The Instrument

Dr. Hongzhou Zhang hozhang@tcd.ie

SNIAM 1.06 896 4655

http://www.tcd.ie/Physics/People/HongZhou.Zhang/Teaching/PY5019/2011.php

http://www.tcd.ie/Physics/People/HongZhou.Zhang/Teaching/PY5019/2011.phpmailto:hozhang@tcd.iehttp://www.tcd.ie/Physics/People/HongZhou.Zhang/Teaching/PY5019/2011.phphttp://www.tcd.ie/Physics/People/HongZhou.Zhang/Teaching/PY5019/2011.phphttp://www.tcd.ie/Physics/People/HongZhou.Zhang/Teaching/PY5019/2011.phphttp://www.tcd.ie/Physics/People/HongZhou.Zhang/Teaching/PY5019/2011.php

Review: Lecture one

• Electron waves (Duality)

– Can be focused – lens

– Simple wave equation

• Applications: High Spatial and Analytical Resolution with Completely Quantitative Understanding

• Limitations: Intepretation, Artefacts, damage, …

Content • Elements of a TEM

– Illumination System : Well-defined reference state

• Electron Sources • Condenser lens

– Sample – The Imaging System : minimize

aberrations • Objective lens

– Apertures/Diaphragms – Image Viewing/Recording – Beam Deflection & Correction – Spectrometers (Lecture 7 and 8) – Supporting Subsystems

• The high voltage system • The vacuum System: cold trap • The cooling system • Radiation shields

– Layer 1: Al, low-E X-ray – Layer 2: Pb, Absorb X-ray

• Electronic and computer controls

• Basic Optics–image formation and ‘modes’

• Basic Alignment

Recording system

~10-7 Torr

~10-8 Torr

~10-8 -10-9 Torr

Imaging system

Illumination

Tecnai F30 Titan

Supporting system

Electron Sources • Types: different ways to excite

electrons – Thermionic

• Good for low magnification • low cost

– Schottky • Better stability: beam current + noise

– Field Emission • high gun brightness and coherence

(Thermionic/FE cannot be interchanged)

• Physics of electron emission • Characteristics Needed

– Brightness – Coherence – Stability – Beam current – Life – Maintenance

http://www.dicomps.com/index.php/en/electron-optics-systems/components/emitters/schottky-emitters

http://www.dicomps.com/index.php/en/electron-optics-systems/components/emitters/schottky-emittershttp://www.dicomps.com/index.php/en/electron-optics-systems/components/emitters/schottky-emittershttp://www.dicomps.com/index.php/en/electron-optics-systems/components/emitters/schottky-emittershttp://www.dicomps.com/index.php/en/electron-optics-systems/components/emitters/schottky-emittershttp://www.dicomps.com/index.php/en/electron-optics-systems/components/emitters/schottky-emittershttp://www.dicomps.com/index.php/en/electron-optics-systems/components/emitters/schottky-emittershttp://www.dicomps.com/index.php/en/electron-optics-systems/components/emitters/schottky-emitters

Physics of Electron emission • Surface Barrier

– work function ~ eV

• Thermionic guns – Richardson’s Law

– Cathodes

• Melt/vaporize with a few eV of thermal energy

– Refractory materials: W, 3660K (Melting P)-2700K(Working T), 4.5 eV, filaments

– Exceptionally low : LaB6, 2483K (Melting P)- 1700K(Working T), 2.4 eV

• J ~ 104 – 105 A/m2 • Diameter of source ~ 10-20 nm • Transverse momentum

• Schottky Emission Guns: – Field assisted thermal emission – ZrO2/W, 1700K, 3.0eV

• J ~ 106 A/m2

• d ~ 15 nm

• FEGs – Fowler-Nordheim theory

– Cathodes • Tip-enhanced Electric field: • Lower the barrier - Electron Tunnelling • Severe stress – mechanically strong (W,

