IMAGING ABERRATIONS IN SCANNING ELECTRON MICROSCOPY

7/27/2019 IMAGING ABERRATIONS IN SCANNING ELECTRON MICROSCOPY

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MR202Electron Microscopy in Materials Characterization

General Introduction, Resolution, Limits on resolution, Lens aberrations

Introduction to SPM/SEM, Electron Optics Electron Guns and Lenses,Probe diameter and probe current

Electron-Specimen Interactions, Interaction volume, elastic and inelasticscattering

Basics of SEM imaging, Imaging modes, Detectors, Image contrast, Imageprocessing

XEDS and WDS Principles and practice, Basics

Case studies in Materials Science Imaging and Analysis

Newer Techniques EBSD, LVSEM, ESEM

Sample Preparation and a special note about digital imaging/processing


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Microscope

Used to see objects not visible to the human eye

Eye can resolve objects ~ 0.1mm apart

For anything closer, we need a means of magnifying

Note : BIGdifference between seeing and resolving

Seeing a car approaching (from its headlights)

Resolving the two headlights as separate sources of light

Optical System - ComponentsSource of Radiation - Visible-light

System of lenses and apertures


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Resolution

Limit to resolution arises from the phenomenon

ofd i f f ract ion

Any system used to form an image uses lenses and

apertures that have a certain dimension

Diffraction from a single slit

Intensity ~ (sin(x)/x)2

A big maxima surrounded by smaller maxima

Point object is not mapped on to a point - spread out


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Image of a circular slit


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Rayleigh Criterion

Profiles from two adjacent point will overlap

To be able to resolve two points as distinct

This is the dif f ract ion- l imited resolution limit

R = sin-1(1.22/d)

To increase resolutionLarge d

Small l


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Resolution

20/20 Vision

In the term "20/20 vision", the

numerator refers to the distance

in feet between the subject and

the chart. The denominator is the

distance at which the lines that

make up those letters would be

separated by a visual angle of 1

arc minute, which for the lowest

line that is read by an eye with no

refractive error
http://en.wikipedia.org/wiki/Fraction_%28mathematics%29http://en.wikipedia.org/wiki/Denominatorhttp://en.wikipedia.org/wiki/Visual_anglehttp://en.wikipedia.org/wiki/Arc_minutehttp://en.wikipedia.org/wiki/Arc_minutehttp://en.wikipedia.org/wiki/Visual_anglehttp://en.wikipedia.org/wiki/Denominatorhttp://en.wikipedia.org/wiki/Fraction_%28mathematics%29


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Images at different resolution


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Limits on Resolution

What diameter of telescope would you require to read

the numbers on a license plate from a spy satellite?


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Lens Aberrations - Other limiting factors for resolution


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Spherical Aberration

Zero

+

-


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Spherical Aberration


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Astigmatism circle becomes an ellipse


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Chromatic Aberration

NoAberration

ChromaticAberration


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Electron moving with a velocity v has a wavelength

associated with it

l = h/mv ~ 12.247/sqrt(E)(kV)

Electrons as Waves - The particle-wave duality

Typical wavelengths

E l

100 kV 0.037 A200 kV 0.025 A


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First Commercial SEM


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Old SEM

Modern day SEM


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Basics of SEM Operation

Electron gun produces a beamThermionic/Field-emission guns

Produce a tight spot on the specimen surfaceCondenser and Objective lenses

Scanning coils raster the beam across the specimenSize of scan -> Magnification

Electron-specimen interactionsProduces a wide variety of signals

Detectors to collect the signalDifferent detectors for different signals


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Magnification

Magnification Area on Sample Pixel Size

10x 1cmx1cm 10 mm100x 1mmx1mm 1 mm

10kx 10mmx10mm 10 nm

100kx 1mmx1mm 1 nm

Magnification = D/d


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Electron Gun


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h


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Thermionic Emission

Jc= AcT2exp(-Ew/kT)

Richardson Equation

Use thermal energy to excite electrons from a metal

EF

EW

vacuum

Ew = 4.5 eV for W, atT = 2700 KJ = 3.4 A/cm2


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Tungsten

Hairpin

FilamentWork Function = 4.5 eV


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This is what happens when

you turn the filament knob


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Effect of bias on the

filament emission


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Other possible gun materials


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LaB6


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LaB6Filament

Work Function = 2.5 eV


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Very high electric fields

Tip with small radius of curvature

Field Emission


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Field EmissionGun


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Comparison of Electron Sources

(Brightness = Current/area/solid angle)


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Source Brightness

(A/cm2

sr)

SourceSize

Lifetime(h)

VacuumLevel

Tungstenfilament

(4.5 eV)

105 30-100 mm 40-100 10-5Torr

LaB6 (2.5 ev)

105

5-50mm 200-1000 10

-7

Torr

Cold FE 108 < 5nm > 1000 10-10Torr

Thermal FE 108 < 5 nm > 1000 10-9Torr

Schottky 108 15-30 nm > 1000


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C f S


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Comparison of Electron Sources

Note that a very small FE probe carries a much larger currentcompared to a W filament.


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Lenses in the Electron Microscope


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Electromagnetic Lens


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Two types of

Objective Lenses

Large working distance

Very small working

distance

(

a) Pin-hole lens variable working distance, no size limitation of sample,good depth of field

(b) Small focal length => High Resolution


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aberrations

Asymmetric


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Demagnification


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aberrations


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Weak

condenser

lens

Strong

condenser

lens


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Small

working

distance

Large

workingdistance


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Three important parameters for image formation

Probe Size -Smaller the probe size, higher the resolution

Smaller the probe size, lower the brightness

Probe Current/Brightness -

Imaging requires large currents

Convergence Angle

Depth of field increases as angle decreases

Aberrations decrease as angle decreasesBrightness decreases as angle decreases

Probe Size dp diameter of beam as it falls on the specimenBrightness b Current density/solid angleProbe convergence a

p angle made by the cone of electrons with the central axis at the sample surface


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Astigmatism


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Astigmatism

A ti ti


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Astigmatism

Astigmatism


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Astigmatism

Astigmatism


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g


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El S i I i


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Electron-Specimen Interactions

Beam-Sample Interactions


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Beam-Sample Interactions


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We need to understand..

Elastic Scattering


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Elastic Scattering

Inelastic Scattering


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Scattering of Electrons


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Scattering of Electrons

Mean Free Path


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Mean Free Path


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Elastic Scattering


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Elastic Scattering


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Inelastic Scattering Bethe Approximation


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g pp


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Energy Loss


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Energy Loss


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Experimental Measurement


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Monte Carlo Simulations


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IMAGING ABERRATIONS IN SCANNING ELECTRON MICROSCOPY

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