Electron Optics

Electron Optics

Introduction

            Electron optics is a mathematical framework for the calculation of particle paths along given electrostatic or magnetostatic fields. Electrons are charged particles (point charges with rest mass). The electron also has an associated spin of + 1/2. While in motion an electron possesses kinetic energy, regardless of any imposed charge field—this could be achieved by accelerating electrons via a voltage differential into a screened "field-free" region, which initially imparts the energy required to accelerate the electron. Given sufficient voltage, the electron can be accelerated sufficiently fast to exhibit measurable relativistic effects, and the velocity must be accounted for relativistically. According to the wave particle duality, electrons can also be considered as wave propagations and therefore have associated wave properties such as wavelength, phase and amplitude.

With respect to electron optics, the nature of the electron as a charged particle causes electrons to interact with imposed electron fields, and their spin causes magnetic field interactions as well. These interactions form the fundamentals

Bethe Formula:

In nuclear physics and theoretical physics, charged particles moving through matter interact with the electrons of atoms in the material. The interaction excites or ionizes the atoms. This leads to an energy loss of the traveling particle. The Bethe formula describes the energy loss per distance travelled of swift charged particles (protons, alpha particles, atomic ions, but not electron) traversing matter (or alternatively the stopping power of the material). The non-relativistic version was found by Hans Bethe in 1930.

For a particle with speed v, charge z, and energy E, traveling a distance x into a target of electron number density n and mean excitation potential I, the relativistic version of the formula reads:

where c is the speed of light and ε₀ the vacuum permittivity, β = v/c, e and m_e the electron charge and rest mass respectively.

Here, the electron density of the material can be calculated by

where ρ is the density of the material, Z its atomic number, N_A the Avogadro number and M_u the Molar mass constant.

In the figure to the right, the small circles are experimental results obtained from measurements of various authors (taken from http://www.exphys.uni-linz.ac.at/Stopping/). The red curve is Bethe's formula. Evidently, Bethe's theory agrees very well with experiment at high energy. The agreement is even better when corrections are applied (see below).

For low energies, i.e., for small velocities of the particle β << 1, the Bethe formula reduces to

At low energy, the energy loss according to the Bethe formula therefore decreases approximately as v⁻² with increasing energy. It reaches a minimum for approximately E = 3Mc², where M is the mass of the particle (for protons, this would be about at 3000 MeV). For highly relativistic cases β ≈ −1, the energy loss increases again, logarithmically due to the transversal component of the electric field.

The mean excitation potential:

In the Bethe theory, the material is completely described by a single number, the mean excitation potential I. In 1933 Felix Bloch showed that the mean ionization potential of atoms is approximately given by

where Z is the atomic number of the atoms of the material. If this approximation is introduced into formula (1) above, one obtains an expression which is often called Bethe-Bloch formula. But since we have now accurate tables of I as a function of Z (see below), the use of such a table will yield better results than the use of formula (3).

The figure shows normalized values of I, taken from a table.^[2] The peaks and valleys in this figure lead to corresponding valleys and peaks in the stopping power. These are called "Z₂-oscillations" or "Z₂-structure" (where Z₂ means the atomic number of the target).

Corrections to the Bethe formula:

The Bethe formula is only valid for energies high enough so that the charged atomic particle (the ion) does not carry any atomic electrons with it. At smaller energies, when the ion carries electrons, this reduces its charge effectively, and the stopping power is thus reduced. But even if the atom is fully ionized, corrections are necessary.

Bethe found his formula using quantum mechanical perturbation theory. Hence, his result is proportional to the square of the charge z of the particle. The description can be improved by considering corrections which correspond to higher powers of z. These are: the Barkas-Andersen-effect (proportional to z³, after Walter H. Barkas and Hans Henrik Andersen), and the Bloch-correction (proportional to z⁴). In addition, one has to take into account that the atomic electrons are not stationary ("shell correction").

These corrections have been built into the programs PSTAR and ASTAR, for example, by which one can calculate the stopping power for protons and alpha particles.^[3] The corrections are large at low energy and become smaller and smaller as energy is increased.

Electron Gun

An electron gun (also called electron emitter) is a device which produces a narrow electron beam of high intensity. It was designed by V. K. Zworykin in 1933. It  is an electrical component that produces an electron beam that has a precise kinetic energy and is most often used in television sets and computer displays that use cathode ray tube (CRT) technology, as well as in other instruments, such as electron microscopes and particle accelerators. Electron guns may be classified in several ways:

·         by the type of electric field generation (DC or RF),

·         by emission mechanism (thermionic, photocathode, cold emission, plasmas source),

·         by focusing (pure electrostatic or with magnetic fields), or

·         by the number of electrodes.

Figure 1 Schematic of an electron gun

Electrons may be emitted from a conducting cathode material either by heating it to the point where outer orbital electrons gain sufficient energy to overcome the work function barrier of the conductor (thermionic sources) or by applying an electric field sufficiently strong that electrons "tunnel" through the barrier (field emission sources). Electron guns used in microprobes employ the former method, in which electrons are effectively evaporated from a resistively-heated tungsten filament; some alternative names for the filament include cathode or emitter.

