1. Chapter 9 “The instrument”
This chapter focuses on the operating mechanisms of TEM lenses, and the procedures to optimize the quality of TEM diffraction patterns and images.

2. TEM components: the “column”
Illumination system
2.   Objective lens & Stage
3.   Imaging system
Transmission Electron Microscopes are generally composed of three parts, which are vertically organized: (from the top) an illumination system, objective lens and sample stage, and finally a system of various lens defined imaging system. All together the instruments looks like a pillar, and for this reason, it is often called “column”.

3. TEM components: the “column”
Illumination system
Objective lens & Stage
Imaging
system
Intermediate, diffraction, projector lenses & detector/CCD/TV
Objective lens & Specimen holder
Parts
Gun & Condenser lenses
As the term “system” implies,  both the first and the third components are composed of sub-parts. The former includes the emission gun and the condenser lenses, while the latter intermediate, diffraction and projection lenses, but also displays to visualize the images or the diffraction patterns.
Each component performs specific tasks. The illumination system is the source of the accelerated electron beam, which is then kept under control by the condenser lenses. The objective lenses permit to regulate the quality of the results, while intermediate and diffraction lenses allow to switch from an image to a diffraction more. And finally, the projector lenses regulate image or DP magnification and focus, but also their visualization on the proper display.
Creation of images or DPs, then magnified and recorded
Magnification, focus and visualization of images and DPs
Emission of the electrons from the cathode towards the specimen
Functions

4. Illumination system Thermionic Electron Gun (TEG)
Parallel electron beam
Electron Gun
Specimen
The path of the electrons begins with their emission from the cathode of the electron gun, but different cathodes are available. Electron guns are generally classified in thermionic and field electron guns, respectively TEG and FEG. TEGs require high temperatures (and high kinetics energy) to overcome the surface energy barrier of the cathode, while FEGs utilize very high voltage field maintaining lower temperatures than the previous category. However, once the electrons are emitted, they follow their path towards the specimen, which can be illuminated with a parallel or a convergent beam.
To explain
In the reality, both these conditions are not absolute: the parallel electron beam is only approximately parallel, while the convergent one may be divergent as well. Convergence angles (α) are small.
Convergent electron beam
Field Electron Gun (FEG)

5. Illumination system Parallel electron beam Broad beam Focused beam
The best classical image contrast.
The sharpest selected-area DPs.
Parallel electron beam
Why?
Out-of-focus condition
Broad beam
Focused beam
C2 focused
Image of the crossover at the FFP of the upper objective lens (C3)
Over-focus
Under-focus
Stronger C2
WeakerC2
Parallel electron beam permits to obtain the best classical image contrast and the sharpest selected-area diffraction patterns.
Considering a simplified scheme with only two condenser lenses, parallel condition can be obtained acting on C2 lens, because C1 is kept at some intermediate setting. For both broad and focused beams, C1 lens provides an image of the gun crossover. However, in the first case, it is recommended to weaken and under-focus the C2 until the illuminated area on the specimen fills the viewing screen. On the other hand, in the second case, C2 is focus in order to obtain an image of the crossover at the front-focal pane (FFP) of the upper polepiece of a c/o (condenser-objective) lens.
C2 aperture allow to regulate the electron current that reaches the specimen. Small apertures decrease the convergence angle, and consequently promote parallel electron beams.
Although parallel electron beams favor high contrast images, sometimes they have to be sacrificed to favor higher magnifications. The latter are obtained strengthening C2, reducing the convergence angle, and illuminating less the specimen.
C3 controls the beam hitting the specimen
More parallel beam!

