01-1 ns length, 1 MHz-05GHz repetition rate)

•Continuous spectrum, high energy access to core levels

• Reliable calculability of absolute intensity

•Emission in clean vacuum, no gas or sputtered materials

•High brilliance unprecedented energy resolution

• High brilliance small spot Spectromicroscopy“The one important complication of synchrotron source is, however, that

while laboratory sources are small appendices to the monochromators, in a synchrotron radiation set-up the measuring devices becomes a small appendices to the light source. It is therefore recommendable to make use of synchrotron radiation only when its advantages are really needed.”

C.Kunz, In Optical properties of solids New developments, Ed.B.O.Seraphin, North Holland, 1976

Radiation-Matter Interaction Polarization and current induction in E.M. field

Matter polarizes in presence of an electric field Result is the establishment in the medium of an electric field function of both external and polarization charges

Matter polarizes in presence of a magnetic field Result is the establishment in the medium of a magnetic field function of both external and polarization currents

•Mechanisms and peculiarities of polarization and currents induction in presence of an E.M. field

•Scheme to calculate the E.M. field established and propagating in the material

•Basis to understand how this knowledge can be exploited to get information on the microscopic properties of matter

The presence of fields induce currents

Basic expressions - Charge polarization

and induced currents

pol P

polJ Pt

magJ c M

cond transport scalar potential optical em wave transport opticalJ E E J J

ii

pP

V

i

i

mM

V

Polarization vectors

Charge and Magnetic/current polarization – closer look

ii

pP

V

i

i

mM

V

-Ze-

+Ze

ip e

E

0P

B

m

magJ

Induced currents

cond transport scalar potential optical em wave transport opticalJ E E J J

+_

e-

( )

transport transport

transport

J qNv E

V

VZe+

( )E

( )B

( ) ( )optical E

Motion of charge under the effect of the electric field of the E.M. field but in an environment where it is present an E.M. field

2

2transport

Ne

m

Expansion of polarisation

Linear and isotropic media

eP E

mM B

4 4 eE P ED E E

4 4 (1 4 )m mH B M B B B

1

1 4 m

1 4 e

Dielectric function Permeability function

iji ij j kj i

jj

P E E higher order termE s Physical meaning Elastic limit the potential is not deformed by the field

Linear versus non linear optics

Formally linear optics implies neglecting terms corresponding to powers of the electric field

Physically it means E.M. forces negligible with respect to electron-nuclei coulomb attraction

9 810 / 10 /E V cm breakdown fields V cm

Nuclear atomic potential is deformed not harmonic (out of the elastic limit) response distortion higher harmonic generation

' ' ' ' ' '( , ) ( , , , ) ( , ) ( , ) ( , )t

All space

D r t dr dt r r t t E r t r t E r t

In very general way

4 extD

-1Responce function

External stimulus

Dielectric function and response

Note is defined as a real quantity

Summary material properties within linear approximation

1

1 4 m

1 4 e

And

transportoptical

Conduction in an e.m. field Conduction under a scalar potential – Usual ohmic conduction

. .E MEJ

staticJ E

4 extE

1E H

c t

0H

14 4optical extH E E J

c t

Corresponding equations for vacuum case

4 extE

0B

B Et

1 4extB E J

c t c

Maxwell equations in matter for the linear case

Wave equation - Vacuum

22

2 2

1E E

c t

22

2q

c

q

c

Vacuum supports the propagation of plane E.M. waves with dispersion / wave vector energy dependence

Wave equation - Matter

Matter supports the propagation of E.M. waves with this dispersion

Formally q is a complex wavevector

22

2 2 2

4 opticalE E Ec t c t

2 2

2 22 2

4( )q i n

c c

Wave vector eigenvalue/dispersion depends on the properties of matter

through (all real quantities)

0 exp ( )qE E i r t

Complex refraction index

0 ˆ ˆexp exp ( )E E s r i ns r tc c

k

Absorption Phase velocity

2

1 2

2 21

2

/

2 / 4 /

i n

n k

nk

Real and imaginary parts not

independent

cv

n

22

22 2

2

4( )q i

c cn

Absorption coefficient

dI Idr 2 4kc

k

2I E( )

0( , ) ( ) dI d I e Lambert’s law

Complex dielectric constant – Complex wave vector2

22

4( )q i

c

0 ˆ ˆ( , ) exp ( ) exp ( )E r t E q r i q r tnc c

k

n n ik 21 2 /i n

2 21 /n k

2 2 / 4 /nk

2 2 4k kI E dI Idr c

Supported/propagating E.M. modes depend on the properties of matter through

The study of modes of the e.m. field supported/propagating in a medium and the related spectroscopical information is the essence of the optical properties of matter

