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Dr. Matthias Krause I Institute of Ion Beam Physics and Materials Research I www.hzdr.de

From micro to nano - fundamentals and recent

developments of Raman spectroscopy

Dr. Matthias Krause, Nanocomposite materials group, Helmholtz-Zentrum Dresden-Rossendorf, Germany

Dr. Matthias Krause I Institute of Ion Beam Physics and Materials Research I www.hzdr.de

Dr. Matthias Krause, Nanocomposite materials group, Helmholtz-Zentrum Dresden-Rossendorf, Germany

Introduction into Raman spectroscopy

Dr. Matthias Krause I Institute of Ion Beam Physics and Materials Research I www.hzdr.de Member of the Helmholtz Association

Outline

1. Introduction into light scattering

2. Vibrational frequency –diatomic molecule, diatomic linear chain, characteristic frequencies

3. Raman activity and intensity – conservation laws, factor group analysis, scattering tensor, double resonance scattering

4. Experimental aspects

5. Instrumentation

6. Literature

7. Summary


1. Introduction into light scattering


Rayleigh scattering

Introduction into light scattering

𝐼450 𝑛𝑚𝐼650 𝑛𝑚

∝

1(450 𝑛𝑚)4

1(650 𝑛𝑚)4

≈ 4.4[2]

[2] https://de.wikipedia.org/wiki/Rayleigh-Streuung

𝐼𝑅𝑎𝑦𝑙𝑒𝑖𝑔ℎ ∝ 1𝜆4 , 𝜈4 [1]

[1] John William Strutt, 3. Baron Rayleigh, nobel prize in physics 1904


"A New Type of Secondary Radiation", Nature 501, 121 (1928)


Nobel prize in Physics 1930


G. Landsberg, L. Mandelstam, "Eine neue Erscheinung bei der Lichtzerstreung in Krystallen", Naturwissenschaften 28, 557 (1928)



Rayleigh and Raman scattering vs. infrared absorption



Lorentz-Line:

𝐼𝜈 = 𝐼𝑚𝑎𝑥

1 + 𝜈 − 𝜈 𝑣𝑖𝑏

Γ

2

FWHM, 2

Imax

𝜈 𝑣𝑖𝑏


A typical Raman line


Imax: amplitude 𝐼𝜈 : integrated area, transition probability of a Raman excitation 𝜈 𝑣𝑖𝑏: Raman shift, ~ transition energy of a Raman excitation 2: full width at half maximum, life time of the excited quantum state

Raman parameter Introduction into light scattering


2. Vibrational frequency – diatomic molecule, diatomic linear chain, characteristic frequencies

𝐸 = ℎ𝜈𝑣𝑖𝑏 = ℎ𝑐0𝜆= ℎ 𝑐0 𝜈 𝑣𝑖𝑏

𝐽 = 𝐽𝑠 𝑠−1 = 𝐽𝑠𝑚𝑠−1

𝑚

𝐸 ∝ 𝜈 𝑣𝑖𝑏 (𝑤𝑎𝑣𝑒 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑐𝑚−1)


Diatomic molecule (classical treatment)

Vibrational frequency – diatomic molecule, diatomic linear chain, characteristic frequencies

𝜈𝑣𝑖𝑏 =1

2𝜋𝑓12

1

𝑚1+

1

𝑚2

𝜈𝑣𝑖𝑏 =1

2𝜋

𝑓12𝜇

𝑠−1 =𝑁𝑚−1

𝑘𝑔=

𝑘𝑔 𝑚 𝑠−2 𝑚−1

𝑘𝑔


Diatomic linear chain


𝜈2 = 𝑓124𝜋2

1

𝑚1+

1

𝑚2±

𝑓124𝜋2

1

𝑚1+

1

𝑚2

2

−2

𝑚1𝑚2 1 − cos 𝑞𝑎

𝜈 = 𝑓 𝑞 , − 𝜋

𝑎 ≤ 𝑞 ≤

𝜋

𝑎


Diatomic linear chain


Optical phonon branch Acoustic phonon branch

H. Ibach, H. Lüth, Festkörperphysik - Einführung in die Grundlagen, 6th ed., Springer Berlin - Heidelberg - New York, 2002


