Limits of OM, SEM, SPM and XRD

BTNN

BT

NN

EDS

G.B.

G.B.

BT-BaTiO3NN-NaNbO3G.B.-Grain boundaryM.G.J.-multiple grain

junction

•Lateral resolution: ~m•Details of microstructure: e.g., domain structure, chemical inhomogeneity phase distribution, grain boundaries, interfaces, precipitates, dislocations, etc.

NN/BT

M.G.J.0.2m

core

shell

Chemical analysis at a nanometer scale

Why TEM?The uniqueness of TEM is the ability to obtain full morphological (grain size, grain boundary and interface, secondary phase and distribution, defects and their nature, etc.), crystallographic, atomic structural and microanalytical such as chemical composition (at nm scale), bonding (distance and angle), electronic structure, coordination number data from the sample.TEM is the most efficient and versatile technique for the characterization of materials.

An Introduction to Transmission Electron Microscopy (TEM)/Scanning Transmission

Electron Microscopy (STEM)• What is a TEM?

• How it works - gun, lenses, specimen stage• Resolution • What can a TEM do?• Imaging and diffraction Imaging-diffraction and phase contrast Diffraction-Selected area electron diffraction (SAED) and Convergent beam electron diffraction (CBED)• Chemical analysis EDS, Electron Energy Loss Spectroscopy (EELS) Energy Filtered Imaging

Basic features of A Modern TEM

Electron Gun

EDS DetectorCondenser Lens

Specimen HolderObjective Lens

Magnifying Lenses

CM200 (200kV)

SAD Aperture

TV MonitorViewing ChamberCamera

Chamber

Cost: $4,000,000

Column

Binocular

A simple analogue

A better comparison

Vacuum The electron microscope is built like a series of vessels connected by pipes and valves separate all the vessels from each other.

The vacuum around the specimen is around 10-7 Torr. The vacuum in the gun depends on the type of gun, either around 10-7 Torr (the tungsten or LaB6 gun) or 10-9 Torr (for the Field Emission Gun).The pressure in the projection chamber is usually only 10-5 Torr (and often worse). This pressure is not very good because the projection chamber holds the negatives used to record images. Even though we dry the negatives before putting them in the microscope, they still will give off so many gases that the vacuum in the projection chamber never gets very good.

Electron Beam Source

The Lenses in TEMCondenser lenses(two)-control howstrongly beam is focused (condensed) onto specimen. At low Mag. spreadbeam to illuminate a large area, at highMag. strongly condense beam.

Objective lens-focus image (imageformation) and contribute most to the magnification and resolution of the image.

Four lenses form magnificationsystem-determine the magnificationof the microscope. Whenever themagnification is changed, the currentsthrough these lenses change.

B

Image Formation in TEM

binocular

negatives

screen

Ray Diagram for a TEM

Control brightness,

convergence

Control contrast

Why Electrons? Resolution!In the expression for the resolution (Rayleigh’s Criterion) r = 0.61/nsin-wavelength, =[1.5/(V+10-6V2)]1/2 nmV-accelerating voltage, n-refractive index -aperture of objective lens, very small in TEM sin and so r=0.61/ ~0.1 radiansGreen Light 200kV Electrons~400nm ~0.0025nmn~1.7 oil immersion n~1 (vacuum)r~150nm (0.15m) r~0.02nm (0.2Å)

1/10th size of an atom!UNREALISTIC! WHY?

Resolution Limited by Lens Aberrations

point is imaged as a disk.

Spherical aberration is caused by the lens field acting inhomogeneously on the off-axis rays.

point is imaged

Chromatic aberration is caused by the variation of the electron energy and thus electrons are not monochromatic.

rmin0.91(Cs3)1/4

Practical resolution of microscope. Cs–coefficient of spherical aberration of lens (~mm)

as a disk.

Beam and Specimen Interaction

(EDS)

(EELS)SAED & CBED diffraction

BF DF HREMImaging

Scanning Transmission Electron Microscopy

                            

  

In STEM, the electron beam is rastered (scan coil) across the surface of a sample in a similar manner to SEM, however, the sample is a thin TEM section and the diffraction contrast image is collected on a solid-state (ADF) detector.

JEOL 2000FX Analytical Electron Microscope

STEM detectoror EELS

HAADF Detector

HAADF-high angleannular dark-field

Scanning beam

specimen

BF ADFADF

BF

DF

(STEM)

Specimen Preparation-DestructiveDispersing crystals or powders on a carbon film on a grid

3mm

Making a semiconductor specimen with a Focused Ion Beam (FIB)

1. a failure is located and a strip of Pt is placed as a protective cover.2. On one side of the strip a trench is milled out with the FIM.3. The same is done on the other side of the strip (visible structure).4. The strip is milled on both sides and then the sides connecting the

strip to the wafer are cut through.5. The strip is tilted, cut at the bottom and deposited on a TEM grid.

