Transmission Electron Microscopy

A typical commercial transmission electron microscope (TEM) costs about $5 for each electron volt (eV) of energy in the beam and, if you add on all available options, it can easily cost up to $10 per eV. As you’ll see, we use beam energies in the range from 100,000 to 400,000 eV, so a TEMis an extremely expensive piece of equipment. Consequently, there have to be very sound scientific reasons for investing such a large amount of money in onemicroscope. In this chapter (which is just a brief overview of many of the concepts that we’ll talk about in detail throughout the book) we start by introducing you to some of the historical development of the TEM because the history is intertwined with some of the reasons why you need to use a TEM to characterize materials. Other reasons for using a TEM have appeared as the instrument continues to develop, to the point where it can seriously be claimed that no other scientific instrument exists which can offer such a broad range of characterization techniques with such high spatial and analytical resolution, coupled with a completely quantitative understanding of the various techniques.

The electron is a low-mass, negatively charged particle. As such, it can easily be deflected by passing close to other electrons or the positive nucleus of an atom. These Coulomb (electrostatic) interactions cause electron scattering, which is the process that makes TEM feasible. We will also discuss how the wave nature of the electron gives rise to diffraction effects. What we can already say is that if the electrons weren’t scattered, there would be no mechanism to create TEM images or DPs and no source of spectroscopic data. So it is essential to understand both the particle approach and the wave approach to electron scattering in order to be able to interpret all the information that comes from a TEM. Electron scattering from materials is a reasonably complex area of physics, but it isn’t necessary to develop a detailed comprehension of scattering theory to be a competent microscopist.

Elastically scattered electrons are the major source of contrast in TEM images. They also create much of the intensity in DPs, so we need to understand what controls this process. First we’ll consider elastic scattering from single, isolated atoms and then from many atoms together in the specimen. To comprehend elastic scattering we need to invoke both particle and wave characteristics of electrons.

In the previous chapter, we discussed elastic scattering of the electron beam in which the incident electrons lost no energy as they traversed the specimen. Inelastically scattered (often termed energy-loss) electrons are equally important and we’ll discuss many of these processes here, but leave the applications till later. Why are we interested in inelastic scattering? Well, such scattering generates a whole range of signals, each of which can tell us more about the chemistry of the specimen than we can find out from the elastic electrons. In addition to the energy-loss electrons themselves, the most important signals are the characteristic X-rays, secondary electrons, and, occasionally, visible light (cathodoluminescence (CL)) and so we’ll emphasize how these arise.

A reliable source of electrons to ‘illuminate’ the specimen is one of themost important parts of a TEM. Fortunately, electron sources are plentiful, but to get the best images and other signals out of our expensive microscope, we need to use the best available source. There are stringent requirements to produce the beam of electrons with the necessary properties and these are best met by only two types of source: thermionic and field-emission sources (or ‘guns’ as they are often called). Thermionic sources are (now rarely) tungsten filaments or (now commonly) lanthanum hexaboride (LaB

6

) crystals, and field emitters are fine tungsten needles. In this chapter we’ll first explain briefly the physics of the different electron-emission processes because then you’ll understand why we operate the sources in certain ways.

Electron lenses are the TEM’s equivalent of the glass lenses in a visible light microscope (VLM) and, to a large extent, we can draw comparisons between the two. For example, the behavior of all the lenses in a standard TEM can be approximated to the action of a convex (converging) glass lens on monochromatic light. The lens is basically used to do two things ■ Take all the rays emanating from a point in an object and recreate a point in an image ■ Focus parallel rays to a point in the focal plane of the lens

If we are studying the structure of a material, when all is said and done, all we have to show for learning how to operate our expensive TEM, the many hours spent in specimen preparation, etc., is an image or a DP. These images and DPs, which are just different distributions of electron intensity, have first to be viewed in some manner. After viewing, we have to decide if we want to save the results for future reference, perhaps so we can print out the data for a presentation, technical report, or scientific publication. Since, as we noted in the opening chapter, our eyes are not sensitive to electrons, we have to find ways to translate the electron-intensity distributions generated by the specimen into visible-light distributions, which we can see. This chapter will explain how we ‘see’ electrons.