Characteristics:

A direct current, electrostatic thermionic electron gun is formed from several parts: a hot cathode, which is heated to create a stream of electrons via thermionic emission, electrodes generating an electric field which focus the beam (such as a Wehnelt cylinder), and one or more anode electrodes which accelerate and further focus the electrons. A large voltage between the cathode and anode accelerates the electrons. A repulsive ring placed between them focuses the electrons onto a small spot on the anode at the expense of a lower extraction field strength on the cathode surface. Often at this spot is a hole so that the electrons that pass through the anode form a collimated beam and finally reach a second anode called a collector. This arrangement is similar to an Einzel lens.

An ion gun consists of a cylinder where gas enters from one end face, undergoes electron bombardment from the side walls, and is subjected to an extraction voltage from the other end face. The entire cage has the role of the cathode; the extractor acts as the anode, and an unnamed ring takes the role of the Wehnelt cylinder.

Most color cathode ray tubes – such as those used in color televisions – incorporate three electron guns, each one producing a different stream of electrons. Each stream travels through a shadow mask where the electrons will impinge upon either a red, green or blue phosphor to light up a color pixel on the screen. The resultant color that is seen by the viewer will be a combination of these three primary colors.

Electrons leave the filament with an average energy of E = kT, where k = Boltzmann's constant (8.617398 x 10^-5 eV/K), and T = filament temperature (K). At 2700 K, the electrons have energies of about 0.23 eV. To escape from the cathode, electrons must have a component of velocity at right angles to the surface and their corresponding kinetic energy must be at least equal to the work done in passing through the surface. The energy required to for a material to give up electrons is related to its work function, E_w. The work function of a material is given by:

E = E_w + E_f

where, E is the total amount of energy needed to remove an electron to infinity from the lowest free energy state, E_f is the highest free energy state of an electron in the material, and E_w is the work function or work required to achieve the difference.

The emission flux can be expressed by the ‘Richardson- Dushman’ equation, dating from 1923, which describes the current density emitted by a heated filament:

The electron flux from a tungsten filament is minimal until a temperature of approximately 2500 K. Above 2500 K, the relationship predicts that the electron flux will increase essentially exponentially with increasing temperature, until the filament melts at about 3100 K. However, in practice, the electron emission reaches a plateau termed saturation due to the self-biasing effects of the Wehnelt cap. Proper saturation is achieved at the edge of the plateau (Figure 2) higher emission currents serve only to reduce filament life.

The electron source in microprobes has a triode configuration, consisting of an emitter/cathode (filament), grid cylinder (Wehnelt) and anode. The filament is usually a thin (about 0.1 mm) tungsten wire bent into an "inverted V." Electrons are preferentially emitted from the bent tip and produce a coherent source of electrons in a fairly small area; however, because the filament is bent in a single plane the geometry of this region is not perfectly circular. Tungsten is used because it withstands high temperatures without melting or evaporating. Unfortunately, as noted above, it has a very high operating temperature (2700 K). Heating is accomplished by running a 3- to 4-amp current through the filament. Higher temperatures can deliver greater beam current, but the tradeoff is an exponentially decreasing lifetime due to thermal evaporation of the cathode material.

Figure 2 shows the emission and sample currents as a function of filament voltage in a self-biased gun (think of voltage as analogous to filament temperature). The operating voltage was 20 keV. Approximate saturation voltages (operating values) are indicated. Notice the false peak at about 3.4 volts caused by region of filament that reaches emission temperature before tip. After Heinrich (1981).

                            Figure 2

Emission currents range from about 50 to 200 mA (1 mA = 10-for electron microprobe, whereas they are much higher (15 to 25 mA) for X-ray fluorescence and much lower (100s pA) for SEM work. The life expectancy, t, of a 0.125-mm-diameter filament (in hours) is approximately:

t = 50 / J,

where J = emission flux (A/cm²).

The cloud of primary electrons is condensed by the Wehnelt cap that surrounds the filament and is biased -200 to -300 V with respect to the filament. The Wehnelt cap has an aperture located below the filament tip and suppresses electron emission from the filament except at the tip.. It is important that the filament be properly centered in relation to the opening of the Wehnelt cap and be the proper distance from the opening. Otherwise, an off center beam that is either weak/condensed or bright/diffuse will be produced. The Wehnelt cap acts as a convergent electrostatic lens and serves to focus the cloud of electrons. The electrons converge at a point (10-100 µm in diameter) located between the base of the Wehnelt cap and the anode plate, This point is called the "cross-over" and is the location of the effective electron source. The distance between the tip of the filament and the Wehnelt aperture is critical in determining the geometry of the lens.

The distance between the Wehnelt and the filament can be adjusted in most microprobes, allowing the shape of the electrostatic field to be changed and optimization of the electron gun.

Figure 3 Configuration of self-biased electron gun (after Goldstein et al. 1981).

