Optical Microscope
MSE 421/521 Structural Characterization
Plan Lenses
In an "ideal" single-element lens system all planar wave fronts are focused to a
point at distance f from the lens; therefore:
• Image near the optical axis will be in perfect focus on a flat image sensor/screen.
• Non-axial rays will come into focus before the image sensor.
• This problem is reduced when the imaging surface is curved, as in the eye.
φ
Most current photographic lenses are
designed to minimize field curvature
(plan lenses), and so effectively have a
focal length that increases with ray angle.
f = f0/cosφ
MSE 421/521 Structural Characterization
Achromatic Lenses
f (focal length) = f(µ)
µblue > µred
(dispersion)
Chromatic aberration means that a lens will not focus different colors in exactly the same
place because the focal length depends on refraction and the index of refraction for blue
light (short λ) is larger than that of red light (long λ).
The amount of chromatic aberration depends on the dispersion of the glass.
MSE 421/521 Structural Characterization
Image Formation
Three ways to form an image:
Projection (shadow)
Optical (with lenses)
Scanning
}
all parts of image simultaneously
Three requirements for image formation:
Brightness
Contrast
Resolution
MSE 421/521 Structural Characterization
Electrons vs Light
Electron “Optics”
Visible
Spectrum
hν
e-
4000 nm ≤ λ ≤ 7000 Å
Wavelength of a photon is inversely proportional to its energy, λ = ch/E
100 Å ≤ λ ≤ 2000 Å
X-Rays
Wavelength of an electron is dependent on its energy (accelerating voltage)
Electrons
JEOL 2100-HR TEM:
λ = 0.0251 Å (200 kV)
Hitachi 4500 SEM:
λ = 0.0859 Å (20 kV)
}
5 orders of magnitude
smaller than for visible light!
Electrons are much more strongly scattered by matter
(EM operates in vacuum)
Lenses are magnetic fields (n = 1)
rd =
Electrons carry a charge
0.61λ
α
MSE 421/521 Structural Characterization
Electrons vs Light
Electron “Optics”
hν
e-
Compared to optical microscopy, electron microscopy offers the following advantges:
Higher resolution
Higher magnification
Greater depth of field
Crystallographic information
Chemical analysis
MSE 421/521 Structural Characterization
Electron Generation
β-
The illumination system in an EM consists of a source of electrons (electron gun)
and a lens system to focus and control emitted electrons.
Electron guns overcome the work function of the electrons by either
resistive heating or a strong electric field (or both).
Thermionic Emission:
A heated wire or crystal is given enough thermal energy to overcome work function (Edison Effect)
plus an electric potential (0.5 – 300 kV) to accelerate the electrons.
Tungsten (hairpin)
W has very high Tm (3422°C) so can have more thermal energy
But work function still high (φ = 4.5 eV) even at operating T ≈ 2500°C
Cheap ($30)
Hitachi S-3400N SEM, LEO 1430 VP SEM
LaB6/CeB6
Lower work function (φ = 2.5 eV) than W at operating T ≈ 1500°C,
so it is easier to pull electrons off and can have beams 30 times
brighter than with W hairpin.
Require high vacuum, suffer from thermal shock, and are expensive ($1000).
Higher T causes increased volatilisation and premature failure.
Tm (LaB6) = 2530°C, Tm (CeB6) = 2540°C.
JEOL 2100 HR TEM
MSE 421/521 Structural Characterization
Electron Generation
Field Effect Emission:
The field effect gun (FEG) uses a W single crystal and high field (> 109 V/m), which lowers the height of
the potential barrier via the Schottky effect. In addition, if the field is sufficiently high, the width of
the potential barrier becomes small enough to allow electrons to escape via tunnelling (field emission).
