ELECTRON OPTICS

II. REVIEW OF EXPERIMENTAL ELECTRON OPTICS AND ITS APPLICATIONS¹

E. Brüche, Berlin

Contents: 1) Electron lenses, 2) Electron-optical instruments, 3) Electron-optical investigations of emission, 4) Development of practical electron optics.

After Busch formulated the foundations of the theory of the electron lens 9 years ago, electron optics developed into a large independent field of theoretical and technical physics. This will become quite clear after we trace the course of its development and the practical results, the most important of which will be discussed by us.

1. Electron Lenses

The basic element of electron optics is a thin ring. Such a ring, charged positively or negatively relative to the surrounding space, forms an electric lens (Fig. 1a); a ring through which a current flows constitutes a typical magnetic lens. A charged ring acts on electron rays in the same way as a glass lens acts on light rays. At a sufficient distance from the electric lens, the potential on both sides of it has the same value, just as does the refractive index in the case of a glass lens. From such a charged

Fig. 1. Main types of electric electron lenses with the distribution of potential along the axis.

ring, the potential initially increases up to the plane of the ring, and then falls again.

one may pass from the ring to the second most important type of electron lenses—to the diaphragm—if this ring is imagined as being surrounded by a row of other rings lying in one plane and having the same potential as the first ring (Fig. 1, b). If we are dealing with an infinitely large charged plane, then the field strength at a large distance from the lens is constant. In the general case the field strength on the two sides of the lens may be either the same or different, and on one side it may become zero. A diaphragm may be either a diverging or a converging lens, in contrast to the ring, which is always a converging lens. Two diaphragms arranged coaxially form a third type of electron lens (Fig. 1, c). This is the so-called immersion lens. In optics it corresponds to a single refracting surface, because the electron-optical refractive index is constant, but different in magnitude on the two sides of the lens. An immersion lens is always converging; it may exert either an accelerating or a retarding action. Of great importance in electron optics is the “immersion objective,” by which is meant an immersion lens placed near a charged plate (Fig. 1, d). The immersion objective is especially important for obtaining images of electron-emitting surfaces (cathode investigations). The designs of electron lenses are very diverse.

Fig. 2. Various designs of simple electron lenses

One may pass from the ring not only to the diaphragm, but also to a cylindrical tube (Fig. 2, a and b), and here it is necessary to consider as fulfilled the condition that the spaces on the two sides of the tube differ in the value of the potential. Further design changes proceeded along the path of compressing the field into the smallest possible space. This is achieved by introducing special electrodes embracing the ring (Fig. 2, c). The use of several electrodes in the case of a diaphragm or cylinder makes it possible to change the optical power of the lens and thus to control the magnification of the system (Fig. 2, d). Design changes, such as, for example, the introduction of funnels or the selection of differently charged electrodes, are made for the purpose of correcting electric lenses*.

In magnetic lenses, the transition from a single turn to longitudinal cylindrical coils, which create

* See the articles by O. Scherzer and V. Glaser.

To E. Brüche’s article

Fig. 4. Electron-optical images obtained in the case of a purely electrical system:
a) at constant voltage; b) at alternating voltage

Fig. 8. Images of gold foil obtained by the methods of light-field and dark-field illumination

Fig. 10. Recrystallization of iron

Fig. 11. Thorium inclusions in crystals of thoriated tungsten

To the article by E. Brüche

Fig. 4. Electron-optical images obtained in the case of a purely electrical system:
a) with constant voltage; b) with alternating voltage.

Fig. 8. Images of gold foil obtained by the methods of bright-field and dark-field illumination.

Fig. 10. Recrystallized iron.

Fig. 11. Thorium inclusions in crystals of thoriated tungsten.

homogeneous magnetic field. (Of course, here one can also proceed to a diaphragm by surrounding the conducting loop with others. In this way one can arrive at a coil in the form of a flat spiral). Reduction of the scattering of the field by means of two coils, one placed inside the other, is used in magnetic lenses just as in electric ones (Fig. 3, c), and in the present case there is also the possibility of changing the field by enclosing the coils in an iron shell (Fig. 3, d). The undesirable rotation of the electron image in some cases can be eliminated by means of a combination of two coils in which currents flow in opposite directions² (Fig. 3, e). Correction of magnetic lenses is carried out with the aid of coils of different magnitude, carrying different currents (Fig. 3, f). In considering

