David Muller 2008

Introduction to Electron Microscopy-IIProf. David Muller, dm24@cornell.eduRm 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

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.

Reciprocity

From L. Reimer, Transmission Electron Microscopy

Reciprocity: Electron intensities and ray paths in the microscope remain the same if (i) the direction of rays is reversed, and (ii) the source and detector are interchanged.

Proof follows from time-reversal symmetry of the electron trajectories and elastic scattering (to all orders).

Reciprocity does not hold for inelastic scattering:Sample is after probe forming optics in STEM - energy losses in sample do not cause chromatic blurring in the image

Sample is before the imaging optics in TEM – energy losses in the sample do cause chromatic blurring in the image. Imaging thick samples in TEM can be improved by energy filtering (so on the zero-loss image is recorded). This is not needed for STEM.

Reciprocity

From L. Reimer, Transmission Electron Microscopy

Image recordedIn parallel

Image recorded serially by scanning the source

Condensoraperture(before sample)

Objective aperture

(after sample)

Controls coherence

Controls resolution

Collectoraperture

Condensoraperture

STEMTEM

ReciprocityReciprocity (or STEM vs. CTEM)(or STEM vs. CTEM)CTEM STEM

Reciprocity (for zero-loss images):A hollow-cone image in CTEM an annular-dark field image in STEM.

Specimen

Illuminationangle α Collector

angle

β

Specimen

Objective Aperture

Objective Aperture

ViewingScreen Gun

Gun Detectors

However: In STEM, energy losses in the sample do not contribute to chromatic aberrations (Strong advantage for STEM in thick specimens)

David Muller 2008Single atom

Sensitivity:

Electron Energy Loss Spectrometer

Annular Dark Field (ADF) detector

yx

200 kV IncidentElectron Beam

(ΔE=1 eV)

Incr

easi

ngen

ergy

loss

1 atom wide (0.2 nm) beam is scannedacross the sample to form a 2-D image

Elastic Scattering ~ "Z contrast"

Scanning Transmission Electron Microscopy

0 0.5 1 1.

ADF Signal Er M4 Edge

Distance (nm)

3 Å

P. Voyles, D. Muller, J. Grazul, P. Citrin, H. Gossmann, Nature 416 826 (2002)U. Kaiser, D. Muller, J. Grazul, M. Kawasaki, Nature Materials, 1 102 (2002)

David Muller 2008

Brightness:Brightness: Not how many electronshow many electrons, but how many electrons go where we want them tohow many electrons go where we want them to

Thermionic Sources:• Large Source• Weak Electric Field• Electrons are “boiled off” in all

directions• Low brightness

Field Emission Guns:• Small Source• Strong Electric Field• Electrons tunnel out along field

lines• High brightness

ElectricField Lines

10 μm 0.1 μm

David Muller 2008

The Brightness Equation

• Brightness is the current density (J=ΔI/ΔS) per solid angle (ΔΩ=πα2) where α is the half angle

2παβ J

SI

=ΔΩΔ

Δ= -(1)

• For a thermal source, the electron current has a maxwellian momentum distribution.

• Transverse momentum Normal to the Field

• Root mean square angle subtended:

• hence ⎟⎠⎞

⎜⎝⎛≈⎟

⎠⎞

⎜⎝⎛ +=

kTeVJ

kTeVJ

ππβ 1 Since eV>>kT

mkTpt 22 = meVmkTpn 222 +=

( )kTeVpp nt +== 11222α

α

E

pt

pn

Brightness increase with beam voltage, decrease with tip temperature

David Muller 2008

• For current density J and probe diameter d0, the probe current is

( ) JdI p2

0 2π= -(2)

A small spot size implies a small beam current or large illumination angle

Brightness as a limit to Spatial Resolution

• From the Brightness equation (1) we also know

• Hence the probe current depends on

2βπα=J

220

2

4αβπ dI p = -(3)

• Rearranging, we find the probe size

αβπ14 21

20 ⎟⎟⎠

⎞⎜⎜⎝

⎛= pI

d -(4)

David Muller 2008

10-10 - 10-1110-8 - 10-910-5 - 10-610-4 - 10-5Vacuum (Torr)

>5 years3-5 years150-300 hrs25-100 hrsLifetime

3001400-18001400-20002500-3000Operating Temp (K)

0.30.522Energy SpreadFWHM (eV)

1091085 x 1065 x 105Brightness at 100 kV

(A/cm2/Sr)

~0.03 nm~0.1 nm~ 2 nm~6 nmSource Size at 10 pA, 100 keV

WCold FEG

ZrO2/WSchottky FEG

LaB6Thermionic

TungstenThermionic

Properties of Electron Sources

David Muller 2008

Tungsten Filament

•Cheap (~$20)•Short lifetime•Low brightness•Works in poor vacuum

David Muller 2008 http://www.kimphys.com/cathode/catalog_PDF/LaB6_cathode_ES423.pdf