In the past three chapters we’ve described the sources, lenses, and detectors that make up a TEM. The only other parts of the instrument you need to know about in detail are those that, if you are not careful, can seriously degrade the quality of the information you generate even if the rest is perfect. These two parts are the holder in which you put your specimen and the vacuum that surrounds it. While there isn’t much you can do to improve the vacuum, beyond buying a better microscope, there is a lot you can do that will degrade the quality of the vacuum in the column and, in doing so, contaminate your specimen. So we’ll tell you a few basics about how the vacuum pumps work, and how the vacuum system is put together. Although the vacuum system is under computer control in most TEMs, you still affect the vacuum by what you put in the microscope. Consequently, you need to know what not to do on those occasions when you might otherwise degrade the vacuum.

Over the preceding four chapters we’ve now introduced all the essential components of the TEM and it’s time to see how the guns (Chapter 5), lenses (Chapter 6), detectors/screens (Chapter 7), and specimen holders (Chapter 8) are combined to form the instrument. Just as we do for the VLM, it’s convenient to divide up the TEM into three components: the illumination system, the objective lens/stage, and the imaging system. The illumination system comprises the gun and the condenser lenses and its role is to take the electrons from the source and transfer them to your specimen. You can operate the illumination system in two principal modes: parallel beam and convergent beam. The first mode is used primarily for TEM imaging and selected-area diffraction (SAD), while the second is used mainly for scanning (STEM) imaging, analysis via X-ray and electron spectrometry, and convergentbeam electron diffraction (CBED).

Specimen preparation is a very broad subject; there are books devoted to this topic alone. The intention here is to summarize the techniques, suggest routes that you might follow, and above all to emphasize that there are many ways to produce a TEM specimen; the one you choose will depend on the information you need, time constraints, availability of equipment, your skill, and the material. So we’ll concentrate on the ‘principles of cooking,’ but won’t try to list all the possible ‘recipes.’ One important point to bear in mind is that your technique must not affect what you see or measure, or if it does, then you must know how. Specimen preparation artifacts may be interesting but they are not usually what you want to study. Incidentally, we’ll make ‘specimens’ from the ‘sample’ we’re investigating so we’ll look at ‘TEM specimens,’ but sometimes we, and everyone else, will interchange the two words.

This chapter will set the stage for our discussion of imaging using diffraction contrast. Put simply, diffraction contrast arises because the intensity of the diffr3acted beams is different in different regions of the specimen. These variations may arise because of changing diffracting conditions or because of differences in specimen thickness. In our study of diffraction in the TEM, we will see spots—lots of them. Sometimes the ‘spots’ will be small faint points and other times they will be large disks, which themselves contain ‘structure’ and more information. Other patterns will contain lines that we will examine in Chapters 19–21.

In the previous chapter, you’ve already encountered vectors

k

and

g

and seen that they have lengths with units of nm

−1

. These vectors are referred to as reciprocal-lattice vectors. Now we are going to discuss what this reciprocal lattice is. The reciprocal lattice is simply a lattice in reciprocal space. Note that this lattice is just as real as the ‘real lattice’ in ‘real’ space. It’s like a new world in

Gulliver’s Travels

but the relationship to ‘our’ world is not a linear scaling factor but a reciprocal one. If something (an object or a length) is large in real space, then it’s small in reciprocal space.

In Chapter 11 we discussed why diffraction occurs; in this chapter we give a more detailed mathematical treatment. It may be more detailed than you need at this stage. Diffraction is one of those phenomena that lends itself directly to a detailed mathematical modeling, but there is a danger:

don’t become so engrossed in the math that you miss the principles involved; conversely, don’t ignore the subject because it is mathematically daunting!

The topic of this chapter is one which causes major problems for many microscopists. The treatment we will follow is known as the ‘dynamical theory.’ Later we will make some gross simplifications, partly because this is instructive and partly because these simplifications do apply to some important special cases; the kinematical approximation is one such simplification. Many other texts begin with the so-called ‘kinematical’ treatment and then advance to the more realistic, more general dynamical case. We will not do this but we will introduce the words and assumptions in Chapter 27.

This topic is rather mathematical, with long sequences of differential equations. The discussion of Bloch waves given here follows the treatment of Hirsch et al. which, in turn, was based on the original analysis of electron diffraction by Bethe (1928). The notation we will use closely follows that used by Bethe. Remember that g can be any reciprocal-lattice vector, although we will also use it to represent a specific vector.