Fig. 3. Magnetic electron lenses

\[ \theta=\frac{1}{2}\left(\frac{E}{U}\right) \]

retarding plates

\[ \frac{1}{\rho}=\frac{1}{2}\left(\frac{E}{U}\right) \]

cylindrical condenser

\[ \frac{1}{f}=\frac{1}{4}\left(\frac{E}{U}\right) \]

diaphragm

Fig. 3a. Paths of electrons in different lenses.

electron-optical systems and electron beams, two points must be taken into account. First, the accelerating field strongly changes the direction of the radiation. Therefore, on the one hand, electric lenses have a great depth of focus, while on the other hand the field of view is limited by the diaphragm standing in the path of the beam. Secondly, only the magnitude of the ratio of two potentials plays a role here, as is shown by the following three examples (Fig. 3, a). When all voltages (including the accelerating one) are increased in the same ratio, the paths of the rays do not change (Fig. 4).

2. Electron-optical instruments

Let us consider the application of the electron-optical method in three examples. First of all, a characteristic example from physics

diffraction of electrons^3. The problem consists in investigating, by means of electron diffraction, the crystalline structure of the foil. It is very difficult to obtain the electron beam required for this purpose with a diameter

Fig. 5. Investigation of the crystalline structure of gold foil:
a) ordinary arrangement; b) arrangement containing a lens

Fig. 6. Diffraction images of different regions of gold foil:
a) enlarged image of the foil; b) diffraction patterns of the marked regions, 0.08 mm in diameter

of 0.1 mm, and also to determine the point at which this beam falls on the foil. The problem is solved in the following way: first, an image of the foil magnified 10 times is obtained. From the plane of this image, a diaphragm with an aperture 1 mm in diameter is used to select,

which is at the same time a fluorescent screen, a beam of rays (Fig. 5). This radiation, too, coming from the region of the foil with a diameter of 0.1 μm corresponding to the given position of the diaphragm on the electron image, gives a diffraction pattern for this portion of the foil (Fig. 6).

An example of the importance of electron optics for the development of long-known technical instruments is provided by the Braun tube, used for oscillography and television.* Electron optics has shown that in the Braun tube the basic problem is that of obtaining an image of the cathode or diaphragm. Before the advent of electron optics, sharp luminous spots (at any rate at low voltages) were achieved only by gas concentration; abandoning this became possible with the advent of electron optics. At present there are various systems of Braun tubes, and, proceeding from the requirement of small dimensions at low magnification, an immersion objective in the form of metallic cylinders is used. In this case the principal collecting lens is moved as far as possible from the cathode (Fig. 7). The result of these improvements has been the obtaining of a sharper image.

Fig. 7. Diagram of a Braun high-vacuum tube: a) change of potential along the axis; b) potential field, c) optical analogy

The most characteristic, one might say classical, application of electron optics is the electron microscope; it can be used for examining biological and other objects, like the microscope in light optics, or for microscopic investigation of electron emission from cathodes. In this field work is being conducted in the direction of surpassing the limits of the resolving power of the light microscope.** Resolution

* See the articles by Gresser on electron optics; Braun and Knoll on electron optics in television.
* See the articles by Ruska*.

the work on this problem was facilitated by the work of the high-voltage laboratory of the Berlin Higher Technical School. Electron-optical investigations have made it possible to study details of the emission process, which is impossible with another method of investigation. This was chiefly the concern of the AEG research institute. Electron microscopes used for solving various problems differ according to the type of object (emitting cathode or illuminated object), and also according to the character of the chosen electric and magnetic system. For obtaining images of cathodes, along with the electric immersion objective, the magnetic microscope has greater practical significance. Recently it has been used to obtain images of wires, after it proved possible to give the equipotential surface near the cathode a plane form. With the aid of a magnetic microscope, images of foil were also obtained by the methods of bright-field and dark-field illumination (Fig. 8)\(^4\).

