§
… thermionic cathode (most common method) … From the late of 1930s until now.
… what requirement do we have?
high brightness, high current efficient = brightness/ total beam current, small source,
long life under available vacuum, stable emission.
(1) Thermionic emission of electrons thermionic emission: At high temp., a large number of electrons with sufficient energy to escape from the walls of the metal.
The electron emission current density

is (Modified Richardson Eq.)
   2 exp(

 w
) k

…………… (1)
where I = emission current density in Amp/cm
2
A = constant (dep. on material)
 w = work function, in eV (electron voltage) k = Boltzmann’s constant = 8.62

10

5 eV/K
T in K
Metal
 w (eV) A (Amp/10
-4 cm
2
K
2
) Melting Temp. (K)
Fe
Ni
Ta
W
LaB
6
4.48
4.61
4.19
4.50
2.66
0.26

10
6
0.31

10
6
0.55

10
6
0.60

10
6
0.29

10
6
1808
1726
3269
3650
2800
→ Choice of emitter materials for EM:
pure W …  the vaccuum near the emitter is poor, (

10

4 ~ 10

3 mbar), W has good oxidation resistance. (1mbar = 0.75torr)
 high A and high melting point & heating temp. = 2600~ 2900K. … Fig.1
… hair-pin filament and point filament
1

LaB
6
(Lanthanum hexaboride) … low value of
 w → to get higher brightness at
T = 1600K, but need high vacuum condition. (

10

6 mbar)
(2) The electron gun
→ Diode gun (2-electrode gun) … consisting a cathode (electron emitter) and a anode (a positively charged plate with a hole).
Relationship between (emission) current and (anode) voltage in a diode:
Saturated emission: because some of the electrons are repelled and returned back into the emitter by the negative charge on the cloud of electrons already in the space between the emitter and the anode.
When
 
saturation
 
V
3
2 … space charge eq. ………… (2)
When
 
saturation
 
V and is temperature dependent …… (3)
In eq.(2), the proportional constant contain a factor
1 / d
2
, where d = the anode-cathode separation,
 d

,
 
.
T
1
, T
2
and T
3
are emitter temperatures.
disadvantage: if d and V fixed, the I can only be varied by altering the filament temp., and the constancy of the beam current dept. on the stability of the filament heating current.

not used in EM
→ Triode gun (3-electrode gun) … used in EM
allowed the I to be varied indept. of filament temp. and anode voltage. The 3 rd
electrode or
Wehnelt grid (or Wehnelt cylinder) is introduced between cathode and anode. The Wehnelt grid is held at a negative potential relative to the filament.
Fig.2 … (a) Configuration of self-biased electron gun (also ref. to Fig.2.2 of Chen’s book).
(b) Schematic diagram.
˙ The effect of the grid is to deflect the electron emitted by a filament into a small cross-over or virtual electron source.
˙ Biased resistor (0~500V): can stabilized the emission current against fluctuations in filament temperature.
Fig.2 … (c) Characteristic behaviour of triode electron gun.
˙ At point 3, beam current saturation, at which the virtual source has the smallest diameter.
2

˙ Heating the filament beyond point 3 shortens its life (  it increases the rate of evaporation) without resulting in any increases in i b
(beam current).
˙
For i b
at saturation (at point 3) and under the same h distance, if more i b
is necessary after saturation, the voltage of the bias resistor should be reduced.
˙ The bias voltage can change the electrostatic potential around the cathode.
˙ In Fig.2(c), at point 2, filament shadow can be observed which can be used to check the filament is aligned with illumination axis or not.
→ Brightness of an (triode) electron gun. d
0
: the cross-over diameter. The intensity distribution of electron at cross-over is usually taken to be Gaussian.
˙ The current density of the electron beam at cross-over J b
(in Amp/cm
2
) is
J b

4 i b
/
 d
0
2 ………………… (4)
where i b
= the total emission current measured from the filament.
˙ The electron beam brightness

is
 
4 i b
/(
 d
0

0
)
2 
J b
/

0
2
………………… (5)
i.e.,

is the current density per unit solid angle. (

in Amp/ cm 2 ster)
˙ The theoretical maximum value for the brightness

is
 m a x
  e

0
/
 k
 ………………… (6) … by Langmuir in 1937
where

is from eq.(1),

0
is the accelerating voltage, k = Boltzmann’s constant.
˙ From eqs.(4) and (5)
J b
 
0
2 ………………… (7)

J b
) max
  max

0
2   e

0

0
2
/ k
 ………………… (8)
where J b
) max
is the max. current density at the cross-over.
˙ Brightness and bias voltage
→ At low bias, since little or no focusing takes place.
 d
0
is large and

obtained is not optimum.
3

→ At high bias, most of the emitted electrons will return to the filament,
 
will
decrease.
→ Fig.3 … relationship between the brightness and bias voltage. There is an optimum bias setting for max. brightness. Two kinds of adjustment: adjust the bias voltage, adjust the h (height) distance.
˙ LaB
6
Rod Cathode: (since 1967)
Fig.4 … LaB
6
tip temp.