1 2 3 4 5

Specimen Preparation-2Ion-milling a ceramic

3mm

Ultrasonic cut grind Dimple center part

of disk to ~5-10mion-mill until a hole appears in disk

Ar (4-6keV, 1mm A)

Jet-polishing metal

Drill a 3mm cylinder

Cut into disks and grind

A disk is mounted in a jet-polishing machine and is electropolished until a small hole is made.

a thin stream of acid

+-

Ultramicrotomy-using a (diamond) knife blade Mainly for sectioning biological materials.To avoid ion-milling damage ultramicrotome can also be usedto prepare ceramic TEM specimens.

Specimen Holder

a split polepieceobjective lens

holder

beam

                        

Heating and strainingTwin specimen holder

Double tilt heating

Rotation, tilting, heating, cooling and straining

Specimen Holder with Electrical Feedthroughs

Imaging

BF and DF imaging

HREM

BF & DF Imaging – Diffraction Contrast

                                                                                                                    

Objective aperture

C-filmamorphous

crystal

D

TBF image

C-filmcrystal

DT

C-filmcrystal

DF image

Diffraction + mass-thickness Contrast

Objective aperture

DDF CDFBeam

tilt

T-transmittedD-diffracted

Hole in OA

OA OA

Diffraction, Thickness and Mass Contrast

Disk specimen

thickness

thinnerthicker

1

2

3

45

6

78

G.B.

. ... . . . .. . .. ... .... .... .. High mass

Lowmass

T TS SS

Bright Dark

Strongdiffraction

Weak diffraction

8 grains are in different orientationsor different diffraction conditions

thicknessfringes

BF images

Bright Field (BF) and Dark Filed (DF) Imaging

                              

                           

   

Incident beam

specimen

transmitted beam

diffracted beam

objective aperture

hole in objectiveaperture(10-100m)

BF imaging-only transmitted beam is allowed to pass objective aperture to form images.mass-thicknesscontrast

BF

DF

DF

DF imagingonly diffractedbeams areallowed to passthe aperture toform images.

Particles in Al-CuAlloy.thin platelets ll eVertical, darkParticles e.

Phase Contrast Imaging High Resolution Electron

Microscopy (HREM)

                              Use a large objectiveaperture. Phases and intensities of diffracted andtransmitted beams are combined to form a phase contrast image.

TD

SiObjective aperture

Electron diffraction pattern recordedFrom both BN film on Si substrate.

BN

Electron Diffraction

Specimen foil

T D

e-

L 2

r

dhkl

[hkl] SAED pattern

L -camera lengthr -distance between T and D spots1/d -reciprocal of interplanar distance(Å-1)SAED –selected area electron diffraction

Geometry fore-diffraction

Bragg’s Law: = 2dsin

=0.037Å (at 100kV)=0.26o if d=4Å

= 2dr/L=sin2as 0r/L = 2

r/L = /d or

r = Lx 1d

hkl

Reciprocal lattice

Reciprocal Lattice

A reciprocal lattice is another way of view a crystal lattice and is used to understand diffraction patterns. A dimension of 1/d is used in reciprocal lattices.

2-D Reciprocal LatticesReal space:Unit cell vectors: a,b d-spacing directiona d10 [10]b d01 [01]

Reciprocal space:Unit cell vectors: a*,b* magnitude directiona* 1/d10 b

b* 1/d01 a

A reciprocal lattice can be built using reciprocal vectors. Both the real and reciprocal construc-tions show the same lattice, using different but equivalent descriptions.

[01]

[10] (10)

(01)

Note: each point in the reciprocal lattice represents a set of planes.

a*b*

0102

1011

1220

21 22

For every real lattice there is an equivalent  reciprocal lattice.

3-D Reciprocal LatticeReal space:Unit cell vectors: a,b,c magnitude directiona d100 [100]b d010 [010]c d001 [001]

Reciprocal space:Unit cell vectors: a*,b* magnitude directiona* 1/d100 b and c

b* 1/d010 a and c

c* 1/d001 a and bNote: as volume of unit cell in real space increases the volume of unit cell in reciprocal space decreases, and vice versa. a*,b* and c* are parallel to corresponding a,b and c, and this is only true for the unit cells of cubic, tetragonal and orthorhmbic crystal systems.

Orthorhombic

Lattice VectorsReal space lattice vectorcorresponds to directions in crystal and it can be defined as:

r=ua+vb+wca,b and c are unit cell vectors,u,v and w are components ofthe direction index [uvw].

A reciprocal lattice vectorcan be written as:

g*=ha*+kb*+lc*a*,b* and c* are reciprocal unit vectors, and h,k and l are the Miller indices of the plane (hkl).