Characteristic frequencies and wave numbers


𝜈𝑣𝑖𝑏 =1

2𝜋𝑓12

1

𝑚1+

1

𝑚2 𝑠−1 ; 𝜈 𝑣𝑖𝑏 = 1303 𝑓12

1

𝑚1+

1

𝑚2(𝑐𝑚−1)

molecular hydrogen, H2: 4167 cm-1

molecular nitrogen, N2: 2330 cm-1

molecular oxygen, O2: 1556 cm-1

bonded hydrogen, Si-H, C-H, N-H, O-H: 2000 - 3700 cm-1

C≡C, C C, CC stretching frequencies: 2100, 1650, 1100 cm-1


𝑓𝐷𝑖𝑎𝑓𝑆𝑖

= 𝑚𝐷𝑖𝑎

𝑚𝑆𝑖 𝜈 𝐷𝑖𝑎2

𝜈 𝑆𝑖2 = 2.8

𝑓𝑆𝑖𝑓𝐺𝑒

= 𝑚𝑆𝑖

𝑚𝐺𝑒 𝜈 𝑆𝑖2

𝜈 𝐺𝑒2 = 1.2



3. Raman activity and intensity in crystals

Raman scattering in crystals – a three step description

1. Absorption of an incoming photon (𝜈0, 𝑘 0), generation of an electron-hole (e/h) pair

2. Scattering of the electron by excitation or de-excitation of a crystal vibration with (𝜈𝑣𝑖𝑏, 𝑘 𝑣𝑖𝑏)

3. Recombination of the e/h-pair, emission of a scattered photon (𝜈1, 𝑘 1) )

S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes - Basic Concepts and Physical Properties, Wiley-VCH, Weinheim, 2004


Raman activity and intensity – conservation laws, factor group analysis, scattering tensor, double resonance scattering

Energy conservation: ℎ𝜈0 = ℎ𝜈1 ± ℎ𝜈𝑣𝑖𝑏


Momentum conservation for Raman scattering in crystals:



Momentum conservation for Raman scattering in crystals:

ℎ𝑘 0 = ℎ𝑘 1 ± ℎ𝑘 𝑣𝑖𝑏,

ℎ𝑘 𝑣𝑖𝑏, 𝑚𝑎𝑥 = ℎ𝑘 0 − −ℎ𝑘 1 ≈ 2 ℎ𝑘 0

2 ℎ𝑘 0 𝜆0 = 500 𝑛𝑚 = 4 𝑥 104 𝑐𝑚−1 ;

0 ≤ ℎ𝑘 𝑣𝑖𝑏 ≤𝜋

𝑎 = 𝜋2.46 𝑥 10−8 𝑐𝑚 = 1.3 x 108 𝑐𝑚−1



Momentum conservation for second order Raman scattering in crystals:

ℎ𝑘 0 = ℎ𝑘 1 ± ℎ𝑘 𝑣𝑖𝑏,

ℎ𝑘 𝑚𝑎𝑥 = ℎ𝑘 0 − −ℎ𝑘 1 ≈ 2 ℎ𝑘 0 = ℎ𝑘 𝑣𝑖𝑏



2 TO

2 TA


W.H. Weber, R. M. E. Raman Scattering in Materials Science; Springer: Berlin - Heidelberg - New York, 2000


Raman activity

first order crystal phonons with 𝑘 𝑣𝑖𝑏 = 0: point phonons, can be treated by factor group analysis for unit cell atoms

second order crystal phonons, resemble phonon density of states



Factor group analysis of -Al2O3, space group 167 (𝐷3𝑑6 , 𝑅3 𝑐)

Number of atoms and vibrations in the primitive cell: 10 (30-3=27)

Site symmetries of Al and O: 4c, C3; 6e, C2 (R.W.G. Wyckoff, Crystal structures, Vol. 1, Interscience Publishers, A Division of J. Wiley& Sons, New York, 2nd edition, 1963)

Irreduzible presentations of corresponding translation vectors (character tables): C3: A (Tz), E (Tx, Ty)

C2: A (Tz), B (Tx, Ty) Correlation with irreproducible presentations of the

factor group (crystal class)



