Chapter 1. Introduction

Transcription

1 Chapter 1 Introduction 1.1 Where are the Atoms? Uncovering objects that are too small to be seen by eye: this is the primary purpose of microscopy. The human eye enables us to resolve objects that are as small as a few tens of micrometers. Many objects and structures that affect and control our daily life are orders of magnitudes smaller than what is observable by eye. In order to explore and understand objects like individual cells or viruses, the grain structure of crystalline materials or the self-organization of nanocrystals, microscopes are the tools that make it possible to surpass our natural physical limits. They enable us to observe the very details of our environment. Microscopes are our keys to the microand nano-universe. Keys that are good for specific purposes but which are neither perfect nor universal. There is no microscope that uncovers the platonic essence of the object being imaged. Every microscope elucidates a very specific characteristic of the object. Indeed, there is no need for a microscope to unravel the whole nature of an object. In most cases we know quite a lot about the object which is analyzed in the microscope. We might know its basic chemical composition, what type of cell it is, or which micro- or crystal structure it is supposed to exhibit. Typically, there is a whole set of aprioriinformation available, and there are very specific questions which need to be addressed when studying an object with a microscope. We expect that a microscope enables us to form a magnified image of a given object that answers one of the questions we have. An image collected in a microscope is supposed to reflect certain characteristics of the object, like its structure, its constitution or, for example, its shape. The microscope provides us with an image of details that we cannot see by eye. Yet an image 1

2 2 Aberration-Corrected Imaging in Transmission Electron Microscopy is never equivalent to the object. An image is an interpretation of the object. This is true for a painting, a photograph and a micrograph. In microscopy, the interpretation strongly depends on the probe or the radiation which is used to explore the object. Different techniques and different microscopes might feature different contrast mechanisms or different resolutions, but the information in the micrograph, regardless of whether a certain feature is resolved, is still supposed to reflect true object information. What should be prevented is that the imaging characteristics of the microscope alter the object information in such a way that the relation between image and object becomes obscure. The microscope must not complicate the relation between object and image. Hence, the interpretation of the object shall be kept simple. The resolving power of a conventional optical microscope is of the order of the wavelength of the light that is used for imaging. By utilizing an optical microscope we can thus expand our observations down to objects that are a bit smaller than a micrometer. Even though this is substantially better than what is doable by the naked eye, it is still by far insufficient to resolve the atomic structure of materials. The basic skeleton of materials thus remains out of reach. In order to be able to derive an understanding about what fundamentally constitutes a material and, in particular, how the structure of a material is related to its physical properties, it is often necessary to measure information about the material s atomic framework. Of course, diffraction techniques such as X-ray or neutron diffraction are extremely powerful in indirectly capturing atomic structure information. But, in general, a diffraction pattern does not contain local information. Whether local atomic information is actually needed depends on the question to be addressed. For a perfect crystal or for a material whose properties can be described from the statistical average of the structure over a large volume fraction, local information is not necessarily needed, and global information is even more valuable. Hence, it is not always necessary to access atomic-scale information to understand a particular property of a material and, indeed, a micro- or even a macroscopic model can provide sufficient depth to explain a particular property. Such micro- or macroscopic approaches are often based on a continuous model where the atomic structure and the atoms individual contributions to the overall properties are averaged. The atomic discontinuity is neglected or levelled out over small sub-volumes. Nevertheless, local information is of crucial importance for the study of individual small objects, like nanoparticles, but also for investigating defects such as