1700 ~ 2100 K, tip radius is about 10 μ m.
advantage disadvantage
－ useful brightness can be achieved at lower temp. (   w lower than W)
－ good vacuum required (

10

6 mbar)
－ cannot be directly heated as in W filament
(

10 times than W’s brightness)
－ junk on surface will increase
 w
－ longer life (

500hrs)
－ less sturdy
－ electron current coming from a smaller area than the W hairpin
－ more expensive
˙ Field emission gun (since 1968)
Fig.5 … Field emitting tip is made from W with tip diameter

100nm
Fig.6 … Schematic diagram of electrode arrangement in the field emission gun.
→ V / V
0
determine the position of the focus (cross-over)of the electron probe.
→ sharp pointed filament get strong electric field at the tip. (

10
9
~ 10
10
V /cm )
→ usually use W as the material,  high mechanical stress on the tip,

need strong material to prevent failure of the tip.
→ Need clean surface,

high vacuum required ( torr

1.333mbar)

10

8
~ 10

9 torr, 1
˙ Summary of filament properties:
Tip radius

(A/cm
2 sr)
Current density
(relative)
Vacuum (torr)
Point filament W
Hairpin W
LaB
6
Field emission
1~ 10
30
1~10
μ
μ
μ m m m
50 nm
2

10
6
5

10
5
7

10
6
10
7
~ 10
8
4
1
14
20

10

5

10

5

10

6

10

8
~ 10

9
4

§
Schematical diagram is shown in Fig.7
The essential components are: (1) Electron gun, (2) Condenser lens, (3) Beam alignment stage, (4)
Specimen stage, (5) objective lens, (6) Intermediate (1 st
projector) lens, (7) Second projector lens,
(8) Viewing chamber and fluorescent screen.
(1) Electron gun
… Consists of a filament and electrostatic lens.
… Cross-over (virtual source) is about 50 ~ 100 μ m.
… Accelerating voltage: typically 40 ~ 400KV by 20KV steps.
… The total current emitted by the electron gun is

100 μ A or more, but only a fraction of this reaches the final image. (the remainder being absorbed by diaphragms)
(2) Condenser lens
( i ) Function: can vary the strength of illumination in the specimen plane to suit the type of specimen and the magnification of the final stage.
For example: enlargement from

500 be varied by a factor of
to

250

10
3
, the illumination at the specimen must
( 500 )
2 
2 .
5

10
5
.
Fig.8 … show how to change the intensity on the specimen.
˙ focused on the specimen plane … max. intensity
˙ underfocused or overfocused on the specimen plane can get lower intensity.
( ii ) Single condenser lens and double condenser lens
… Fig.9: (a) single lens, (b) double lens with C1 strongly excited, (c) double lens with C1 weakly excited.
˙ single condenser lens (Fig.9(a)) … the focusing image of cross-over

the size of cross-over, i.e. 50 ~ 100 μ m, which is >> the diameter of the field actually appearing on a micrograph, e.g., for

10
5
, will only be about 1 μ m appear.
˙ double condenser lens … C1 is the additional lens, can strongly excited and from a diminished image of the cross-over (e.g., for Elmiskop I type. A max. factor of about 100), which is then projected on the specimen by C2 (C2 has a magnification of about 2).
… Fig.9(b)
˙ by adjusting the strength of C1, the spot size on the specimen can be varied.
… Fig.9(b) and (c)
( iii ) Determination the current density obtained at the specimen
˙ From eq.(5)
 
J b
/

0
2
. It has shown that

is constant at any point in an optical system.
(ref. R.S. Longhurst, “Geometrical and Physical Optics”, p.374, London, Longmans, Green and Co.)
If we let J b
)
0
: current density

0
)
0
: divergence of the beam
J b
) : current density

0
) s
: divergence of the beam
}
} at the specimen at the crossover (beam source)
5

then from eq.(5), one can get
J b

0
)
0
)
0
2

( J b
(

0
) s
) s
2
………………… (9)
The right term of eq.(9) is just determined by the parameter of electron gun.

It is a constant for both single and double condenser operation.

