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) Smal