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Microscopy: Overview of Different Methods

EML 5930 (27-750) Advanced Characterization and Microstructural

AnalysisA. D. Rollett, P.N Kalu

Spring 2008

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(MACRO)TEXTURE

Review:

Recall that X-ray texture (macrotexture):

• Provides an overview of the crystallographic texture of material - only texture information is obtained.

• Provides the volume fraction of the specimen, which has a particular orientation.

• Does not tell how grains are distributed in the material.

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• Lack of a direct connection between the study of texture and microstructure.

• Parallel but separate investigations are needed in order to obtain microstructural data.

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• Microtexture technique provides concurrently the spatial location and the orientation of individual grains in a sample.

• This technique can be referred to as the modern approach to texture investigation.

• Until recently, the orientation of individual crystals can only be determined by Selected Area Diffraction Pattern (SADP) technique on TEM - very tedious.

MICROTEXTURE

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• Phenomena that can be investigated using microtexture:– Effect of property variation as a function of orientation

– Misorientation between neighboring grains or distribution of grain boundary geometry, which can result in the grain boundary/property relationship.

– Correlations between geometrical and orientational parameters of the grains

– Orientation variations within individual grains– Phase Identification/Relationships

– Direct ODF measurement

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• Macrotexture or Microtexture analyses techniques rely on the diffraction of radiation by a crystal lattice.

• The exploring radiation can be used as an experimental tool for microtexture measurement only if the probe size is smaller than the microstructural unit.

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Diffraction:

• Crystal structure analysis is usually based on diffraction phenomena caused by the interaction of matter with X-rays, electrons, or neutrons.

• Therefore, when either X-rays or electrons interact with crystalline material, they are:

(a) Subject to diffraction – have similar wave properties.

(b) Monochromatic radiation - produce a series of strongly diffracted beams leaving the crystal in defined and predicted directions.

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• The resultant diffraction pattern is given by Braggs Law, and this is given by

…….. 1

where, d: Interplanar spacing

: Grazing angle of incidence (Bragg angle)

n: Integer (0, 1, 2, 3 ….. )

: Wavelength of the incident electrons

• Note

– With diffraction, we use Reciprocal lattice in which sets of lattice planes are represented simply by a set of points in reciprocal space.

sin2dn

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The Reciprocal Lattice• Very useful in metric calculations

• Let a, b, c be the elementary translations of a space lattice (direct lattice)

• A second lattice, reciprocal to the first one, is defined by translations a*, b*, c*, which satisfy the following conditions:

a*. b = a*. c = b*. a = b*. c = c* . a = c* . b = 0

and

a*. a = b*. b = c*. c = 1

• Equation 2a suggests that a* is normal to the plane (b,c),

b* is normal to the plane (a,c), and

c* is normal to the plane (a,b),

(2b)

(2a)

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• The magnitude and sense of a*, b*, c* are fixed by (2b)

• According to (2a), a* may be written as:

a* = p (b ^ c)

where p is a constant.

The value of p is obtained by if the scalar product of both sides of (3a) by a is taken:

a* . a = 1 = p (b ^ c . a) = pV

• Therefore, p = 1/V, and equation (3a) can be written as:

a* = { (b ^ c)}1/V ………

(3a)

(3b)

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Table 1. The Characteristics of Light and Various Radiations Used for Texture Measurement by Diffraction.

• Electrons are the only radiation in which their penetration depth and interaction volume is small enough to allow diffraction from individual grains (very small volume).

• Therefore, only electrons can be used for MICROTEXTURE

Light Neutrons X-rays ElectronsWavelength [nm] 400-700 0.05 - 0.3 0.05 - 0.3 0.001 - 0.01Energy [eV] 1 1.00E-02 1.00E+04 1.00E+05Charge [C] 0 0 0 -1.60E-19Rest mass [g] 0 1.67E-24 0 9.11E-28Penetration depth [mm] 0 10 - 100 0.01 - 0.1 1.00E-03

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• Microtexture technique can either be TEM-based or SEM-based.

• Until mid-1980, the TEM-based was the major microtexture technique, although an SEM-based Selected Area Channeling technique was available.

• Modern SEM-based technique known as can now be classified into two:– manual

– automated

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Principles of Electron Microscopy

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MICROSCOPY

Introduction:

• Several new microscopy-based microcharacterization techniques have been developed over the last four decades, which have significantly extended the ability to study the microstructure of materials.

• In addition to Optical Metallography, there is a range of Electron Optical techniques.

• Electron microscope (developed in 1931) was initially used for the study of biological systems, but thin foil techniques in the mid-1950’s enabled microstructural investigations to be undertaken on metals and alloys.

