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On completion of this tutorial you should be able to:
Before starting this TLP users should be familair with electron properties and magnetic fields, how optical lenses work and diffraction.
Transmission electron microscopy is an immensely valuable and versatile technique for the characterisation of materials. It exploits the very small wavelengths of high-energy electrons to probe solids at the atomic scale. In addition, information about local structure (by imaging of defects such as dislocations), average structure (using diffraction to identify crystal class and lattice parameter) and chemical composition may be collected almost simultaneously. However, use of the microscope is highly skilled, and along with the interpretation of the information gained requires a good understanding of the processes occurring in the microscope, and the structure of materials.
This TLP provides a solid basis for learning the theory behind the electron microscope and the concepts needed to begin learning to use one.
The figure shows a typical TEM system. Click on the various sections to learn about what they do.
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At the top of the TEM column is the electron gun, which is the source of electrons. The electrons are accelerated to high energies (typically 100-400 keV) and then focussed towards the sample by a set of condenser lenses and apertures.
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The source is chosen so that the rates of electrons incident on the sample per unit area and leaving the source per unit solid angle (brightness) are maximised. This is so that the maximum amount of information can be extracted from each feature of the sample.
There are two major types of electron source. Guns of the cheaper and more common of the two generate electrons by thermionic emission. If enough thermal energy is added to a material its electrons may overcome the energy barrier of the work function and escape. Unfortunately, to avoid the source melting, the material used must either have a very high melting point (such as W) or an exceptionally low work function (certain rare-earth boride crystals such as LaB6 are widely used).
Another way of extracting electrons from a material is by applying a very large electric field. By drawing tungsten wire to a very fine point (<0.1 μm), application of a potential of 1 kV gives an electric field of 1010 A m-1 which is large enough to allow electrons to tunnel out of the sample. This is called field emission.
Field emission guns are around twice as expensive as thermionic electron guns, and must be used under ultra-high vacuum conditions. They are favourable for applications in which a high brightness and low energy-spread of incident electrons is needed. (eg. HRTEM, FEG.)
The shape of the beam of electrons emanating from the source can be approximated to a cone. Manipulation of the electron beam is the key to getting information from the sample. This is achieved using electromagnetic lenses. Here we shall see how the paths of electrons in the microscope can be modified by the lenses to focus the beam as required.
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Fortunately, despite operating in a very different way, we may use electron lenses in the same way as light-optical lenses. The way of describing the function of a lens in an optical system is by means of a ray diagram, which is a slight abstraction based on the thin lens approximation. This geometric construction allows us to see the behaviour of different rays incident on a lens.
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By using a small number of lenses in series we can achieve very high magnifications very quickly, since the magnifications multiply. For example, three lenses each giving a magnification of 50× give a 503 = 125000× magnification when placed in series. Any magnification may be achieved in theory. However, beyond a limit any increase in magnification becomes meaningless, as the amount of information available is limited by resolution.
The resolution of an image is the smallest distance between two points at which they may be distinguished as separate. The limit on resolution arises because by passing a beam of light through a lens of finite size it is diffracted. Due to the interference of waves coming from different parts of the lens, and also due to the fact that there are always some rays from the object which fall outside the lens, what begins as a point on the sample becomes a series of concentric circles in the image. These patterns of concentric maxima and minima are called "Airy Rings".
To reduce the effects of diffraction it is favourable to increase the size of the lens. Unfortunately, this leads to further problems.
Unfortunately, no lens is perfect. Apart from diffraction effects, resolution is limited by artefacts in the image due to the magnification process, "aberrations". These are due to the fact that rays entering the lens from different angles, or of different wavelength are bent differently. In practice, the aberrations due to the lenses become the limiting factor in the resolution of the electron microscope. We shall deal briefly with two major aberrations: spherical and chromatic aberrations.
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By using a more expensive FEG electron source, the effects of the chromatic aberrations may be reduced substantially - at least before the beam hits the specimen. Afterwards some will remain because energy is lost (and thus the wavelength changed) as the beam passes through the specimen. Unfortunately the monochromatic aberrations such as spherical aberration will almost always be present. Resolution may be increased by restricting the electrons used to those falling close to the optic axis. As seen in the simulation, an aperture placed above the lens limits the angles at which electrons are incident on the sample, reducing the spherical aberration.
Reducing the aperture size will also reduce the beam current, and increase the amount of diffraction experienced by the beam. There is, therefore, an optimum aperture size for the greatest resolution.
A typical TEM uses a system of two condenser lenses to control the beam incident on the sample. The first lens demagnetises the source, either to increase the brightness or decrease the area of the specimen that is illuminate. A second lens with an aperture above it controls the convergence angle, α, of the beam at the specimen.
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It is possible to reduce the effects of spherical aberration dramatically through the use of a large number (as many as 50) of finely adjustable lenses acting in series, much like the lenses in a camera lens are arranged to reduce chromatic aberration. With the computing power available today it is possible to adjust the lenses simultaneously to find the optimum combination of strengths. This has made it possible to construct aberration-corrected microscopes with a resolution better than 0.1 nm (1 Å).
In the central section of the microscope the electron beam interacts with the specimen, and the resulting electrons are gathered and focussed ready for further magnification of the desired images.
As the electrons are incident on the sample they may be scattered by several mechanisms.
