Introduction to Electron MicroscopyProf. David Muller, dm24@cornell.edu Rm 274 Clark Hall, 255-4065

Ernst Ruska and Max Knoll built the first electron microscope in 1931(Nobel Prize to Ruska in 1986)

T4 Bacteriophage

Electron Microscopy bridges the 1 nm 1 m gap David Muller 2008 between x-ray diffraction and optical microscopy

Tools of the Trade

AFM

MFM

Scanned Probe Microscope (includes Atomic Force Microscope)

Transmission Electron Microscope

Scanning Electron MicroscopeDavid Muller 2008

Biological and Electronic Component DimensionsBiological1

Electronic ComponentsLogic Board Computer chip Optical Microscope

Tool

10-2

SEM

Size (m)

10-4

Mammalian cell

10-6

Bacterial cell Virus Transistor AFM/STM Gate Oxide Atom

TEM

10-8

Gene Protein

10-10 David Muller 2008

Comparison 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 and 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 MicroscopesLight Microscopesource 1st condenser 2nd condenser

TEM

SEM or STEM

Viewing screen Or CCD

specimen Objective lens Projector lenses

CA condenser aperture OA objective aperture SA selected area aperture

Image formed by scanning a small spot

David Muller 2008

Viewing screen Or CCD

Inside a Transmission Electron MicroscopeHigh tension cable (100-200 kV) Filament Accelerating stack Double condenser lens

condenser aperture

objective aperture Selected area aperture

Sample sits here

Viewing chamberDavid Muller 2008

An Electron Lens

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An Electron Lens

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Geometric Optics A Simple LensFocusing: angular deflection of ray distance from optic axis

x

x

Object planeDavid Muller 2008

front focal plane

Lens at z=0

Back focal plane

image plane

Geometric Optics A Simple LensWavefronts in focal plane are the Fourier Transform of the Image/Object

1 1x x

Object planeDavid Muller 2008

front focal plane

Lens at z=0

Back focal plane

image plane

X-ray and Electron Diffraction from a Silicon CrystalBraggs Law:

n = d sin 200 keV Electrons

10 keV x-rays

=1.54 David Muller 2008

=0.0251In Si d220 = 1.92

Electron Velocity and Wavelength

De Broglie Wavelength:

h = p

Where h is Plancks constant And p=mv are the momentum, mass and velocity of the electron

If an electron is accelerated through a potential eV, it gains kinetic energy

1 2 mv = eV 2

So the momentum is

mv = 2meV

Electron wavelength

=

h2 1.23nm = 2meV V

(V in Volts)

( relativistically correct form:David Muller 2008

h 2c 2 = eV ( 2m0c 2 + eV )

)

Electron Wavelength vs. Accelerating Voltage

0.05 Relativistic Non-relativistic

0.04 (Angstroms)

Accelerating Voltage 1V

v/c 0.0019784 0.0062560 0.062469 0.019194 0.54822 0.69531 0.77653 0.81352

()12.264 1.2263 0.38763 0.12204 0.037013 0.025078 0.019687 0.0087189

0.03

100 V 1 keV

0.02

10 keV 100 keV 200 keV 300 keV 1 MeV

0.01

0 0 200 400 600 800 1000 Electron Kinetic Energy (keV)

David Muller 2008

Resolution Limits Imposed by Spherical Aberration, Cs(Or why we cant do subatomic imaging with a 100 keV electron) LensCs>0

Plane of Least Confusion

Cs=0

d min

Gaussian image plane

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 , the minimum blur is

d min

1 = Cs 3 2

Typical TEM numbers: Cs= 1 mm, =10 mrad dmin= 0.5 nmDavid Muller 2008

Resolution Limits Imposed by the Diffraction Limit(Less diffraction with a large aperture must be balanced against Cs) Lens

d00

Gaussian image plane The image of a point transferred through a lens with a circular aperture of semiangle 0 is an Airy Disk of diameter

0.61 0.61 d0 = n sin 0 0

(0.61 for incoherent imaging e.g. ADF-STEM, 1.22 for coherent or phase contrast,. E.g TEM)

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(for electrons, n~1, and the angles are small)