J b
)
0
= constant

(

0
)
0
2 ………………… (10)
i.e., the current density J b
)
0
is determined simple by the divergence of the beam at the specimen, which will be determined by the geometry of the system (e.g., condenser aperture) and the excitations of C1 and C2. (e.g., Fig.10)
˙ Let D = aperture diameter of C2 l = distance between C2 and specimen.
}
Fig.9(b) then

0
)
0

D
………………… (11) l
For example: as shown in Figs.9(a) and (b), (b) and (c), both have the same

0
)
0
.

They also have the same J b
)
0
, i.e., double condenser lens does not increase the intensity in the illuminated area, it simple reduced the size of the illuminated area.
˙ When C2 is underfocused or overfocused (see Fig.8), the divergence

0
)
0
decreases as shown in Fig.10.
where I = beam current in C2
I
0
= beam current in C2 for just focus
Fig.10

under-focused or over-focused, both of them will decrease

0
)
0

J b
)
0
also decrease, in which the J b
)
0
of double condenser decreases more rapidly than that of single condenser.
(3) Beam alignment stage
… for best performance, the illumination axis coincides with the axes of the objective lens and the following lenses.
… Misalignment: lateral displacement between two parallel axes. … corrected by translating. angular difference between two axes. … corrected by tilting into parallelism and the translating.
… Fig.11 shows the principle of electromagnetic beam tilt and shift stages.
(4) Specimen stage
… use circular metallic grid ψ =3mm to support the specimen or just use the thin foil with
ψ = 3mm as the specimen.
6

… specimen must be positioned at right angle to the optical axis, near the focus of the objective
lens.
… movable in x and y direction (
 
1mm)
… top entry type
side entry type
}
Fig.12
… Goniometer stages are available with top or side entry, can tilt up to 60 ° , rotate up to 360 ° and indep. tilt about two axes at right angle.
… Eucentric Goniometer stage … the field of view and image focus remain unchanged when the specimen plane is tilted and rotated.
… Stages for allowing specimens to be heated (hot stage), cooled (cold stage), stretched (tensile stage), compressed etc. under observation. … should be mechanical and thermally very stable.
(5) Objective lens
… the most important lens in the column. … also called as focusing lens. (  objective lens
距離
試片最近，故其對試片之 image 負有第一次放大之責，對於最後 image 之品質的影響也
最大。)
… focal length = 1~ 5mm, the shorter the focal length, the smaller the aberrations and the better the resolving power.
… objective aperture (O.A.) － In or near to the back focal plane of the objective lens. A metal disc with a central circular hole centered on the lens axis. … Fig.13 …
可阻擋從試片 scattering
出來所不要之電子，如此可以減少
C.A.
及 spherical aberration
。
… the diameter d of O.A.
2
  d f
where f = the focal length of the lens
e.g. f = 4.0mm,
 opt

5

10

3 rad.
 d = 40 μ m …… for the best resolution but for most practical specimens, the d is closen for its effect on image contrast rather than its effect of image resolution.
… bright field image and dark field image.
} more discussed in (10) of this section
… selected area aperture
… stigmator or astigmatism corrector is fitted between the O.A. and the next lens in the column.
7

(6) Intermediate or 1 st projector lens (P1) …
又稱放大鏡
(Magnifying lens).
主要功能有二 決定放大倍率， 選擇以繞射點
(
繞射圖形
)
或顯微影像
(image)
在螢光幕上
顯現。
… 陳力俊書圖
2-16.
… In a 3-lens column (e.g. Fig.14), the intermediate lens generally operates over a wider range of focal lengths than the other lens may play either a reducing or a magnifying role.
… In a 4-lens column (e.g. Fig.17), an additional weak lens, called the diffraction lens, is fitted between the objective and the intermediate lens. This enable

50

10
4
upward to be achieved more
conveniently, and introduces greater flexibility into the magnification range as a whole.
(7) 2 nd
Projector lens (P2)
: 主要功能為對影像作最後的放大工作，將影像投影於下方之螢光幕。
… The lowest values of magnification are obtained by altering the strengths of one or both projector lens. … Fig.14
… to balance the distorsions, the two lens (P1 and P2) against each other and obtain distorsion-free images at all magnifications.
… “zoom focusing” … In EM, all lens currents, including the objective lens are pre-programmed into a microprocessor so that the image is made to remain essentially in focus throught the entire magnification range.
(8) Viewing chamber and fluorescent screen and photographic recording camera … Fig.15
(9) Wobbler focusing aid … Fig.16
… This device deflects the illuminating beam alternately between two tilted positions on opposite sides of the optical axis at a frequency of 10 or 20 cycles each second.
(10) The image and diffraction pattern in TEM
… For 4-lens column: … Fig.17
The image … the 1 st
image is imaged by the diffraction lens. (i.e., the diff. lens focused on the 1 st
image plane)
… For 3-lens column: … Fig.18
The image … the 1 st
project lens (P1) focused on the 1 st
image plane .
The diff. pattern … the P1 focused on the back focal plane.
… objective aperture (O.A.) … in or near the back focal plane of the objective lens to ensure that only one beam contributes to the formation of the electron image.
若此 “one beam” 是
8

