Transmission Electron Microscopy

David Stokes2DX Workshop

University of Washington8/15-8/19/2011

Kinds of Electron Microscopes

TEM transmissive resolution determined by optics analogous to bright field light microscope detector is film or CCD

SEM reflective, surface imaging resolution determined by spot size x-ray microanalysis or EELS possible

STEM transmissive, small spot with scan coils resolution determined by spot size analogous to confocal detector is PMT x-ray microanalysis or EELS possible

SEM vs. TEM

TEM sectioned cell

TEM metal shadowed molecules

250 nm

TEM of frozen, isolated macromolecules

TEM of 2D membrane protein crystal

TEM images are 2D projections

Source of electrons

Tungsten: - outer electrons of W are made free by heating the metal. - W has excellent yield when heated just below its melting temp of 3653K. - Heat to 2600K for good yield without melting and evaporating tip (saturation point) - 100 hrs with W wire. - Make filament (cathode) at neg potential (e.g. -100 kV). - As electrons boil off the W, they are repelled by the cathode. - Potential difference relative to the anode provides the accelerating voltage - Make Weihnolt several hundred volts more negative electrons pass through the aperture in the Weihnolt cap. bias controls output of electrons and shapes field - Anode is grounded so electrons are accelerated towards it. - Electrostatic field causes crossover at the anode - this is effective source size

LaB6 - has lower work function: amount of energy necessary to free electrons. - 1000K with higher electron yield and longer life. - get small beam crossover size with high flux (10x emission of W)

Field emission - single crystal of W oriented relative its xtal lattice - no heating - series of high voltage anodes draw electrons out of lattice - electrostatic lens of anodes -> 10 nm source size - need very high vacuum -> contamination - Zirconium to reduce work function, heating to reduce contamination

from Reimer

Properties of Electrons

c

a

c

a

ac

c

a

eUedsedsEedsFWP )(

U=accelerating voltagecharge on electron is -1.602x10-19 Coulombs, when accelerated through 1V potential difference has kinetic energy of 1.602x10 -19 Nm (joule)define this kinetic energy as 1 eV.

With accelerating voltage of 200kV – electrons have energy of 200keV (= 3.2x10 -14 joules)compare to C-C bond of 5.8x10-19 joules (3.6 eV) or lattice binding energy of 1-2 eV

Energy of electrons is work W required to move electron from anode to cathode against force F=-eE:

Speed of electrons at 100kV: v=1.64x108m/sec more than 1/2 speed of light Have to consider relativity1MeV = 2Eo m=3m0

Wavelengths of electrons ()0.0349 Å at 120kV, 0.025 Å at 200 kV, 0.01969 Å at 300 kV

compare with wavelength of light: 2000 Åor X-rays:1.5 Å for Cu K1 Å synchrotron radiation

diffraction limit forresolution ofany optical system:D = /2

Force on an electron

electrostatic: EqF

0

electromagnetic: BvqF

0

Typical electron lensesTypical electron lenses

single lens (e.g. condensor)single lens (e.g. condensor) split lens (e.g. objective)split lens (e.g. objective)

Magnetic lenses like Glass lenses Magnetic lenses like Glass lenses are governed by Newton’s lens equationare governed by Newton’s lens equation

and

http://members.shaw.ca/quadibloc/science/opt05.htm

Focal length of Electromagnetic lens

electromagnetic lens: can change focal length by changing current

glass lens: change focus by moving specimen up and down change magnification by switching lenses

)/( 2iUKf

f = focal length K = lens const, U = voltage, i = current

Lens Strength affects focal lengthLens Strength affects focal length

A stronger lens demagnifies the image!!!

)/( 2iUKf f = focal length K = lens const, U = voltage, i = current

Trajectory of electrons through a homogeneous B fieldBveF

sinevBF

where is angle between v and B

Generally, path is spiral, with v|| and v components

So electrons passing through given point P will intersect again at point P'

Energy of electron conserved – no change in |v|If force is to v: electron moves in a circleIf force is || to v, path unchanged.

