Transcript Raman spectroscopy
RAMAN SPECTROSCOPY
Scattering mechanisms
Random motions Vibrations Rotations Rayleigh Mie 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
E
0 cos
P
E
E
0 cos Displacement
q
q
0 cos Polarizability Raman active modes: Small amplitudes
q
0 : 0
q
q
0 -e +e
Raman Lines Polarization
P
0
E
0 cos 0
E
0 cos
q
1 2
q
q E
0 0 cos
q E
0 0 cos
t
t
cos
t
First term: Rayleigh scattering 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 molecule.
2 1 is Raman active: the polarizability is different at the two extremes.
On the other hand 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
h
0 16
THz
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 1
D
Raman spectrum Faraci et al. PRB 73, 033307 (2006) Intensity :
I
BZ
, : Raman frequency : Fourier amplitude of phonon wavefunction L ,
q
: Lorentzian, linewidth Γ Introduce confinement function
F C
Fourier amplitude : 1 3
F C
Spectrum :
I
2
a
0 2
dq
2 2
Confinement function
F C
k n
n
n
,
D
sin
n k r n
for r
D
2
n
max
n
max
smallest
int
eger less than
2
D a
nm
0.543
nm
7.4,
n
max 4 Decays towards edge of nanocrystal
Calculating spectrum
C n
3 3 sin 2 2
n
q
2 Spectrum:
I n
1
n n
D
1
D
Confinement effect on q :
n
D C n
2 2
dq
2 1
D n
D
D
1 Average phonon mode of Si :
A
5
cm
1
B
2 cos
q a
4 5
cm
1
Calculated spectra Line width for bulk Si: 3cm -1 Large shift with size Asymmetric shape of spectrum
Comparison to experiments
a
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= H 2 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 8 th semester report 𝐶 ℎ = 𝑛 1 + 𝑚 2 ( 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