1st part Classical scheme / macroscopic picture

2nd part Quantum mechanics / microscopic picture

Relation between (r,t), (r,t) (r,t) or (q,) (q, ) (r ) and the properties of matter

Spatial dispersion

2ˆq q

extension on which the average is made

a 2

ˆ 0q q

( , ) ( 0, ) (0, )q q

2ˆ 0q q

Note 0 wavevector does not mean lost of dependence on direction anisotropic materials excited close to origin

Unknowns and equations

(real quantities) are the unknowns related with the material properties

(r,t) is close to unity at optical frequencies magnetic effects are small

magJ c M

(not to be confused with magneto-optic effects: i.e. optics in presence of an external magnetic field)

Generally a single spectrum – f.i. absorption – is available from experiment

(An ellipsometric measurement provides real and imaginary parts at the same time.

It is based on the use of polarizers not easily available in an extended energy range)

Real and imaginary parts are related through Kramers – Kronig relations

Sum rules

Kramers – Kronig dispersion relations

' ''2

1 ' 2 20

( )21

( )P d

'1 '

2 ' 2 20

( ) 12( )

( )P d

Under very general hypothesis including causality and linearity

Models for the dielectric constant / Lorentz oscillator

2202 Loc

d dm r m r m r eE

dt dt

Induced dipole

Mechanical dumped oscillator forced by a local e.m. field

Neglecting the magnetic term /Localev B c

2

2 20

1( )

( )Loc

Loc

e Ep E

m i

2

2 20

1( )

( )Loce E

m i

Out of phase – complex/dissipation – polarizability (Lorentzian line shape)

( )LocalE e-

Complex dielectric function

1 2( )( ) 1 4 ( ) ( )i

2

2 2

4 11

( )o

Ne

m i

4 4 eE P ED E E

P N E

From

2 22

1 2 2 2 2 2

( )41

( )o

o

Ne

m

2

2 2 2 2 2 2

4

( )o

Ne

m

Lorentz oscillator Dielectric function

Lorentz oscillator Refraction index

Lorentz oscillator Absorption Reflectivity Loss function

EEL spectroscopy

Physics

Difference between transverse and longitudinal excitation

Optical spectroscopy

Non linear Lorentz oscillator

0

22 2

22 Loc

d d er r r E

dt dtr

m

0 0

2 2 22 2 2

1( )

2 2 22n

n n nn

e

m i i

20

1

(

( ) 2

) ni

n

tn

n

Er

m

ee

i

1 2 ....r r r

21 1 2 2r E r E

22

1 1 0 122

d d er r r E

dt dt m

22 2

2 2 0 22 12d d

r r rdt dt

r

• induced dipole at frequency and 2

• the system is excited by a frequency but oscillates also at frequency 2

• re-emitting both and 2

Anarmonic potential

Lorentz oscillator in a magnetic field 1/2

2202

( ) (0,0, )Loc Ext Ext

d d drm r m r m r e E B B B

dt dt dt

2 20

2 20

2 20

( )

( )

0

x

y

m im m eE eB i

m im m eE eB i

m z im z m

x x x

x

z

y

y y y

2 220

22 2 20

2

4

x y

x

L

L

i E i EeP n

m i

2 220

22 2 20

2

4y

L

Ly xi E i EeP n

m i

2L

eB

m

x and y motions are coupled

Larmor frequency

;x yP Nex P Ney Solving for x and y

0 ( 1)P E �

0 1

0

1

1

xx xy xz

yx yy yz

zx

x x

z zz

y

zy

y

P E

P E

P

( 1)x xx x xy y xz zP E E E

2 220

22 2 20 0

( 1) ( 1)4

x

L

yx y

ien

m i

2

22 2 20 0

2

4x

L

Ly

ien

m i

2

22 2 20 0

2

4

Lyxxy

L

ien

m i

1zz

Lorentz oscillator in a magnetic field 2/2

( )ij B�

Lorentz oscillator in a magnetic field 1/3

0 ( 1)P E

(0,0, )

0

0 ;

0 0

xx

yy

zz

xy

xy B B

�

2 220

22 2 2 20 0

2

22 2 2 20 0

2

22 2 2 20 0

1 14

2

4

2

4

yy

L

L

y

L

x xy

L

L

xx

xy

ine

m i

ine

m i

ine

m i

The dielectric function is a tensor

[ Physically lost of symmetry for time reversal ]

