The transmission electron microscope

Additional web resources

• http://nanohub.org/resources/3777– Eric Stach (2008), ”MSE 528 Lecture 4: The instrument,

Part 1, http://nanohub.org/resources/3907

MENA3100 V08

Objective lense

Diffraction plane(back focal plane)

Image plane

Sample

Parallel incoming electron beamSi

a

b

cP

ow

derC

ell 2.0

1,1 nm

3,8

Å

Objective aperture

Selected area aperture

Simplified ray diagram

JEOL 2000FX Wehnelt cylinderFilamentAnode

Electron gun 1. and 2. beam deflectors

1.and 2. condenser lensCondenser apertureCondenser lens stigmator coilsCondenser lens 1. and 2. beam deflector

Condenser mini-lensObjective lens pole pieceObjective apertureObjective lens pole pieceObjective lens stigmators1.Image shift coilsObjective mini-lens coils (low mag)2. Image shift coils

1., 2.and 3. Intermediate lens

Projector lens beam deflectorsProjector lensScreen

Mini-lens screws

Specimen

Intermediate lensshifting screws

Projector lensshifting screws

Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1, http://nanohub.org/resources/3907

Eric Stach (2008), ”MSE 528 Lecture 4: The instrument, Part 1, http://nanohub.org/resources/3907

The requirements of the illumination system

• High electron intensity– Image visible at high magnifications

• Small energy spread– Reduce chromatic aberrations effect in obj. lens

• Adequate working space between the illumination system and the specimen

• High brightness of the electron beam – Reduce spherical aberration effects in the obj. lens

The electron gun

• The performance of the gun is characterised by:

– Beam diameter, dcr

– Divergence angle, αcr

– Beam current, Icr

– Beam brightness, βcr

at the cross over

Cross over

α

d

Image of source

Brightness

• Brightness is the current density per unit solid angle of the source

• β = ie/(πdcαc)2Cross over

α

d

Image of source

The electron source

• Two types of emission sources– Thermionic emission

• W or LaB6

– Field emission• W ZnO/WCold FEG Schottky FEG

The electron gun

Bias -200 V

Ground potential

-200 kV

Anode

Wehneltcylinder

Cathode

dcr Cross over

αcr

Equipotential lines

Thermionic gunFEG

Thermionic gunsFilament heated to give Thermionic emission-Directly (W) or indirectly (LaB6)

Filament negativepotential to ground

Wehnelt produces a small negative bias-Brings electrons to cross over

Thermionic guns

Thermionic emission

• Current density:

– Ac: Richardson’s constant, material dependent– T: Operating temperature (K)– φ: Work function (natural barrier that prevents electrons from leaving the solid)

– k: Boltzmann’s constant

Jc= AcT2exp(-φc/kT)Richardson-Dushman

Maximum usable temperature T is determined by the onset of the melting/evaporation of material.

Field emission

• Current density: Fowler-Norheim

Maxwell-Boltzmann energy distribution

for all sources

Field emission• The principle:

– The strength of an electric field E is considerably increased at sharp points.

E=V/r

• rW < 0.1 µm, V=1 kV → E = 1010 V/m

– Lowers the work-function barrier so that electrons can tunnel out of the tungsten.

• Surface has to be pristine (no contamination or oxide)– Ultra high vacuum condition (Cold FEG) or poorer vacuum if tip is

heated (”thermal” FE; ZrO surface tratments → Schottky emitters).

Characteristics of principal electron sources at 200 kV

W LaB6 FEG Schottky (ZrO/W)

FEG cold (W)

Current density Jc (A/m2) 2-3*104 25*104 1*107

Electron source size (µm) 50 10 0.1-1 0.010-0.100

Emission current (µA) 100 20 100 20~100

Brightness B (A/m2sr) 5*109 5*1010 5*1012 5*1012

Energy spread ΔE (eV) 2.3 1.5 0.6~0.8 0.3~0.7

Vacuum pressure (Pa)* 10-3 10-5 10-7 10-8

Gun temperature (K) 2800 1800 1800 300

* Might be one order lower

Advantages and disadvantages of the different electron sources

W Advantages: LaB6 advantages: FEG advantages:

Rugged and easy to handle High brightness Extremely high brightness

Requires only moderate vacuum

High total beam current Long life time, more than 1000 h.

Good long time stability Long life time (500-1000h)

High total beam current

W disadvantages: LaB6 disadvantages: FEG disadvantages:

Low brightness Fragile and delicate to handle

Very fragile

Limited life time (100 h) Requires better vacuum Current instabilities

Long time instabilities Ultra high vacuum to remain stable

Electron lenses

• Electrostatic– Require high voltage - insulation problems– Not used as imaging lenses, but are used in modern monochromators or

deflectors

• Magnetic– Can be made more accurately – Shorter focal length

F= -eE

F= -e(v x B)

Any axially symmetrical electric or magnetic field has the properties of an ideal lens for paraxial rays of charged particles.

General features of magnetic lenses

• Focuses near-axis electron rays with the same accuracy as a glass lens focuses near axis light rays.