Intensity of Raman excitations

𝐼 𝑅𝑎 = 𝐶 𝜈0 − 𝜈14 𝐼0 𝑞𝑖

2

𝑁

𝑖=1

𝛼𝜚𝜎2

𝑥𝑦𝑧

𝜚𝜎

𝐼0 = 1

2 𝜀0 𝑐 𝐸 0

2 𝑊𝑚−2, 𝑒𝑥𝑐𝑖𝑡𝑎𝑡𝑖𝑜𝑛 𝑙𝑖𝑔ℎ𝑡 𝑝𝑜𝑤𝑒𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦

𝑞𝑖: 𝑖 − 𝑡ℎ 𝑅𝑎𝑚𝑎𝑛 𝑎𝑐𝑡𝑖𝑣𝑒 𝑐𝑟𝑦𝑠𝑡𝑎𝑙 𝑣𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛


𝐼𝑅𝑎 ℎ𝑎𝑠 𝑢𝑛𝑖𝑡 𝑊

𝑠 𝑑Ω


Raman scattering tensor

𝐼 𝑅𝑎 = 𝐶 𝜈0 − 𝜈14 𝐼0

𝛼𝑥𝑥′ 𝛼𝑥𝑦

′ 𝛼𝑥𝑧′

𝛼𝑦𝑥′ 𝛼𝑦𝑦

′ 𝛼𝑦𝑧′

𝛼𝑧𝑥′ 𝛼𝑧𝑦

′ 𝛼𝑧𝑧′

𝑞𝑖

2𝑁

𝑖=1


At least one tensor element must be non-zero


Our example: -Al2O3, factor group 𝐷3𝑑

𝛼𝜚𝜎′ (𝐷3𝑑) = 𝛼′ 𝐴1𝑔 + 𝛼′ 𝐸𝑔, 1 + 𝛼′ 𝐸𝑔, 2

𝛼𝜚𝜎′ (𝐷3𝑑) =

𝑎 0 00 𝑎 00 0 𝑏

+𝑐 0 00 −𝑐 𝑑0 𝑑 0

+0 −𝑐 −𝑑−𝑐 0 0−𝑑 0 0

2 Raman-active irreproducible representations: A1g, Eg 4 Raman-active tensor elements: a, b; c, d 𝜞𝑹𝒂𝒎𝒂𝒏, 𝜶−𝑨𝒍𝟐𝑶𝟑

= 𝟐𝑨𝟏𝒈 + 𝟓 𝑬𝒈



How can the tensor elements of -Al2O3 be measured?

Alignment of crystal and light E-vector coordinates

Porto notation: [a(bc)d] a: propagation direction of exciting light b: polarization direction of exciting light relative to crystal coordination system c: polarization direction of scattered light relative to crystal coordination system d: propagation direction of scattered light



How do the Raman spectra of -Al2O3 look like?



Factor group analysis may work fine, but...

Second order scattering can hide first order modes

Vibrations of polar crystals split in TO- and LO-components

Raman modes show dispersion, i.e. change their frequency in dependence of exciting light wavelength



How are these effects manifested in the Raman spectra?


Resonance Raman scattering

𝐼𝑅𝑎 ∝ 𝐾2𝑓,102

𝐼𝑅𝑎 ∝ 𝑐𝑜𝑛𝑠𝑡2

𝐸0 − 𝐸𝑎𝑖𝑒 2

𝐸0 − ℎ𝜈𝑣𝑖𝑏 − 𝐸𝑏𝑖𝑒 2 ≈

𝑐𝑜𝑛𝑠𝑡2

𝐸0 − 𝐸𝑎𝑖𝑒 4




Resonance Raman scattering



Double Resonance Raman scattering




Double Resonance Raman scattering in graphite

1525 1550 1575 1600 2600 2700 2800

= + 141 cm-1

1.17 eV

1.58 eV

2.41 eV

2.47 eV

2.54 eV

2.60 eV

2.71 eV

1064 nm

785 nm

514 nm

501 nm

488 nm

476 nm

457 nm

Dispersion of D*-Line: 46 cm

-1/ eV

Ra

ma

n in

ten

sity (

arb

. u

n.)