The potential difference between the filament and Wehnelt is maintained using a bias resistor, which allows the gun to be self-regulating. Recall from high-school physics that V = I R, where V = voltage, I = current, and R = resistance. As the filament emits electrons, an emission current (I) flows from filament to Wehnelt. Any increase the emission current causes a larger voltage drop (V) across the bias resistor and a larger negative voltage is applied to the Wehnelt, reducing the current. As the emission increases, so does the voltage difference between Wehnelt and filament, causing the emission to plateau. Proper bias voltage also optimizes the electron beam brightness (current density per solid unit angle) providing the the most focused electron beam (Figure 4).

Figure 4. Schematic relationship between bias voltage, emission current, and beam brightness. (after Goldstein and Yakowitz, 1975, p. 25.).

The electrons emitted from the filament are drawn away from the cathode by the positively charged anode plate, which is a large circular plate with a central aperture.  The anode has a hole in its center and is biased from +1 to +50 keV with respect to the filament-Wehnelt. (Actually the electron gun is held at a negative voltage relative to the anode.). The voltage potential between the cathode and the anode plate accelerates the electrons down the column and is known as the "accelerating voltage" and is given in terms of KeV. Together the Wehnelt cylinder and anode plate serve to condense and roughly focus the beam of primary electrons.

Movement of the filament tip is the major source of beam instability and even a displacement of 1^o will produce a significant change. The electron gun is aligned by shifting the position of the filament relative to the anode and column beneath it. This position may have to be periodically checked. Most machines (including the Cameca MBX) are aligned mechanically by moving the filament with setscrews or knobs. However, the most modern Cameca microprobes use electromagnets to align the gun. This is accomplished with alignment coils consisting of two sets of four radially oriented magnets one above the other.

Applications:

 The most common use of electron guns is in cathode ray tubes, which were widely used in computer and television monitors. An electron gun can also be used to ionize particles by adding or removing electrons from an atom. This technology is sometimes used in mass spectrometry in a process called electron ionization to ionize vaporized or gaseous particles. More powerful electron guns are used for welding, metal coating, 3D metal printers, metal powder production and vacuum furnaces.

Electron Lens:

An electrostatic lens is a device that assists in the transport of charged particles. For instance, it can guide electrons emitted from a sample to an electron analyzer, analogous to the way an optical lens assists in the transport of light in an optical instrument. Systems of electrostatic lenses can be designed in the same way as optical lenses, so electrostatic lenses easily magnify or converge the electron trajectories. An electrostatic lens can also be used to focus an ion beam, for example to make a microbeam for irradiating individual cells.

Figure 5 Electrostatic lenses in an electron diffraction experiment

Cylinder lens

A cylinder lens consists of several cylinders whose sides are thin walls. Each cylinder lines up parallel to the optical axis into which electrons enter. There are small gaps put between the cylinders. When each cylinder has a different voltage, the gap between the cylinders works as a lens. The magnification is able to be changed by choosing different voltage combinations.

Although the magnification of two cylinder lenses can be changed, the focal point is also changed by this operation. Three cylinder lenses achieve the change of the magnification while holding the object and image positions because there are two gaps that work as lenses. Although the voltages have to change depending on the electron kinetic energy, the voltage ratio is kept constant when the optical parameters are not changed.

While a charged particle is in an electric field force acts upon it. The faster the particle the smaller the accumulated impulse. For a collimated beam the focal length is given as the initial impulse divided by the accumulated (perpendicular) impulse by the lens. This makes the focal length of a single lens a function of the second order of the speed of the charged particle. Single lenses as known from photonics are not easily available for electrons.

The cylinder lens consists of defocusing lens, a focusing lens and a second defocusing lens, with the sum of their refractive powers being zero. But because there is some distance between the lenses, the electron makes three turns and hits the focusing lens at a position farther away from the axis and so travels through a field with greater strength. This indirectness leads to the fact that the resulting refractive power is the square of the refractive power of a single lens.

Einzel lens

An einzel lens is an electrostatic lens that focuses without changing the energy of the beam. It consists of three or more sets of cylindrical or rectangular tubes in series along an axis.

Quadrupole lens

The quadrupole lens consists of two single quadrupoles turned 90° with respect to each other. Let z be the optical axis then one can deduce separately for the x and the y axis that the refractive power is again the square of the refractive power of a single lens.

A magnetic quadrupole works very similar to an electric quadrupole. But the Lorentz force increases with the velocity of the charged particle. In spirit of a wien filter a combined magnetic, electric quadrupole is achromatic around a given velocity. Bohr and Pauli claim that this lens leads to aberration when applied to ions with spin (in the sense of chromatic aberration), but not when applied to electrons, which also have a spin. See Stern-Gerlach experiment.

Magnetic lens

The magnetic lens consists of three parts: a radial field with a flux decreasing towards the optical axis, which makes particles at the outer rim perform a spiraling motion, a homogeneous magnetic field along the optical axis which leads to the focusing Lorentz force, and a second part with a radial field undoing the spiraling. Again the indirectness leads to the fact that the resulting refractive power is the square of the refractive power of a single lens.