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Typical Information from Electron Microscope:• Chemical composition of materials can be obtained using

electron microprobes to produce characteristic X-ray emissions and electron energy losses.

• Imaging (surface) can be characterized using secondary electrons, backscattered electrons, photo-electron, Auger electrons and ion scattering.

• Crystallography or crystal structure information can be obtained from backscattered electrons (diffraction of photons or electrons).

The various studies of materials exploit at least one of the above information, as well as the excellent spatial resolution of electron microscopes.

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Figure 1. Summary of the various signals obtained by interaction of electrons with matter in an electron microscope

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Comparison between Optical and Electron Microscopy:

• In many ways, electron microscopes (Scanning and Transmission) are analogous to light microscopes.

• Fundamentally and functionally, electron microscopes (EM) and optical microscopes (OM) are identical.

• That is, both types of microscopes serve to magnify minute objects normally invisible to the naked eyes.

• Basically, component terminology of an EM is similar to that of an OM. Both microscopes consist the following (see Figures 2 and 3):

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Figure 2. A simple optical, transmission microscope system comprising a condenser and objective lens.

19Figure 3. Comparison of image formation.

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(a) Source of Illumination as light source

–Electron Gun produces an electron beam by thermionic or field emission - EM

–Lamp produces light beam (including uv rays) - OM

(b) Condenser Lens system projects a near parallel radiation on to the specimen

–Electro-magnets of variable focal length are the lenses in EM.

–Curved transparent substance - OM

(c) Series of Imaging Lenses form the Image of the specimen

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• Although (a) to (c) above address the basic differences between the two types of microscopes, a detailed comparison is provided in Table 1.

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TABLE 1. EM and OM Comparison Chart

PARAMETERS OPTICAL MICROSCOPE ELECTRON MICROSCOPE

Illuminating Beam Light Beam Electron Beam

Wavelength7,500Å (visible)~2,000Å (ultraviolet)

0.859Å (20 kV)~0.0370Å (100 kV)

Medium Atmosphere Vacuum

LensOptical lens(glass)

Electron Lens(magnetic or electrostatic)

Resolving PowerVisible: 3,000ÅUltraviolet: 1,000Å

Point to point: 3ÅLattice: 1.4Å

Aperture Angle 70o ~35’

Magnification10x ~ 2,000x(lens exchange)

90x ~ 800,000x(continuously variable)

Focusing Mechanically Electrically

ContrastAbsorption,Reflection

Scattering absorption -SEMDiffraction, phase - TEM

Sample Type Bulk sampleBulk sample - SEMThin foil ( 3 mm dia. and electron transparent,i.e. 1000 atoms in thickness) -TEM

InformationGrain size and shapeDistribution of phases (particles)

Grain size and shapeDistribution of phases (particles)Chemical composition, e.g Identify phasesCrystal and defect structure

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ELECTRON MICROSCOPES

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ELECTRON EMISSION

• The liberation of electrons from the surface of a solid into vacuum.

• The process of electron emission is similar to that of ionization of a free atom– The energy of the electrons in an atom is lower than that of an

electron at rest in vacuum; consequently, in order to ionize an atom, energy must be supplied to the electrons in some way or other.

• A solid can only emit electrons if some of the electrons have energies equal to, or larger than, that of an electron at rest in vacuum. This may be achieved by various means, such as by – heating, irradiation with light (photoemission), – bombardment with charged particles (secondary emission), or – using of a strong electric field (field, or cold, emission).

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ELECTRON SOURCES

• Electron sources in electron beam instruments are required to provide either – a large total current beam of about 50 m diameter - low

magnification TEM, or

– a high intensity probe of electrons as small as 0.5 nm in diameter - SEM

• There are three different types of electron source available

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a) Thermionic tungsten hairpin filament This is usually heated to about 2800 K by direct

resistance heating. The surrounding grid, known as the Wehnelt cylinder, and the anode, which is at earth potential, act as an electrostatic lens.

For an operating condition of 100 kV, the brightness is about 3 x 105 A cm-2 sr-1.

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(a)

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(b)

Figure 4. Schematic diagram of a conventional tungsten thermionic source. (a) the filament F and Wehnelt cylinder (b) schematic ray path showing focusing action.

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b) Lanthanum hexaboride crystal (LaB6)

The only difference between the conventional assembly illustrated in Figure 4 and a modern LaB6 assembly is that extra pumping holes are present in the Wehnelt cap to ensure a better pumping speed near the tip.

Higher current (greater than the tungsten) is obtainable in small probes.

The brightness of a LaB6 can be as high as 107 A cm-2 sr-1 at 100kV.

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c) Field emission source

• The emission of electrons from a metal or semiconductor into vacuum under the influence of a strong electric field.