• Same aberrations as glass lenses.• Converging lenses.• The bore of the pole pieces in an objective lens is about 4 mm or less.• A single magnetic lens rotates the image relative to the object.• Focal length can be varied by changing the field between the pole pieces

(changing magnification).

http://www.matter.org.uk/tem/lenses/electromagnetic_lenses.htm

Electromagnetic lensBore

Soft Fe pole piece

gap

Cu coil

Current in the coil creates A magnetic field in the bore.

The magnetic field has axialsymmetry, but is inhomogenious along the length of the lens.

The soft iron core can increase the field by several thousand times.

Electron ray paths through magnetic fields

B

See fig 6.9

r

θv v2

v1

The electron spirals through the lens field: A helical trajectory.

For electrons with higher keV, we must use stronger lenses (larger B) to get similarray paths.

Simple ray diagrams• Electron lenses act like a convex glas lens• Thin lens • β: variable giving the fractionof rays collected by the lens~ 10 m rad ~0.57o

β

α

Point obj

Point image

Never a perfect image

Changing the strength of the lens

• The further away rays are from the optical axis the stronger they are bent by a convex lens.

• What happens to the focal and image plane when the strength of the lens is changed?

• What happens to the image?

• Under conditions normally found in the TEM, strong lenses magnify less and demagnify more (not in VLM).

• When do we want to demagnify an object?

The strength of the lens

Spherical aberration

ds = 0.5MCsα3 (disk diameter, plane of least confusion)

ds = 2MCsα3 (disk diameter, Gaussian image plane)

M: magnificationCs :Spherical aberration coefficientα: angular aperture/ angular deviation from optical axis

r1

r2

Plane of least confusion

α

Gaussian image plane

2000FX: Cs= 2.3 mm2010F: Cs= 0.5 nm

Highest intensity in the Gaussian image plane

Chromatic aberration

vv - Δv

Diameter for disk of least confusion:

dc = Cc α ((ΔU/U)2+ (2ΔI/I)2 + (ΔE/E)2)0.5

Cc: Chromatic aberration coefficientα: angular divergence of the beamU: acceleration voltageI: Current in the windings of the objective lensE: Energy of the electrons

2000FX: Cc= 2.2 mm2010F: Cc= 1.0 mm

Thermally emitted electrons: ΔE/E=kT/eU, LaB6: ~1 eV

Disk of least confusion

The specimen will introduce chromatic aberration.

The thinner the specimen the better!!

Correcting for Cc effects only makes sense if you are dealing with specimens that are thin enough.

Lens astigmatism• Loss of axial symmetry

y-focus

x-focusy

x

This astigmatism can not be

prevented, but it can be

corrected! Disk of least confusion

Diameter of disk of least confusion:da: Δfα

Due to non-uniform magnetic fieldas in the case of non-cylindrical lenses. Apertures may affect the beam if not precisely centered around the axis.

Depth of focus and depth of field (image)

• Imperfections in the lenses limit the resolution but give a better depth of focus and depth of image.– Use of small apertures to minimize aberrations.

• The depth of field (Δb or Dob) is measured at, and refers to, the object.– Distance along the axis on both sides of the object plane within which

the object can move without detectable loss of focus in the image.

• The depth of focus (Δa, or Dim), is measured in, and referes to, the image plane. – Distance along the axis on both sides of the image plane within which

the image appears focused.

αim

DobDim

dob dim

1 12 2

Depth of focus and depth of field (image)

βob

Ray 1 and 2 represent the extremes of the ray paths that remain in focus when emerging ± Dob/2 either side of a plane of the specimen.

αim≈ tan αim= (dim/2)/(Dob/2) βob≈ tan βob= (dob/2)/(Dim/2)

Angular magnification: MA= αim/ βob

Transvers magnification: MT= dim/ dob MT= 1/MA

Depth of focus: Dim=(dob/ βob)MT2 Depth of field: Dob= dob/ βob

αim≈ tan αim= (dim/2)/(Dob/2) βob≈ tan βob= (dob/2)/(Dim/2)

Angular magnification: MA= αim/ βob

Transvers magnification: MT= dim/ dob MT= 1/MA

Depth of focus: Dim=(dob/ βob)MT2 Depth of field: Dob= dob/ βob

Depth of field: Dob= dob/ βob

Carefull selection of βob

• Thin sample: βob ~10-4 rad

• Thicker, more strongly scattering specimen: βob (defined by obj. aperture) ~10-2 rad

Depth of field

Example: dob/ βob= 0.2 nm/10 mrad = 20 nmExample: dob/ βob= 0.2 nm/10 mrad = 20 nm

Example: dob/ βob= 2 nm/10 mrad = 200 nmExample: dob/ βob= 2 nm/10 mrad = 200 nm

Dob= thickness of sample all in focusDob= thickness of sample all in focus

Depth of focus

Depth of focus: Dim=(dob/ βob)MT2

Example: To see a feature of 0.2 nm you would use a magnification of ~500.000 x

(dob/ βob)M2= 20 nm *(5*105)2= 5 km

Example: To see a feature of 0.2 nm you would use a magnification of ~500.000 x

(dob/ βob)M2= 20 nm *(5*105)2= 5 km

Example: To see a feature of 2 nm you would use a magnification of ~50.000 x

(dob/ βob)M2= 200 nm *(5*104)2= 500 m

Example: To see a feature of 2 nm you would use a magnification of ~50.000 x

(dob/ βob)M2= 200 nm *(5*104)2= 500 mFocus on the wieving screenand far below!Focus on the wieving screenand far below!