Multipole lenses

Multipoles beyond the quadrupole can correct for spherical aberration and in particle accelerators the dipole bending magnets are really composed of a large number of elements with different superpositions of multipoles.

Usually the dependency is given for the kinetic energy itself depending on the power of the velocity. So for an electrostatic lens the focal length varies with the second power of the kinetic energy, while for a magnetostatic lens the focal length varies proportional to the kinetic energy. And a combined quadrupole can be achromatic around a given energy.

If a distribution of particles with different kinetic energies is accelerated by a longitudinal electric field, the relative energy spread is reduced leading to less chromatic error for example in the electron microscope.

Applications:

Electro lens is the most important component of an electron gun used for producing the narrow intense electron beam. Electron lens action is utilized in particle accelerators to focus charged particles into a narrow beam. The recent development of electron spectroscopy makes it possible to reveal the electronic structures of molecules. Although this is mainly accomplished by electron analysers, electrostatic lenses also play a significant role in the development of electron spectroscopy. Since electron spectroscopy detects several physical phenomena from the electrons emitted from samples, it is necessary to transport the electrons to the electron analyser. Electrostatic lenses satisfy the general properties of lenses.

Cathode Ray Tube (CRT)

The cathode ray tube (CRT) is a vacuum tube containing one or more electron guns (a source of electrons or electron emitter) and a fluorescent screen used to view images. It has a means to accelerate and deflect the electron beam(s) onto the screen to create the images. The images may represent electrical waveforms (oscilloscope), pictures (television, computer, monitor), radar targets or others. CRTs have also been used as memory devices, in which case the visible light emitted from the fluorescent material (if any) is not intended to have significant meaning to a visual observer (though the visible pattern on the tube face may cryptically represent the stored data).

The CRT uses an evacuated glass envelope which is large, deep (i.e. long from front screen face to rear end), fairly heavy, and relatively fragile. As a matter of safety, the face is typically made of thick lead glass so as to be highly shatter-resistant and to block most X-ray emissions, particularly if the CRT is used in a consumer product.

Figure 6 Cathode Ray Tube showing its deflection coils and electron guns

CRTs have largely been superseded by newer display technologies such as LCD, plasma display, and OLED, which as of 2012 offer lower manufacturing and distribution costs. The vacuum level inside the tube is high vacuum on the order of 0.01 Pa to 133 nPa.

In television sets and computer monitors, the entire front area of the tube is scanned repetitively and systematically in a fixed pattern called a raster. An image is produced by controlling the intensity of each of the three electron beams, one for each additive primary color (red, green, and blue) with a video signal as a reference. In all modern CRT monitors and televisions, the beams are bent by magnetic deflection, a varying magnetic field generated by coils and driven by electronic circuits around the neck of the tube, although electrostatic deflection is commonly used in oscilloscopes, a type of diagnostic instrument.

Oscilloscope CRTs

In oscilloscope CRTs, electrostatic deflection is used, rather than the magnetic deflection commonly used with television and other large CRTs. The beam is deflected horizontally by applying an electric field between a pair of plates to its left and right, and vertically by applying an electric field to plates above and below. Oscilloscopes use electrostatic rather than magnetic deflection because the inductive reactance of the magnetic coils would limit the frequency response of the instrument.

Phosphor persistence

Various phosphors are available depending upon the needs of the measurement or display application. The brightness, color, and persistence of the illumination depends upon the type of phosphor used on the CRT screen. Phosphors are available with persistences ranging from less than one microsecond to several seconds. For visual observation of brief transient events, a long persistence phosphor may be desirable. For events which are fast and repetitive, or high frequency, a short-persistence phosphor is generally preferable.

Micro channel plate

When displaying fast one-shot events the electron beam must deflect very quickly, with few electrons impinging on the screen; leading to a faint or invisible image on the display. Oscilloscope CRTs designed for very fast signals can give a brighter display by passing the electron beam through a micro-channel plate just before it reaches the screen. Through the phenomenon of secondary emission this plate multiplies the number of electrons reaching the phosphor screen, giving a significant improvement in writing rate (brightness), and improved sensitivity and spot size as well.

Graticules

Most oscilloscopes have a graticule as part of the visual display, to facilitate measurements. The graticule may be permanently marked inside the face of the CRT, or it may be a transparent external plate made of glass or acrylic plastic. An internal graticule eliminates parallax error, but cannot be changed to accommodate different types of measurements. Oscilloscopes commonly provide a means for the graticule to be illuminated from the side, which improves its visibility.