• Field emission - electrons tunnel through a potential barrier, rather than escaping over it as in thermonic emission.• The effect is purely quantum-mechanical, with no

classical analog.

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• In most cases, it is a <111> orientation crystal of tungsten, and a Wehnelt cylinder, which is raised to an extraction potential up to about 4 kV in order to cause emission from the tip of the crystal.

• There is a requirement of high vacuum for this source• The brightness of cold or thermal emission source can

be about 104 times of a conventional tungsten filament.• The high brightness of this source make them preferable

for scanning instruments.• Cold, thermal or Schottky

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Schotty Field Emission Source Electron Gun for SEM

• Source:– Schotty field emitter (ZrO/W – High brightness – Highly-stable electron beam

• High current density • 100 nm spot size at 5 nA sample current • The field emission source – current density can be

maximize and still produce a 100 nm spot size at 5 nA. – Optimised for Auger analysis at very high spatial

resolution with SEM.

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ELECTRON LENSES AND OPTICS

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• Electron lenses in microscopes are generally electromagnetic.

• There are three types of magnetic lenses in uses (refer to Figure 5):

(a) a multi-layer coil; i.e., an air-core solenoid coil

(b) a coil enclosed by soft iron plates (in order to reduce leakage flux) containing a gap (in order to concentrate the induction field) and

(c) a coil enclosed by soft iron plates containing a gap and internal soft iron pole pieces (in order to ensure a high intensity magnetic field)

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Figure 5. Types of magnetic electron lenses.

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• Almost all modern electron microscopes use pole pieces for high resolving power and high magnification.

• The function of such an electron lens is more or less the same as that of horse-shoe magnets symmetrically arranged about an axis.

• Accordingly, all the parallel electron beams incident to the curved magnetic field converge at one point.

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ELECTRON OPTICS

• The action of a magnetic field on an electron is described by a well-known right hand rule where thumb, first and second finger are used to represent the terms in a vector product

• The force F which an electron of charge -e experiences when travelling with velocity v, due to a magnetic field B, is given by:

…………(4a))( BveF

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Figure 6. Schematic diagram of the action of a cylindrical magnetic lens on the path of non-axial electrons.

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and the magnitude of the force is then given by

…………..(4b)

where is the angle between B and v.

If the initial velocity of an electron is divided into two components, vp parallel to B and vo perpendicular to B, then the value of vp will be unchanged by B (since will be zero) and the force resulting from B and vo will result in a circular motion of the electron about B (see Figures 7 and 8).

sinevBF

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Figure 7. Electrons passing through magnetic lens

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• Figs. 7 & 8 shows the trajectory of an electron passing through such a magnetic field.

• Although the electron beam path in a magnetic lens is not the same as the light ray path in an optical lens, the results are similar.

• As shown in Figs. 7 & 8, the electron travels rectilinearly, crosses the axis, moves through the magnetic field along a spiral orbit, approaches the axis, crosses the axis again, and travels rectilinearly.

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Figure 8. Schematic diagram showing the trajectory of an electron through a magnetic lens.

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The radius r of this spiral motion is given by:

……….(4c)

Since generally, in electron microscopes, electron beams near the axis are used for forming an image, is extremely small.

This effect is similar to the converging action of an optical convex lens, and if the revolution of the electron about the axis is omitted, the converging action of an electron lens can be considered to be identical to that of an optical lens.

sineBmv

r

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• A magnetic lens containing pole pieces magnetized to near-saturation for concentrating magnetic flux in a very narrow space constitutes a thin lens.

• The focal length f and rotation angle are given as follows:

…….. 5

where, V => Accelerating voltage

= specific charge of electron e/m

dxxBV

dxxBVf

)(8

81 2

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RESOLUTION OF LENS• Resolution defines the smallest separation of two points in the

object, which may be distinctly reproduced in the image.Light Microscope: The resolving power for light microscope

is determined by diffraction aberration and can be defined as 1,2

……….. 6

• where is the wavelength of the illumination, n is the refractive index of the medium in front of the lens, is the semi-angle (aperture angle) subtended by the object at the lensNA = n sinα = numerical aperture = measure of light-gathering ability

= 0.95 (max. with air). Higher (~1.515) for oil-immersion objtvs.k is a constant usually taken to be 0.61.

sinnk

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Optical Microscope –

= 50 nm (for white light Illumination)

n sin = 0.135 (when fitted with an oil immersion lens)

Therefore, it is possible to achieve a resolution of about 250 nm in Optical Microscopes.

• Filters can also be used to enhance the resolving power of an objective. For light:– The shorter wavelengths are at the violet-blue-green end of

the spectrum

– The higher wavelengths are at the orange-red of the spectrum.