6. Illumination system Convergent electron beam Basic mode
Why?
Higher focus of the beam due to higher beam intensity.
Image through scanned beam & low contrast
Basic mode
Probe/Spot mode
Creation of a focused convergent beam at the specimen
Probe size << 1 nm
FEGs use C1 and C2
TEGs need to demagnify the gun crossover using C3 or c/o lens
Another kind of compromise is that between illuminated area and focus. To obtain higher focuses, it is necessary to use an intensified convergent electron beam, which also minimize the area under investigation.
Two are the ways to obtain a convergent electron beam.
The basic mode changes C2 until the image of the C1 crossover in formed at the specimen. This process lists both pros and cons. Because the source image is immediately visible, it is possible to regulate both the dimension of the beam and the image saturation. Moreover, C2 focusing can be an useful mean to compensate low transmissions due to too thick samples. However, image contrast is low, and sharped selected-area diffraction patterns are not feasible.
The second strategy to produce a convergent electron beam is called probe/spot or convergent-beam mode, and it is based on a convergent beam (or probe) whose size is below 1 nm. This dimension is easier to obtain with field electron guns rather than with thermionics, because the latter require a demagnification of the beam. For this reason, FEGs utilize only C1 and C2, while TEGs require also C3 or c/o lens. As visible in the scheme, the demagnification process is function of the C3 distance (di) and the object distance (do). When C1 is strong, C2 is weak or not in use, and C3 or c/o is strong, di is lengthened, do is shortened, and the demagnification is increased.
TEM Probe/spot mode can be improved by the addition of more lenses; however, unlike the basic mode, it does not provide an immediate visualization. The image is visible only after the scanning of the beam.
Visible source image
C2 focusing can compensate thick specimens
Low image contrast
No SADP
C1 strong
C2 weak/off
C3 or c/o strong

7. Illumination system Condenser-Objective Lens min C2 strength max
Parallel
Convergent
Divergent
Parallel
High magnetic field of the objective lens.
Dual function:
Convergence of the beam on the specimen(as C3)
Focusing
BUT almost never parallel beam
As already mentioned, condenser-objective lenses are an useful combination of an objective lens and a condenser mini-lens (twin-lens). The first converge and focus the beam on the specimen, but it does not easily allow a parallel beam. Thus, in order to fulfill also this condition, the condenser mini-lens is added to the system, and this produces a parallel beam when c/o lens is over-focus.
In presence of a c/o lens, C2 strengthening has several interconnected consequences:
- the focus of the beam at the specimen varies;
C2 crossover moves up (red circles);
C3 can add its own crossover (violet circles).
Thus, it is possible to pass from a one-crossover parallel electron beam to a convergent, a divergent and a two-crossovers parallel one.
C/o lenses are also characterized by a specific excitation that allows simultaneous focus and visualization. However, out of this condition, the beam convergence is low, and the electron beam generates only a halo.
Addition of a condenser mini-lens (twin-lens)

8. Illumination system C2 aperture alignment From distorted images to
constant circular beam images which expand/contract about the optic axis
C2 aperture alignment
Translations and tilts
WOBBLING:
Focus-Defocus C2 aperture (repeated)
To avoid distorted images, the illumination system has to be properly aligned. This means that the gun crossover has to be on the optic axis to let the electron travel down the column in a straight line.
Different TEMs have specific alignment procedures. However, these are usually based on translations and tilts. The former move the beam to a different area of the specimen, while the latter illuminate the same area altering the angle of coincidence. Both these operations allow to align the illumination system by centering the C2 aperture. However, they could also be useful for other operations, such as the investigation of specific specimen features.
C2 aperture is aligned interchanging its focus and defocus states for several times (wobbling) till the image of the beam remains circular and expands/contracts about the optic axis (see image on the right). To facilitate the process, it is recommended to start at a low magnification. The desired magnification range is progressively reached during the focus-defocus iteration.

9. Illumination system Condenser – Lens Defects Spherical Aberration
Chromatic Aberration
Astigmatism
Increased refraction of the beam
Not all colors converge to the same point
Deflection of the beam due to misaligned C2 aperture, contamination or charge
Problem for convergent electron beam
Like all lenses, also condenser lenses might incur in defects. Among these there are spherical and chromatic aberration and astigmatisms.
Spherical aberration is defect given by an increased refraction of the beam. It does not affect parallel beam formation, but it interferes negatively with convergent one. In particular, finest probes are not possible when spherical aberration affects C3. This defect can be partially corrected optimizing C2 aperture, but this is not always possible.
Differently, chromatic aberration occurs when the beam is not effectively monochromatic as it is supposed to be. This can be corrected applying a monochromation of the beam.
Finally, astigmatisms represents a deflection of the beam that might be caused by a misaligned C2 aperture, a contamination or an excessive charge. This defect can be detected by wobbling the beam without the need of any specimen. If the image is elliptical rather than circular and it rotates through 90° either side of focus, astigmatism is confirmed. Its correction requires the use of condenser stigmators compensating field. These are iteratively applied on over-focused and under-focused beams till the image remains circular. However, if the stigmators do not correct the defect neither at their maximum strength, this means that there is a contamination.
Correction:
Monochromation of the beam
Correction:
Adjustment of beam image to circular at over and under-focus by stigmators
Correction:
optimum C2 aperture