Propagation in a magnetised medium 1/2

22

0 2

22

0 0 1,

2

,322 2

( )

ij j ij j ij j

iD

E E Dt

Ett

E

Wave equation

2 20 0i j j i ij j

j j

k k E k E E Eigenvalue equation

2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2

/ / /

/ / / 0

/ / /

x xx y x xy z x xz

y x yx y yy y z yz

z x zx z y zy z zz

n n k k n k k k n k k k

n k k k n n k k n k k k

n k k k n k k k n n k k

0

kn

kwith

Note ≠ 0 in anisotropic media

Propagation in a magnetised medium 2/2

2

2

0

0

0 0

xx xy

yx yy yz

zz

n

n

Considering the medium with B||z

2xx zyn i

Magneto-optics effects

Dichroism N+ Right circular polarized wave

N- Left circular polarized wave

Magneto-optic effects e.g. Faraday and Kerr effects/geometries

Linear polarized Elliptically polarized

Rotation according to n+-n-

M M

Longitudinal geometry

Two waves propagating with two different velocities and different absorption

Dielectric tensor

are in general tensorial quantities

4 4 eE P ED EE � �

4x x xx xy xz x

y y yx yy yz y

z z zx zy zz z

D E P

D E P

D E P

( , ), ( , ), ( , ), ( , ), ( , )e mq q q q q ����������

Dielectric tensor

4xx xy xz xx xy xz xx xy xz

yx yy yz yx yy yz yx yy yz

zx zy zz zx zy zz zx zy zz

xx yy zz 0 0

0 0

0 0

xx xy xz

yx yy yz

zx zy zz

0

0 0

xx xy

xy yy yz

zz

Scalar medium

Magnetized medium

Longitudinal and transverse dielectric constant 1/2

Any vector field F can be decomposed into two vector fields one of which is irrotational and the other divergenceless

0

0

L

L

T

T

F

F F

F

F F

If a field is expanded in plane waves FT is perpendicular to the direction of propagation.

0

0

D D k

B E

B

k

E

D

Longitudinal and transverse dielectric constant 2/2

( , ) (1 )4L L L

iJ q E

22

2 2

1 4(1 ) (1 ) ( , ) ( , )T T Tq E q i J q

c c

22

2

1(1 ) ( )T Lq

c

( , ) (1 ) ( , )4T T T

iJ q E q

The description in terms of longitudinal and transverse dielectric function is equivalent to the description in terms of the usual (longitudinal) dielectric function and magnetic permeability. They are both/all real quantities together with conductivity. They combine together to forming the complex dielectric constant defined here.

Optics EELS/e- scattering

Transverse and longitudinal modes 1/3

Modes can be transverse or longitudinal in the same meaning of transverse and longitudinal E.M. field searching for transverse waves is equivalent to searching for transverse modes

Propagating waves and excitation modes of matter are two different

manifestation of the same physical situation

Plasmon is a charge oscillation at a frequency defined by the normal modes oscillation produces a field only a field of this kind is able to excite this mode

+_

q

q( )E

Transverse and longitudinal modes 2/3

ˆ ˆ( , ) 0 ( , ) 0s D q s E q

ij�

NE k

c

Searching for modes eigenvectors of

Transverse modes Polaritons

Longitudinal modes

ˆ 0E Es E

( , ) ( , ) ( , ) 0i ij jD k k E k �

( , ) 0ij k

the quantum particles are coupled modes of radiation field and of the elementary excitations of the system: Plasmons, longitudinal opical phonons, longitudinal excitons,….

The quantum particles are coupled modes of radiation field and of the elementary excitations of the system, called Polaritons including transverse (opical) phonons, excitons,….

Transverse and longitudinal modes 3/3

( , ) 0E k

0D

4

DP

10 ( , ) ( , )i ij ijE k D k

1 1( , ) 0( , )ij

ij

kk

Polarization waves

Sum rules for the dielectric constant

' ' ' 2

0

1Im ( )

2 pd

' ' 2

0

Re 1 2 (0)d

Examples of sum rules

Of use in experimental spectra interpretation

Quantum theory of the optical constants

Macroscopic optical response Microscopic structure

Transition probability

Ground state HRADIATION + HMATTER perturbed by radiation-matter interaction

Two approaches

• fully quantum mechanics

• semi classical

Three processes

• Absorption

• Stimulated emission

• Spontaneous emission

O ° O

O ° O ° ° O

Microscopic description of the absorption and emission process

R M IH H H H

2 2 21( )

