Electron microscopy
 
Electron Scattering from a Specimen in EM Measurements
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Electron-scattering from specimens in EM measurements can be grouped in different ways. However, the very common and important classification is sorted by elastic and inelastic scattering as listed in Table 1219.

Table 1219a. Electron scattering from a specimen in TEM measurements (Incoherent does not imply inelastic scattering; however, inelastic scattering is necessarily incoherent in EM measurements).
Scattering type
Energy loss
Wave (phase) property
Scattering direction
Scattering angle
Electron property
Full name
Elastic No energy change of the wave after scattering Usually coherent (when the specimen is thin and crystalline) Forward scattering 1° ~ 10° Wave Coherent elastic scattering
Incoherent > 10° Particle Incoherent elastic scattering
Back scattering  
Inelastic There is energy change of the wave after scattering Almost always incoherent Forward scattering < 1° Incoherent inelastic scattering
Coherent Does not exist in EM measurement, but it shows in neutron scattering     Coherent inelastic scattering
*   Incoherence does not imply inelastic scattering, while inelastic electron scattering is incoherent in electron microscopy.
** Inelastic scattering is not necessarily incoherent in neutron scattering.

Table 1219b. Coherency of scattered electrons from a specimen in EM (electron microscope) measurements.

Coherency
Property
Coherent In phase: preserves the relative phases of the wavelets scattered from different locations in a material; namely, well-defined phase relationship between incident and scattered radiation
Fixed wavelength
The resolution for coherent imaging is much worse than that for incoherent imaging
Useful for diffraction experiments
Incoherent No phase relationship: does not preserve a phase relationship between the incident wave and the scattered wavelets
Not useful for diffraction experiments
The spatial distribution of the scattered intensity is obtained by summing up the intensities from independent scattering events
Incoherent elastic scattering follows the Rutherford scattering law
The resolution for incoherent imaging is much greater than that for coherent imaging due to squaring an amplitude distribution
Incoherent cases: e.g. difference in wavelength
More coherent beam Sharper diffraction pattern can be obtained
* When the electrons are treated as waves, their coherency becomes important.

Table 1219c. Electron forward- and back-scattering from a specimen in EM (electron microscope) measurements.

Scattering direction
Scattering angle
Forward scattering < 90°
Back scattering > 90°

 

Table 1219d. Application/effects of electrons scattered from a specimen in forward direction in EM (electron microscope) measurements. The scattered wave is strongest in the forward direction.
Application/effects
Energy loss
Specimen
Coherency
Full name
Diffraction Elastic scattering Crystals Coherent scattering Coherent elastic scattering
Amorphous solids Incoherent scattering Incoherent elastic scattering
Disordered materials
Diffuse background in diffraction pattern Mixture of incoherent elastic and inelastic scattering Thick specimen Mainly created by incoherent elastic scattering
Partially created by incoherent inelastic scattering Incoherent inelastic scattering
Thermal diffuse scattering   Incoherent  
Compton scattering   Incoherent and inelastic  
HOLZ Elastic scattering   Coherent Coherent elastic scattering
HRTEM  
Weak-beam dark-field images   Contrast after elimination of the incoherent inelastically scattered background  
Kikuchi lines Inelastic + elastic scattering Thick specimen Two electron scatterings: incoherent scattering (sometimes inelastic) is followed by coherent elastic scattering (Bragg diffraction).  
Practical diffraction pattern     An incoherent summation of independent scattering for millions of electrons due to averaging atomic vibrations during acquisition  
Thickness fringes in TEM images   Crystals Fringes become less visible for thicker specimens due to effect of absorption or a loss of coherent  
Fresnel fringes   Coherent  
Electron holography Elastic scattering Coherent beam and scattering are needed Coherent elastic scattering
Scattering from single atoms Any Incoherent  
Scattering from small objectives of ≤1.5 nm in size   Crystals Could be coherent  
Spectroscopy, e.g. EELS Inelastic scattering Any Incoherent scattering: occur with a transfer of energy from the wave to the material  
Plasmon Primay means of inelastic scattering    
Scattering angle < 3° Elastic scattering Crystals Coherent  
Bright field STEM with overlap of diffracted discs  
Larger scattering angle As the scattering angle becomes larger, the coherency degree becomes less Incoherent elastic
scattering (Rutherford scattering)
> 50 mrad (~3°) for 300 kV Any Dominated by incoherent thermal diffuse scattering
Scattering angle > 5° Incoherent and Bragg scattering is normally negligible
High angle Rutherford scattering Incoherent
HAADF
Z-contrast STEM
Z-contrast STEM of silicon at θ > 40 mrad*
Mass-thickness contrast Crystals
Secondary electrons    Any Incoherent  
Atomic vibration   Create an incoherent or partially coherent intensity distribution  
Fluctuations in lens
currents
    Causes incoherence  
Energy spread of electrons from the gun      
Fluctuations in the high
voltage
     