PP' = v||Tc = vTccos,

where Tc is time to complete circle, which is independent of

P'

P

If many angles focused in same plane, get image formed

For small angles of , cos ~1 and get image formed at P'. Larger angles of reduces the distance to P' (cos = (1 - 2/2 + . . .) and thus gives rise to spherical aberration

Real lens is non-homogeneous field - so-called bell-shaped field

Aberrations: astigmatism, coma, spherical, field curvature, distortion (pincushion/barrel)

chromatic and Contrast Transfer Function

TEM lens configuration

Condenser Lenses:Demagnifies sourceDefine “spot size”

Objective lens:Defines image focusHas fixed magnification (20-50x)

Intermediate lens:Controls whether Image or diffraction patternIs recorded

Projector lenses:Controls image magnificationorDiffraction “camera length”

Condenser lenses

C1 lens produces image of sourceC2 lens demagnifies onto sample

C2 aperture reduces beam currentand makes beam more parallel

C1 lens controls spot size

Strong C1 lens produces small probe size and weak beam

Weak C1 lens produces larger probe size and bright beam

This is known as “spot size”

C1 crossover produces image of source andMag = u/v for C2 lens

Beam convergence

UpperObjectivelens

Increasing strength of C2 lens

~parallel convergent divergent parallel

magnification of objective: 20-50xangle for 2.5 Å resolution at 200kv: = /d = 0.025/2.5 = 10 mrad = 0.5°

most of mag range achievedwith projection lensesMuch smaller angles andaberrations therefore lessimportant

Back focal plane of objective lens corresponds to diff pattern

Selected area aperture is at first image plane

Intermediate lens selects either BFP or 1st image plane as its object

Diff pattern or 2nd image serves as object for projector lens

Diffraction vs. Imagingcontrolled by

Intermediate lens

Coma

For high resolution images, you want the apparent source aligned with the real source on the optical axis and the beam to run parallel to this axis. This is coma-free alignment.

Deflectors

electrostatic electromagnetic

Deflectors produced by transverse fields: E field (parallel plate capacitor) B field (electromagnetic lens)

deflector coils generally come in pairs

pivot points aligned pivot points misaligned

gun tilt coils

condensorlens

specimen

source

Apertures

condensor

aperture

A typical scattering eventA typical scattering event

( , , ) ( , )ikr

ikzi s

er e f

r

i s

Proportionality constant for scattering:is scattering cross-section for one atom (cm2/atom)

elastic, inelastic, absorption, fission

Electron Scattering

Elastic Scattering: Rutherford scattering

+ + + + + + + +

R

zb

F

F

2

2

221

44 R

Ze

R

qqF

electrostaticforce:

Z = atomic number,but, actually need to consider screening of electrons on nuclear charge

N.B. Elastically scattered electrons have same wavelength as incident beam and are most effective for generating phase contrast image because they interfere with the unscattered beam

42 2 2 3

0

1 1( )tot

Z RZ

a

Solving Scrodinger’s equation for the potential and making approximations for screening of nuclear charge by electron cloud:

Inelastic Scattering

1. Oscillations of molecular bonds and phonon excitations: 20 meV – 1 eV too small to generally observe given ~1 eV spread of beam energy2. Excitation of outer electrons and valence/conduction band electrons (metals): 1-50 eV3. Ionization of inner electrons (K,L,M shells) to unoccupied shells: 10 – 100s eV

Energy transferred from incident electrons to the specimen

Why do we hate inelastic collisions?Why do we hate inelastic collisions?

Inelastic electrons are focused at “undesirable” placesAnd therefore produce a blurred image due toChromatic aberration

Inelastic scattering produces chemical changes radiation damage

differential scattering vs. 25 keV electrons with Ar gas

scattered outside 2.4 A aperture

inelastics within aperture

elastics within aperture

unscattered

total scattering cross-sectiondifferential cross-section

The inelastic scattering “blurs” the low spatial frequenciesThe inelastic scattering “blurs” the low spatial frequencies

electrons X-rays

But they can be filtered out (after they damaged the specimen)But they can be filtered out (after they damaged the specimen)

-filter +filter