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“Avoiding stereological bias inherent to the
appearance of 3-D objects on 2-D sections is
essential for the estimation of total object
number in a defined reference space.
Recognition and avoidance of these sources of
bias requires a thorough understanding of bias
introduced by assumptions, models, and
correction factors. The goal of unbiased
sampling and assumption-free stereology
designs to estimate number is to overcome this
and other sources of systematic error that can
introduce systematic error into sample
estimates.”
However, good stereology is efficient stereology.
Over-sampling beyond the point of diminishing
returns it is not good use of resources. As noted
by the esteemed Swiss stereologist, Professor
Ewald Weibel, the most rational approach is:
Do More Less Well. That is, optimize sampling
to achieve stable estimates with minimal time,
effort, and resources.
Unbiased Stereology
• Systematic error / stereological error
“Blind” Structural Characterization
SPM (Scanning Probe Microscopy):
1. STM (Scanning Tunneling Microscopy)
2. AFM (Atomic Force Microscopy)
Surface imaging technique
+
Nanoindentation
http://en.wikipedia.org/wiki/Image:ScanningTunnelingMicroscope_schematic.png
STM
STM
• Developed in 1981-1982 by Binnig and Rohrer
• Based on electron tunneling (QM)
• Extremely sharp tip (PtIr) on Piezoelectrics
AFM
• Modification of STM for not only
electronically conductive materials.
• Measures:
– Van der Waals
– Capillary
– Chemical bonding
– Electrostatic
– Magnetic
http://en.wikipedia.org/wiki/Image:Atomic_force_microscope_block_diagram.png
MORE AFM
Operating Modes
Contact Non-contact Tapping
http://www.mechmat.caltech.edu/~kaushik/
Gerber and Lang, Nature
Nanotechnology 1, 3 - 5 (2006)
Un dimanche après-midi à l’Ile de la Grande Jatte
Resolution
• Airy Disc and Rings
• Concept of resolution and depth of field
• Optical vs Electrons
www.aguntherphotography.com/files/tutorial/diffraction/
www.aguntherphotography.com/files/tutorial/diffraction/
Rayleigh Criterion for resolution
Resolution (nm) = d1 / 2 = 0.61λ / μ sinα
http://www.seemsartless.com/guides/camera-dof.php
http://photography.about.com/od/takingpictures/ss/DOF_2.htm
Taken from J.I. Goldstein et al., eds., Scanning Electron Microscopy
and X-Ray Microanalysis, (Plenum Press,NY,1980).
SE images afford improved depth of focusOptical Image SEM Image
Tip of a screw(Brundle)
Erythrocytes(Flegler)
Optical Image SEM Image
Rayleigh Criterion for resolution
Resolution (nm) = d1 / 2 = 0.61λ / μ sinα
Depth of Field (nm) = Res/tan α
There is the need for smaller wavelength to
achieve high resolution microscopy.
→ The introduction of electron microscopes
Electron Gun
Thermionic emission Field emissionElectrons can be emitted
from a filament (emitter or
cathode) by gaining
additional energy from heat
or electric field.
Commonly used emitters:
Tungsten wire
LaB6 filament
Field emitter.
The common properties of
the emitters are low work
function, high melting point,
and high mechanical
strength W wire LaB6
Field emitter
TEM Sample Preparations
• Specimen must be thin enough to transmit sufficient
electrons to form an image (100 nm)
• It should be stable under electron bombardment in a high
vacuum
• Must fit the specimen holder (i.e. < 3 mm in diameter)
• Ideally, specimen preparation should not alter the
structure of the specimen at a level observable with the
microscope
• Always research (i.e. literature search) the different
methods appropriate for your sample prep first
TEM Specimen PreparationSpecimen Requirements
• 3 mm diameter (Nom. 3.05 mm) grids used for non self-supporting specimens
• Specialized grids include:
− Bar grids
− Mixed bar grids
− Folding grids (Oyster grids)
− Slot grids
− Hexagonal grids
− Finder grids
− Support films (i.e. C or Holey C, Silicon Monoxide, etc.)
• Mesh is designated in divisions per inch (50 – 2000)
• Materials vary from copper and nickel to esoteric selections (Ti, Pt, Au, Ag etc.) based on various demands
TEM Grids
TEM Specimen Preparation
Cut into slicesCore into 3 mm disk and
polish to about 100 mm thickGlue to a metal
support ring
Make a dimple(~ 10 mm in the center)
Ion mill to make thin (< 0.1mm) area or hole
Ar +
• Usually used for polymers, polymer
matrix composites, various particles
embedded in epoxy resin, etc.
