2. Presentation Layout
What are plasmons
Plasma Frequency
Physical meaning of surface plasmon
Bulk plasmon and surface plasmon
Mean free path
3. What are Plasmons
Plasmons are a unit of collective oscillations of electrons
Or
Quantum of plasma oscillation
Photons-
electromagnetic
vibrations
Light is a wave that is oscillating electro-magnetic field, plasmons
can be excited by light under specific conditions. (And conversely,
in some cases light can be emitted by plasmons as well.)
Phonons-
mechanical
vibrations
4. Plasma Frequency
Classical Explanation:
Determined by oscillations of the valence electrons in a metal with respect to
the positively charged cores.
δr - Fluctuation in radial distance r from a
positive core of a free electron gas with n
concentration of electrons
δn = 4πnr2 .δr
Electric field
E= e/r2δn =4πne. δr
Retarding force created by expansion
F = -eE = -4πne2 .δr
Frequency of the harmonic oscillator due to the retarding force
me - mass of the electron
5. Plasmon Energy
Eplasmon = ћωp
Energy lost by the electron beam when it
generates a plasmon
Typical Plasmon Energies
6. Bulk Plasmon and Surface Plasmon
• Collective oscillation of conducting
electrons
• Bulk plasmon energy depends only on
electron density n
Bulk Plasmon
• Wave nature: Charge density waves
at surface.
Surface Plasmon
ωp= bulk plasmonfrequency
ωp(s)= surface plasmonfrequency
7. Physical Meaning of Surface Plasmons
Nanoparticles- Lattice
of ionic cores with
conduction electron
moving almost freely
inside the NP.
Particle illumination:
EMF of the light exerts
a force on these
conduction electrons
moving them towards the
NP surface.
Electrons are confined
inside NP, negative
charge and positive
charge accumulate on
opposite side, creating
an electric dipole
Dipole generates an electric
field inside the NP opposite
to that of the light that will
force the electrons to
return to the equilibrium
position.
electrons are displaced from the
equilibrium position and the field is
removed later, they will oscillate
with a certain frequency that is
called the resonant frequency called
plasmonic frequency.
8. Mean Free Path of Electron
Electron energy loss in a solid of n electrons/unit volume
B represents a ratio of particle energy to excitation energy
Therefore,
If we treat the plasmon as the major source of energy loss in determining
the mean free path λ for electrons:
9. Mean free path, λ for Al
Given:
ћωp = 15eV
Incident energy of electron = 350eV
This implies,
E = ½ mv2 or v2= 2E/m
Therefore, v = 2 x 350 x 1.6 x 10-19/ 9.1 x 10 -31
= 1.23 x 1018 cm2/s2
Putting these values in equation below gives λ = 0.92nm
10. Electron energy loss spectra of Al
Energy loss spectrum for electrons reflected from Al for incident primary electron
energy of 2 keV. The loss peaks are made up of a combination of surface and bulk
plasmon
Bulk Plasmon= 15.3 eV
Surface Plasmon= 10.3 eV