) • Pristine: contamination/oxide free

(Ultrahigh Vacuum< 10-9 Pa) • J ~ 109-1010 A/m2 • d ~ 2.5 nm

kTATJ

exp2

V/m10~ 9

r

VE

Strong field

Image potential

Effective potential

w

E

kEkJ

2/3

22

1 exp

Titan: Extraction: 1.8 ~ 7 kV r ~ 0.1 um Emission current: ~ mA – 200 uA

Characteristics: Gun/beam Brightness

2

j

S

I

dSr

nrS

S

3

22

0

2

4pp dI

– Invariance of axial gun brightness

I1, S1, 1 1

2

11

11

S

I

2

1

2

12

II

I2, S2, 2

2

2

22

22

S

I

u

v

Transverse Magnification: 12

2 SMS T

Angular Magnification: M21MMT

12122

1

2

12

22

22

1

MSMI

S

I

T

2

2

0

2p

e

d

i

–STEM/EDX/EELS: using a probe

• Why do we need a high brightness source?

Diameter d0 Beam current: ie Divergence angle: p

• The current density (j = I/S) per unit solid angle • The apparent surface size: the area subtended by a surface S when looking at that surface from a reference point, divided by the square of the distance to that surface • Brightness (A/m2 sr) Intensity

• What determines gun brightness?

Probe current:

Detector signal-to-noise ratio: pin ISNR Ip > ~ pA

- High emission current density, FE (1010 A/m2) – Thermal (104 A/m2)

- Small : Wehnelt electrode/suppressor cap

Characteristics: Beam Coherence

- The Heisenberg uncertainty: htE

E ~ 0.3-3 eV ( 10 meV with the monochromator) t ~ 4 X 10-15 s: interval shorter than t , as if monochromatic

• The temporal/Longitudinal coherence: how similar the wave packets are

20/11

1,EE

cvtvtc

- Electrons: 200kV (E ~ 1 eV), tc = 861 nm; Lasers: cms – metres - Spacing

Gun Characteristics

• Brightness (A/m2 sr) – Invariance – Probe size

• Coherency ( in step) • Small source size, FE gun • Small energy spreading • Small illumination aperture • Increase wavelength

• Stability – High voltage supply – Current:

• Thermionic/Schottky – stable ~ ± 1%/hr • CFE < ± 5%/hr

– FE: Better UHV

• Life/Cost

Measuring the Gun Characteristics: • The beam current (nA - pA)

– Faraday cup in a sample holder – Picoameter in the earth line – Calibrate ib vs exposure meter/EELS shield current – Schottky: stable, no need to monitor it constantly – ib ~ the beam size (C1, C2 aperture) – Emission current (uA) vs. Beam current

• The angle of convergence – CBED – Important in CBED, STEM, XEDS, EELS

• The beam diameter – No universal accepted definition – Manufacturer: calculated values for C1 setting – Measuring the Beam diameter

• C1: control the beam size • Form an image of the beam…? • FWHM, 50% intensity – STEM • FWTM = 1.82 X FWHM, 90% intensity – XEDS • STEM: scanning across an atomically-sharp edge – ADF

b

aB 22

2

j

S

I

Measuring the Gun Characteristics

• Spatial Coherency –Image of hole (holy carbon)

• Fresnel Fringes –Slightly out-of-focus

•Thermionic: one/two fringe •FE: Numerous!

• Temporal coherency- E –EELS: use an electron spectrometer –FWHM of the Zero loss peak

Defocus: z

x

x

Path difference:

A

B

z

x

z

xxxzABP

2

Constructive interference: nz

xP

2

znx Positions of the bright rings: 2.1~1 nnzx nm 50 sCz(300kV, Cs = 1.2 mm)

um 1z 6~x

Lens Optical Axis

Back Focal Plane

Object Plane

Image Plane

Zo

fo

fi

Zi

u

v

vuf

111

ioio ffZZ

Gaussian form

Electromagnetic lens • Coil current – focus strength • Fixed location • Rotation of the images • Severe Spherical/Chromatic aberrations • Limited collection angle

Optical Convex lens • BFP: parallel rays to form a point • Conjugate points and image formation: all rays from a point in object to a point in an image •Image: 180o rotation with respect to the object • Lens Equation

Newtonian form

• Magnification

Transverse: u

vM T

Angular: TM

M1

Longitudinal: 2TL MM

Eugene Hecht, Optics, Addison Wesley

Magnetic Lens: Round Lens

Lens gap

The magnetic field at any point is determined by B(z)