Image Storage Tube

These are found in analog phosphor storage oscilloscopes. These are distinct from digital phosphor storage oscilloscopes which rely on solid state digital memory to store the image. The use of a long persistence phosphor may allow the image to be observed after the event, but only for a few seconds at best. This limitation can be overcome by the use of a direct view storage cathode ray tube (storage tube). A storage tube will continue to display the event after it has occurred until such time as it is erased. A storage tube is similar to a conventional tube except that it is equipped with a metal grid coated with a dielectric layer located immediately behind the phosphor screen. An externally applied voltage to the mesh initially ensures that the whole mesh is at a constant potential. This mesh is constantly exposed to a low velocity electron beam from a 'flood gun' which operates independently of the main gun. This flood gun is not deflected like the main gun but constantly 'illuminates' the whole of the storage mesh. The initial charge on the storage mesh is such as to repel the electrons from the flood gun which are prevented from striking the phosphor screen.

When the main electron gun writes an image to the screen, the energy in the main beam is sufficient to create a 'potential relief' on the storage mesh. The areas where this relief is created no longer repel the electrons from the flood gun which now pass through the mesh and illuminate the phosphor screen. Consequently, the image that was briefly traced out by the main gun continues to be displayed after it has occurred. The image can be 'erased' by resupplying the external voltage to the mesh restoring its constant potential. The time for which the image can be displayed was limited because, in practice, the flood gun slowly neutralizes the charge on the storage mesh. One way of allowing the image to be retained for longer is temporarily to turn off the flood gun. It is then possible for the image to be retained for several days. The majority of storage tubes allow for a lower voltage to be applied to the storage mesh which slowly restores the initial charge state. By varying this voltage a variable persistence is obtained. Turning off the flood gun and the voltage supply to the storage mesh allows such a tube to operate as a conventional oscilloscope tube.

Color CRTs

Color tubes use three different phosphors which emit red, green, and blue light respectively. They are packed together in stripes (as in aperture grille designs) or clusters called "triads" (as in shadow mask CRTs). Color CRTs have three electron guns, one for each primary color, arranged either in a straight line or in an equilateral triangular configuration (the guns are usually constructed as a single unit). (The triangular configuration is often called "delta-gun", based on its relation to the shape of the Greek letter delta.) A grille or mask absorbs the electrons that would otherwise hit the wrong phosphor. A shadow mask tube uses a metal plate with tiny holes, placed so that the electron beam only illuminates the correct phosphors on the face of the tube. Another type of color CRT uses an aperture grille to achieve the same result.

Other CRTs

Cats Eye

In better quality tube radio sets a tuning guide consisting of a phosphor tube was used to aid the tuning adjustment. This was also known as a "Magic Eye" or "Tuning Eye". Tuning would be adjusted until the width of a radial shadow was minimized. This was used instead of a more expensive electromechanical meter, which later came to be used on higher-end tuners when transistor sets lacked the high voltage required to drive the device. The same type of device was used with tape recorders as a recording level meter.

Charactrons

Some displays for early computers (those that needed to display more text than was practical using vectors, or that required high speed for photographic output) used Charactron CRTs. These incorporate a perforated metal character mask (stencil), which shapes a wide electron beam to form a character on the screen. The system selects a character on the mask using one set of deflection circuits, but that causes the extruded beam to be aimed off-axis, so a second set of deflection plates has to re-aim the beam so it is headed toward the center of the screen. A third set of plates places the character wherever required. The beam is unblanked (turned on) briefly to draw the character at that position. Graphics could be drawn by selecting the position on the mask corresponding to the code for a space (in practice, they were simply not drawn), which had a small round hole in the center; this effectively disabled the character mask, and the system reverted to regular vector behavior. Charactrons had exceptionally long necks, because of the need for three deflection systems.

Nimo

Nimo was the trademark of a family of small specialized CRTs manufactured by Industrial Electronics Engineers. These had 10 electron guns which produced electron beams in the form of digits in a manner similar to that of the charactron. The tubes were either simple single-digit displays or more complex 4- or 6- digit displays produced by means of a suitable magnetic deflection system. Having little of the complexities of a standard CRT, the tube required a relatively simple driving circuit, and as the image was projected on the glass face, it provided a much wider viewing angle than competitive types (e.g., nixie tubes).

Williams tube

The Williams tube or Williams-Kilburn tube was a cathode ray tube used to electronically store binary data. It was used in computers of the 1940s as a random-access digital storage device. In contrast to other CRTs in this article, the Williams tube was not a display device, and in fact could not be viewed since a metal plate covered its screen.

Zeus thin CRT display

In the late 1990s and early 2000s Philips Research Laboratories experimented with a type of thin CRT known as the Zeus display which contained CRT-like functionality in a flat panel display. The devices were demonstrated but never marketed.

Advantages

·         High contrast ratio (over 15,000:1), excellent color, fairly wide color gamut and low black level.

·         No native resolution; the only current display technology capable of true multisyncing (displaying many different resolutions and refresh rates without the need for scaling).

·         No input lags.

·         No ghosting and smearing artifacts during fast motion due to sub-millisecond response time, and impulse-based operation.

·         Near zero color, saturation, contrast or brightness distortion.

·         Excellent viewing angle.

·         Allows the use of light guns/pens.