The analysis of Bloch waves given in the previous chapter is closely related to the classic analysis of waves that you’ve seen in condensed-matter physics or semiconductor theory. In semiconductors in particular, we often talk of band diagrams and indirect or direct band gaps. We use terms like conduction bands, valence bands, and Brillouin-zone boundaries (BZBs). We visualize these quantities by drawing diagrams of

E

(

k

), the electron energy (which is a function of

k

) versus

k

, the wave vector.

Since our emphasis is on crystalline materials, we will first discuss how the details of the crystal symmetry affect the DPs we expect to see. What we’re doing here is taking the concepts of the reciprocal lattice and applying it to particular examples. There are two basic lessons.

A very important concept in TEM is that we only ever diffract from small volumes. These volumes are now called nanoparticles, nanograins, nanobelts, etc. By definition, no TEM specimen is infinite in all directions and all defects are small. Of course, the beam is also never infinitely wide! This chapter therefore discusses how the size of what we are examining influences the appearance of the DP.

The core strength ofTEMis that you can obtain both a DP and an image from the same part of your specimen (not to mention various spectra). To obtain the crystallographic data, a method for interpreting and indexing the DP is essential and this aspect is the theme for the next four chapters. We’ll start in this chapter by considering classic selected-area diffraction (SAD) patterns (SADPs) and how to index them, but also introduce other related, if less widely used, parallel-beam diffraction methods.

In this chapter and the following two, we will discuss two special cases of electron diffraction. We’ll see that incoherently scattered, divergent beams of electrons give rise to paired arrays of lines in SADPs, known as Kikuchi patterns. In the next two chapters, we will form DPs with a convergent rather than a divergent (or, as in the previous chapter, parallel) beam. These two techniques have a lot in common. In the first, the electrons are initially being scattered by the atoms in the crystal so that they ‘lose all memory of direction’ and may also lose energy.

We know that SAD, while giving us useful information about the specimen, has two severe limitations.

In the preceding chapter, we described how to obtain a variety of CBED patterns under various experimental conditions. In this chapter you will find out why these patterns are so useful: they contain a wealth of quantitative data, much of which you can’t obtain by any other technique and many of which augment standard X-ray crystallographic methods (but always at higher spatial resolution). The established techniques largely depend on simple observation of the patterns whereas newer techniques involve quantitative simulations of the patterns.

We’ve already mentioned in Chapters 2–4 that TEM image contrast arises because of the scattering of the incident beam by the specimen. The electron wave can change both its amplitude and its phase as it traverses the specimen and both types of change can give rise to image contrast. Thus a fundamental distinction we make in the TEM is between

amplitude contrast

and

phase contrast

. In most situations, both types of contrast actually contribute to an image, although we usually select conditions so that one will tend to dominate. In this chapter, we’ll discuss only amplitude contrast and we’ll see that there are two principal types, namely,

mass-thickness contrast

and

diffraction contrast

. This kind of contrast is observed in both TEM and STEM and in both BF and DF images. We’ll discuss the important differences between the images formed in each of these two modes of operation.

We see phase contrast any time we have more than one beam contributing to the image. In fact, whenever we say “fringes,” we are essentially referring to a phase-contrast phenomenon. Although we often distinguish phase and diffraction contrast, this distinction is generally artificial. For example, in Chapters 24 and 25, we will examine thickness fringes and stackingfault fringes; both types of contrast result from interference of waves so both are phasecontrast images although we usually think of them as two-beam, diffraction-contrast images.

We see diffraction contrast in an image for two reasons: either the thickness of the specimen varies or the diffraction conditions change across the specimen: the t effect and the s effect! The

thickness

effect: when the thickness of the specimen is not uniform, the coupling (interference) of the direct and diffracted beams occurs over different distances, thus producing a thickness effect. Don’t confuse diffraction contrast due to thickness changes with mass-thickness contrast discussed in the previous chapter. The effects are very different. The diffraction contrast changes with small changes in tilt, but the mass-thickness contrast doesn’t.

Internal interfaces (grain boundaries, phase boundaries, stacking faults) or external interfaces (i.e., surfaces) are surely the most important defects in crystalline engineering materials. Their common feature is that we can usually think of them as all being two-dimensional, or planar, defects (even though they’re not really). The main topics of this chapter will be ■ Characterizing which type of internal interface we have and determining its main parameters. ■ Identifying lattice translations at these interfaces from the appearance of the diffractioncontrast images.