2R k k kk

H P Q

,

1( )

2k kk

E n .... ....k

n

mi,ei mj,ej

21

( ) ( )2

iM i j i i j i spin

i j i j ii

eH p A r e r H

m c

�

Term neglected for non relativistic particles

System

Radiation

Matter

•Interaction Hamiltonian HI

•Effect of the interaction on the states of the unperturbed HR + HI

Hamiltonian of a charged particle in E.M. field

1H A E A

c t

1F e E v H

c

2 2 21

2R x x y y z z

e e eH p A p A p A e

m c c c

xp ix

22

22

212

2R

e eH i i e

m c c

eAA

cA

2 2

22 2 2 2

22

1 12 2

2 2

2

R

e eH i i

m c m c

e

m m

e

A

A

p

cA A

c

0A

Particle radiation interaction

22

22

22 ( )

2

2 ( ) ( )2

2 ( )

ii R i i j i spin

i i j i

i i j i spini

i j ii i

i

R i

R

e r H

eH i A r e

eA

c

m

ei A

rc

c

Hm

r

Matter Hamiltonian + perturbation Hamiltonian

H E Problem to be solved

Eigenstate and eigenvector of the matter radiation system in interaction

Important notes

M R n n nH H E

• it is assumed here – formally - that the problem in absence of interactions has been solved.

• In practice this can be done with more or less severe approximations.

• The calculation of the electronic properties of the ground state is a special and important topic of the physics of matter

( , ... ...n n i i k nr s n

( , )n i ir s

Many particles state

Generally obtained by approximate methods

The solution is found by a perturbative method

Transition between states of ground state due to the perturbation term

The effect of perturbation HI on the eigenstates of H0

Obtained by time dependent perturbation theory

..... .... ( , )n k n i inn r s

' '

'( )

0

( ) ( )

( )

n

n t nn

mm I n

m

t

t c t

dc ti H

dt

Matrix elements 1/3

(0) 1 (0)n m nc The evolution of the state m is obtained calculating the matrix element

( ) (0) (0) (0)m n m I nt c H

... .... ( , )n k n i in r s

System states under perturbation due to

Changes of photon occupation and matter (f.i. electronic) state

0 exp ( )kA A i k r i t

Matrix elements 2/3

It is found that for photon mode k, only

' 1k kn n

contribute linear terms to matrix elements

Probability of transition of the system from state

'n n

+1 photon emission -1 photon absorption

Matrix element 3/3

'

' ' '

'

'

' ' '

'

2

22

2

2

22

2

1sin

8 ( ) 2( ) ( , )

1sin

8 ( 1) 2( ) ( ) ( )

(

,

)kn n

kn nk

nn n

knn n n n

kn

n n

kn n

n

tn

c t M k E E Emis

tn

c t M k E E Absorption

si nV

V

o

' ' exp( )(ii nn n n

i i

eM ik r i

m

Transition probabilities

' '

2 24 ( 1)( , ) ( )k

nn n nk

nM k E E Emission

V

' '

2 24 ( )( , ) ( )k

nn n nk

nM k E E Absorption

V

Spontaneous emissionStimulated emission

Spontaneous emission present only in quantum mechanics treatment

Integrating in time from 0 to infinity for the transition probabilities

per unit time

Dielectric function and microscopic properties

2

0

1( )

T

P J E dt ET

2

4

4( ) 1 4 ( ) i

( )f n probability of finding the state in a state n, at thermodynamic equilibrium ( ) ( ')f n f n for 'n nE E

' ' exp( )inn n i ia ni

i

eM ik r p

m

2

8knE

V

Dissipated

power

' '

'

22

24( ) ( ) '

4( )

8 knnn n

k

nn

nV

nM E E f n f

VVn

Microscopic expression of the dielectric function

'

22

' '2

4 1Im ( ) ( ) ( ) ( ')n n n n k

nn

M E E f n f nV

Physical meaning Sum of all the absorbing channels at that photon energy

Note dissipation originates from non radiative de-excitation channels

Intuitive meaning of the expression for absorption coefficient

'

22

' '2

4 1Im ( ) ( ) ( ) ( ')n n n n k

nn

M E E f n f nV

' ' 'Im ( ) ( ) ( ) ( ) ( ) ( ')n n n kn nnN E N E M E E f n f n

'( )n

N E

En

En’

( )nN E

N(E) density of states(Number of states/eV)

