David Muller 2008
Introduction to Electron MicroscopyIntroduction to Electron MicroscopyProf. David Muller, [email protected] 274 Clark Hall, 255-4065
Ernst Ruska and Max Knoll builtthe first electron microscope in 1931
(Nobel Prize to Ruska in 1986)T4 Bacteriophage
Electron Microscopy bridges the 1 nm – 1 μm gap between x-ray diffraction and optical microscopy
David Muller 2008
Tools of the TradeTools of the Trade
Transmission Electron Microscope
Scanned Probe Microscope(includes Atomic Force Microscope)
AFM MFM
Scanning Electron Microscope
David Muller 2008
Biological and Electronic Component Dimensions
Electronic ComponentsBiological Tool
Siz
e (m
)
10-10
10-8
10-6
10-4
10-2
1
Mammalian cell
Bacterial cell
Virus
GeneProtein
Atom
Logic Board
Computer chip
Transistor
Gate Oxide
OpticalMicroscope
TEM
AFM/STM
SEM
David Muller 2008
Comparison of Optical and Electron MicroscopesComparison of Optical and Electron Microscopes
• Electron microscopes are operated in vacuum because the mean free path of electrons is air is short – this mean biological samples should not degas – they can either be dehydrated or frozen – pathology, not in-vivo.
•Electron microscopes have higher resolution than optical microscopes –atomic resolution is possible.
•Chemical imaging and spectroscopy – mapping π and σ bonds at 1nm resolution can be done.
•Radiation damage is severe and limits the image quality and resolution (not as bad as x-rays or neutrons though! – see R. Henderson, Quarterly Reviews of Biophysics 28 (1995) 171-193.)
David Muller 2008
Comparison of Optical and Electron MicroscopesComparison of Optical and Electron Microscopes
TEMLight Microscopesource
1st condenser
CA condenser apertureOA objective aperture
SA selected area aperture
2nd condenser
Objectivelens
Projectorlenses
Viewing screenOr CCD
Viewing screenOr CCD
specimen
SEM or STEM
Image formed by scanning a small spot
David Muller 2008
Inside a Transmission Electron Microscope
High tension cable(100-200 kV)
Filament
Double condenser lenscondenser aperture
Viewing chamber
Sample sits hereobjective aperture
Selected areaaperture
Accelerating stack
David Muller 2008
An Electron Lens
David Muller 2008
An Electron Lens
David Muller 2008
Geometric Optics Geometric Optics –– A Simple LensA Simple Lens
x x
Objectplane
imageplane
Backfocalplane
frontfocalplane
Lensat z=0
θ
Focusing: angular deflection of ray α distance from optic axis
David Muller 2008
Geometric Optics Geometric Optics –– A Simple LensA Simple Lens
x x
Objectplane
imageplane
Backfocalplane
frontfocalplane
Lensat z=0
θ1
θ1
Wavefronts in focal plane are the Fourier Transform of the Image/Object
David Muller 2008
X-ray and Electron Diffraction from a Silicon Crystal
λ=0.0251Å
200 keV Electrons
λ=1.54 Å
10 keV x-rays
θλ sindn =
In Si d220 = 1.92 Å
Bragg’s Law:
David Muller 2008
Electron Velocity and Wavelength
De Broglie Wavelength:ph
=λ Where h is Planck’s constantAnd p=mv are the momentum, mass and velocity of the electron
If an electron is accelerated through a potential eV, it gains kinetic energy
eVmv =2
21
So the momentum is meVmv 2=
Vnm
meVh 23.1
2
2
==λElectron wavelength
( relativistically correct form: )2( 2
0
22
eVcmeVch
+=λ )
(V in Volts)
David Muller 2008
Electron Wavelength vs. Accelerating Voltage
0.00871890.813521 MeV
0.0196870.77653300 keV
0.0250780.69531200 keV
0.0370130.54822100 keV
0.122040.01919410 keV
0.387630.0624691 keV
1.22630.0062560100 V
12.2640.00197841 V
λ (Ǻ)v/cAccelerating Voltage
0
0.01
0.02
0.03
0.04
0.05
0 200 400 600 800 1000
RelativisticNon-relativistic
λ (A
ngst
rom
s)
Electron Kinetic Energy (keV)
David Muller 2008
Resolution Limits Imposed by Spherical Aberration, Cs(Or why we can’t do subatomic imaging with a 100 keV electron)
Lens
3min 2
1 αsCd =
Plane ofLeast Confusion
Gaussian image plane
Cs=0
Cs>0
For Cs>0, rays far from the axis are bent too strongly and come to a crossover before the gaussian image plane.