3 Introduction 3 dislocations, grain boundaries or individual precipitates. Indeed, it is often the case that local deviations from perfect crystallinity define the real functionality of a material. Knowing where which species of atom does what, observing the location of each individual atom, measuring which element it is and how it is connected to the neighboring atoms: this is the fundamental level at which materials science starts. As a matter of fact, the properties of a material are determined by the atomic constitution, by its skeleton and, in particular, by the configuration and density of defects. Eventually, it is the agglomerate of discrete atoms that constitutes the material and defines its macroscopic physical properties. The smaller a system, the higher the importance of the building blocks that constitute the system. This is true for any kind of network, and it is especially applicable to nanomaterials. Nanomaterials are in principle ordinary materials, except for the fact that their physical extension in at least one direction is of the order of nanometers to tens of nanometers. Nanomaterials are small systems. Therefore, when we deal with nanomaterials, such as clusters of atoms that consist merely of hundreds or thousands of atoms, it is undeniable that atomic-scale information is of the highest importance. Unlike bulk materials whose intrinsic physical properties do not depend on the size of the piece of material under consideration, for nanomaterials this can be fundamentally different. A bulk semiconductor has a characteristic bandgap energy which neither depends on the volume nor mass of material that is inspected. Like many other properties of materials, the bandgap energy is an intrinsic physical property. The type of atoms forming the bulk material and the way they are arranged define its physical properties. But for a semiconductor nanocrystal this can be different. Below a critical size of the nanocrystal, say for instance 10 nm, the bandgap energy can become a function of the size of the crystal. The bandgap essentially transforms into an extrinsic physical property which of course still depends on the type of atoms constituting the nanocrystal and how these atoms are arranged, but also on the number of atoms that are in the system. In order to relate the property of the material to its structure, it is then mandatory to know how many atoms of which type form the nanocrystal. Of course, this is not limited to the case of quantum confinement effects of nanocrystals. Nanomaterials can in general exhibit physical properties which depend strongly on the size, shape or, for instance, on the surface configuration of the atoms. Similarly, the core structure of a dislocation, the surface structure of solids or the

4 4 Aberration-Corrected Imaging in Transmission Electron Microscopy arrangement of precipitates in an alloy for all these cases it can be of crucial importance to know how the atoms are arranged on the skeleton of the solid. Hence, there are many cases where we need to know where which atomic species does what. It is for these cases that atomic-resolution imaging is an indispensable tool in materials science. Electron microscopes enable us to observe objects that are smaller than what is accessible by optical microscopes. Instead of using optical light for imaging, transmission electron microscopes and scanning transmission electron microscopes employ electrons with energies in the range of about 50 to 1,000 kev. The wavelength of such electrons is between 5 and 1 pm. While in light optics it is feasible to access structural information that is of the order of the wavelength of the optical light that is used for imaging, this is not the case in electron optics. Though the wavelength of the electrons is in the range of a few picometers, the resolution of conventional highresolution microscopes is roughly two orders of magnitude larger. Since the spacing between atoms arranged on a crystal lattice is in the range of the order of 200 pm, the resolution is sufficient to access some kind of atomicresolution information. Indeed, both modes, the broad-beam transmission mode and the scanning transmission mode, have been employed to resolve the atomic structure of crystals. Even the detection of individual heavy atoms on thin support films has been possible. Since electron microscopy enables atomic-resolution imaging, one is tempted to say that by having a small enough wavelength the problem of atomic-resolution imaging is solved. This conclusion is indeed partially true. The higher the energy of the electrons used for imaging, the better the resolution. However, especially when working with small materials whose many surface atoms are removable quite easily, the damage the electrons can cause to the material is significant. Hence, one cannot simply increase the electron energy to see more details of the specimen one also needs to make sure that the object is not severely modified by probing it with electrons. Furthermore, the resolution problem in conventional electron microscopy is not directly related to the electron wavelength. There are numerous factors which can affect the resolution of a microscope, regardless of whether this is a light optical or an electron microscope. One ofthese factors is the effect of aberrations, i.e. the non-ideal imaging characteristics of lenses. An aberration describes an imaging characteristic which causes the image to carry false or truncated object information. The image is no longer a simple interpretation of the object.