Balancing Spherical Aberration against the Diffraction Limit(Less diffraction with a large aperture must be balanced against Cs)

For a rough estimate of the optimum aperture size, convolve blurring terms -If the point spreads were gaussian, we could add in quadrature:

d

2 tot

0.61 1 3 + Cs 0 d +d = 0 22 0 2 s

2

2

100 Probe Size (Angstroms)

10

d 1 1

d

0

s

Optimal aperture And minimum Spot size1 d min = 0.66 Cs / 43 / 4

David Muller 2008

(mrad)

10

Balancing Spherical Aberration against the Diffraction Limit(Less diffraction with a large aperture must be balanced against Cs) A more accurate wave-optical treatment, allowing less than /4 of phase shift across the lens gives Minimum Spot size:1 d min = 0.43Cs / 43 / 4 1 d min = 0.61Cs / 4 3 / 4

(Incoherent image - e.g. STEM) (coherent image - e.g. TEM)

Optimal aperture:

opt

4 = C s

1/ 4

At 200 kV, =0.0257 , dmin = 1.53 and opt = 10 mrad At 1 kV, =0.38 , dmin = 12 and opt = 20 mradDavid Muller 2008

Electron Diffraction and Imaging a [100] Silicon Crystal

Image

Diffraction Pattern

220 400

=0.0251David Muller 2008

In Si d220 = 1.92

Depth of Field, Depth of Focus

d D0 = tan 0

For d=3nm, =10 mrad, D0= 300 nmDavid Muller 2008

For d=200nm, =0.1 mrad, D0= 2 mm!

Lenses in a Transmission Microscope(and deflection coils to correct their alignment)Gun: electron source If misaligned, low intensity & other alignments may also be out Condensor: uniformly illuminate the sample If misaligned, you will lose the beam when changing magnification 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

http://www.rodenburg.org/RODENBURG.pdf

Caustics in a LensOn-axis

Tilted

http://www-optics.unine.ch/education/optics_tutorials/aspherical_surface.htmlDavid 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. NyeDavid Muller 2008

Common AberrationsAstigmatism -x&y focus at different planes -fix by adjusting stigmators Bad Coma -beam is tilted off axis -fix by centering aperture Bad

-f

f=0

+f

Good Good

Check lens alignment by going through focus (change lens strength)David Muller 2008

Lens AlignmentCorrecting for a gun shift misalignment How do we align one lens, when all lenses are misaligned?

Step 1: Strongly excite C1 (small spot size) cross-over moves to lens & optic axis. Use beam shift D2 to bring spot to to axis below C2

Step 2: Weaken C1 (large spot size) cross-over moves away from optic axis Use gun shift D1 to bring spot to to axis below C2. Iterate until spot stops moving

David Muller 2008

http://www.rodenburg.org/RODENBURG.pdf

Focusing using Fresnel Fringes2 m underfocus In focus 2 m overfocus

bright fringe

Minimum contrast

dark fringe

Check lens alignment by going through focus (change lens strength)David Muller 2008

Correcting Objective Astigmatism using Fresnel FringesAstigmatic & best focus Stigmated& focused

dark fringe

bright fringe

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Materials Microscopy Resources on Campus(http://www.ccmr.cornell.edu/facilities/) TypeAtomic Force Microscopy

ApplicationsTopographic Imaging on wafers Accurate height measurements on flat surfaces (~ 0.5 nm vertical) Lateral Resolution 10-20 nm In-situ no vacuum required Imaging of complex structures at 120 nm resolution X-ray mapping at 100-500 nm In-vacuum Clark: High spatial resolution Snee/Bard: best x-ray mapping, OIM 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)

LocationDr. Jonathan Shu D-22 Clark Hall Prof. Kit Umbach SB-60C Bard Hall CNF Clean Room Clark: Mick Thomas F3 Clark Hall Bard/Snee: John Hunt SB56 Bard/1149 Snee Duffield: John Grazul 150 Duffield (TEM+STEM) Clark: Mick Thomas F3 Clark (STEM+EDX)

Scanning Electron Microscopy

Transmission Electron Microscopy