3. Electron-optical investigations of emission

Four most important methods of extracting electrons are known: extraction by heating, by ionic impact, by electronic impact, and by light radiation. The first object of electron-optical investigation was the incandescent cathode. It soon became possible to elucidate the crystalline structure of the cathode in the case of a pure metal or of a thin (monomolecular, and smaller) layer of metal deposited on the cathode, lowering the work function (Ba, Cs). These investigations show that individual crystals may have different values of the work function, differing by tenths of a volt. This result is experimental material confirming Schottky’s theory of the nonuniform distribution of emission over the cathode surface, and may serve to explain deviations from Schottky’s straight lines\(^5\). If it is assumed that the surface of the wire is composed of crystals having different potentials, then, when a small external field is applied, retarding fields will be created over some crystals, making the escape of electrons difficult (Fig. 9). Owing to this, the total electron current proves to be smaller than can be expected from the theory of emission. In addition, electron optics gives metallographers a method for investigating\(^6\) the process of crystallization at high temperatures, as, for example, the crystallization or recrystallization of iron (Fig. 10). Electron-optical methods make it possible to investigate the structure of the emitting surface, for example—

Fig. 9. Schematic image of the surface of a wire, the crystals of which possess surface potentials \(+1\) or \(-1\ \mathrm{V}\), and of the fields near it

for example, the structure of thoriated tungsten (Fig. 11)\(^7\). With a photoelectric cathode it is impossible to determine its crystalline structure, since the light quanta contribute energy much greater than the work function. The practical significance of this method in this case is as follows: on the one hand, it makes it possible to detect slight contamination of the cathode surface; on the other hand, it makes it possible to investigate the inhomogeneity of layers. In some cases it proves possible to observe the crystalline structure of secondary-emission cathodes\(^8\). By means of secondary emission the internal structure of thin metallic foil can be investigated\(^9\).

The investigations described were of direct importance for all instruments in which cathodes with thermionic, photoelectric, or secondary emission were used (electron tubes, electron multipliers, etc.).

4. Development of Practical Electron Optics

Electron optics has had several stages of development. The first stage should be considered the discovery of cathode rays, their careful investigation, and the study of the influence of electromagnetic fields on them. To this period also belong the discovery of photoelectric and thermoelectric phenomena and of X-rays. Cathode rays first found technical application in Braun tubes and X-ray tubes. Later, electron tubes with heated cathodes joined them. The most complex of these devices from the point of view of technical realization is the Braun tube, since the task of constructing it is connected with the necessity of obtaining a point-like luminous spot. This latter task inevitably had to lead to the development of electron optics.

The aim of the further development of geometrical electron optics was definitively determined after the discovery of the properties of fields with axial symmetry. It was shown theoretically and experimentally that such fields as, for example, fields created by magnetic coils, can act as lenses; moreover, electrostatic systems made it possible to solve the problem of obtaining sharp electron images. Thus the further development of electron optics proceeded in the following directions: first, the construction of electron instruments analogous to optical ones (electron telescope, microscope, and spectrograph), and the use of new instruments for solving problems that cannot be solved by optical methods (increasing the resolving power of an instrument, investigating changes in the structure of matter in the incandescent state, etc.); second, the study from a new point of view of already existing electron devices in which electron radiation is used (X-ray tubes, electron tubes, photoelectric cells, Braun tubes); third, the creation of devices of the type of an electronic image converter,

secondary-electron multiplier, etc. Achievements in the field of television, electron multipliers, and image converters are examples of the modern development of electron optics, whose possibilities are still far from exhausted.

Literature

1. For older works see Brüche and Scherzer, Geometrische Elektronenoptik und ihre Anwendungen, Springer, 1934.
2. H. Stobnow, Z. Physik, 96, 634, 1935.
3. H. Boersch, Ann. d. Phys., 27, 75, 1936.
4. Boersch, Ann. d. Phys., 26, 631, 1936; Mahl, Z. Physik, 98, 321, 1935.
5. See J. A. Becker, Rev. Mod. Phys., 7, 95, 1935; Brüche, Z. Physik, 98, 77, 1935.
6. Brüche and Knecht, Z. techn. Phys., 15, 461, 1934; 16, 95, 1935; W. G. Burgers and J. J. A. Ploss van Amstel, Nature, 136, 721, 1935.
7. E. Brüche and H. Mahl, Z. techn. Phys., 16, 623, 1935; 17, 262, 81, 1936; R. P. Johnson and W. Shockley, Phys. Rev., 49, 436, 1936.
8. M. Knoll, Z. techn. Phys., 16, 467, 1935.
9. R. Behne, Ann. d. Phys., 26, 383, 1936.