As we discussed in Chapter 24, bending of the lattice planes causes a change in the diffraction conditions and therefore a change in the contrast of the image. The presence of a lattice defect in the specimen causes the planes to bend close to the defect. The special feature here is that the bending varies not just laterally, but also through the specimen. Since the details of the bending generally depend on the characteristics of the defect, we can learn about the defect by studying the contrast in the TEM image. This simple principle has led to one of the main applications of TEM, namely, the study of defects in crystalline materials. We can claim that our understanding of the whole field of dislocations and interfaces, for example, has advanced because of TEM. We have even discovered new defects using TEM—like the stacking-fault tetrahedron, the faulted dipole, and the multipole.

The term ‘weak-beam microscopy’ refers to the formation of a diffraction-contrast image in either BF or DF where the useful information is transferred by weakly excited beams. The DF approach has been more widely used, in part because it can be understood using quite simple physical models. It also gives stronger contrast; we see white lines on a dark gray background. This chapter will be concerned only with the DF approach. Historically, the weak-beam dark-field (WBDF often abbreviated to WB) method became important because under certain special diffraction conditions, dislocations can be imaged as narrow lines which are approximately 1.5nm wide. Equally important is the fact that the positions of these lines are well defined with respect to the dislocation cores; they are also relatively insensitive to both the foil thickness and the position of the dislocations in the specimen. The technique is particularly useful if you are studying dissociated dislocations where pairs of partial dislocations may only be ~4 nm apart and yet this separation greatly affects the properties of the material.

We will now rethink what we mean by a TEM, in a way that is more suitable for HRTEM, where the purpose is to maximize the useful detail in the image. (Note the word

useful

here.) You should think of the microscope as an optical device that transfers information from the specimen to the image. The optics consists of a series of lenses and apertures aligned along the optic (symmetry) axis. What we would like to do is to transfer

all

the information from the specimen to the image, a process known as mapping. There are two problems to overcome and we can never be completely successful in transferring

all

the information. First, as you know from Chapter 6, the lens system is not perfect so the image is distorted and you lose some data because the lens has a finite size (Abbe’s theory). The second problem is we have to interpret the image using an atomistic model for the material.

Much of what we’ve discussed in the preceding imaging chapters is what we might call ‘classical’ TEM imaging. It began with BF and DF techniques and quickly expanded to include many beams. Diffraction contrast, phase contrast, and to a lesser extent, mass-thickness contrast are the mechanisms we use to characterize our specimens. We control the contrast by inserting the objective aperture, or a STEM detector, and excluding or collecting electrons that have been scattered by the different processes. However, there are variations to the standard ways in whichwe can extractmore information from aTEMimage; in this chapter, we’ll present a brief overview of some of them. Most of these operational modes that we’ll discuss here are somewhat esoteric and have rather specialized applications. Nevertheless, you should know that they exist because they may be just what you need to solve your particular problem.

When we need to obtain information about the specimen in two directions, we need to align the specimen close to a low-index zone axis. If theHRTEMimage information is going to be directly interpretable, the specimen must be oriented with the incident beam exactly aligned with both the optic axis of the TEM and the zone axis of the specimen. Thus, we will have many reflections excited and the simple two-beam analysis of Chapter 27 cannot be used.

In this chapter we will equate processing with the use of the computer to analyze our data. We will simply use image processing to extract more information from the data than we can obtain by eye. The data will generally be an HRTEM image but could be other images or DPs. We’ll quantify spectra after we describe them in Part 4 of this text. In the past, the optical bench was also used for this purpose, but the number of optical benches is negligible compared to the number of computers now found in every TEM lab. Optical benches did allow us to form DPs which we could then modify to produce a processed image. This analog approach has now largely been replaced by its digital counterpart. The computer can be much cheaper than the optical bench and is far more flexible. The number of software packages which are designed for, or can easily be adapted to, TEM is also growing.

To make use of the X-rays generated when the beam strikes the specimen, we have to detect them and identify from which element they originated. This is accomplished by X-ray spectrometry, which is one way to transform the TEM into a far more powerful instrument, called an analytical electron microscope (AEM). Currently, the only commercial spectrometer that we use on theTEM is an X-ray energy-dispersive spectrometer (XEDS), which uses a Si semiconductor detector or sometimes a Ge detector. New detector technologies are emerging, which we’ll describe briefly. While some of these may render the Si detector obsolete, we’ll nevertheless emphasize this particular detector.