·         Can be used or stored in both extreme hot and cold temperature conditions without harm to the system.

·         Large size and weight, especially for bigger screens (a 20-inch (51 cm) unit weighs about 50 lb (23 kg)).

·         Geometric distortion caused by variable beam travel distances.

·         High power consumption. On average, a CRT monitor consumes 2–10× the power that an identically sized LCD monitor would consume, depending on the type of backlight used in the LCD screen, and its brightness setting.

·         A lot of heat can be emitted during operation, due to relatively high power consumption.

·         Can suffer screen burn-in, though not as quickly as Plasma displays.

·         Produces noticeable flicker at refresh rates lower than 85 Hz.

·         Hazardous to repair/service.

·         Maximum size for direct-view displays is limited to about 40 inches due to practical and manufacturing restrictions (a CRT display of this size can weigh about 300 pounds), though the sizing can be increased with an array of separate displays, such as the original Jumbotron used at sports arenas.

·         The glass envelope contains toxic lead and barium as X-ray radiation shielding. The phosphors can also contain toxic elements such as cadmium. Many countries treat CRTs as toxic waste and prohibit their disposal in landfills or by incineration.

·         Purity and convergence in color tubes, affected by the Earth's magnetic field, usually roughly factory preset (biased) for operation in either the northern hemisphere, the southern hemisphere, or the equatorial area, but may require trimming at final location. Adjustment at final location requires a high degree of technical skill, as well as safety precautions associated with opening the display housing.

·         Sensitive to magnetic interference, which can cause the image to shimmer (e.g. if a transformer or other electro-magnetic source is too close to the screen) or the colors to shift (e.g. if an unshielded speaker is too close to the screen).

·         Slightly blurry image compared to the razor sharp stationary image an LCD can produce.

·         A “halo” may appear around bright objects on a mostly dark screen.

Cathode Ray Oscilloscope Principles

The Figure shows the structure and the main components of a cathode ray tube (CRT) are shown in figure 7(a). The face plane of the CRO screen is shown in figure 7(b).

Electron beam generated by the electron gun first deflected by the deflection plates, and then directed onto the fluorescent coating of the CRO screen, which produces a visible light spot on the face plane of the oscilloscope screen.

                                       Figure 7(a)                                             Figure 7(b)

A detailed representation of a CRT is given in Figure 7(c). The CRT is composed of two main parts,

i). Electron Gun,  ii). Deflection System

Figure 7(c)

Electron Gun

            Electron gun provides a sharply focussed electron beam directed toward the fluorescent-coated screen. The thermally heated cathode emits electrons in many directions. The control grid provides an axial direction for the electron bean and controls the number and speed of electrons in the beam. The momentum of the electrons determines the intensity, or brightness, of the light emitted from the fluorescent coating due to the electron bombardment. Because electrons are negatively charged, a repulsion force is created by applying a negative voltage to the control grid, to adjust their number and speed. A more negative voltage results in less number of electrons in the beam and hence decreased brightness of the beam spot. Since the electron beam consists of many electrons, the beam tends to diverge. This is because the similar (negative) charges on the electrons repulse each other. To compensate for such repulsion forces, an adjustable electrostatic field is created between two cylindrical anodes, called the focussing anodes. The variable positive voltage on the second anode cylinder is therefore used to adjust the focus or sharpness of the bright spot.

The Deflection System

The deflection system consists of two pairs of parallel plates, referred to as the vertical and horizontal deflection plates. One of the plates in each set is permanently connected to the ground (Zero volt), whereas the other plate of each set is connected to input signals or triggering signal of the CRO.

Figure 7 (d)

As shown in Figure 7 (d), the electron beam passes through the deflection plates.

Figure 8

In reference to the schematic diagram in Figure 8, a positive voltage applied to the Y input terminal causes the electron beam to deflect vertically upward, due to attraction forces, while a negative voltage applied to the Y input terminal causes the electron beam to deflect vertically downward, due to the repulsion forces. Similarly, a positive voltage applied to the X input terminal will cause the electron beam to deflect horizontally toward the right, while the negative voltage applied to the X terminal will cause the electron beam horizontally toward the left of the screen.

Cyclotron

A cyclotron is a type of particle accelerator in which charged particles accelerate outwards from the center along a spiral path. The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying (radio frequency) electric field.

Principle of Operation

Cyclotrons accelerate charged particle beams using a high frequency alternating voltage which is applied between two "D"-shaped electrodes (also called "dees"). An additional static magnetic field  is applied in perpendicular direction to the electrode plane, enabling particles to re-encounter the accelerating voltage many times at the same phase. To achieve this, the voltage frequency must match the particle's cyclotron resonance frequency

,

with the relativistic mass m and its charge q. This frequency is given by equality of centripetal force and magnetic Lorentz force. The particles, injected near the centre of the magnetic field, increase their kinetic energy only when recirculating through the gap between the electrodes; thus they travel outwards along a spiral path.

Figure 9 Diagram of cyclotron operation from Lawrence’s 1934 patent.

