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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
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