Transmission Electron Microscopy (all content)

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Contents

Aims

On completion of this TLP you should be able to:

• explain to someone with A-level physics how a TEM works and how it forms a) an image and b) a diffraction pattern;
• name the essential components of a TEM and define the meaning and significance of important terms such as resolution, magnification, image contrast...
• explain the operation of electromagnetic lenses in terms of ray diagrams, particularly in the illumination system and the objective/intermediate system;
• explain to a materials undergraduate how different types of contrast arise from beam-specimen interactions, and how these can be used to study materials in the TEM.

Before you start

Before starting this TLP users should be familair with electron properties and magnetic fields, how optical lenses work and diffraction.

Introduction

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.

TEM structure

The figure shows a typical TEM system. Click on the various sections to learn about what they do.

Illumination: Electron Source

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.

Source

The source is chosen so that the emitted current density per solid angle (brightness) is 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, thermionic emitters and electron field emitter. Electron guns based on thermionic emission are cheaper and more robust, hence often found on older instruments. If enough thermal energy is added to a material its electrons may overcome the energy barrier of the work function and escape. 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 V m^-1 which is large enough to allow electrons to tunnel out of the sample. This is called electron field emission.

Field emission guns are more expensive than 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. high resolution TEM, electron energy loss spectroscopy)

Illumination: Condenser System

The shape of the beam of electrons emitted by 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.

The action of electron lenses can be described 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.

Electromagnetic lenses in a TEM By using a small number of lenses in series we can achieve very high magnifications/demagnification very quickly, since these 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.

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, \(\alpha\), of the beam at the specimen.

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).

Image formation

In the central section of the microscope the electron beam interacts with the specimen, and the transmitted electrons are gathered and focussed ready for further magnification of the desired images.

Sample Stage

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 tranferred to the sample and dissipated as heat). By analysing the changes to the electrons transmitted through the specimen we can gather information about the material, and in particular we can study its morphology, crystal structure, and composition.

The sample itself is inserted into the path of the electrons, and for the best resolution must be extremely thin; a few nanometers. This is to maximise the number of transmitted electrons, and minimise multiple scattering events which make it more difficult to deduce information about the material.

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 good imaging. Common specimen holders allow rotation about two horizontal axes, along with lateral movement. Other holders might include heating or cooling elements, or nano-indenters to deform the specimen as it is imaged.

Specimen holders

Objective/Intermediate Lens System

The objective lens takes electrons transmitted through the specimen and forms a diffraction pattern (in the back focal plane) and an image of the specimen (in the image plane).

In the conventional TEM we have the option of magnifying either the image or the diffraction pattern formed by the objective lens. This is achieved by changing the settings of the intermediate lens from the imaging mode to the diffraction mode. The ease with which the microscopist can move between the two modes is one of the things which makes the TEM such a useful and versatile instrument.

In imaging mode, the microscopist focuses the intermediate lens onto the image plane of the objective lens to produce a magnified version of the image further along the optic axis and on the viewing screen. To view a diffraction pattern, the intermediate lens is adjusted so that its object plane coincides with the back focal plane of the objective lens, where the first diffraction pattern is formed. The diffraction pattern is then displayed on the viewing screen.

Viewing images

After the electrons have passed through the specimen and been scattered to varying degrees, the information is converted into a macroscopic image. The simplest way of doing this is by simply magnifying the image or diffraction pattern until it is of the required size for analysis. This is the basis of conventional TEM.

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).

TEM

Projector System

The projection system magnifies the images or diffraction patterns formed from the specimen, projecting them onto the viewing screen, where the electron density is converted into light-optical images for the microscopist to see.

Screen

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 (to protect the users from X-rays generated in the microscope).

Image contrast

The information contained in a TEM 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:

• Mass absorption contrast
  • On passing through matter, a beam of electrons is gradually attenuated. The degree of attenuation increases with the thickness of the specimen and its mass, so variations of mass and thickness across the sample give rise to contrast in the image.
• Diffraction contrast
  • Diffraction of electrons from Bragg planes causes a change in their direction of travel (elastic scattering). Hence, contrast can arise between adjacent grains or between different regions near the core of a dislocation.
• Phase contrast
  • Scattering mechanisms often cause a change in the phase of the scattered electrons, as well as a change in direction. Interference between electrons of different phase which are incident on the same part of the image will cause a change in intensity and give rise to contrast. This is normally only visible at high magnifications and for microscopes that can achieve atomic resolution (HRTEMs).