The D shaped electrodes are enclosed in a flat vacuum chamber, which is installed in a narrow gap between the two poles of a large magnet. Their radius will increase until the particles hit a target at the perimeter of the vacuum chamber, or leave the cyclotron using a beam tube, enabling their use e.g. for particle therapy. Various materials may be used for a target, and the collisions will create secondary particles which may be guided outside of the cyclotron and into instruments for analysis.

Relativistic considerations

In the non relativistic approximation, the frequency does not depend upon the radius of the particle's orbit, since the particle's mass is constant. As the beam spirals out, its frequency does not decrease, and it must continue to accelerate, as it is travelling a greater distance in the same time period.

In contrast to this approximation, as particles approach the speed of light, their relativistic mass increases, requiring either modifications to the frequency, leading to the synchrocyclotron, or modifications to the magnetic field during the acceleration, which leads to the isochronous cyclotron. The relativistic mass can be rewritten as

,

Where,  is the particle rest mass

 

is the relative velocity, and

 

is the Lorentz factor

The relativistic cyclotron frequency and angular frequency can be rewritten as

, and

,

Where,

 , would be the cyclotron frequency in classical approximation,

 , would be the cyclotron angular frequency in classical approximation.

The gyro radius for a particle moving in a static magnetic field is then given by

,

because

Where, v would be the (linear) velocity

Synchrocyclotron

A synchrocyclotron is a cyclotron in which the frequency of the driving RF electric field is varied to compensate for relativistic effects as the particles' velocity begins to approach the speed of light. This is in contrast to the classical cyclotron, where the frequency was held constant, thus leading to the synchrocyclotron operation frequency being

,

where  is the classical cyclotron frequency and  again is the relative velocity of the particle beam.

The rest mass of an electron is 511 keV/c², so the frequency correction is 1% for a magnetic vacuum tube with a 5.11 keV/c² direct current accelerating voltage. The proton mass is nearly two thousand times the electron mass, so the 1% correction energy is about 9 MeV, which is sufficient to induce nuclear reactions.

Isochronous cyclotron

An alternative to the synchrocyclotron is the isochronous cyclotron, which has a magnetic field that increases with radius, rather than with time. Isochronous cyclotrons are capable of producing much greater beam current than synchrocyclotrons, but require azimuthal variations in the field strength to provide a strong focusing effect and keep the particles captured in their spiral trajectory. For this reason, an isochronous cyclotron is also called an "AVF (azimuthal varying field) cyclotron". This solution for focusing the particle beam was proposed by L. H. Thomas in 1938.

Recalling the relativistic gyro radius

and the relativistic cyclotron frequency , one can choose  to be proportional to the Lorentz factor, .

This results in the relation

which again only depends on the velocity , like in the non-relativistic case. Also, the cyclotron frequency is constant in this case.

The transverse de-focusing effect of this radial field gradient is compensated by ridges on the magnet faces which vary the field azimuthally as well. This allows particles to be accelerated continuously, on every period of the radio frequency (RF), rather than in bursts as in most other accelerator types. This principle that alternating field gradients have a net focusing effect is called strong focusing. It was obscurely known theoretically long before it was put into practice. Examples of isochronous cyclotrons abound; in fact almost all modern cyclotrons use azimuthally-varying fields. The TRIUMF cyclotron is the largest with an outer orbit radius of 7.9 metres, extracting protons at up to 510 MeV, which is 3/4 of the speed of light. The PSI cyclotron reaches higher energy but is smaller because of using a higher magnetic field.

Applications

For several decades, cyclotrons were the best source of high-energy beams for nuclear physics experiments; several cyclotrons are still in use for this type of research. The results enable the calculation of various properties, such as the mean spacing between atoms and the creation of various collision products. Subsequent chemical and particle analysis of the target material may give insight into nuclear transmutation of the elements used in the target.

Cyclotrons can be used in particle therapy to treat cancer. Ion beams from cyclotrons can be used, as in proton therapy, to penetrate the body and kill tumors by radiation damage, while minimizing damage to healthy tissue along their path. Cyclotron beams can be used to bombard other atoms to produce short-lived positron-emitting isotopes suitable for PET imaging.

More recently cyclotrons currently installed at hospitals for particle therapy have been retrofitted to enable them to produce technetium-99. Technetium-99 is a diagnostic isotope in short supply due to difficulties at Canada's Chalk River facility.

Mass spectrometer

In 1919 Aston developed the first really good mass spectrograph, an instrument for measuring the masses of isotopes. His apparatus gave accuracies of one part in 1000.
A simpler form of the mass spectrograph than Aston's is that due to Bainbridge (1933) and a plan view of this is shown in Figure 10. 