TheX-ray spectrumgenerated within your specimen consists of element-specific characteristic peaks with well-defined energies superimposed on a non-characteristic background. While the XEDS system is a remarkable piece of technology, we’ve already described its limited resolution and we will see in this chapter that it is also prone to creating small artifact peaks in the spectrum. Furthermore, the unavoidable presence of scattered electrons and X-rays within the AEM conspire to degrade the quality of the generated spectrum and increase the number of false peaks in the displayed spectrum. The AEM illumination system and specimen stage are rich sources of powerful radiation, not all of it by any means coming from the area of interest in your specimen. So you have to take precautions to ensure that the X-ray spectrum you collect comes predominantly from the area of the specimen that you want to analyze and we describe several tests you should perform to ensure that the XEDSTEM interface is optimized.

It is a waste of time to proceed with

quantitative

analysis of your XEDS spectrum or image without first carrying out

qualitative

analysis. Qualitative analysis requires that

every

peak in the spectrum be identified unambiguously, with statistical certainty, otherwise it should be ignored for both subsequent quantitative analysis and imaging. We emphasize this point because of the many opportunities for the misidentification of small peaks in the spectrum. In this chapter, we’ll deal initially with acquisition and identification of the elemental information in spectra and images. First, we will show you how to choose the best operating conditions for your particular AEM and XEDS system. Then we’ll explain the best way to obtain a spectrum for qualitative analysis. You have to acquire a spectrum with sufficient X-ray counts to allow you to draw the right conclusions with a given degree of confidence. There are a few simple rules to follow which allow you to do this.

Now you’ve got an idea of how to acquire XEDS spectra and images from thin foils. You understand what factors limit the useful information they may contain and what false and misleading effects may arise. Also you know how to be very sure that a certain characteristic peak is due to the presence of a certain element and the occasions when you may not be so confident. Having obtained a spectrum or image that is qualitatively interpretable, it turns out to be a remarkably simple procedure to convert that information into quantitative data about the distribution of elements in your specimen; this is what we describe in this chapter.

Often when you do X-ray analysis of thin foils you are seeking information that is close to the limits of spatial resolution. Before you carry out any such analysis you need to understand the various controlling factors and in this chapter we explain these. Minimizing your specimen thickness is perhaps the most critical aspect of obtaining the best spatial resolution, so we summarize the various ways you can measure your foil thickness at the analysis point, but the quality of the TEM-XEDS system is also important.

Electron energy-loss spectrometry (EELS) is the analysis of the energy distribution of electrons that have come through the specimen. These electrons may have lost no energy or may have suffered inelastic (usually electron-electron) collisions.

The term ‘energy loss’ implies that we are interested only in inelastic interactions, but the spectrum will also contain electrons which have not lost any discernible energy, so we need to consider elastic scattering as well. In this chapter, we’ll focus on the low-energy portion of the EEL spectrum which comprises.

The high energy-loss spectrum (

E

>50 eV) consists primarily of ionization or core-loss edges on a rapidly decreasing plural-scattering background. Elemental-composition data and elemental maps can be extracted from these ionization edges. In this chapter, we’ll examine how to get this information, quantify it, and image it. A good use for such data is lightelement analysis wherein EELS complements XEDS. First, we’ll remind you of the experimental variables over which you have control, because these are rather critical. Then we’ll discuss how to obtain a spectrum and what it should look like if you’re going to quantify it.

In the previous chapter, we described elemental analysis using ionization edges, but there is much more than just elemental information in the ionization edges and this distinguishes EELS from XEDS. There are detailed intensity variations in the core-loss spectra called energy-loss near-edge structure (ELNES) and extended energy-loss fine structure (EXELFS). From this fine structure, which we can resolve because of the high-energy resolution inherent in EELS, we can obtain data on how the ionized atom is bonded, the coordination of that specific atom, and its density of states. As always, we can use any intensity changes to create filtered images which show the distribution of, e.g., regions of different bonding states. Furthermore, we can probe the distribution of other atoms around the ionized atom (i.e., determine the radial-distribution function (RDF) which is very useful for the study of amorphous materials) and we can study momentum-resolved EELS, observe the anisotropy of chemical bonds, combine EELS with tomography, inter alia.