Thermionic LaB6 Filament

•~$1000•Longer life, but can be damaged by thermal shock•Medium brightness•Needs moderate vacuum

David Muller 2008

Schottky Tip design

ZrZr reservoirreservoir

TipTip

Tungsten wire Tungsten wire filamentfilament

•Expensive (~$20,000?)•Long lifetime (years)•High brightness•Needs good vacuum

David Muller 2008

Electron Scattering

Incident electron

Elastic scattering(large angle, α Z2)

Inelastic scattering(small angle, α Z)

•Elastic scattering can only change the direction of the electron,•Only inelastic scattering can slow it down (by losing energy in the sample)

Valence electrons can be excited(detected as secondary electrons)

David Muller 2008

Beam Spreading

E0=200 keV E0=20 keV

1 μm of Carbon

Electron Range (in μm):

5.10

064.0 ERρ

≈

(density ρ in g/cm3, E0 in keV)

R~ 100 μm at 200 keV

David Joy’s simulation code is available at http://web.utk.edu/~srcutk/htm/simulati.htmA more detailed simulator can be found at http://www.gel.usherbrooke.ca/casino/What.html

David Muller 2008

Beam Spreading

For thin films:

5.1

0%90

625 tZAE

b ρ=

At 100 kV:0.16 nm for 10 nm thick C1.8 nm for 50 nm thick C

E0 in kVt in cm, ρ in g/cm2

A in g/mol

0

0.5

1

1.5

2

0 1 2 3 4 5 6

FWHM of feature90% beam radius

Res

olut

ion

(μm

)

Si thickness (μm)

200 keV Electrons in Silicon

David Muller 2008

Imaging Buried Atoms (Sb in Si)

Sb source turned on here No Sb in substrate

1 nm

Null test:No Sb in substrate

P. Voyles, D. Muller, J. Grazul, P. Citrin, H. Gossmann, Nature 416 826 (2002)

160

140

120

100

80

60

40

20

0

num

ber o

f ato

mic

col

umns

1.41.31.21.11.00.90.8normalized intensity

Si columns Si/Sb columns singly-occupied doubly-occupied

David Muller 2008

CTF

PSF

(200 kV, C3=1.2 mm)

Effect of defocus and aperture size on an ADF-STEM image

David Muller 2008

ADF of [110] Si at 13 mr, C3=1mm

Strong {111} fringes Strong {311} fringes

2 clicks overfocus

Best 111 and 311 fringes occur at different focus settingsIf the aperture is too large

What happens with a too-large aperture?

David Muller 2008

Aperture Size is Critical(200 kV C3=1mm)

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8

13 mrad10 mrad

CTF

k (1/A){111}

Si

{220}Si

30% increase in aperture size ~50% decrease in contrast for Si {111} fringes

David Muller 2008

Aperture Size is Critical

0

5

10

15

20

25

30

0 0.2 0.4 0.6 0.8 1

10 mrad13 mrad

Bea

m C

urre

nt E

nclo

sed

(pA

)

Radius (nm)

r80%

= 0.25 nm

r80%

= 0.8 nm

r64%

= 0.1 nm

All the extra probe current falls into the tails of the probe – reduces SNR

(200 kV C3=1mm)

David Muller 2008

Finding the Aperture with the smallest probe tails

(Kirkland, Fig 3.11)

4/1

3

22.1 ⎟⎟⎠

⎞⎜⎜⎝

⎛=

Coptλα

( ) 21

min 8.0 λSCf =Δ

David Muller 2008

Summary

Contrast Transfer Functions: Coherent:

Lower resolution, higher contrastEasy to get contrast reversals with defocusAperture size only affects cutoff in CTF

Incoherent:

Higher resolution, lower contrastHarder to get contrast reversals with defocusAperture size is critical – affects CTF at all frequencies

4/34/13min 43.0 λCd =

4/1

3

4⎟⎟⎠

⎞⎜⎜⎝

⎛=

Coptλα

4/34/13min 77.0 λCd =

4/1

3

6⎟⎟⎠

⎞⎜⎜⎝

⎛=

Coptλα

David Muller 2008

3D Tomography of Nanostructures?3D Tomography of Nanostructures?

J. Harms et al., Structure Fold Des 7, 931-41. (1999)

• 3D: 1 nm resolution• 2D: 0.4 nm•Low dose imaging of individual particles

•Don’t need crystals!

Kirrmoycin stalled ribosome at 13Å

Herpes simplex

Z.H. Zhou et al, J. Mol. Bio.

(Biologists have been doing this for 30 years with TEM)

David Muller 2008

Tomography in Materials Science

Ta/TaN liner around a copper interconnect

Si nanocrystals in SiO2 Au clusters on Carbon Nanotubes

(Examples from researchers in my group)

M. Weyland, A. Yurtserver, P. Ercius, J. Cha 2005

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/)