Beam convergence      
Smaller source size     Better coherency  
Spatial coherence     Smaller electron sources give better coherency (at best only ~ 1 nm)  
Spread of focus due to chromatic aberration     Causes incoherence  
Field emission guns     High degree of coherence  
LaB6 electron guns     Low degree of coherence  
* θ is the inner angle of HAADF.
** For a LaB6 electron gun with an emission spot of 10 μm in diameter to achieve the same coherence length as a field emission source additionally requires a source demagnification of several hundred times.

 

Table 1219e. Thickness dependence of electron scattering from a specimen in EM (electron microscope) measurements.
Scattering direction
EM method
Scattering event/angle
Scattering direction
Electrons
Wave (phase) property
Electron property
Contrast interpretation
Thin specimen TEM Less scattering events and then smaller scattering angle
Forward scattering More electrons Strong coherent signal Strong wave property Easy

Back scattering Fewer electrons Weak incoherent signal Weak particle property  
Thick specimen TEM/SEM   Forward scattering Fewer electrons Weak coherent signal Weak wave property Middle
Electron is scattered more than once (plural scattering), and then scattering angle is greater Back scattering More electrons Strong incoherent signal Strong particle property  
Very thick or bulk specimen SEM More scattering events and then greater scattering angle Forward scattering Fewest electrons Weakest coherent signal Weakest wave property Difficult
Electron is scattered >20 times (multiple scattering), and then scattering angle is greatest Back scattering Most electrons Strongest incoherent signal Strongest particle property  

Table 1219f. Factors which affects coherency in EM (electron microscope) measurements.

Factors
Coherency
Larger angular spread of illumination Less coherent
Smaller angular spread of illumination More coherent
Larger chromatic aberration Less coherent
More beam convergence
Smaller collector aperture in STEM More coherent
The spacing of Bragg planes is less than the atomic vibration amplitude Coherent Bragg scattering cannot occur
* In STEM mode, the electron coherence is defined by the coherence length seen at the condenser aperture.

Table 1219g. Coherency effects in EM (electron microscope) measurements.

Coherency
Phase contrast
Image sensitivity
More coherent Enhanced Improved
Partially coherent Limit interference effect  

Table 1219h. Types of coherencies in EM (electron microscope) measurements.

Types of coherencies
Mechanisms
Temporal Coherency All the electrons have the same wavelength, just like monochromatic light.
Spatial Coherency Spatial coherency is related to the size of the electron source. Perfect spatial coherence would imply that the electrons were all emanating from the same point at the source. Therefore, source size governs spatial coherence and smaller source size gives better coherency.

 

Coherence of various scattered electron rays Coherence of various scattered electron rays
Figure 1219. Coherence of various scattered electron rays: (a) Thin film specimen in TEM and/or STEM modes, and (b) Bulk specimen in SEM mode. The electron rays in red are incoherent, while the rays in green are coherent.

 

 

 

 

 

 

 

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