5 Introduction 5 With respect to aberrations, light and electron optics are not equivalent; the imaging characteristics of electron lenses is not perfect. Of course, neither is any real light-optical lens perfect. But the difference between light and electron optics lies in the fact that in light optics the dominant lens aberrations can be compensated by, for example, serially arranging convex and concave lenses. In electron optics, on the other hand, this is not the case. There are no concave electron lenses. The inherent lens errors of electron lenses cannot be corrected simply by adding a complementary lens of opposite error. Instead, the errors add up. Electron lenses, and in particular round electron lenses (i.e. lenses which are rotationally symmetric about the optical axis), suffer from aberrations which cannot be compensated in a simple way. Though affected by aberrations, this does not imply that electron micrographs necessarily show false object information. By strongly narrowing the path of the electron beam through the microscope, it is possible to approach a nearly perfect imaging characteristic. False information is minimized and the micrographs show true object information. Minimizing the impact of the aberrations on the image comes, however, at the expense of a very limited resolution. The resolution limitation imposed by the aberrations does not mean that there is no object information beyond the resolution limit contained in a micrograph. The resolution limit is a quantity that describes the smallest object detail that can be interpreted directly in a micrograph. This is not necessarily the smallest object detail that contributes to the image. Indeed, modern but conventional electron microscopes transfer object information to the image which reaches beyond the actual resolution limit. However, since this high-resolution information is not free of aberrations, we cannot read it directly from a micrograph. Hence, although atomic-resolution imaging is feasible with conventional (scanning) transmission electron microscopes, lens aberrations can cause image artifacts which obscure the object information contained in a micrograph. Whether an atom is imaged as a bright or as a dark spot in the image is a question of the imaging characteristics of the microscope, which can be dominated by the lens aberrations. But it is not only the image contrast that depends on the imaging characteristics. Object details can even be imaged into areas of the micrograph such that a simple relation between image and object is lost. Under these circumstances the micrographs do not tell us where the atoms are. Aberration correction is about correcting the intrinsic aberration(s) of round electromagnetic electron lenses which are typically used in conventional electron microscopes. Aberration-corrected imaging is about

6 6 Aberration-Corrected Imaging in Transmission Electron Microscopy the formation of micrographs which no longer suffer from unwanted aberrations, which thus show an improved resolution and which contain information that is a true and simple interpretation of the object. The improved resolution and the simplified image interpretation are only two aspects of the benefits of aberration-corrected electron microscopy. The smaller electron probes, which can be formed in aberration-corrected probe-forming instruments, enable a higher beam current. This enhances the signal-to-noise ratio in analytical measurements. Furthermore, since the improved resolution reduces the instrument-specific blurring of the object information contained in a micrograph, the object information can be imaged with a higher signal-to-noise ratio. This simplifies quantification of micrographs, as, for instance, the derivation of quantitative chemical information or distortion measurements on grounds of atomic-resolution micrographs. Hence, there is a whole set of side effects which comes along with the enhanced resolution of aberration-corrected electron microscopes. 1.2 Brief Historical Overview Compared to other fields in physics, electron optics is a rather young discipline. It might not be wrong to state that its launch happened when Louis de Broglie (1924) postulated the wave characteristic of the electron in his doctoral thesis. Shortly thereafter, Hans Busch (1926) described the focusing characteristics of electromagnetic fields on pencils of electrons. Busch s result can be considered as the discovery of the electromagnetic lens. Both findings were crucial for electron microscopy; while de Broglie (1924) showed that electrons possess a characteristic which is similar to the wave characteristic of optical light, Busch (1926) revealed that the trajectories of electrons can be controlled by electromagnetic fields similar to the way glass lenses can control optical light. What occurred during the following five to ten years was a technological and scientific breakthrough that is undoubtedly astonishing. In less than a decade, the fundamental principles of electron optics were developed. Devices were constructed that generate electrons of high flux and instruments were developed that modify the trajectories of electrons in a controlled manner. The development of electron sources and electron lenses was crucial for the invention of the electron microscope in 1932 by Ernst Ruska and Max Knoll (Knoll and Ruska, 1932). Already in his diploma work in Knoll s group in Berlin, Ruska successfully elaborated on new types of electron lenses for a cathode oscilloscope (Ruska, 1930). Then, after finishing his diploma thesis, the job situation in Germany was