10. Illumination system Calibration C1 setting C2 aperture Probe Size
Probe Current
Convergence angle
The major calibration variables are probe size and convergence angle (α), which are respectively related to C1 settings and C2 aperture. As visible from the scheme, probe size decreases with increasing C1 strength, and convergence semi-angle increases linearly with C2 aperture size. Moreover, both C1 setting and C2 aperture act on the probe current. In fact, the latter increases with larger C2 apertures, but its maximum is also proportional to the cube of the probe diameter.
Decreasing probe size with increasing C1 strength.
Maximum probe current proportional to the cube of probe diameter, and larger C2 apertures increase probe current.
Larger C2 apertures increase convergence (semi) angle.

11. Objective lens & Stage Top-entry holder Side-entry holder
Different geometry
Different flexibility
Stage
Sample holder
Conditions
At these conditions,
tilts around sample axis do not move the image across the projection screen
The specimen feature under analysis has to be placed:
Close to the tilt axis of the specimen rod
At the reference/eucentric plane and height
Symmetric to the upper and lower objective polepiece fields
Moving to the second component of TEM, we meet the stage and the objective lens.
The stage is where the specimen holder is placed. There are two types of specimen holders, which are characterized by different geometry and operating flexibility: top-entry and side-entry holders. Apart this, it is essential to position the sample according to few rules:
The part of the specimen under analysis has to be placed close to the tilt axis of the specimen rod.
While positioning the sample, it is necessary to define the reference plane, which is normal to the optic axis and contains the axis of the specimen-holder rod. In case of side-entry holders, this is called “eucentric plane”, and its position within the objective lens is called “eucentric height”. When the sample is at the eucentric plane and height, the objective-lens current is standard and reproducible.
The eucentric plane position should be symmetric to the upper and lower objective polepiece fields, otherwise images and DPs have different magnification and focus setting in TEM and STEM.
The eucentric plane is obtained by selecting a recognizable feature of the sample at ca x magnification, finding the tilts limits (tilting clockwise and anticlockwise the stage to see when the feature is no more visible), and adjusting the sample height till when the z-control can compensate ±30° tilt either side. This setting is regulated first at low and then at high magnification.
In case of o/c lenses, the eucentric position has almost to coincide with the optimal c/o lens excitation point. The two values should differ by < 3-10 µm. This occurs when the lens is set at c/o excitation point and focused with the z-control.

12. TEM Imaging system Diffraction Mode Image Mode
Electrons from the specimen
DP in the back-focal plane (BFP)
Recombination of electrons in an image in the image plane
Diffraction Mode
Image Mode
Once the electrons leave the sample, they are dispersed by the objective lens to create a DP at the back-focal plane below the sample. Then, they are newly combined into an image at the image plane.
The sample can be visualized through two different primary modes: the diffraction mode and the image mode. The difference between these two is given by the object plane of the intermediate lens. In the first case, this is the back-focal plane, while in the second the image plane. Finally, for both the cases, the object plane is projected onto the viewing screen or CCD.
The BFP is the object plane of the intermediate lens
The image plane is the object plane of the intermediate lens

13. TEM Imaging system DPs Electrons from the whole area
Electrons from selected area
Buckled patterns & too high intensities
DPs
Possible parallel electron beam
Fixed magnification
Min selected area ca. 0.4 µm
No parallel electron beam
No sharp DPs
SAD
patterns
CBED
patterns
By an aperture in the image plane of the objective lens
Reducing the beam by means of C2 and C3
When diffraction patterns are generated by all the electrons from the specimen, they result buckled, and the intensity can be too high. However, these problems can be overcome selecting a certain area of electrons. This can be done using a smaller beam regulated by C2 and C3, or an aperture/diaphragm in the image plane of the objective lens. The first process produces the so-called CBED patterns, while the second the SAD patterns.
CBED patterns list two limits: they are not sharp, and they cannot utilize a parallel electron beam. SADPs solve these limits, and in particular they are recommended for selected spots, when DP spots are too close, in case of fine structures, and when the specimens are sensitive to the beam. They are produced according to the following procedure. We start in image mode. C2 is under-focused, the objective diaphragm is removed, and SAD one is inserted. When the largest available aperture is found, SAD diaphragm is conjugated with the objective lens and we switch to diffraction mode. Finally, SADPs are focused using the controls and under-focusing further C2.
In order to facilitate DP interpretation, it is possible to regulate another parameter: the camera length (L). However, this might result complex in case of c/o lenses.
SADPs are characterized by fixed magnification and a minimum selected area measuring ca. 0.4 µm.
To use expecially for:
Selected spots
When DP spots are too close
Fine structures
Sensitive specimens