Joint Density Of States N(E) N(E’)

Dipole approximation

' '

22 8 ( )

( , ) exp( )k ii i nn n n

ik i

n eM k ik r p

V m

exp 1ik r

' '

' '

( ) iin n n n

i i

i in n n ni

eM p

m

i e r

Matrix elements of position operator

Semi classical approach

0 exp ( ) 2 ( )R ki

R iA A i k r ie

i A rtc

Note that the same result can be obtained by considering the transition probability between quantized states of the matter system under the effect of classical external perturbation of the E.M. field with given by the same expression of

This semi classical approach gives identical results for absorption and stimulated emission probabilities, but does not account for spontaneous emission

Selection rules for Hydrogen atom

' in nii

e r ˆ ( ,sin sin ,sin cos cos )

' ' '

' ' '

' ' '

' ' ' co

si

ˆ s

n sin

in o

ˆ

ˆ s

c s

nlmn l m

nlmn l m

nlmn l m

nlmn l m

er

ie er

je er

ke er

( ) (cos )m imnlm lR r P e

Generic light polarization

nlm

' ' 'n l m

Selection rules/2

' ' '

' ' ' c sˆ o

nlmn l m

nlmn l m

er

k er

' '

' '

' '

' '

2 ( )

2 ( )

cos sin sin ( ) ( )

cos ( ) ( ) ( )

m m i m mn ln l

m m i m mn ln l

drd d r R R P P e

drr R R d P P d e

' ' 1m m l l

For radiation polarized along z

Expressions valid in any central field

nlm

''' 1n l l m

[linear polarized light ]

Hydrogen - Selection rules Circular polarization

sin ( ) sin ( )r x iy or r x iy

2

E

2

ie i

1 1l m

Calculation of matrix elements - Optical properties of matter

' '

' '

( ) iin n n n

i i

i in n n ni

eM p

m

i e r

The basic step in calculation involves

many particles wavefunctions

Born - Oppenheimer approximation

( , ) ( , ) ( )n n nr R r R R

Nuclear motions separated from electronic motions

'

*

,( ) ( , )( ) ( , )mm k mk

eM dr k r i k r

m r

One electron description

One electron WF Solution of motion in an average potential generated by all other electrons

Dielectric function in one electron approximation

' '

'

'

' ' '

2

32 ,

2 2

, ,

4 2Im ( ) ( ) ( ( ) ( )

2

( ( )) ( ( ))

( ) ( ( ) ( ) ( )

mm k mk mm m BZ

F m F m

mm k mk m m k mkBZ

dk M E k E k

f E k f E k

M dk E k E k M JDOS

'*

,( ) ( , )( ) ( , )mm k mk

eM dr k r i k r

m r

Crystal states E(k) K reduced vector within the Brillouin zone

Case of crystals

Joint Density of States - JDOS

Phenomenology of absorption

•Interband transitions

-direct/indirect

-Intraband absorption

-Phonon contribution

•Core/localized (e.g. molecular) level absorption

Local field effects - Local (Lorentz) field corrections

03L

PE E

Decay and relaxation of excited states

' '

'

22

, ,

4 ( 1)1( , ) ( )k

m kn n nn kR k

nM k E E

V

Probability of relaxation/decay of excited state as integral on all the spontaneous emission channels of field and matter states

As a consequence the dependence of Im () has to be modified

1 1 1( )

e phR e e

•Lorentzian broadening

function substituted for by Lorentzian curve

(e.g. see Lorentz oscillator)

Lorentzian broadening

'

2 20

( )

1

( )

m knE E

i

Exploitation of emission / radiative decay

Total/Partial yield measurement of absorption through electron (Secondary, Auger,..) and photon (fluorescence, luminescence,…) yields

De-excitation spectroscopies

•Fluorescence

•Luminescence XEOL

•Auger electron and photon induced – Selection rules and surface sensitivity

233 *

1

( ) ( ( ) ) ( , ) ( ) ( ( ))c n c n c F nn

I dk E k E dr k r er r f E k

matrix element ~ constant I Density of states and 3

Boundaries reflectivity

From material filling the whole space to material with boundaries and matter-vacuum interfaces

Reflectivity - Measure of the reflected intensity as a function of incident intensity

Fresnels relations based on boundary conditions of fields link

reflected intensity with dielectric function

Reflectivity from a semi-infinite homogeneous material

Surface plane Normal to surface

Modellisation of surfaces and interfaces

Multiple boundaries

S and p reflectivity

Diffuse scattering 1/2

2 2 2 (( , ) , ) 0(, )n rE r k E r

Scalar theory of scattering (single Cartesian component)

