Raman Effect

1
Raman Effect

• The Scattering of electromagnetic radiation by
  matter with a change of frequency

2
Outline

• Introduction
• Classical Description
• Quantum Description
• Resonant Raman Scattering
• Conservation of energy and momentum
• Symmetry of Raman Tensor
• Selection Rules
• Experimental Setup and results

3
Introduction

• When light enters a medium it is part reflected
  part refracted part scattered and part absorbed.

Scattering is due to inhomogeneities inside the
medium. When these inhomogeneities are not
static (density fluctuations) the scattered light
can have a change of frequency. This is called
Raman scattering.
4
Introduction

• There are many non static inhomogeneities, due to
  Temperature, that can be described as elementary
  excitations of the medium Phonons, Plasmons,
  Spin-Waves, Electronic states etc.

Phonons dispersion relation of Si
5
The Dielectric function
Of a collection of simple harmonic oscillators
with density N, charge Q, Mass M and natural
frequencies ?i is
The SHO can be electronic or from lattice
vibrations. The response of the SHO to an
electric field with frequency ? depends on the
difference (?-?i). if
Lattice contribution is negligible, and the
electronic contribution doesn't depend on ?
6
Classical Macroscopic theoryDefinitions and
results from electrodynamics

• In a dielectric medium the electric force is
  different from the one in vacuum due to
  polarizability
• Radiation of an oscillating dipole P

7
Classical Macroscopic theoryPolarizability

• Atomic thermal vibrations (or any other density
  fluctuations) denoted ?(r,t) can be expanded as
  plane waves
• The electric susceptibilty is fluctuating due to
  these thermal vibrations and can be expanded
  from zero temperature value (treating separately
  each normal mode) as

8
Classical Macroscopic theoryPolarizability

• Since the polarizability also
  fluctuate

Pind is an oscillating dipole and therefore it
radiates. This radiation is Raman Scattering.
9
Classical Macroscopic theoryPolarizability
There are two frequencies of oscillation, which
give two different scattering lines

• Power radiated by Pind

10
Quantum description
Oscillating dipole doesnt radiate. Quantum
transitions do.

• transition probabilities are calculated with
  fermi golden rule

with
11
Quantum DescriptionWho interacts with what

• phonon-photon interaction is weak, since
  
• semi classical approach ignore Hrad
• HeR is treated in the electric dipole
  approximation.
• adiabatic approximation. Electrons are in the
  ground state before and after the scattering
• The state of the crystal is separated to a
  product of electrons state and phonon states.

12
Quantum descriptionschematic representation
Incoming Photon interacts with an electron. the
Photon is annihilated and the electron is
excited to an intermediate virtual state bgt. The
excited electron interact with a phonon, and
returns to the electronic ground state creating a
scattered Photon.
13
Quantum DescriptionFeynman Diagrams
There are six processes that contributes to the
one phonon stokes Raman scattering. Three of the
m are shown.
14
Quantum descriptiontransition probability
15
Resonance term

• the resonance term in the transition probability
  leads to an enhancement of the scattering
  intensity when the incident light is close to an
  electronic energy level. This allows to explore
  the energy spectrum of the mater in the light
  energy range.
• Only one term contribute the most, because it is
  the multiply of two resonances that of the
  incoming beam and that of the outgoing beam.

16
Energy and momentum conservationone phonon
process

• Conservation of energy and crystal momentum
  requires (for one-phonon process)

• Sizes of k,q,?i and ? 0
• Wavevector of a visible light photon 105cm-1
• Wavevector of phonons range typically 0-107cm-1
• Photons can exchange momentum only with zone
  center phonons (q0) and Q0

17
What is the Raman Tensor

• In the classical viewpoint, the induced dipole
  moment is proportional to the Raman tensor, and
  to the fluctuation amplitude. Quantum mechanics
  replaces the amplitude with occupancy. The
  scattering intensity of a certain process
  (certain Phonon branch) is proportional to the
  Raman tensor squared of that process.
• To find the intensity of a certain frequency
  shift we need to find the Raman tensors for all
  phonons which give that shift.
• l is the incident photon polarization m is the
  scattered photon polarization and k is the phonon
  polarization

18
Raman Tensorexample

• The third rank tensor for the diamond structure
  crystal (for even-parity Phonons belonging to
  ?25 representation) is

• For scattering from yz plane (100). From
  wavevector conservation q is along the x axis. If
  ki , ks are also along the x axis, then the Raman
  tensor will be Ryz and scattering intensity will
  be proportional to dLO2 and the scattering is
  only from LO phonons. If the photons goes in
  (110) direction q will also be in (110) the Raman
  tensor will be a combination of Ryz and Rzx and
  TO Phonons also participate in the scattering.

19
Selection Rules

• Phonons wavefunction symmetry for q0 can be
  characterized by the irreducible representation
  of the crystal symmetry group.
• A Phonon can participate in a scattering process
  only if its symmetry X the symmetry of the third
  rank tensor contains the A1 fully symmetric
  represnentation.
• Therefore, Certain polarizations and geometries
  gives no Raman scattering, because of symmetry
  requirements.
• For example odd-parity Phonons in a crystal with
  center of inversion symmetry (diamond) are
  forbidden.

20
What can we learn from Raman Scattering

• The investigation of the Raman spectrum of a
  crystal should include the angular and
  polarization dependence of the scattering
  intensity, and also the width of peak and the
  efficiency. From this information can be
  extracted
• The frequency of an optic phonon
• The symmetry of the phonon
• Electron-Phonon interaction
• Two Phonon scattering process give information
  about Phonon density of states
• From the incident light frequency dependence of
  the intensity we can find electronic energy
  levels

21
Experimental setup
22
Temperature dependence of Raman scattering in
silicon T. R. Hart, R.T Aggarwal, Benjamin Lax,
Phys Rev B. 1 638 (1970)
Stokes and anti Stokes lines In different T.
Ratio of the anti Stokes to Stokes.
23
Scattering intensity as a function of photon
energy in GaP
24
Exciton mediated RRS in CdTe
25
Scattering from electronic states of a Doped GaP
Energy levels of Zn acceptor in GaP
Raman Spectrum of GaP dopped with Zn
26
Spin Flip Raman Scattering in CdS
Florescence spectrum that shows the bound exciton
lines, which are close to the Ar 4880Å laser
line.
Raman Spectrum due to magnetically split ground
state of the exciton
27
Spin Flip Raman Scattering in CdS
28
Spin Flip Raman Scattering in CdS
Measurement of the electron g factor, with the
separation of the Stokes and anti Stokes lines
vs. the magnetic field
29
ResultsSi and C from Modis Lab