RAMAN SPECTROSCOPY
Scattering mechanisms
Rayleigh
Mie
Random motions
Vibrations
Rotations
Elastic
Raman - local modes, vibrations, rotations
Brillouin - collective modes (sound)
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 scattering
Interaction between applied field and normal modes
Applied optical field:
Induces polarization
Vibrations:
E  E0 cos t 
P   E   E0 cos  t 
Displacement
Raman active modes:
Small amplitudes
Polarizability 
q  q0 cos  t 
  
q0 :    0  
 q0 
 q 
-e
+e
Raman Lines
Polarization
  
P   0 E0 cos t   
 q0 E0 cos  t  cos  t 
 q 
1   
  0 E0 cos t   
 q0 E0 cos     t   cos     t 
2  q 

First term: Rayleigh scattering
Second term: Stokes  ω-Ω 
Anti Stokes  ω+Ω 
Raman lines
Momentum sele ction rule:
k₀ - k  q +G=0
Only transitions at q=0

Selection rules – Raman active modes:
Polarizability ellipsoids
1
of CO2 molecule.
 1 is Raman active: the
polarizability is different at
the two extremes.
On the other hand 2 and  3
are not Raman active.

Raman scattering from Si nanocrystals
Bonds in Si (Diamond structure)
S1: Vibrational frequencies (0.1 eV)
S2: Optical frequencies (3.4 eV)
Raman spectrum of Si
Phonons in bulk Si
    0   16THz
h  0.066 eV
1  525 cm1

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
– q  0 selection rule lifted -
q 
1
D
Raman spectrum
Intensity : I   
Faraci et al. PRB 73, 033307 (2006)
 C  q  L  , q  dq
2
BZ
 : Raman frequency
C  q  : Fourier amplitude of phonon wavefunction
L  , q  : Lorentzian, linewidth Γ
Introduce confinement function FC  r , D 
Fourier amplitude : C  q  
2
Spectrum : I   

0
a
1
 2 
3
 iq r
F
r
,
D
e


C

C  q  dq
2
 
    q    
2
2
2
Confinement function
FC  r , D   
n
kn 
sin  kn r 
kn r
for r  D
2
n
, n  2, 4, 6, , nmax
D
nmax smallest int eger less than
2 D  2  2nm


7.4,
n

4
max


a  0.543nm

Decays towards edge of nanocrystal
Calculating spectrum
n th component of FT: Cn  q   3
Spectrum:
I    
n 1
D

sin  q D2 
 3 D 3q  kn2  q 2 
Cn  q  dq
2
 
2
    q    
2
n 1
n 1
Confinement effect on q :
 q

D D
D D
n
n 1
D
2
2
 a
Average phonon mode of Si :   q    A  B cos  q 
 4
A  1.714 105 cm 1 B  1.00 105 cm 1
Calculated spectra
Line width for bulk Si: 3cm-1
Large shift with size
Asymmetric shape of spectrum
Comparison to experiments

a
Richter model  RWL  :     
 D
  52.3 cm1 ,   1.586
Bond charge model
Bond charge model
Transition from amorphous to nano crystalline Si film
Yue, Appl. Phys. Lett., 75, 492 (1999)
PECVD deposition at 230˚C
on glass
Dilution rate R=
H2
SiH 4
varied
PL spectra: a-Si at 1.3 eV
c-Si at 0.9 eV
Temperature dependence
Si nc’s on graphite. Shift of Stokes and Anti Stokes lines.
Ratio between Stokes and Anti Stokes determine temperature
Faraci et al. PRB 80 193410 (2009)
Raman spectroscopy on carbon nanotubes
Jung, Bork, Holmgaard, Kortbek
8th semester report
𝐶ℎ = 𝑛𝑎1 + 𝑚𝑎2
(n,m)
tube
Metallic and semiconducting tubes
Radial and transverse modes
Radial breadingmodes
Conclusions
Raman spectroscopy
•
•
•
•
Elemental specific optical technique
Fast and reliable
Distinguish crystalline and amorphous phases
Size sensitive for nc’s ~1-10 nm