2 2( , ) ( , ) ( , ) ln( , ) 0( , )E r rE r k r E r

2 21( , ) ( , ) 1

4F r k n r

2 2( , ) ( , ) , )(4 ) ( ,U r k U r U rF r

Defining: Scattering potential

Incident field

scattering medium

Scattered wave

Inhomogeneous filling of spaceTerm neglected if dimensions

Small and/or rough objects

Diffuse scattering 2/2

0ˆˆ

1( )

0ˆˆ( , )ˆ( ) si r

ik rks

fe

U rs er

ss

0' '( )' 3 ' ' 3 'ˆ ˆ

1 0ˆ ˆ( , ) ( ) ( )s rsik i rqf s s F r e d r F r e d r

The scattering amplitude is the Fourier transform of the scattering potential

Inverting F(r) n(r)

Born approximation

s

0s

0ˆks ksq

q

Conclusions

Classical scheme Introduction of the dielectric function

Microscopic (quantum mechanics) treatment of emission and absorption

Relation between macroscopic dielectric function (measured quantity) and microscopic properties

http://www.gfms.unimore.it/

Calculation of ij elements

Source Source: 3.3 m of arc, 3.1 m x 3.3 m vertical x horizontal

two fields – vertical and horizontal – out of phase of ±/2 according to the sign of take off angle (J.Schwinger PR 75(1949)1912)

2 22 23 3

0

0

3 3( ) ( ) [( ) (1 )]

4 42z i

c c

eE i A

cr

1 2' 2 23 3

0

0

3 3( ) ( ) [( ) (1 )]

4 42y i

c c

eE A

cr

Electric fields

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 1012

320eV r = 1 m

0.1% BW

(mrad)

Eoy

N/C

//320eV

r = 1 m 0.1% BW

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-3

-2

-1

0

1

2

3 T

Eoz

N/C

x 1012

(mrad)

≈ 103 photons/bunch - bunch duration ≈ 20 ps

-250

-200

-150

-100

-50

0

I(A

*e-1

2)

45 40 35 30 25 20 15 Z c

E = 100 eV Exit slits 900um * 30 um

-0.4

Electric field at E= 100 eV +0.4

-0.4 +1 -1 Horizontal

Vert

ical

Selector fully open: Zc= 45 mm, Zg = 1 mm

S1=-0.9 S2=0.011 S3=-0.068

Ey=0.95 Ez=0.04 =-1.4

-250

-200

-150

-100

-50

0

I , A

*e-1

2

403020

Zc, mm

100 eVZg = 41

Zc = 34

-1

+0.4

+1

0

Electric field at E = 100eV Erepresentation

Horizontal

Ve

rtic

al

-0.4

Ellipticity, =0.04

Polarization selector position: Zc = 34 mm, Zg = 41 mm

(aperture 4 mm) S1=-0.97 S2=0.011 S3=0.082

Ey=0.98 Ez=0.04 =-1.44

-250

-200

-150

-100

-50

0

I , A

*e-1

2

403020

Zc, mm

100 eVZg = 31

Zc = 31

-1 +1 -0.4

+0.4 Electric field at E = 100 eV

Horizontal

Ve

rtic

al

Ellipticity, =0.33

     Polarization selector position: Zc = 31 mm, Zg = 31 mm

(aperture 14 mm) S1=-0.77 S2=0.08 S3=-0.57

Ey=0.93 Ez=0.31 =1.43

Polarimetry 100 eV ellipse

Transport and conditioning optics

BPM

P1

MONO

EXIT SLITS

GAS CELL

Helicity selector

P2

Intensity monitor

Light spot

Energy range 3- 1600 eVEnergy resolution E/E ≈ 3000 (peak 5000) at vertical slit (typically 30 μm) x 400 μm (variable) Variable

divergence (maximum, variable) 20 m vert x hor

ellipticity variable horizontal/vertical (typically in the range 1.5 – 3.5, Stokes parameters (normalized to the beam intensity) S1 0.5 - 0.6, S2 0 - 0.1, S3 0.75 -0.85 )

helicity variable (typical value for rate of circular polarization P or S3 0.75 – 0.95)

Source 4 m HxV

Mirrors in sagittal focusing reduction of slope errors effects in the dispersion plane

plane-grating-plane mirror monochromator based on the Naletto-Tondello configuration

