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