“ 直射電子束 ” (transmitted beam) ，則為
bright field image (B.F)
；若此 “one beam” 是 “ 繞射電子束 ”
(diffracted beam)
， 則為 dark field image (D.F.)
。
… Selected area aperture (S.A.) … an aperture is inserted at the 1 st
image plane of the objective lens so that the area of the specimen which is giving rise to the diffraction pattern (D.P.) is defined.

SADP (selected area diffraction pattern)
… ref. to Fig.2-16 of Chen’s book.
… Bright field image and dark field image.
… Fig.19 (a) bright field image
(b) centred or axis dark field image
(c) off-axis dark field image … poor resolution.
… ref. to Figs.2-18 and 2-19 of Chen’s book.
§
Fig.20 … the essential parts of the SEM column
(1) Electron gun
… conventional triode gun, usually with W filament, or field emission gun as in the TEM.
… 1~ 30KV with current of up to 250 μ A. The effect of voltage on the resolution: An example was supplied with one particular SEM: gun voltage (KV) resolving power (nm)
1
140
3
70
10
30
30
20
(2) Double condenser lens system
… to obtain the demagnified image of the “crossover” of the electron source. (Two C1 can demagnify the crossover to 10
-4
. In TEM, one is C1, the other is C2, but in SEM, two C1 are used.)
… similar to those already described in TEM, can be likened to a double C1 system.
(3) Final or 3 rd condenser lens (sometimes called the objective lens)
… Functioning similarly to the C2 of the TEM.
… Fig.21 (a) C1, C2 are only weakly excited, the final probe has a large diameter and the current in it is also high.
(b) C1, C2 are strongly excited, only small spot on the specimen, but it can be seen that only a small proportion of the available electrons actually end up on the specimen.

the resolving power is better in (b), but the signal-to-noise ratio is lower in (b).
… The size of diaphragm (at C3) and the working distance together determine the depth of focus of the probe beam.
˙ Fig.22 … let D = depth of focus (e.g., the probe diameter reaches twice the minimum spot size)
9

(a) and (b): D

by

the diameter of aperture.
(b) and (c): D

by

the working distance.
˙ the depth of focus of the C3 is in fact the depth of field of SEM.
… C3 also contains the deflection system responsible for the scanning action of the electron probe.
Fig.23 … scanning coil are supplied with current from the scan generator.
Scan generator: is an ascillator which provides separate frequencies for the line scan (X deflection) and the frame scan (Y deflection).
(4) Electron collection system:
Fig.24 … photon and charged particle emission phenomena which take place at an electron-bombarded surface.
… The 2 nd
electron detector is the most common in all SEM system.
… 2 nd
electron detector or ET detector … based on the design of Everhart and Thornley in 1960.
Fig.25 … ET detector
… backscattered electron collector
(5) Specimen chamber and stage … Fig.26
… This chamber accommodates the specimen holder and mechanisms for manipulating it, detectors for various emissions.
… specimen stage is able to move in x, y, z direction. The specimen can be tilted and rotated.
… Eucentric goniometer stage … once the specimen level has been adjusted to the eucentic point, all successive tilts and rotations take place about the centre of the field of view.
§
Transmission microscopy on a dedicated SEM … by fitting a transmission stage and detector to
SEM. (at least 30KV is required )
Scanning microscopy on a dedicated TEM or analytical TEM … the most common usage of
STEM
˙ Scanning microscopy on a dedicated TEM or analytical TEM
… using the scanning attachment to a dedicated TEM, which enables a finely focused illuminating probe to be scanned across the specimen.
… fitted detectors, such as 2 nd electron, backscattered electron, transmitted electron and X-ray etc.
… for forming a suitable small focused probe, STEM needs C3, in addition to C2 and C1, to get the probe with 15


diameter can be formed from the electron gun.
Fig. 27 … (a) Riecke-Ruska condenser-objective lens (1966).
(with prefield of objective lens as the C3)
10

(b) Double-deflection scanning of the beam.
Fig.28 … Multi-mode possibilities of the analytical TEM.
having: BS detector
EDS X-ray detector
2 nd
electron detector … compared to SEM, STEM is formed mainly by true 2 nd
electron, with very little BS electron.
 
get a strictly surface image, without the depth contribution provided by the higher energy electron.
Transmitted electron detectors
specimen-current imaging
Fig.29 … STEM
11