1. Light Scattering Spectroscopies
Raman Scattering
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2. Macroscopic Theory of Phonon Scattering
System : infinite, isotropic medium
: Plane electromagnetic wave
: Induced sinusoidal polarization
: Electric susceptibility
(fluctuates at T >0)
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3. Macroscopic Theory of Phonon Scattering
Atomic displacements associated with a phonon
Adiabatic approximation:Characteristic electronic frequencies are>> ω0
(ki,wi,Qi)
Taylor expansion in Qi(r,t)
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4. Macroscopic Theory of Phonon Scattering
12/3/2018
Macroscopic Theory of Phonon Scattering
Thus, the polarization of the medium in the presence
of atomic vibrations is obtained as
where
(Polarization vibrating in phase with F)
&
(Polarization wave induced by the phonon)
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5. Macroscopic Theory of Phonon Scattering
Now rewriting the equation as
The induced polarization consists of two sinusoidal waves!
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6. Macroscopic Theory of Phonon Scattering
Pind
Stokes shifted sinusoidal
ks=(ki-q) and s=(i- o)
Anti-Stokes shifted wave
kAS=(ki+q) and AS=(i+o)
The light produced by these polarization waves
Stokes scattered anti-Stokes scattered
light
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7. Macroscopic Theory of Phonon Scattering
Terminology
phonon
frequency =
ph
incident photon
frequency i -
scattered photon s
Energy and momentum are conserved
One phonon scattering probes zone center phonons
Higher order terms lead to ± ωa ±ωb (ωa>ωb)
Hence two phonon scattering. Combination and difference modes. If two phonons are identical, the two phonon peak is called an overtone.
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8. Raman Tensor and Selection Rules
Intensity of scattered rad can be calculated from time
averaged induced polarizations Pind into solid angle.
Intensity of the scattered radiation depends on the polarization of the scattered as well as of the incident radiation.
Define a complex second rank tensor with q=Q/|Q| as
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9. Macroscopic Theory of Phonon Scattering
(R : the Raman tensor)
Raman scattering can be used to determine
frequency and symmetry of a zone center phonon mode
Raman tensors for zincblende structure
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10. Macroscopic Theory of Phonon Scattering
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11. Nonclassical View of Raman Scattering
The quantity measured in experiments =  (scattering efficiency)
L:scattering length
V=AL
s:frequency of
the scattered light
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12. Nonclassical View of Raman Scattering
Raman scattering inelastic scattering of photons by quantized excitations in the medium
: total scattering cross section
Ni:flux of incident photon beam per unit area
Ns:flux of scattered photon beam per unit area
(non classical result)
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13. Nonclassical View of Raman Scattering
 : total cross section corresponding to |ei.R(i, s). es|
 Ns=  (i, s)Ni
Assuming that the incident photon flux is such that only one scattered phonon is produced
 Ni= 1/ (i, s)
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14. Nonclassical View of Raman Scattering
Raman scattering possesses time-reversal symmetry
Ns= (Ni-1) + Ni A (s, i)
From the time reversal symmetry we have the requirement
Ns= Ni  1= NiA (s, i)
(i, s) = A(s, i)
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15. Experimental Setup
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16. Selected Results
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17. 13:50

18. 13:50

19. 13:50

20. Frequency Shift
 (T) = 0 + 1(T )+ 2(T ),
where 0 + 2(0) is the Raman frequency as T approaches 0 K, 1(T ) represents the volume dependence of the frequency due to the thermal expansion of the crystals and 2(T ) specifies the contribution of anharmonic coupling to phonons of other branches.
1(T ) can be written as
1(T) = 0
where (T ) is the coefficient of linear thermal expansion.
In general, the purely anharmonic contribution to the frequency shift can be modeled as
2(T ) = A
which represents the optical phonon coupling to two different phonons (three-phonon processes). Here, x1 = hc1 / kBT and x2 = hc2 / kBT .
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21. Linewidth
The temperature dependence of the phonon linewidth can be described as follows
 = C
where C is the broadening of the phonon line due to the cubic anharmonicity at absolute zero (the decrease in phonon lifetime,  , due to the decay of the optical phonon into two different phonons).
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22. TlInS2
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23. TlInS2: At BZCenter Group Theory gives: 10 Ag +14 Bg + 10 Au + 14 Bu ,
where Au + 2 Bu modes are acoustic. There should be 10 Ag + 14 Bg Raman-active modes
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24. Most modes shifts to smaller frequencies as temperature increases.
Modes in TlInS2
Most modes shifts to smaller frequencies as temperature increases.
Modes at ans cm-1 sohws hardening with increasing temperature
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25. Translational Mode Frequency at 57.1 cm-1
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26. Intramolecular Mode at 292.3 cm-1
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27. 57.1 and 292.3 cm-1 Curve 1:Exp freq shift
Curve 2: Purely thermal expansion 1(T)
Curve 3:Purely anharmonic contribution, 2(T)
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28. Frequency and Lineshift Analysisν0 ν1 ν2 A C
37.6
18.8
0.40
0.32
61.8
30.9
0.67
0.29
83.8
41.9
-0.57
1.06
139.1
69.5
69.6
-0.79
0.44
278.3
104.6
173.7
1.34
0.79
284.4
78.9
205.5
4.86
0.70
303.8
48.2
255.6
2.46
0.98
347.5
48.9
298.6
0.59
1.54
348.3
139.3
209.0
2.11
0.93
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