14. TEM Imaging system BF image DF image CDF image DADF image
The visualization of SADPs depends on direct-beam electrons (bright central spot) and scattered electrons. The first can generate a bright-field (BF) image, while the second a dark-field (DF) one. The process to get these image starts with the production of a SADP. Remaining in diffraction mode, the objective diaphragm is used and this aperture selects the direct beam or the scattered electrons. Finally, both BF and DF images can be obtained at any magnification.
It is useful to remember that the objective aperture controls both the aberrations and consequently the resolution.
It is also possible to displace the objective aperture from the optic axis. In this case, the transmitted beam is intercepted, and the diffracted beam adds information giving a displaced aperture dark field image (DADF). However, this image is affected by defects, such as spherical aberration and astigmatism.
Higher quality DF images are anyway possible if we use centered dark field images (CDF). In this case, the incident beam is tilted in order to hit the sample at an angle equal and opposite to the scattering angle.
However, both DADF and CDF images have the limit to analyze only a small fraction of scattered light. To see all the portions of the specimen, other solutions should be applied, such as a hollow-cone diffraction.

15. TEM Imaging system Hollow-Cone Diffraction Hardware Software
Annular condenser aperture
Scan coils
Selectable cone semi-angles and rotation speed
Fixed cone semi-angles
To obtain hollow-cone DF images, the objective aperture has to collect certain diffracted beams, and this happens when the conical-scanning beam satisfies Bragg reflection condition. Then, they are processed into images through hardware or software.
The “hardware” is based on an annular condenser aperture. The specimen is illuminated by a cone of electrons, whose angle to the optic axis is fixed. The direct beam (000) that crosses the specimen generate several diffracted beam, which result in a multiple DPs.
On the other hand, the “software” uses scan coils to make rotate the incident electron beam around the optic axis. This spin is regulated via computer control, allowing the selection of both the specific cone semi-angles and the speed of the rotation. Finally, instead than multiple DPs, the scattered electrons are integrated into a single DF image.
Multiple DPs
Integrate DF

16. STEM Imaging system STEM Images Depends on the probe
Only probe aberration
STEM Images
The signal is
Generated at the specimen
Detected
Amplified
Visualized
Pivot the beam at FFP
Scan Coils
Computer display BF
ADF
If scanned constantly parallel to the optic axis, probes can generate also STEM images.
The probe is scanned on the specimen. Two pairs of scan coils regulate the probe and pivot the beam approximately at the front focal pane (FFP) of the upper objective polepiece. At this point, the C3 guides the electrons in parallel to the optic axis till the image of the C1 crossover is generated in the specimen plane. At the same time, the scan coils accomplish also a second function, that is the scan the computer display. Thus, on the contrary than TEM images, STEM images depend only on the probe. Consequently, quality and magnification depend on the beam. The aberrations are those of the probe, which can overcome using aberration corrections, and lens defects are avoided (in particular chromatic aberration). On the other hand, STEM images are much slower than those of TEM: their recording is serial instead than parallel.
An important role of STEM imaging is associated to the electron detector, which allows the selection of those electrons that have to contribute to the STEM image. A specific example of electron detector are BF detectors, which select the direct beam. Then, this signal is amplified and modulated to produce the final signal that permits the image display.
STEM images can be both bright- and dark-field based. As for TEM images, DF conditions require the selection of a part or all the scattered electrons. In case the image had to include only a determined range of scattered electrons, it is possible to obtain the DF image acting on the stationary DP. Because the detector is placed into a conjugate plane to the stationary DP, the latter has to be shifted. In this way the scattered beam is on the optic axis and falls on the BF detector. On the other hand, it is possible to use an annular detector, whose resulting image is defined annular dark-field (ADF) image. Generally, this detector is placed on the optic axis, surrounds the BF one, and generates a final ADF image complementary to BF image. However, more complex detectors can be designed in size and shape to pick up also those electrons that scatter at higher angles.
BF image
DF image
ADF image
complementary

