JBG CMS nanoprobes2003 Lecture2 - UvA · 2014-10-08 · Microsoft PowerPoint -...

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1 CMS Masters: Nanoprobes, spectroscopy & scattering © Jeroen Goedkoop 2003 Spectroscopy rules Spectroscopy rules Lecture 2 Nanoprobes, spectroscopy and scattering

Transcript of JBG CMS nanoprobes2003 Lecture2 - UvA · 2014-10-08 · Microsoft PowerPoint -...

Page 1: JBG CMS nanoprobes2003 Lecture2 - UvA · 2014-10-08 · Microsoft PowerPoint - JBG_CMS_nanoprobes2003_Lecture2.ppt Author: mgolden@PC-WZI05 Created Date: 9/5/2003 11:11:10 AM ...

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Spectroscopy rulesSpectroscopy rules

Lecture 2Nanoprobes, spectroscopy and

scattering

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Energies andEnergies and momentamomenta of condensed matter probesof condensed matter probes

Mass Energy Value for λ= 2Å(k=1010 π m-1)

Phonon

IRVisibleUVX-ray

0

λω hc=h

1 meV - 3 eV3-5 eV

5-100 eV0.1 - 100 keV

5 x 104 eV

Electron 9.1 x10-31 kg

mk

2

22h 40 eV

Neutron 1.67x10-27 kg

mk

2

22h 0.02 eV

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Energy scalesEnergy scalesin spectroscopyin spectroscopy

3d band

4spband

1s

2s2p

3s3p

Bind

ing

ener

gy (e

V)

60

600

6000

Visib

leUV

M L2 3

K

X-ray Edges

Abso

rptio

n

L1

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Time & energyTime & energyscalesscales

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

SpectroscopySpectroscopy

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

SpectroscopesSpectroscopes

Spectroscope - A Kruss, Hamburg c.1910swww.dundee.ac.ukWollaston (1802)

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

An early exampleAn early example

www.humboldt.edu

Hawk, Philip B. Practical Physiological Chemistry. P. Blakiston's Sons & Co., Philadelphia (1913) pp. 215-218.

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

A pedestrian course in electromagnetismA pedestrian course in electromagnetism

• A bit of Ibach and Lueth, Ch.11

• Conservation, selection rules

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Maxwell equationsMaxwell equations

jEB

BE

B

E

000

0

0

µµε

ερ

+∂∂=×∇

∂∂

−=×∇

=⋅∇

=⋅∇

t

t

jEB

BE

B

E

000

0

0

µµε

ερ

+∂∂=×∇

∂∂

−=×∇

=⋅∇

=⋅∇

t

t

Ej σ=

Condensed matter hides in σ

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Light basicsLight basics

Plane wave

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Light basicsLight basics

Wave equation in vacuum

Phase velocity

)/~( cxntie −−= ω0EE

Wave equation in medium

)( kxtie −−= ω0EE

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

AbsorptionAbsorption

2

122

)/~(

2

)()(~

εκεκ

ωεκω

ω

==−

=+=

= −−

nn

inn

e cxnti0EE

Complex refractive index:Complex refractive index:

LawBeerLambert.

:intensitydTransmitte)/()/2(*

)/~(

2 dco

dco

dcni

eIeII

e

ωεκω

ω

−−

≈==

=

EE

EE 0

0

2 log1)()(

:tcoefficienAbsorption

II

dcK −== ωωεω

In medium: Ibach & Lüth

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Kramers KronigKramers Kronig relationsrelations

ε for system ofharmonic oscillators

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Kramers KronigKramers Kronig relationsrelations

How to get Kr. Kr.Ibach & Lüth

Ibach & Lüth

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Resonance

∫∞

−=

=

++=

022

2

'''

)(1)('

2)()("

)()()(

εεεσε

π

λεσε

εεε

dEhcr

Ef

rf

iffZf

a

e

e

a

atomic scattering amplitude:

real part: Kramers-Kronig

Gd M4,5From absorption cross sectionto scattering cross section

imaginary part: absorption

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

The dielectric constant for two simple casesThe dielectric constant for two simple cases

• Harmonic oscillator

• Free electron gas

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

Dielectric function for Damped Harmonic OscillatorsDielectric function for Damped Harmonic Oscillators

dampingResonant frequency

Field induced dipole

Real and imaginary parts

Ibach & Lüth

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

How to measure the dielectric functionHow to measure the dielectric function

1. Transmission measurement of ε2 + K.K. transform2. Reflection measurement + simulation

Reflection coefficient:

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The free electron gas,The free electron gas, plasmonsplasmons

Plasma frequency

Explains reflectivity of metalsPlasma resonances damped by interband resonances

>> model has no practical use for metalsWorks well for semiconductors

Ibach & Lüth 11.9

Drude damping term

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C M S M a s t e r s : Nanoprobes, spectroscopy & scattering© Jeroen Goedkoop2003

EELSEELS

Surface and bulk plasmon