7 Introduction 7 difficult and Ruska gladly accepted an unpaid position as a doctoral student in Knoll s group (Ruska, 1987). Ruska s doctoral studies led to the invention of the transmission electron microscope. In parallel with these technical achievements, the theoretical tools needed to understand the path of electrons exposed to well-characterized electromagnetic fields were developed and thus the fundamentals of electron optics were established. In 1932, Knoll and Ruska had already predicted that the theoretical resolution limit of the electron microscope is of the order of 2 Ångström (Knoll and Ruska, 1932). The first electron microscopes that were built in the 1930s did not reach a resolution that even came close to the Ångström scale though. However, it was clear that similar to light optics, the inherent imaging properties of the electron lenses need to be fully understood in order to be able to gather the fundamental characteristics of the imaging process in a multi-lens electron optical system and to reveal the resolution limiting factors. A first theoretical derivation of the inherent aberrations of an electrostatic electron lens was carried out by Otto Scherzer (1933). Shortly after that, Scherzer (1936b) showed that for stationary round electron lenses which are free of charges, the constant of spherical aberration and the constant of chromatic aberration are finite positive. This result is known as the Scherzer theorem. At the time Otto Scherzer came to this conclusion, the electron microscopes were not limited by these unavoidable lens aberrations but by other factors, such as the brightness of the electron sources, the (mechanical) stability of the systems or by the lack of axial symmetry of the round lenses, which arose due to mechanical and materialspecific imperfections. Roughly ten years after Scherzer s theoretical study of the aberration characteristic of round electron lenses and their impact on the resolution limit (Scherzer, 1939), the first report on approaching the theoretical resolution of an electron microscope was published by James Hillier (1946). By developing a new electron source that enabled an electron intensity that was a factor of twenty better than previoussources,aswellasbyimproving the axial symmetry of the magnetic electron lenses, Hillier (1946) reported a spatial resolution of about 10 Å. This was the first report of an electron microscope that approached its theoretical resolution determined by the lens aberrations, which, according to Scherzer (1936b), were unavoidable. From then on, the performance of electron microscopes had continuously improved, but still their ultimate resolution performance had always been limited by the unavoidable aberrations of round electron lenses.

8 8 Aberration-Corrected Imaging in Transmission Electron Microscopy As pointed out by Scherzer (1936b), the aberrations of round electron lenses impose a practical but not a fundamental barrier. In 1947, Scherzer laid out strategies to correct for the chromatic and the spherical aberration of a round electron lens. One of these strategies involved non-round optical elements, i.e. optical lenses which are not rotationally symmetric about the optical axis but which produce an electromagnetic field of reduced azimuthal symmetry. The application of such multi-pole lenses turned out to be the most promising way of correcting lens aberrations. Scherzer s work (1947) was the starting point of a 50-year period of various attempts to design and build electron optical units which would correct the lens aberrations and thus enable for an enhanced resolution. Indeed, a first corrector was built by Scherzer s student Robert Seeliger (1949, 1951, 1953), who essentially showed that the spherical aberration can be decreased by employing three so-called Korrekturstücke, i.e. correction units, which consist of electrostatic octupole fields. This corrector was then further developed by Möllenstedt (1956). Even though the corrector was functional, it could not improve the resolution. There were other attempts, for instance the one from Deltrap (1964), who built a corrector based on a design suggested earlier by Archard (1955), or a corrector based on a fundamentally different principle which was suggested by Beck (1979) and further advanced by Crewe and Kopf (1980), Crewe and Salzman (1982), Crewe (1984) and Rose (1981). The variety of approaches was so large that it was even necessary to mention HowNotToCorrectAnElectronLens as the title of a short note by Scherzer (1982) suggests which was a response to a less fruitful idea. The first aberration correctors that proved to increase the resolution of electron microscopes were built in the 1990s. The very first of these workable aberration correctors was installed in a scanning electron microscope (Zach and Haider, 1995). Shortly after that, aberration correctors for transmission electron microscopes were brought to application: one for a dedicated scanning transmission electron microscope (Krivanek et al., 1997) and one for a broad-beam illumination transmission electron microscope (Haider et al., 1995, 1998b). These pioneering inventions were the starting point of a new era in electron microscopy, an era that has led to electron microscopes which are indispensable in the research of (nano-)materials. This very brief introductory overview is certainly not complete and more snapshots about the chronological evolution of today s working aberration correctors are elucidated in Chapter 8. For now it shall suffice to point out that the development of working aberration correctors has a long history.