Examples and experimental arrangements at BEAR (Bending magnet for Absorption Emission and Reflectivity)

Bulk materials

Surfaces

Interfaces

Absorption

Reflectivity

Fluorescence

Luminescence – XEOL

Diffuse scattering

Experimental arrangements

BEAR (Bending magnet for Emission Absorption Reflectivity) beamline at Elettra

Experimental/scattering chamber

(Positive -Differentially pumped joints)

Goniometers

Sample manipulator

6 degree of freedom

VIS Luminescence

monochromator

Detection

e- analyser / photodiodes

(2 solid angle)

M,A 0.001°A 0.01°S 0.05°C 0.1°

Rotation around beam axis any position of E in the sample frame

Optical constants of rare hearths

1 0 - 2 1 0 - 1 1 0 0 1 0 1 1 0 2 1 0 3 1 0 4 1 0 5 1 0 6

p h o t o n e n e r g y ( e V )

1 0 - 1 3

1 0 - 1 2

1 0 - 1 1

1 0 - 1 0

1 0 - 9

1 0 - 8

1 0 - 7

1 0 - 6

1 0 - 5

1 0 - 4

1 0 - 3

1 0 - 2

1 0 - 1

1 0 0

1 0 1

1 0 2

k

K

L 1 , 2 , 3

M 4 , 5

N 4 , 5

O 2 , 3

D r u d e E n d r i z

L a r r u q u e r t

C u r r e n t

H e n k e

C h a n t l e r

E x t r a p o l a t i o n

See f.i. Mónica Fernández-Perea, Juan I. Larruquert, José A. Aznárez1, José A. Méndez Luca Poletto, Denis Garoli, A. Marco Malvezzi, Angelo Giglia, Stefano Nannarone, JOSA to be published

Interfaces & surface physics in periodic structures(multilayer optics)

(Optical technology Band pass mirrors)

At Bragg Z dependent standing e.m. field establishes both inside the structure and at the vacuum-surface interface modulated in amplitude and position

ML : Artificial periodic stack of materials

Z

ultra-thin deposited films

buried interface spectroscopy•Devices of use in spectroscopy

BRAGG

See also poster P III 26

Standing waves & excitation

Physics of mirror/Reflection

Spectroscopy of interfaces

Scanning through

Bragg peak

In energy or angle

Local modulation of excitation

Photoemission, Auger, fluorescence, luminescence etc..

Si Mo

Si

Cr/Sc Cr-Oxide interface (As received )

Qualitative analysis-Opposite behavior of Cr and Sc-Different chemical states of the buried Sc-Two signals from oxygen: one bound to Cr at the surface, the second coming from the interface- Carbon segregation at the interface

Cr2

O3

(6 Å)

Cr

(15 Å)

Sc

(25 Å)

X 60

573 eV

Ru (Clean) -Si buried interface

silicide

Inte

nsity (

arb

. units)

620600580560Kinetic energy (eV)

740736732728

h = 838 eV

Ru 3d

Mo 3d

Si 2p

Peak

are

a (

arb

. units

)

7.57.06.56.05.55.0Grazing angle (°)

1st component

2nd

componentRu 3d

Inte

nsity

(ar

b. u

nits

)

290288286284282280278Binding energy (eV)

Ru 3d

1st

component

2nd

component background

Ru

(15 Å)

Si

(41.2 Å)

Mo

(39.6 Å)

Angular scan through the Bragg peak

at 838 eV

X 40

Model – Ru-Si interface• Interface morphology

• Calculation of e.m. field inside Ml

•Photoemission was calculated, (Ek= h - EB)

Minimum position and lineshape depend critically on the morphology profile

Ru

Ru-Si

Mo-Si ML & i.f. roughness

Wavelength [nm]

Mo/Si61.2 %

58.4 %

Motivation role of ion kinetic energy and flux during ML growth

Ions EK: 5 eV (1st nm), 74 eV > 1nm Controlled activation of surface mobility

Ion assistance

ML (P 8 nm, 0.44) Performance- R (10°)

Performance & diffuse scattering

Performance differences are to be related to interface quality

Diffuse scattering around the specular beam was measured

KS= Ki + qZ + q//

diffuse scattering - MLs

f.i. Stearns jAP 84,1003

RqiRHq

q

z

edeq

qSz

z

//

2222 )(

2

1

2// eR1

)(

In plane Fourier transform on q// of potential

Single interface – Autocorrelation function

MLs : S(q) two terms

I.f.roughnes produces diffuse scattering around the specular beam

I.f.roughnes can/can not be coherently correleted through the ML

Description on a statistical base, ….fractal properties

R

eRHyyxxH

12)()','( 2

KS= Ki + qZ + q//

• incoherent scattering by single interfaces

• correlated/coherent scattering among i.f. (interlayer replica of roughness)

