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