Round: Cylindrical coordinates

zz

ry

rx

sin

cos

Electrons in the Lens • Stationary magnetic field

– Only change the direction – Energy of the beam

unchanged – Direction of the field only

change the rotation angle

• Rotationally symmetric B field – B = 0

• Electrons acquire azimuthal velocity (v) by Br – The electron rotating, i.e.

the meridional plane rotating

• A radial force due to the v and Bz bends the electron closer to the axis

Electron Trajectory The motion of an electron in a magnetic field: BveBvEeF

dt

pd

CBre

mr z 22

2

The radial equation:

The azimuthal equation ():

0

180

0

22

2

2

r

E

EEm

zBe

dz

rd z

r‘’ < 0 : negative curvature Bend towards the Optical Axis

2

0

1

a

z

BzB

Glaser’s bell-shaped field- analytical solution:

B0 ~ T, a ~ mm

alLongitudin

azimuthal

radial2

z

r

Fzm

rFdt

mrd

mrFrm

Meridional plane rotating, C = 0: zL Bm

e

2

Larmor Frequency

The paraxial approximation: z

BrB zr

2

02

222

z

B

m

rereBzm zr

0

122

2

2

2

yx

k

dz

yd

Reduced coordinates, y=r/a, x=z/a:

0

0

22

0

22

18E

EEm

aBek

21;cot kx

Substitution- simplified 0cot2 2 ykyy

The trajectory r(z) The solution

sin

cos

sin

sin21 CCy

Case 1: A parallel incident ray

Initial conditions: zrr 0

Z

k2 =2.26 w=1.8

a0 = 0.1 mm B0 = 2 T E0= 300keV r0 =1 , 3, 5 um

r0 =3 um B0 = 2 T E0= 300keV a0 = 0.1, 0.15, 0.2 mm

k2 =2, 5, 9

sin

sin0

a

rr Trajectory:

Focal point: 0sin

sin0

a

rr

3;21 22 kkStrength parameter:

Case 2: the ray passes through: 000 ,yP

Image point: 111 ,yP if 0sin 01

,...2,1,01 nnn

More than one image point

The position of the object: 00 cotaz

The position of the Images: nn az 11 cot

Newton’s Lens Equation:

nanaznaz n

22

10 coseccotcot

1010 ffZZ

naFzFznaffFzzZFzzZ cot;cosec;; 1010101000

This is not a thin lens

Lens Aberrations

Fidelity!

Including higher-order terms in the ray equation: third-order aberration

• Chromatic Aberration • insufficient stabilization of V • Energy spread of the gun • Energy loss in the sample • insufficient stabilization of lens current

naff cosec10

21 k 00

22

0

22

/18 EEEm

aBek

: E< 1 eV: Schottky/FE better for HRTEM ME

ECd occ

• Spherical Aberration • Gaussian image plane (paraxial) • a plane of least confusion

On-axis On-axis

Off-axis

Off/on-axis

• Coma, Field curvature, Distortion

• Aberration : requires small objective apertures: 10-25 mrad (for 0.1-0.3nm)

3

2

1oss Cd

• Astigmatism • off-axis: different focusing strength:

meridional and sagittal (can be ignored) • on-axis: not rotationally symmetric, stigmator

Apertures, Beam Deflection, and Stigmator

- Aperture/Diaphragm •Control divergence/convergence of electron beam – aberration •Select diffraction beam •Select regions to contribute to DPs

-Deflecting beam – shift/tilt; scanning • Alignment • STEM • Blank the beam: electrostatic lens, us

Short field – interrupt change

- Quadruple lens: two orthogonal planes of symmetry

Force is tangent to the equipotential lines for

electron travelling // the optical axis

Change the shape of the beam

Illumination System

• Small probe for analytical modes and STEM: 0.2-100 nm

• Obtain sufficient intensity • Irradiated area corresponds to the viewing

screen • Variation of illumination aperture

• Low-medium mag: ~ 1 mrad (10 mrad ≈ 0.57o) • HRTEM: < 0.1 mrad • Lorentz/holographic/small-angle ED:

Probe Formation • X-ray analysis and EELS, microbeam-diffraction, STEM

• Two-/three- stage of demagnification of the electron-gun crossover • Schottky: 15 nm (r ~ 0.5 – 1 um)