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Electron Microscope –

• De Broglie relationship relates the wavelength of electrons, , to their momentum, mv (m is the mass and v is velocity), by h – Planck’s constant, such that:

……… 7

• Since electrons are accelerated by a potential difference of V volts and have a kinetic energy K, where K is given as –

……... 8

Therefore,

……… 9

mvh

2

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mvK

eVmv 22

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By considering equations (7) and (9), we have –

……. 10

The energy term eV is expressed in electron volts and represents that energy required to pass an electron through a potential difference of one volt ( 1 eV = 1.602 x 10-19 J).

2/12meV

h

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When the velocity of the electron approaches the speed of light, v c, a relativistic correction is required for the voltage, such that

………………….. 11

where mo is the mass of the electron at rest. It is important to use this correction for cases when V 105 volts. Table 2 presents a chart of electron wavelength in relation to applied voltage.

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1cm

eVVV

o

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Table 2. Variation of Electron Wavelength with applied voltage

Applied Voltage (keV) Wavelength, nm)

20 0.008588

50 0.005355

80 0.00418

100 0.003702

200 0.002508

500 0.001421

1000 0.00872

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• If diffraction aberration is considered (see equation (6)), the resolving power of 100 and 300 keV electron microscopes will be about 0.0025 nm and 0.0017 nm respectively. These values are not realistic!

• The ultimate resolution of an electron microscope is dictated by the defects in the imaging system rather than by the wavelength (diffraction aberration) of the radiation employed.

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Lens defects: • Chromatic aberration is related to energy losses within the

specimen. This is generally of little importance except for very thick regions of thin foils or bulk specimens.

• Astigmatism may arise from

– intrinsic defects in the objective lens, or

– from contamination on the lens and the objective aperture.

Microscope manufacturers have developed methods for correcting this defect

– small set of coils are used to produce uniform magnetic field.

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• Spherical aberration is the main factor, which limits the performance of electromagnetic lenses used in microscopes. – It is a function of the lens design and the acceptance

angle () for electrons entering the lens. – This angle must be kept at a minimum, however this

decreases the resolution limit due to diffraction. The best resolution is accomplished with a compromise value of , and is given by

……… 12

– where cs is the coefficient of spherical aberration, and min is typically less than 3 Å on modern microscopes.

4/14/14/14/3min

ss candc

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Current state-of-the-art TEM capability

Current state-of-the-art TEM capability

1. Analytical Probe sizes less than 1A

2. TEM resolution 0.8A or better

3. Holographic reconstructions less than 1A

4. FEG: cold/thermal/Schottky

5. Energy resolution in EELS less than 20meV – more typical values less than 100meV – routine values of 700 – 800meV. Monochromators help.

6. WDS resolution less than 1 eV (1000meV)

7. CCD Camera images 4K x 4K (8K under development at UCSD-commercial version just delivered to Fujiyoshi)

8. Contemporary computer control – contemporary means TODAY

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Current state-of-the-art TEM capability

Current state-of-the-art TEM capability

9. Accelerating voltages up to 3.0 MeV

10.A variety of energy filters: Omega, Mandoline, Gamma, single-sector (GATAN)

11.Goniometer Automation (searching, recording, tilting (tomography/kspace tilting and navigation))

12.Detector Automation - autoinsertion, autoconfiguration of instrument modes

13.Piezo elements for nanopositioning

14.SPM – Nanofactory

15.Remote control – taking the operator away from the microscope

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• Before the Cs corrector became a practical invention, the TEM/STEM went through the final transition to an FEG instrument capable of uncorrected extended information limit and smaller, higher current probes.

• This happened in the early part of 1990 and set the stage for the development of the TEM/STEM Cs corrector.

Resolution/Cs Correction

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Directions for the future:

• Areas of Future directions for Improvements include:resolution (image/analytical – spatial/energy), computer control, automation, vacuum, in-situ capability, remote control

• The question is “How will these improvements be effected?”

• Most instruments today are available with a variety of resolution enhancers: • Cs correctors for TEM and STEM image and

analytical resolution• Monochromators for improved energy resolution.

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Directions for the future:

Other subjects to consider include: A. Tomography: Image series acquisition, Image

reconstruction, and 3D rendering.B. Lorentz: objective minilens with a resolution of

about 2nm that can be used as an objective lens

C. Remote controlD. Data managementE. EDS and EELS/Imaging, and F. Integration of all functions.

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Today Electron Microscopes represent state-of-the-art technology incorporating:

• Clean High vacuum and Ultra-high vacuum

• Extreme electronic stability - lenses and high voltage

• Machining accuracy to 1um or better, and

• Unsurpassed mechanical stability

They remain the highest lateral spatial resolution spectroscopy devices in the world

They can currently resolve sub-angstrom features and can perform spectroscopy on single atomic columns or even single atoms.