Field reduces the work function by ∆φ = 3.8x10-5F ½ eV
Cold FEG
operates at room temperature, but requires flashing
Thermally-Assisted FEG (Schottky emitter)
pointed W crystal (coated with ZrO2) is welded to V-shaped W filament and heated to 1500°C
ZrO2 lowers work function (φ = 2.8 eV)
improved stability and no flashing
enhanced emission by giving some thermal energy, which reduces tunneling distance
(really a field-assisted thermionic source)
MSE 421/521 Structural Characterization
Thermionic Emission
Current density at filament surface:
j = AT 2e-φ/kT [A/m2]
A = 1.20173x106 [A/m2/K2] (Richardson’s constant)
T = absolute temperature [K]
increases rapidly as T increases & φ decreases (so use high-Tm low-φ material W)
Brightness: B = j/(πα2) (j = beam current density, α = convergence semi-angle)
(at cross-over: Langmuir equation):
B = (jV)/(πkT)
[A/m2/sr]
V = voltage [V]
k = 8.617x10-5 eV/K
Example:
For W (φ = 4.5 eV) operating at T = 2500 K and V = 100 kV:
j = (1.20173x106 A/m2K2)(2500 K)2exp(-4.5 eV/[(8.617x10-5 eV/K)(2500 K)] = 6364 A/m2
B = (6364 A/m2)(100000 eV)/[(π sr)(8.617x10-5 eV/K)(2500 K)] = 9.4035x108 A/m2/sr
~9x104 A/cm2/sr
MSE 421/521 Structural Characterization
Field Effect Emission
Current density = j = 6.2x10-10
Temperature-independent
-2
(Ef /φ)½F 2 exp-6.8x109φ3/2 Acm
Ef + φ
F
Ef ≈ 5 eV for W at R.T.
For a field F >
5x109
V/m, field emission exceeds thermionic emission.
To apply such a high field, W has to be prepared as a sharp point of diameter ≈100 nm, which makes it
very delicate; therefore, ultra-high vacuum systems (10-8 – 10-9 torr) are necessary – adds cost
(JEOL 2100 LaB6 TEM operates at ≈10-7 torr).
Low energy spread (δE ≈ 0.3 eV) for improved resolution and better interpretation of EELS data
More coherence
Highly sensitive to contamination - cold FEG must be flashed every few hours
MSE 421/521 Structural Characterization
Electron Generation
A comparison of electron emission characteristics of
W, LaB6, CeB6 and FEG guns
W wire
LaB6
<100>
CeB6
<100>
2500
1500
4.5
2.7
3
Brightness (A cm-2 sr-1)
Crossover diameter (mm)
Short-term beam current
stability (%RMS/hr)
<1
<1
<1
3-5
<1
Energy spread at 100 kV (eV)
2
1.5
1.5
0.2 - 0.4
0.5
Typical service life (hr)
30-100
1000
1,500
103 – 104
10,000
Operating vacuum (torr)
10-5
10-7
10-7
10-10
10-9
Evaporation rate (g cm-2s-1)
NA
2.2 x 10-9
1.6 x 10-9
NA
NA
Operating temperature (°C)
Work function (eV)
Emission current density (A/cm2)
Brightness
increases
linearly with
voltage.
FEG
(cold)
FEG
(Schottky)
1500
27
1500
~2.5
4.5
2.8
30
30
17,000
5,300
104
105
105
2x107
107
30
10
10
0.01
0.02
Resolution determined largely by diameter of beam and δE
Thermionic guns have large areas of emission – beam is demagnified x10-4 – very stable and insensitive to contamination
Cold FEG has small area of emission – beam is reduced just 5-10x to 1 nm – unstable and very sensitive to contamination,
but nearly coherent
MSE 421/521 Structural Characterization
Triode Electron Gun
cathode
(heating)
(gun bias)
Wehnelt kept at slightly more –V
(repels electrons)
filament kept at large -V
>1 mm hole in Wehnelt
directly below filament
gap between filament and Wehnelt cap
is critical to electron focusing and
filament lifetime
anode and rest of column are earthed
The triode produces a beam of electrons which comes to focus (cross-over) just below the Wehnelt cap
with a diameter of d0 ≈ 30 µm for W and ≈ 10 µm for LaB6 or CeB6.
MSE 421/521 Structural Characterization