EM Course – Inelastic Scattering
Professor Rodney Herring
Inelastic Scattering - Introduction
Quasiparticle Property Measurements
Two reasons why we can generate and detect:
1) Since the fast electrons passing through a material can create
plasmons, phonons, magnons, etc., i.e, signal generating, their
resulting energy-loss electrons (used for signal detecting) carry the
information of their properties.
2) Every electron that scatters off the same quasiparticle mode picks
up the same scattering phase.
- if an electron scatters off the quasiparticle, this electron
carries information about the quasiparticle.
e.g., the phonon gluing Cooper pair electrons together
to make the superconducting fluxon.
Inelastic Scattering - Introduction
Electron Scattering
Inelastic Scattering - Introduction
We will focus on the collective interactions produced by inelastic scattering
since no new information concerning x-rays and secondary electrons is
available in Williams and Carter.
Electron Energy Loss Spectrum (EELS)
Elastically scattered electrons – Bragg diffracted
and diffuse elastically scattered electrons
Zero-loss + phonon loss
,I
(Bulk Plasmons)
Low-energy, diffuse inelastically
scattered electrons
(Surface Plasmons)
(excitons,
bandgap,
dopants,
defects)
,E
g hkl
000 beam
g hkl E
Diffracted beam
EELS spectrum of elastically & inelastically scattered electrons
Zero-loss & Phonon-loss Intensities for
GaAs
10
total
8
Intensity
Aplanatic STEHM required
6
Zero-loss
4
2
444
222
666
atomic planes
Phonon-loss
0.2
0.4
0.6
0.8
1.0
s (1/Å)
0
10
f (mrad)
Doyle and Turner Acta Cryst. (1968). A24, 390
20
Similar intensity loss for
plasma loss electrons
Inelastic Scattering - Introduction
Plasmons and Phonons
Plasmons and Phonons
(next slide)
*
Longitudinal Waves
* for bulk
plasmons,
which exist
inside the
material.
There is also a
surface
plasmon,
which can be
delocalized on
the surface and
exist for microseconds
Recall: the electron emitted from the source is a transverse wave.
Bulk Plasmons
If the specimen is >100 nm, then another bulk plasmon can be created.
The diffracted beams can also produce bulk plasmons.
Surface Plasmons
The surface plasmon energy is equal to the bulk plasmon energy
(10s of eV) divided by square root 2.
For some specimen and certain conditions, surface plasmons
can have a high intensity, e.g., gold nanoparticles, carbon
nanotubes, etc., anything where the surface dominates over the
volume of the specimen. Their creation by the electron beam
creates a high intensity of surface plasmon loss electrons.
Plasmons
1. Localized Surface Plasmons
Surface Plasmon
2. Propagating Surface Plasmons
Localized Surface Plasmons
Simple semi-classical model:
electron wave
Surface plasmon densities around differently
shaped nanoparticles
A.J. Haes, C.L. Haynes, et al, MRS BULLETIN, 30 368 (2005)
Surface Plasmon Polariton
The smaller the wavelength of surface plasmon, the shorter
length it travels or propagates over the surface!
H.A. Atwater, S. Maier, et al, MRS BULLETIN, 30 385 (2005)
Plasmons Loss Electrons
Phonon Loss Electrons
Interband and Intraband Loss Electrons
plus the presence of
dopants and defects
(electronic and
photonic defects)
in the band gap
Elastically & Inelastically Scattered Electrons
Elastically scattered electrons – Bragg diffracted
and diffusely scattered
Zero-loss + phonon loss
,I
(Bulk Plasmons)
(Surface Plasmons)
(excitons,
bandgap,
dopants,
defects)
,E
g hkl
000 beam
g hkl E
Diffracted beam
What is the better electron source that represents elastically and
inelastically scattered electron coming from material specimens?
Lorentzian:
Represents
electrons from
specimen that have
lost energy such as
inelastically
scattered electrons
including plasmon
loss electrons and
phonon loss
electrons.
Lorentzian
Gaussian:
Represents
electrons from
electron emitter
plus Bragg
diffracted beams,
which have no
energy loss.
Gaussian
The mean is and the half-width is . The Lorentzian distribution has
very extended wings and is not defined as the integral is unbounded!
Lateral coherence enables
continued interfere of beams
as they are separated by
changing voltage on electron
biprism.
New position on source, RS’1
and RS’2 enable the source
size, shape and coherence to
be determined.
Perhaps, first time to
aB
measure properties of
electron source coming from
specimen.
Primary Beam
Condenser Aperture
ac
RS’1
Crystal Specimen
2qB
RS’2
Apparent Sources, Rs’
(virtual sources)
Electron Biprism ( )
Main Beam
Diffracted Beam
Region 1
Region 2
Fringe Contrast versus Beam Separation
86V
82V
a)
b)
79V
74V
The Lateral spatial
coherence, do, is given
as a function of electron
source size, Rs, to be:
d 

 2 Rs
The reduced fringe
contrast as the beams
separate gives a
measure of the shape of
the electron sources.
2
1
2
c)
d)
Beam Damage
Beam Damage
Beam Damage
Beam Damage - Heating
Beam Damage - Heating
Beam Damage – Polymers
Beam Damage - Polymers
Beam Damage – Covalent & Ionic Materials
*
* cathodoluminescence
Beam Damage in Metals
Beam Damage
Beam Damage
Beam Damage
Inelastic Scattering - Sputtering
Inelastic Scattering - Summary
Surface Plasmon Polariton
Propagating Surface Plasmons: Surface Plasmon Polaritons (SPPs)
SPP are electromagnetic modes
bound to metal/dielectric interface
which propagates as a longitudinal
wave along the surface.
Localized Surface Plasmons
Surface Plasmon Polaritons
Nanoparticles size: 10-200 nm Metal thickness : 10-200 nm
Field enhancement
100-10,000 times
10-100 times
Field spatial range
10-50 nm
~1000 nm
A.J. Haes, C.L. Haynes, et al, MRS BULLETIN, 30 368 (2005)
Plasmon Polariton Propagation in Gold Rod
Plasmon Polariton Propagation in stripe with d < λ
Surface Plasmon Bio Sensors (SPR-like experiment )
Sensor chip
with gold film
Advantages:
Evanescent field interacts with adsorbed molecules only
Coupling angle strongly depends on εd
Bandgap Engineering
0.95 eV
0.78 eV
Figure 9: Energy band diagram versus lattice constant.