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