9 Introduction 9 A long history of attempts, which were not all as successful as hoped for, yet all these practical attempts and the theoretical knowledge that was developed in parallel helped to build electron microscopes which are no longer limited by the intrinsic aberrations of round electron lenses (Zach and Haider, 1995; Krivanek et al., 1997; Haider et al., 1998b). Indeed, from the beginning of electron microscopy in 1932 until the first working aberration correctors were built, a period passed which is identical to the time that passed between the first flying motorized manned aircraft built by the Wright brothers in 1903 and the moment the first man put a foot on the moon. Of course, these two evolutionary processes are not comparable, neither on the relevant scale of length nor in the money that was needed to warrant a certain degree of progress. The point, however, is that building a working aberration corrector needed the results of technological advancements that span more than half a century. As in many areas of science and technology, the basic principles are often quite straightforward. The difficulty lies in realizing them. Indeed, the complexity of the correctors is not just defined by the ingenious optical elements employed but also arises from the fact that once a potential corrector is available, it needs to be set up such that the corrector does what it is supposed to do without doing things it should not do. 1.3 Scope of the Book The scope of this book is to provide an introduction to aberration-corrected atomic-resolution transmission electron microscopy. The book covers both the scanning transmission mode and the broad-beam transmission mode. Preferably, the reader is familiar with the concepts of electron diffraction and conventional electron microscopy, and has some practical experience with electron microscopes. The text does not focus on the mathematical derivation of how an aberration corrector works. It is a book intended, but not exclusively, for experimentalists and students who want to know how this black box on an aberration-corrected microscope works and who want to know the guidelines on how (and why) to optimize the experimental conditions on aberration-corrected microscopes. It aims at making the reader familiar with concepts, strategies and terms which are used in the daily handling of aberration-corrected microscopes, as well as in the specific literature about it. Although the book does not aim at treating the concepts about electron optics, aberrations and aberration correction from a strictly mathematical point of view, it shall make the reader familiar with some of

10 10 Aberration-Corrected Imaging in Transmission Electron Microscopy the fundamental ideas in electron optics which are applied in conventional as well as in aberration-corrected microscopy. The text can also serve as a guide for readers who want to start with atomic-resolution imaging on conventional electron microscopes. This work shall bridge the gap between texts focusing on electron and charged-particle optics on the one hand and application-oriented books on the other hand, whose focus is on materials science. It shall motivate the reader to dig deeper into the literature about aberration-corrected electron microscopy and electron optics. It is an introductory text it is a primer. This book provides an image of aberration-corrected electron microscopy from a more application-oriented rather than a purely theoretical point of view. As any image, it is an interpretation of the subject. 1.4 General Outline The text is structured in three main parts, each comprising two to three chapters. Part I, entitled Fundamentals, introduces the reader to the fundamental concepts of the two most widely used atomic-resolution electron microscopy techniques: phase contrast imaging in the broad-beam illumination mode (Chapter 2) and scanning transmission electron microscopy (Chapter 3). The focus lies on conventional electron microscopes which are not equipped with aberration correctors. Chapter 4 illustrates the limits of conventional electron microscopes. The title of the second part is Electron Optics. It is split into two chapters. Chapter 5 introduces the reader to some of the fundamental concepts of electron optics, discussing topics like the Hamiltonian analogy, the point eikonal, the refractive index of electrons and geometrical wave surfaces. Chapter 6 deals with the Gaussian dioptrics of a round electron lens with a straight optical axis. The path equations of a round electromagnetic lens are derived, the theorem of optical imaging is discussed and cardinal elements, as well as some of the fundamental rays, are defined and illustrated. This chapter also elucidates the sources of aberrations in conventional electron microscopy. The third part of the book, Aberration Correction, comprises three chapters. Chapter 7 introduces the concepts of image and wave aberrations, and discusses axial and off-axial as well as geometrical and, more briefly, chromatic aberrations. It deals with the isoplanatic approximation and defines the axial aberration function. Chapter 8 deals with the basic concepts of aberration correctors. It first illustrates the effect of

11 Introduction 11 multi-pole lenses and then introduces the reader to the basic concepts of the quadrupole octupole and the hexapole spherical aberration corrector. The chapter also contains a more detailed historical overview and it provides a brief outlook to the latest generation of aberration correctors. As such, the basic principles underlying correctors for off-axial aberrations and for the chromatic aberration are introduced. Chapter 9 focuses on practical aspects when working with aberration-corrected electron microscopes. It describes the methods of aberration diagnosis and discusses in detail the effect of aberration correction on the imaging characteristics. It also provides practical guidelines on how to work with an aberration-corrected microscope and how the imaging performance can be optimized. Though the three parts of the book provide a comprehensive introduction to aberration-corrected electron microscopy, the individual parts of the book can in principle be read independently from each other. Each part of the book is largely self-contained.