These scattering mechanisms will change the angle the electrons are moving at relative to the optic axis, and may be elastic (conserving energy) or inelastic (with energy dissipated as heat). It is by measuring the changes to the electrons on passing through the sample, either by measuring the angle that they have been scattered through (such as by studying diffraction patterns or images) or by measuring the amount of energy that they have lost, that we can gather information about the sample.
The specimen itself is inserted into the path of the electrons, and for the best resolution must be extremely thin; a few nanometers. This is to minimise multiple scattering of the electrons which decreases the number of electrons detected, and makes it more difficult to deduce information about the sample.
Once inside the microscope, the specimen sits right inside the objective lens and must therefore be small - typically less than 3 mm in diameter. It is necessary to align the specimen very accurately with the electron beam to achieve the required images. Common specimen holders allow rotation about two horizontal axes, along with lateral movement. Other holders might include heating elements or nano-indenters to deform the specimen as it is imaged.
Specimen holders
This lens takes the electrons leaving the specimen and forms a diffraction pattern in the back focal plane of the lens, and an image of the specimen in the image plane.
In the conventional TEM we have the option of magnifying the image of the sample formed by the objective lens, or the diffraction pattern. The ease with which the microscopist can move between the two modes (imaging mode and diffraction mode) is one of the things which makes the TEM such a useful and versatile instrument.
To view an image, the microscopist focuses the intermediate lens onto the image plane of the objective lens. To view a diffraction pattern, the lens is refocused onto the back focal plane of the lens. In this plane the diffraction pattern of the sample forms, and may be magnified for viewing on the screen.
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After the electrons have passed through the specimen and been scattered to varying degrees, the information from the system is converted into a macroscopic image. The simplest way of doing this is by simply magnifying the diffraction pattern or image formed of the sample until it is of the required size for analysis. This is the basis of conventional TEM (CTEM).
Alternatively, if a very fine beam of electrons is rastered across the sample, the amount of scattering from each point may be measured separately and successively, and an image gradually built up. This technique, requiring no lenses after the specimen, is called scanning TEM (STEM).
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The projection system magnifies the images or diffraction patterns formed from the specimen and focuses images in the plane of the screen, where the electron density is converted into light-optical images for the microscopist to see.
It is here that the effects of spherical and chromatic aberrations in the lenses are most significant. The chromatic aberrations are much more pronounced since the interactions of the electrons with the sample often absorb energy, so the beam of electrons passing through the projector lenses contains electrons of a much wider range of energies.
Beneath all the lenses is a phosphorescent screen that glows when it is struck by electrons, displaying the image or diffraction pattern. The screen is viewed through a lead-glass window.
In the transmission optical microscope, we may think of colour images being formed as light of different colours is absorbed at each point of the sample. The degree of absorption leads to the contrast in the image.
In the electron microscope, we cannot usually see the effect of the wavelength of the electrons (the "colour") in each image, so we only have "black and white" images. Hence, the information contained in an electron micrograph is solely due to the difference in the flux of electrons through each point in the image - the contrast. The electron microscopist must understand the reasons for contrast in order to gather information from the sample. We shall deal briefly with the main sources of contrast in the following:
Instead of recording the image from a sample all at once, we can illuminate a very small segment of the sample at one time and record the magnitude of electron scattering from the point. This can by done rapidly and an image built up in the same way as on a television screen by scanning the beam across the sample. This technique is called scanning transmission electron microscopy (STEM).
Since the whole image is not collected and focussed at the same moment, no lenses are needed after the sample. Instead, a set of annular detectors is used. An advantage in image formation is that electrons scattered through large angles (Rutherford scattering) may be detected using a high-angle annular dark-field (HAADF) detector and a fourth mechanism of contrast exploited. At large angles the intensity of scattering,
I ∝ Z x .
This allows structure to be imaged, as contrast will appear between areas of different elemental composition.
Finally, the absence of the projection lenses means that there is a lot of left over space in the chamber of the microscope, and this can be filled with analytical detectors, which may measure the energies of the scattered electrons. STEM is used for high resolution chemical analysis of specimens.
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Through this TLP we have seen how a beam of electrons is generated, manipulated and detected in an electron microscope. We have explored the various components of the electron microscope, and seen how they work together to extract information from a sample on the nanometre scale.
Finally, we can begin to appreciate the power and versatility of electron microscopy, and how it may be useful in the study of materials.
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You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!
Explain why the image rotates when the strength of an electromagnetic lens is changed.
Which of these lens conditions gives the smallest convergence angle?
If an object is placed 1 mm from a (convex) lens of focal length 0.25 mm, where will the image be located?
How can chromatic aberrations be minimised in a TEM?
Which imaging technique requires the smaller objective aperture?
What is the minimum magnification needed to make visible the {111} planes in silicon?
Goodhew, Humphreys and Beanland, Electron Microscopy and Analysis 3 rd Edition, Taylor and Francis 2001.
Williams and Carter, Transmission Electron Microscopy Kluwer/Plenum Press, 1996 to 2004
Academic consultant: Peter Goodhew (University of Liverpool)
Content development: James Chivall
Photography and video: Brian Barber
Web development: Lianne Sallows and David Brook
DoITPoMS is funded by the UK Centre for Materials Education and the Department of Materials Science and Metallurgy, University of Cambridge
Additional support for the development of this TLP came from the Worshipful Company of Armourers and Brasiers'