Raman shift (cm-1)



Beyond crystalline solids




in situ Raman study of a-Si/ Ag at 500°C

R. Wenisch, PhD thesis, in preparation

30 nm Ag

60 nm a-Si


Particle-size and stoichiometry effects


V. Swamy et al., APL 89, 163118 (2006), Size-dependent modifications of the Raman spectrum of rutile TiO2,

𝜈 𝑟𝑒𝑓 𝐴1𝑔 = 612 𝑐𝑚−1

J.C. Parker, R.W. Siegel, APL 57, 943 (1990), Correlation of the Raman spectrum to the oxygen stoichiometry of nanophase TiO2,


4. Experimental aspects

Method Light source

Beam optics Sample stage

Analyzer Detector

Raman Laser Plasma line and Rayleigh filter

Micro-scope

Grating CCD (256x1024)

FTIR Black-body

IR optics, Au-mirrors

T+R stages

Inter-ferometer

DTGS, Photodiode

UV-Vis-NIR

Black-body

BMS, UV-Vis-NIR optics

T+R stages

Grating Photodiode,

XRD X-Ray X-Ray optics CCD

Ion beams

2 MeV He+

Magneto optics Si diodes


Illumination and scattering beam optics

Experimental aspects


Diffraction and detection



Measured quantity: wavelength of scattered light



Measured quantity: wavelength of scattered light

Determined quantity: Raman shift



5. Instrumentation


Labram HR Raman spectrometer, 2 gratings, microscope stage

Lateral resolution: ~ 0.5 µm Lateral reproducibility: ≤ 1 µm Spectral resolution, 532 nm: ~ 1.5 cm-1 (3 Pixels, 1800/ mm

grating) Laser wavelength 532 nm and 632.8 nm Polarization measurement equipment LN2 cooled front-illuminated CCD, QE ≤ 50%

Instrumentation


in situ Raman spectrometer iHR 550 at cluster tool, 3 gratings

Spectral resolution, 532 nm: ~ 2 cm-1 (3 Pixels, 1800/ mm grating) Laser wavelength 473 nm and 532 nm no polarization measurement equipment LN2 cooled deep-depleted CCD, QE ≥ 90%

Lateral resolution: ~ 5 µm Lateral reproducibility: ~ 1 µm

Instrumentation


in situ Raman spectrometer iHR 550 at cluster tool

Lateral resolution: ~ 60 µm Lateral reproducibility: ~ 1 µm Depth resolution: ~ 250 µm

Instrumentation


6. Literature

1. J. Weidlein, U. Müller, K. Dehnicke, Schwingungsspektroskopie - Eine Einführung, Georg Thieme Verlag Stuttgart, 2. Aufl., 1988

2. S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes - Basic Concepts and Physical Properties, Wiley-VCH, Weinheim, 2004

3. H. Kuzmany, Solid State Spectroscopy - An Introduction, Springer-Verlag, Berlin, 1998

4. R.W.G. Wyckoff, Crystal structures, Vol. 1, Interscience Publishers, A Division of J. Wiley& Sons, New York, 2nd edition, 1963

5. Hellwege, K.-H. Einführung in die Festkörperphysik, Springer Berlin, Heidelberg, New York, 1976

6. Harald Ibach, H. L. Festkörperphysik - Einführung in die Grundlagen, 6th ed., Springer Berlin - Heidelberg - New York, 2002

7. Misra, P. K. Physics of condensed matter, Academic Press Amsterdam, 2012 8. W.H. Weber, R. M. E. Raman Scattering in Materials Science, Springer Berlin -

Heidelberg - New York, 2000


7. Summary - Raman spectroscopy

1. Non-destructive, fast, easy-to-operate method for the analysis of gases, liquids, surfaces, amorphous and crystalline solids

2. High energy-resolution, ~1µm lateral resolution, ~ 3µm depth resolution

3. Chemical composition, bond strength, molecular and phase structure, degree of long-range ordering, defects, molecular and crystal orientation

4. Low and high temperatures, high pressures, high electric or magnetic fields, sealed air-sensitive samples

5. Coupling techniques with AFM and electrochemistry available

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