Effect of Spacing of planes in Real Space on Length of Reciprocal Vector, g

In a crystal of any structure, ghkl is normal to the (hkl)plane and has a length inversely proportional to the interplanar spacing of the planes.

(111)-d111-

[111]-

Why are there so many spots?The Ewald Sphere and Diffraction Pattern

Reciprocal lattice

High energyelectron case

k – wave vectorlkl = 1/ – wavelength of electron

Ewald’s Sphere

Ewaldcircle

0

incident beam

diffracted beam

2

C

ki Gg130

H

Ewald’s sphere is built for interpreting diffraction

CG-C0=0G or kd-ki=g Laue equation

lkl=1/

kd

Wherever a reciprocal lattice point touches the circle, e.g., at G, Bragg's Law is obeyed and a diffracted beam will occur. At H, no diffraction.

Construction of Ewald’s SphereEwald’s sphere is built for interpreting diffraction patterns and it shows which sets of planes are at (or close to) their Bragg angle for diffraction to occur.

•Incident wave is represented by a reciprocal vector k (lkl=1/ and points in the direction of wave).•Construct a circle with radius 1/ (i.e., k), which passes through origin of reciprocal lattice, 0.•Wherever a reciprocal point touches the circle, Bragg’s law is obeyed and a diffracted beam will occur.•C0–incident beam and CG–diffracted beam. The angle between C0 and CG must be 2.•0G is the reciprocal vector g130 and has magnitude of 1/d130.

0G/2=lklsin, 0G=2/sin, 1/d130=2/sin130

=2d130sin130

Ewald’s Sphere Construction in 3D

In a single crystalonly a few sets ofplanes are orientedat their Bragg angle at any one time.

Polycrystalline sample

ZOLZ

FOLZ

SOLZ

ZOLZ, FOLZ and SOLZ are zero order, first order and second orderLaue zone, respectively.

SAED

A TEM technique to reduce both the area and intensity of the beam contributing to a diffraction pattern by the insertion of an aperture into the image plane of the objective lens. This produces a virtual diaphragm in the plane of the specimen.

SADaperture

Virtualaperture

specimen

Objectivelens

Diffractionpattern

Back focalplane

Selected Area Electron Diffraction

parallel beam

Focusing SAED Pattern at Fixed Screenby changing magnetic lens strength

specimen lensscreen

Transmitted beam

Diffracted beam

Spot patternSAED (ZOLZ) gives 2-D information

SAED Patterns of Single Crystal, Polycrystalline and Amorphous Samples

a b c

a. Single crystal Fe (BCC) thin film-[001]b. Polycrystalline thin film of Pd2Sic. Amorphous thin film of Pd2Si. The diffuse

halo is indicative of scattering from anamorphous material.

r1 r2200

020110

Diffraction Spot IntensitySpot intensity: Ihkl lFhkll2

Fhkl - Structure Factor

Fhkl = fn exp[2i(hu+kv+lw)]N

n=1

fn – atomic scattering factor

fn Z, sin/h,k,l are Miller indices and u,v,w fractional coordinates

Indexing Diffraction Pattern-ratio techniqueAny 2-D section of a reciprocal lattice can be defined by two vectors so only need to index 2 spots. 1.Choose one spot to be the origin and measure r12.measure the spacing of a second spot r2

3.measure the angle, 4.prepare a table giving the ratios of the spacings of permitted diffraction planes in the known structure5.take measured ratio r1/r2 and locate a value close to this in the table6.assign more widely-spaced plane (lower indices) to the shorter r value7.calculate angle between pair of planes of the type you have indexed8.if measured agrees with one of possible value, accept indexing. if not, revisit the table and select another possible pair of planes9.finish indexing the pattern by vector addition.

Indexing Electron Diffraction Patterns

If we know the index for two diffraction spotsIt is possible to index the rest of the spots byUsing vector addition as shown. Every spotsCan be reached by a combination of these twoVectors.

Zone Axis of A SAED Pattern

Take any two g vectors, g1 (h1k1l1) and g2 (h2k2l2) from the diffraction patter. The zone axis is given by the vector product:

The zone axis is parallel to the electron beam direction.

Indexing-example1.Choose T as the origin, r1-7.75mm

2.r2-12.87mm

3.~72O

4.Get a table giving relative reciprocal lattice spacings

5.r2/r1=1.66 gives several possible pair of planes in the table

r1

r2

T

r=L/d r2/r1=d1/d2

6.From the table of interplanar angle in cubic, ~72O gives only one matched pair of planes, {100} (or {200}) and {311} for a face-centered lattice. {100} diffraction is not allowed in a face-centered structure.

7.Calculating interplanar angles leads to (131) or (113) and (200) since angle between (311) and (200) is 25.2O.8.Zone axis of pattern: r1 x r2 = [013] for (131) and (200) pair

Cubic

200

131 (311)?

_

[013]_