• Automated high precision cutting
machine using glass or diamond
knives capable of cutting specimens
as thin as 10 nm
TEM Specimen Preparation
Ultramicrotomy
F. Shaapur, “An Introduction to Basic Specimen Preparation Techniques for Electron Microscopy of
Materials”, Arizona State University, (1997) http://www.asu.edu.class/csss
Ultramicrotomy
TEM Specimen Preparation
• Specimen arm holds and slices a sample with a tapered end (to reduce the cutting cross-section) by lowering it against the sharp edge of the knife
• Cutting strokes combined with simultaneous feeding of the sample toward the cutting edge produce ultra-thin sections
Glass Knife Boat
• Sections of material are
collected on the surface of
a trough filled with liquid
(usually water)
• Sections lifted off onto
TEM grids which provide
support
• Cryo-Ultramicrotomy:
Freeze materials (i.e. for
rubbery elastic
materials,etc.) with lN2 to
below glass transition
temperature to make hard
enough to cut
Glass Knives
http://www.emsdiasum.com/Diatome/knife/images/
Caring for diamond knives:
http://www.emsdiasum.com/Diatome/
diamond_knives/manual.htm
Diamond Knives
• Much harder than glass
• Costs in the range of
$1,500-$3000
• Final angle of the knive
can vary between 35-60°
− Smaller angled
knives capable of
cutting thinner
sections of soft
material
− Larger angled knives
suitable for cutting
harder specimens
but not as sharp
• Cutting edge is extremely
thin (~ several atoms or a
few nm) and easily
susceptible to damage
• Very similar to (SEM)
– Uses ions instead of electrons
– Field emission of Liquid Metal Ion
Source (LMIS)
– Usually Ga or In source
– Rasters across sample
– 5-30 keV Beam Energy
– 1 pA to 20 nA
– 10-500 nm spot size
• FIB can be used to image, etch, deposit,
and ion implant site specifically
Focused Ion Beam
FIB Schematic
• Sample diced or polished to 50 mm or less
• Mounted on TEM slot or U-shaped grid
• FIB or gas assisted FIB (GAE) etched on both sides until region of interest
is thin
A. Yamaguchi and T. Nishikawa, J. Vac. Sci. Technol. B 13(3), 962-966 (1995).
TEM Specimen Prep with FIB
Trench Technique
A. Yamaguchi and T. Nishikawa, J. Vac. Sci. Technol. B 13(3), 962-966 (1995).
• Low magnification bright-field
TEM of InP prepared by
conventional FIB
Low Mag. TEM of InP
TEM Specimen Prep with FIB
http://www.amerinc.com/html/sample_preparation.html
TEM Specimen Prep with FIB
FIB Image of IC Sample
Basic TEM Imaging
HRTEM image of single crystals of (Ce0.5Zr0.5)O2, prepared by high-temperature flame spray synthesis.
Image from website of Dr. Frank Krumeich, ETH Zürich, Switzerland
HRTEM image of an Ag particle supported on ZnO.
Image from website of Dr. Frank Krumeich, ETH Zürich, Switzerland
Electron Diffraction
(ED)
High-Resolution
Transmission Electron
Microscopy
(HR-TEM)
Bright- and Dark-Field Imaging
(BF/DF imaging)
• Crystallographic Info• Internal ultrastructure
• Nanostructure dispersion
• Defect identification
• Interface structure
• Defect structureEnergy-Dispersive
X-ray Spectrometry
(EDS)
• Elemental composition,
mapping and linescans
• Chemical composition
• Other Bonding info
Electron Energy Loss
Spectroscopy
(EELS)
TEM Capabilities
Transmission Electron
Microscope
(TEM)
Bright field imaging
http://www.microscopy.ethz.ch/TEM_BF.htm
Bright field imaging
http://www.microscopy.ethz.ch/TEM_BF.htm
Contrast mechanism
Mass and thickness contrast 3
Contrast mechanism Diffraction contrast 7
Contrast mechanism
Diffraction contrast 8
Contrast mechanism
Diffraction contrast 9
Contrast mechanism
Diffraction contrast 11
• Line defect
Moire Fringes
Check out animation at:
http://www.matter.org.uk/tem/dark_field.htm
BF and DF
images of ZrO2
http://www.microscopy.ethz.c
h/BFDF-TEM.htm
EpilayerTwins
Meletis et al, 2008.
Double-layered Nanostructure of Ba(Zr,Ti)O3 Epilayer
[100]
[010]
[001]
(111)
(111)-
(111)- -
(111)-
Epilayer
Twin-1
Twin-2
Twin-3
Twin-4
MgO
a1b1
c1
a2
b2
c2
a3
b3
c3
a4
b4
c4
[100]
[010]
[001]
(111)
(111)-(111)-
(111)- -(111)- -
(111)-
(111)-
Epilayer
Twin-1
Twin-2
Twin-3
Twin-4
Epilayer
Twin-1
Twin-2
Twin-3
Twin-4
MgOMgO
a1b1
c1
a1b1
c1
a2
b2
c2
a2
b2
c2
a3
b3
c3
a4
b4
c4
a4
b4
c4
Epitaxial Ba(Zr,Ti)O3 film
William and Carter
STEM and
Annular
Darkfield
Ul-Hamid, 2004.
Chui et al, Nanotechnology 2006.
SEM Imaging
Al2O3/Ni composite
Courtesy of Prof. T. Sekino, ISIR, Osaka Univ.
BSE SE
Backscattered electron (BSE) image Secondary electron (SE) image
Al2O3/Ni composite
X-ray Energy Dispersive Spectroscopy
(EDS) in SEM
EDS spectrum: Characteristic X-ray peaks on continuum bk
http://www.geosci.ipfw.edu/cgi-bin/sem/techinfo.cgi?choice=xmap EDS elemental maps
RGB
Secondary effects 2
Interaction volume
• Interaction volume is the region that electrons penetrate into the
specimen which depends on
– Atomic number,
– Accelerated voltage,
– Tilted angle
– and so on.
Interaction volume 2
Carbon Iron Uranium
Effect of atomic number
Effect of accelerated voltage
Interaction volume 3
10 keV
20 keV
30 keV
Interaction volume 4Effect of tilted angle
0o tilt
60o tilt
45o tilt
Summary: Signals in EM
TEM
Bright field, Dark field,
Electron Diffraction* and
Energy dispersive- x-ray.
SEM
Secondary e, Back-scattered e, EDX
and Electron back-scattered diffraction
