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Raman Effect

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Title: 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
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