RAMAN SPECTROSCOPYScattering mechanisms

Random motionsVibrationsRotations

RayleighMie

Raman - local modes, vibrations, rotations

Brillouin - collective modes (sound)

Elastic

Raman scattering

• Detects normal modes– Vibrations or rotations in gases or liquids– Phonon modes in solids

• Fingerprint of bonds (elements)• Sensitive to

– State of matter, crystalline or amorphous– Defects– Particle size– Temperature– ….

• Experimental: narrow laser line + good spectrometer

Raman lines of semiconductors

Raman scatteringInteraction between applied field and normal modes

0 cosE E t

0 cosP E E t

Applied optical field:

Induces polarization Polarizability

Vibrations: Displacement 0 cosq q t

Raman active modes:Small amplitudes 0 0 0:q q

q

-e

+e

Raman Lines

0 0 0 0

0 0 0 0

cos cos cos

1cos cos cos2

P E t q E t tq

E t q E t tq

First term: Rayleigh scatteringSecond term: Stokes ω-Ω

Anti Stokes ω+Ω

Raman lines

Polarization

Momentum sele ction rule:k₀ - k q +G=0

Only transitions at q=0

Selection rules – Raman active modes:

Polarizability ellipsoids

of molecule.

is Raman active: the polarizability is different at the two extremes.

On the other hand and are not Raman active.

1

2CO

1

2 3

Raman scattering from Si nanocrystalsBonds in Si (Diamond structure)

S1: Vibrational frequencies (0.1 eV)

S2: Optical frequencies (3.4 eV)

Raman spectrum of Si

1

0 16

0.0661 525

THz

h eV

cm

Phonons in bulk Si

Experiments:Neutron scattering

Size effects in phonon modes

• Well-known for thin films• 0-D systems:– No band gap in amorphous matrix - reduce

confinement effects– Fluctuations in size, shape, and orientation

• Effect on Raman spectrum:– Shift of peak– Broadening of line– selection rule lifted -

0q 1q

D

Raman spectrum

2Intensity : ,

: Raman frequency: Fourier amplitude of phonon wavefunction

L , : Lorentzian, linewidth Γ

BZ

I C q L q dq

C q

q

3

2 2

220

Introduce confinement function ,1Fourier amplitude : ,

2

Spectrum :

2

C

iq rC

a

F r D

C q F r D e

C q dqI

q

Faraci et al. PRB 73, 033307 (2006)

Confinement function

max

max max

sin, 2

, 2, 4, 6, ,

2 2 2int 7.4, 40.543

nC

n n

n

k r DF r D for rk r

nk n nD

D nmn smallest eger less than na nm

Decays towards edge of nanocrystal

Calculating spectrum

23 3 2 2

12

221

2

5 1 5 1

sinn th component of FT: 3

Spectrum:

21 1Confinement effect on q :

Average phonon mode of Si : cos4

1.714 10 1.00 10

D

nn

nD

n

n nD

qC q

D q k q

C q dqI

q

n nqD D D D

aq A B q

A cm B cm

Calculated spectra

Large shift with sizeAsymmetric shape of spectrum

-1Line width for bulk Si: 3cm

Comparison to experiments

1Richter model RWL : 52.3 , 1.586a cmD

Bond charge model

Bond charge model

Yue, Appl. Phys. Lett., 75, 492 (1999)Transition from amorphous to nano crystalline Si film

PECVD deposition at 230˚C on glass

2

4

HDilution rate R= variedSiH

PL spectra: a-Si at 1.3 eV c-Si at 0.9 eV

Temperature dependence

Faraci et al. PRB 80 193410 (2009)

Si nc’s on graphite. Shift of Stokes and Anti Stokes lines.Ratio between Stokes and Anti Stokes determine temperature

Raman spectroscopy on carbon nanotubesJung, Bork, Holmgaard, Kortbek8th semester report

𝐶h=𝑛𝑎1+𝑚𝑎2

(n,m) tube

Metallic and semiconducting tubes

Radial and transverse modes

Radial breadingmodes

ConclusionsRaman spectroscopy

• Elemental specific optical technique• Fast and reliable• Distinguish crystalline and amorphous phases• Size sensitive for nc’s ~1-10 nm