• Assumption: All discs - Gaussian intensity distribution

2

0

2

0 exp)(r

rjrj

The probe current: pp jdI

2

04

This will result in a correction factors of

the order of unity

Brightness invariance: 220

2

4pp dI

The ideal useful probe size

pp

p CId

0

2/1

20

14

Diffraction due to finite aperture: p

dd

6.0

Spherical aberration: 32

1pSs Cd

Chromatic aberration: pcc

EE

EE

E

ECd

0

0

21

1

2

1

Quadratic superposition of error discs: 622

22

0

222

0

2

4

116.0 ps

p

sdp CCdddd

Optimum aperture for minimum-sized probe with a fix probe current:

0

p

pd

4/1

0

8/1

3

4

s

optC

C

Minimum probe: 4/1

3

0

8/3

min3

4

sC

Cd

Koehler Illumination

• Sample must be evenly illuminated – Each source point

contributes equally to the illumination plane

– image contrast not due to the nonuniform irradiation

• Fixed positions of the focal planes of the microscope optics

• Size of illuminated field at the specimen

Illumination

FFP

IMG

IMG

BFP

Condenser

Objective

FFP Sample

BFP

IMG

Douglas B. Murphy, Fundamentals of Light Microscopy and Electronic Imaging, John Wiley & Sons, Inc

Uniform Illumination

Titan Condenser System

Six Lens: • Gun lens: Beam current • C1- C2: Beam current/Spot size • C2-C3: Illuminated area/convergence angle • MC: Microprobe/nanoprobe • Obj: probe formation

Condenser Zoom

Spot size – C1-C2 Zoom Illuminated Area – C2-C3 Zoom

1

111

fvU

U

V

D

2

111

fVvD

vf1 vf2

vD

v

U

VMMvM TTT

21

C2 aperture

Specimen • Cc and Cs ~ the focal length of the lens:

Immersed into the magnetic field of the objective lens

• Useful Thickness – HRTEM(interference): thick sample

attenuates the amplitude ~ single atom/layered samples…

– Lattice imaging: one/more Bragg waves • Direct interpretable: 10 nm • Thick samples: dynamical effect –

simulation

– BF/DF: ~ 1nm resolution • Energy loss by inelastic scattering +

chromatic aberrations ~ 100 -300 nm (100kV)

• Specimen mounting – Grids of 3mm diameter:

• http://www.agarscientific.com/ • http://www.2spi.com/catalog/grids/

• Specimen Manipulation – Goniometer: single/double tilt holder – In-situ holders

http://www.agarscientific.com/http://www.2spi.com/catalog/grids/

Imaging System – Objective Lens • Magnification: MT ~ 20-50 times • Highest performance demanded

- The aperture (convergence angle)

T

oo

MM

• Change o: ‘Objective aperture’ • Diaphragm: heat-resistant materials, Pt… • Large current density: 105 A/m2

• Contaminated: additional astigmatism •Small o: increase diffraction contrast

- Astigmatism

• Ensures rays travel at small angles to the optical axis in all subsequent lense.

– Cs (3) /Cc are important only for OL – Projection lens: distortion not impair the sharpness

Image formation – Abbe’s Theory

Plane wave: rki exp0

rkirirar seexpexp~ 0 Exit wave:

u

q

r

A B

f dSrqirqF

S

e

exp

r: radius vector in the specimen plane

q: radius vector in the diffraction plane

Fourier transform

rM

qdrqiqFM

r sS

m

1exp

1 2

Inverse Fourier transform

qdrqiqHqFM

rS

m

2exp1

Pupil function: aberration/aperture/defocus

Basic Modes • Lenses: Fixed

position

• Imaging and diffraction mode

• BF/DF

• HRTEM

Fixed OL, BFP/IMG they are object plane

for DL

Fixed PL image plane

Using DL: More than one ways to achieve the same Mag –

minimize overall aberration

Basic Modes: BF and DF

Imaging: Depth of Field/Focus

• Depth of Field: object remains in focus

• Depth of Focus: image remains in focus

• Sample in Focus from the top to the bottom

• Cs- allows use of large apertures: reduce Depth of Field/Focus

A blurring of the image

A blurring of the image

SMs

o

ss MMS

2

M=10k, o=10mrad, s=5 nm S > 50 cm

Focused image on viewing screen and CCD

Depth of Image

Depth of focus

A resolution sM = 50 um (recording)

