Plasmons

Presented By:

Anuradha Verma

Research Scholar

Presentation Layout

What are plasmons

Plasma Frequency

Physical meaning of surface plasmon

Bulk plasmon and surface plasmon

Mean free path

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

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

Plasmon Energy

Eplasmon = ћωp

Energy lost by the electron beam when it generates a plasmon

Typical Plasmon Energies

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

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.

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:

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

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