STEM

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 is 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. The spatial resolution of this technique is given by the size of the electron beam at the specimen surface (controlled by the gun and condenser system). 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 where x~2.

STEM HAADF images display compositional contrast, and can be used to quantitatively assess elemental composition up to the atomic scale.

Using a STEM in conjunction with analytical detectors it is possible to collect compositional maps of specimens, for example by energy dispersive X-ray spectroscopy (EDS) or electron energy loss spectroscopy (EELS). EM is used for high resolution chemical analysis of specimens.

Image resolution

The resolution of an image is the smallest distance between two points at which they may be distinguished as separate. The resolution of perfect optical lenses is limited by diffraction effects: the finite size of the lens(aperture) causes a modulation of transmitted light intensity collected on a viewing screen some distance away. The pattern of intensity, known as an Airy pattern, displays a strong central maximum (i.e. the Airy disk), surrounded by concentric minima and maxima.

A similar effect can be expected for electron lenses in the TEM: the intensity transmitted by the objective lens will be affected by diffraction such that a point-like object in the specimen plane will produce an Airy disk in the image plane. Two point-like objects in the specimen will be distinguished as separate, if their distance \(r_d \leq {0.61 \lambda \over \alpha}\), where \(\lambda\) is the wavelength of the electron beam and \(\alpha\) is the semi-angle subtended by the lens(aperture). This can be defined as the resolution of a perfect electron lens, based on the Rayleigh criterion.

Electron lenses are not perfect. They suffer from astigmatism, as well as chromatic and spherical aberrations, which arise from the spread of electron velocities in the beam, their angular distribution, and their distance for the optic axis as they travel through the magnetic field generated by the lenses.

Lens astigmatism is corrected by adjusting lens stigmators to compensate image distortions.

The effect of chromatic aberrations is seen when electrons travelling at different velocities experience a different Lorentz force as they cross the lens, and are focused at different distances along the optic axis. This degrades the resolution of the image. The effect can be reduced substantially by using a FEG electron source with a small energy spread. It is important to note that the beam energy distribution always broadens when electrons interact with the specimen through inelastic collisions. Hence small chromatic distortions are unavoidable in TEM images.

A lens is said to display spherical aberration when the field of the lens behaves differently for electrons travelling near the optic axis, and those travelling off-axis. The image resolution is degraded by \(r_s = C_s \alpha^3 \) , where \(C_s\) is the spherical aberration coefficient (usually expressed in mm), and \(\alpha\) is, again, the semi-angle subtended by the lens(aperture). Spherical aberration may be reduced by forming images just with electrons that travel close to the optic axis, i.e. minimising \(\alpha\). As you can see in the animations this can be accomplished using a small aperture to exclude electron trajectories that cross the lens far from its centre.

Reducing the aperture size reduces the beam current and increase the diffraction experienced by the beam. There is, therefore, an optimum aperture size for the greatest resolution. The optimum resolution can be expressed as: \(r_{opt} = \lambda^{1/4}C_s^{3/4}\).

Conventional TEMs can achieve resolutions of 0.2 nm, and hence allow imaging of atomic lattices. Aberration corrected TEMs, where additional electron-optic components are introduced to compensate for spherical and chromatic aberrations, can achieve point resolutions below 0.1 nm (in phase contrast images).

Summary

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.

Questions

Quick questions

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!

1. Explain why the image rotates when the strength of an electromagnetic lens is changed.

2. Which of these lens conditions gives the smallest convergence angle?

   	a	over-focus
   	b	in focus
   	c	under-focus

3. If an object is placed 1 mm from a (convex) lens of focal length 0.25 mm, where will the image be located?

4. How can chromatic aberrations be minimised in a TEM?

5. Which imaging technique requires the smaller objective aperture?

   	a	diffraction contrast
   	b	phase contrast

6. What is the minimum magnification needed to make visible the {111} planes in silicon?

Going further

Books

Goodhew, Humphreys and Beanland, Electron Microscopy and Analysis 3 rd Edition, Taylor and Francis 2001.

Williams and Carter, Transmission Electron Microscopy Kluwer/Plenum Press, Second edition 2009

Academic consultant: Peter Goodhew (University of Liverpool)
Content development: James Chivall
Photography and video: Brian Barber
Web development: Lianne Sallows and David Brook

This DoITPoMS TLP was 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'.