M=10k, o= 1 mrad, T = 5 um

Difficult to focus… use large aperture

Calibration and Alignment

• A well-calibrated system: – Magnification – Camera length

• An aligned system: – Imaged centred for

• different magnifications • Focus conditions

– Uniform and centred illumination for a range of illumination conditions

– Proper illumination maintained when switching between modes

Startup and Alignment

• Startup (AML training) – Load the sample in the sample holder – Clean the sample holder… if it can be cleaned – Insert the holder into the column: vacuum! – Turn on the beam

• Gun alignment: gun tilt – maximum brightness • Condenser aperture: C2

– High current: large aperture – High coherence: small aperture

• Illumination stage: C1 & C2, spot size, beam shift, gun shift

• Condenser astigmatism: C2: circular – in focus • Eucentricity:

– primary tilt axis – holder axis (height of the sample) – Smallest Cs for OL

• Current centre: OL • Diffraction centring: DF mode • OL astigmatism

Summary

• Physics of TEM Elements

– Sources

– Lens

• Optics of the system

– Illumination

– Image formation

• Basic modes

• Simple operational notes

Lecture 3

• Sample-specimen interaction

– Elastic scattering

• Kinematic Diffraction Theory

SUPPLEMENTARY

Electron Guns: Thermionic guns

• Thermionic guns – LaB6 – Rhenium heating – Triode:

• Cathod (-100kV) • Wehnelt cylinder (small negative bias < 2kV):

form crossover • Anode (earthed)

– Emission current vs. beam current – Operate at/just below the saturation

condition (no structure is visible within the source image) that would result in

• Longer Gun life • Optimised Brightness (Self-biasing)

– if low → Vw low → d0 large; if high → Vw high → ie low

– CTEM: no need to optimize – Increase current: decreasing Vw (gun emission

control)

– Gun alignment – optical axis • Symmetrical image (instauration image)

Electron Guns: Field Emission Guns

• FEGs – W – Two anodes (electrostatic lens)

• 1st Anode: positively charged ~ kV (respect to the tip – extraction voltage) increase it slowly – thermal-mechanical shock

• 2nd Anode (accelerate the beam to 100keV)

– A magnetic lens: controllable beam and

– Contamination • Vacuum 10-9Pa • Flashing the tip (reversing the

potential)

Geometrical Optics

• Perfect image and real image

– Finite sizes of an optical device: diffraction-limited

• Geometrical optics: rectilinear propagation

– Homogeneous media

– 0: neglect diffraction effects

– Manipulation of wavefronts (rays)

Huygens’ Principle Secondary spherical wave – dS of a wavefront:

2

cos1,

exp

A

R

ikRdS

i

Ad

Any point P in front of the secondary waves interference – sum the amplitude

dS

R

ikR

i

Ad

SS

P exp

cos2 02

0

22 RrrRrrR dRrrRdR sin22 0

rdrdS sin2RdR

Rr

rdS

0

2

max

0

expexp2

0

R

R

Q

P RdikRARri

ikrA

r

ikrAQ

exp

The amplitude-phase diagram: adding dR with increasing phase: kR

The first Fresnel-zone: R-R0 = /2

Radius of the circle decrease: A()

Form ‘Circle’:

The ‘Circle’ converges to the centre:

Half of the first Fresnel-Zone: 0

2/

exp1

exp2

1exp

0

0

max

0

ikRik

RdikRRdikRAR

R

R

R

0

0exp

Rr

RrikAQP

Fresnel Diffraction at the edge

2

0

22

0

2/1222

02

1r

yxryxrrParaxial rays:

000

002

00

002

00

00

2exp

2exp

exp

x

Q

P dxdyRr

Rriky

Rr

Rrikx

Rri

RrikA

)()()()(

2

1exp

0

00

00viSvCuiSuC

Rri

RrikAu

Q

P

00

002

Rr

Rrxu

00

002

Rr

Rryv

Intensity distribution of Fresnel pattern

Reimer, TEM, 5th, Springer

Reimer, TEM, 5th, Springer