Fraunhofer and Fresnel diffraction

• Fraunhofer diffraction: far-field diffraction– The electron source and the screen are at infinite distance

from the diffracting specimen.• Flat wavefront

• Fresnel diffraction: near-field diffraction– Either one or both (electron source and screen) distances

are finite.

Electron diffraction patterns correspond closely to the Fraunhofer case while we ”see” the effect of Fresnel diffraction in our images.

Airy discs (rings)

• Fraunhofer diffraction from a circular aperture will give a

series of concentric rings with intensity I given by: I(u)=Io(JI(πu)/ πu)2

http://en.wikipedia.org/wiki/Airy_disk

Strengths of lenses and focused image of the source

If you turn up one lens (i.e. make it stronger, or ‘over- focus’ then you must turn the other lens down (i.e. make it weaker, or ‘under-focus’ it, or turn its knob anti-clockwise) to keep the image in focus.

http://www.rodenburg.org/guide/t300.html

Magnification of image, Rays from different parts of the object

If the strengths (excitations) of the two lenses are changed, the magnification of the image changes

http://www.rodenburg.org/guide/t300.html

The Objective lens

• Often a double or twin lens• The most important lens

– Determines the resolving power of the TEM• All the aberations of the objective lens are magnified

by the intermediate and projector lens.

• The most important aberrations– Astigmatism – Spherical – Chromatic

Astigmatism

Can be corrected for with stigmators

• Cs can be calculated from information about the shape of the magnetic field– Cs has ~ the same value as the focal length (see

table 2.3)• The objective lens is made as strong as possible

– Limitation on the strength of a magnetic lens with an iron core (saturation of the magnetization Ms)

– Superconductiong lenses (give a fixed field, but need liquid helium cooling)

The objective lens

Apertures

AperturesWe use apertures in the lenses to control the divergence or convergence of electron paths through the lens which, in turn, affects the lens aberrations and controls the current in the beam hitting the sample.

A.E. Gunnæs MENA3100 V08

Use of aperturesCondenser apertures: Limit the beam divergence (reducing the diameter of the discs in the convergent electron diffraction pattern).Limit the number of electrons hitting the sample (reducing the intensity).

Objective apertures: Control the contrast in the image. Allow certain reflections to contribute to the image. Bright field imaging (central beam, 000), Dark field imaging (one reflection, g), High resolution Images (several reflections from a zone axis).

BF image

Objectiveaperture

Objective aperture: Contrast enhancement

All electrons contribute to the image.

Si

Ag and Pb

glue(light elements)hole

Only central beam contributes to the image.

Bright field (BF)

Small objective aperture Bright field (BF), dark field (DF) and weak-beam (WB)

BF image

Objectiveaperture

DF image Weak-beam

Dissociation of pure screw dislocation In Ni3Al, Meng and Preston, J. Mater. Scicence, 35, p. 821-828, 2000.Diffraction contrast

Large objective aperture High Resolution Electron Microscopy (HREM)

HREM image

Phase contrast

Use of aperturesCondenser aperture: It limits the beam divergence (reducing the diameter of the discs in the convergent electron diffraction pattern).It limits the number of electrons hitting the sample (reducing the intensity).

Objective aperture: It controls the contrast in the image. It allows certain reflections to contribute to the image. Bright field imaging (central beam, 000), Dark field imaging (one reflection, g), high resolution images (several reflections from a zone axis).

Selected area aperture: It selects diffraction patterns from small (> 1µm) areas of the specimen.It allows only electrons going through an area on the sample that is limited by the SAD aperture to contribute to the diffraction pattern (SAD pattern).

Selected area diffraction

Objective lense

Diffraction pattern

Image plane

Specimen with two crystals (red and blue)

Parallel incoming electron beam

Selected area aperture

Pattern on the screen

Diffraction with no aperturesConvergent beam and Micro diffraction (CBED and µ-diffraction)

Convergent beam Focused beam

Convergent beam Illuminated area less than the SAD aperture size.

CBED pattern µ-diffraction pattern

C2 lens

Diffraction information from an area with ~ same thickness and crystal orientation

Small probe

Shadow imaging (diffraction mode)

Objective lense

Diffraction plane(back focal plane)

Image plane

Sample Parallel incoming electron beam

Magnification and calibration

Microscope Lens Mode Magnification

JEM-2010 Objective MAG 2 000-1 500 000

LOW MAG 50 - 6 000

Philips CM30 Twin TEM 25 - 750 000

Super twin TEM 25 - 1 100 000

Twin SA 3 800 - 390 000

Super twin SA 5 600 - 575 000

Resolution of the photographic emulsion: 20-50 µm

Magnification depends on specimen position in the objective lens

Magnification higher than 100 000x can be calibrated by using lattice images.

Rotation of images in the TEM.