17. Alignment 1. Alignment of the objective lens center of rotation
2. Alignment of the DP on the optic axis
Why?
To avoid:
Off-axis electrons (which cause aberrations)
Off-axis rotation of the electrons
Why?
To avoid the movement off-axis of the pattern.
How?
Reference feature
Wobbling at low magnification
Beam tilts
Wobbling at high magnification
Manual defocus of the objective lens
How?
Reference feature
Projector lens adjustment
There are two main alignments to carry out: that of the objective lens center of rotation and that of the DP on the optic axis. Both aim at stabilize the pattern or the image from off-axis movements.
Any alignment requires to select a reference feature, whose patter or image has to be stabilized. Moreover, in general, it is recommended to start at low magnification.
To align the objective lens center of rotation, the first step is to wobble (focusing and defocusing) while monitoring if the feature rotates off-axis. If this happens, beam tilts are used till the phenomenon stops. When the rotation persists, but the point remains in the middle of the screen, the magnification is increased. The adjustment process is repeated, and at its end, the objective lens might require a manual defocusing till the feature is stable about the center.
On the other hand, the alignment of the DP on the optic axis is based on the projector lens adjustment till the central spot of the DP remains around the axis while the camera length is changed.

18. Stigmation Astigmatism in the objective lens
2. Astigmatism in the intermediate lens
When?
Misaligned objective aperture
Contaminations
Small orthogonal distortion under wobbling.
Stigmation
Reference: small hole/rough corner
Parallel electron beam
BF image at high magnification
Monitoring of Fresnel fringe while wobbling
Objective stigmators
Repeat at high magnification
Stigmation
Reference feature
Incident beam underfocus
Intermediate stigmators
Two kinds of stigmation might be needed: for the objective and the intermediate lens.
In the first case (previously mentioned in slide 9), the procedure is based on the stabilization of the Fresnel fringe of the reference detail (small hole or rough corner) BF image. When the fringe is uniform, there is no more astigmatism. On the other hand, if its intensity varies with the focus, the objective stigmators have to be used. The process begins at a magnification of ca. 10^5x. Then, the process is repeated at higher values >250000x.
Similarly, also the astigmatism of the intermediate lens is adjusted with the stigmators (in this case “intermediate stigmators”). However, this defect is much less relevant and visible than the previous, and it affects only the DP.
Astigmatic distortion of Fresnel fringe

19. Calibration Magnification calibration 2. Camera length calibration
3. Rotation of the image relative to DP
Like for any instrument, TEM has to be calibrated when installed, then periodically, and in case of modifications. Despite this, it remains an instrument for relative measurements (not absolute), and its calibration is the tool we have to obtain a reasonable accuracy (ca. ±5%).
There are three major calibrations: for the magnification, the camera length, and the rotation of the image relative to DP. To these, other three can be added: for the accelerating voltage, the specimen tilt axis and the sense of tilt, and the focal increments of the objective lens.
Magnification calibration can use different references depending on the range under study: carbon-film replica of an optical-diffraction grating of known spacing, small latex spheres, and phase-contrast images of known crystal spacings. The calibration specimen is placed at the eucentric height and illuminated with a parallel beam. The objective aperture is aligned, and then we pass to the image mode. The BF image is focus and recorded. Finally, the magnifications are calculate from the acquired images, whose true spacings are known. Theoretically, this procedure should be carried out at each measurement in order to reduce the lens hysteresis.
Similarly to the previous case, also the camera length (L) calibration begins with the reference (known crystal spacing –d-) at the eucentric height and the BF in focus. Then, SAD aperture is inserted, and we switch to diffraction mode. The beam has to be parallel, and the focus is obtained with the first intermediate lens control. At this point, because we know the ring radius and the wavelength, we can calculate L using the Bragg equation: Rd=λL. Particular attention should be paid if a c/o lens is used, because L can easily change as a function of convergence or divergence. To avoid this error, it is recommended to select and maintain one condition for every calibration.
The calibration of the rotation of the image relative to DP uses α-MoO3 as reference. Once placed it at the eucentric plane, inserted the SAD diaphragm and put in focus, the system passes to diffraction mode with parallel electron beam. The focus is optimized to have sharpest diffraction. A double exposure of the DP is taken at different magnifications. Finally, for each time, angle φ is measured and its variation plotted. Because at high magnification one of the imaging-system lenses might switch off, it is suggested to control eventual 180° inversions of the images. If present, they should be reported.
4. Accelerating voltage
5. Specimen tilt axis and the sense of tilt
6. Focal increments of the objective lens