See f.i. Stearns JAP, 84, 1003, 1998

Diffuse scatteringDetector

qdetector 0.003 nm-1

At 0.48 nm (13.1 eV)

Incident beam

Divergence

qdiv 0.0005 nm-1/m

At 0.48 nm (13.1 eV)

- scan

Rocking scan

Mo/Si

Mo-Si ML diffuse scattering

Ion assistance

In plane correlation function - absence of interface correlation

hRRC 22 /exp)(

ξ , correlation length h, fractal dimension/jaggedness

Correlation function

ξ=400 Å

ξ=200 Å

ξ= 300 Å

ξ=120 Å

See also poster Borgatti et al. P III 17

Pentacene on Ag(111)

Premise about C22H14/substrates•He scattering on pentacene deposited by hyperthermal beams 1ML planar

•Morphology and electronic properties ( delocalization of the electrons) transport properties highly anisotropic;

•on Metals: nearly planar orientation a condition hindering the formation of an ordered overlayer;

on semiconductors/oxides: SiO2 standing GeS lying.

Chemisorption morphology - tilt angle & electronic structure

( Concentrating on 1 Mono layer )

See also poster Pedio et al. P II 33

C3 symmetry

Oblique cell Periodicity (6 x 3) ,

1 monolayer

Surface Cell( By He scattering )

Danışman et al. Phys. Rev. B 72, 085404 (2005)

XAS

298296294292290288286284

Photon Energy (eV)

31 5

6

4

2

0.3 ML

0.5 ML

1 ML

2 ML

3 ML

Multilayer

C K-edge

gas phase13 56

4

2

10°

27°

25°

resonances

LUMO

LUMO+1

Redistribution of the oscillator strength in the C1s – LUMO excitation region (1-3 of gas phase)

(At magic angle 54.7°)

Tilt angle

Gas phase XAS

(Alagia et al.JChemPhys 122(05)124305)

VB photoemissionLDA calculations C22H14/Al(100)

Simeoni et al. S.Science 562,43 (2004)

Redistribution of states upon chemisorption

HOMO-LUMO gap increasing-4 -3 -2 -1 0 1

Kinetic Energy (eV)

Photoemission

0.3 ML

0.5 ML

1 ML

2 ML

3 ML

3b2g

2au

3b3g

clean

h=30 eV

3b2g

2au

3b3g

EV

0

6.6 eV

7.4

8.3

EF

abs

orpt

ion

coe

ffic

ient

a. u

.

310305300295290285280Photon Energy (eV)

Nex_185_int Nex_186_6_int Nex_187_6_int Nex_188_6_int Nex_189_int

C=0°

C=90°

1 Ml C22H14/Ag(111)

resonances

resonances

xM

yM

zM

bea

m

XAS 1 ML - precession scan

ε= EV/EH = 0.29

Dichroism/Bond directionality & Tilt angle of the molecule

i= 10°

XAS – 1 ML - deconvolution

0.5

0.4

0.3

0.2

0.1

0.0

abso

rpti

on

co

effi

cien

t a.

u.

294292290288286284

Photon Energy (eV)

C=54.7°

data fit

i

iCi

Step

1 Ml C22H14/Ag(111)

A

BE

ACA BCB

CCC

C

D

F

2 2 2

22 2 2

2 2 2 2 2

2 2 2

cos sin 2 cos sin cos sin sin cos cos cos

cos sin 2 cos sin cos sin sin

2 cos sin 1 cos cos sin

sin sin cos cos cos sin sin

H

C C C C M M

C C C C

C C C C

M M

E p p E

Precession scan - FormulaeFit function for Single domain

Fit parameter: θ (polar angle of dinamic dipole )

0.5

0.4

0.3

0.2

0.1

0.0

abso

rpti

on

co

effi

cien

t a.

u.

294292290288286284Photon Energy (eV)

C=54.7°

data fit i

iCi

Step

1 Ml C22H14/Ag(111)

A

BE

ACA BCB

CCC

C

D

F

P

Tilt angle - Fit Coverage Tilt angle precession scan

Tilt anglePolar scan

0.3 25° +/- 5°

0.6 27° +/- 5° 28° +/- 4°

1.0 10° +/- 4° 8° +/- 4°