For a lens with aperture angle α, the minimum blur is
mind
Typical TEM numbers: Cs= 1 mm, α=10 mrad → dmin= 0.5 nm
David Muller 2008
Resolution Limits Imposed by the Diffraction Limit(Less diffraction with a large aperture – must be balanced against Cs)
Lens
000
61.0sin61.0
αλ
αλ
≈=n
d
Gaussian image plane
The image of a point transferred through a lens with a circular aperture of
semiangle α0 is an Airy Disk of diameter
0d
(for electrons, n~1, and the angles are small)
α0
(0.61 for incoherent imaging e.g. ADF-STEM, 1.22 for coherent or phase contrast,. E.g TEM)
David Muller 2008
Balancing Spherical Aberration against the Diffraction Limit(Less diffraction with a large aperture – must be balanced against Cs)
230
2
0
220
2
2161.0
⎟⎠⎞
⎜⎝⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛=+≈ α
αλ
sstot Cddd
For a rough estimate of the optimum aperture size, convolve blurring terms-If the point spreads were gaussian, we could add in quadrature:
1
10
100
1 10
Prob
e Si
ze (A
ngst
rom
s)
α (mrad)
ds
d0
Optimal apertureAnd minimum
Spot size
4/34/1min 66.0 λsCd =
David Muller 2008
Balancing Spherical Aberration against the Diffraction Limit(Less diffraction with a large aperture – must be balanced against Cs)
4/34/1min 43.0 λsCd =
A more accurate wave-optical treatment, allowing less than λ/4 of phase shift across the lens gives
Minimum Spot size:
4/14
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sopt C
λαOptimal aperture:
At 200 kV, λ=0.0257 Ǻ, dmin = 1.53Ǻ and αopt = 10 mrad
At 1 kV, λ=0.38 Ǻ, dmin = 12 Ǻ and αopt = 20 mrad
4/34/1min 61.0 λsCd =
(Incoherent image - e.g. STEM)
(coherent image - e.g. TEM)
David Muller 2008
Electron Diffraction and Imaging a [100] Silicon Crystal
λ=0.0251Å
Diffraction Pattern
In Si d220 = 1.92 Å
Image
220
400
David Muller 2008
Depth of Field, Depth of Focus
00 tanα
dD =
For d=3nm, α=10 mrad, D0= 300 nm For d=200nm, α=0.1 mrad, D0= 2 mm!
David Muller 2008
Lenses in a Transmission Microscope(and deflection coils to correct their alignment)
http://www.rodenburg.org/RODENBURG.pdf
Condensor: uniformly illuminate the sampleIf misaligned, you will lose the beam when changing magnification
Gun: electron sourceIf misaligned, low intensity & other alignments may also be out
Objective: image sample – determines resolution. If misaligned, the image will be distorted, blurry.
projector: magnifies image/ forms diffraction pattern – should not alter resolution. If misaligned, the image will be distorted, diffraction pattern may be blurry.
David Muller 2008
Caustics in a Lens
http://www-optics.unine.ch/education/optics_tutorials/aspherical_surface.html
On-axis
Tilted
David Muller 2008
Caustics(remove extreme rays and caustics by putting in an aperture)
From “Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations” by J. F. Nye
David Muller 2008
Common AberrationsAstigmatism Coma
Bad
Good
-Δf +ΔfΔf=0
-x&y focus at different planes-fix by adjusting stigmators
Check lens alignment by going through focus (change lens strength)
Bad
Good
-beam is tilted off axis-fix by centering aperture
David Muller 2008
Lens AlignmentCorrecting for a gun shift misalignment
Step 1:Strongly excite C1(small spot size)cross-over movesto lens & optic axis.
Use beam shift D2to bring spot toto axis below C2
Step 2:Weaken C1(large spot size)cross-over movesaway from optic axis
Use gun shift D1to bring spot toto axis below C2.
Iterate until spotstops moving
How do we align one lens, when all lenses are misaligned?
http://www.rodenburg.org/RODENBURG.pdf
David Muller 2008
Focusing using Fresnel Fringes
Check lens alignment by going through focus (change lens strength)
In focus
Minimum contrast
2 μm underfocus 2 μm overfocus
bright fringe dark fringe
David Muller 2008
Correcting Objective Astigmatism using Fresnel Fringes
Stigmated& focused
bright fringedark fringe
Astigmatic & best focus
Duffield: John Grazul150 Duffield(TEM+STEM)
Clark: Mick ThomasF3 Clark (STEM+EDX)
•1 nm (polymers) –> atomic resolution of crystals in thin samples•X-ray mapping at 1 nm•EELS at < 1 nm•Requires sample thinning (except for nanoparticles)
Transmission Electron Microscopy
•Clark: Mick ThomasF3 Clark Hall
•Bard/Snee:John Hunt SB56 Bard/1149 Snee
•Dr. Jonathan ShuD-22 Clark Hall
•Prof. Kit UmbachSB-60C Bard Hall
•CNF Clean Room
Location•Topographic Imaging on wafers•Accurate height measurements on flat surfaces (~ 0.5 nm vertical)•Lateral Resolution 10-20 nm•In-situ – no vacuum required
Atomic Force Microscopy
•Imaging of complex structures at 1-20 nm resolution•X-ray mapping at 100-500 nm •In-vacuum•Clark: High spatial resolution•Snee/Bard: best x-ray mapping, OIM
Scanning Electron Microscopy
ApplicationsType
Materials Microscopy Resources on Campus(http://www.ccmr.cornell.edu/facilities/)
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