Figure 10 Mass spectrometer

Ions are formed at D and pass through the cathode C and then through a slit S₁. They then travel between two plates A and B, between which a potential (V) is applied. A magnetic field (strength B) is applied at right angles to the electrostatic field and so the electrostatic and electromagnetic forces act in opposite directions to each other. 
A particle with a charge q and velocity v will only pass through the next slit S₂ if the resultant force on it is zero – that is it is traveling in a straight line. That is if:

Electromagnetic force (Bqv) = Electrostatic force (qE)

Therefore, for the particle to pass through S₂: 

Velocity of particle (v) = E/B

But this is a constant, and so only particles with a certain velocity enter the deflection chamber F. For this reason the combination of slits and deflecting plates is called a velocity selector.
In the deflection chamber the ions are affected by the magnetic fields alone and so move in circular paths, the lighter ions having the larger path radius. If the mass of an ion is M, its charge q and its velocity v then:

Bqv=Mv²/r
where r is the radius of the path. Therefore r = Mv/(Bq)    and so: Mass of ion (M) = rB²q/E
The radius of the path in the deflection chamber is directly proportional to the mass of the ion. The detection is by either a photographic plate or a collector that produces a small current when the ions fall on it. The magnetic field may be varied, so changing the radii of the particles' paths so that ions of different masses fall on a fixed collector.

This method of analysis is very accurate and can detect differences in the masses of two ions as small as one part in 10⁹.

Figure 11 shows the appearance of the photographic plate when a gas containing two isotopes is used. Note the wider line for the mass m₁, showing its relatively greater abundance.

Figure 11

Electron Microscope:

An electron microscope (EM) is a type of microscope that uses an electron beam to illuminate a specimen and produce a magnified image.

An EM has greater resolving power than a light microscope and can reveal the structure of smaller objects because electrons have wavelengths about 100,000 times shorter than visible light photons. They can achieve better than 50 pm resolution and magnifications of up to about 10,000,000x whereas ordinary, non-confocal light microscopes are limited by diffraction to about 200 nm resolution and useful magnifications below 2000x.

Figure 12 Electron Microscope fabricated by Siemens

The electron microscope uses electrostatic and electromagnetic lenses to control the electron beam and focus it to form an image. These electron optical lenses are analogous to the glass lenses of a light optical microscope.

Electron microscopes are used to investigate the ultrastructure of a wide range of biological and inorganic specimens including microorganisms, cells, large molecules, biopsy samples, metals, and crystals. Industrially, the electron microscope is often used for quality control and failure analysis. Modern electron microscopes produce electron micrographs, using specialized digital cameras or frame grabbers to capture the image.

Types of Electron microscope:

i). Transmission electron microscope (TEM)

The original form of electron microscope, the transmission electron microscope (TEM) uses a high voltage electron beam to create an image. The electron beam is produced by an electron gun, commonly fitted with a tungsten filament cathode as the electron source. The electron beam is accelerated by an anode typically at +100 keV (40 to 400 keV) with respect to the cathode, focused by electrostatic and electromagnetic lenses, and transmitted through the specimen that is in part transparent to electrons and in part scatters them out of the beam. When it emerges from the specimen, the electron beam carries information about the structure of the specimen that is magnified by the objective lens system of the microscope. The spatial variation in this information (the "image") may be viewed by projecting the magnified electron image onto a fluorescent viewing screen coated with a phosphor or scintillator material such as zinc sulfide. Alternatively, the image can be photographically recorded by exposing a film or plate directly to the electron beam, or a high-resolution phosphor may be coupled by means of a lens optical system or a fiber optic light-guide to the sensor of a CCD (charge-coupled device) camera. The image detected by the CCD may be displayed on a monitor or computer.

Figure 13 Layout of optical components in basic TEM

Transmission Electron Microscope (TEM)

Resolution of the TEM is limited primarily by spherical aberration, but a new generation of aberration correctors has been able to partially overcome spherical aberration to increase resolution. Hardware correction of spherical aberration for the high-resolution transmission electron microscopy (HRTEM) has allowed the production of images with resolution below 0.5 angstrom (50 picometres) and magnifications above 50 million times. The ability to determine the positions of atoms within materials has made the HRTEM an important tool for nano-technologies research and development.

An important mode of TEM utilization is electron diffraction. The advantages of electron diffraction over X-ray crystallography are that the specimen need not be a single crystal or even a polycrystalline powder, and also that the Fourier transform reconstruction of the object's magnified structure occurs physically and thus avoids the need for solving the phase problem faced by the X-ray crystallographers after obtaining their X-ray diffraction patterns of a single crystal or polycrystalline powder. The major disadvantage of the transmission electron microscope is the need for extremely thin sections of the specimens, typically about 100 nanometers. Biological specimens typically require be chemically fixing, dehydrating and embedding in a polymer resin to stabilize them sufficiently to allow ultrathin sectioning. Sections of biological specimens, organic polymers and similar materials may require special `staining' with heavy atom labels in order to achieve the required image.

ii). Scanning electron microscope (SEM)

Unlike the TEM, where electrons of the high voltage beam carry the image of the specimen, the electron beam of the scanning electron microscope (SEM) does not at any time carry a complete image of the specimen.

Figure 14 Schematic of SEM

 The SEM produces images by probing the specimen with a focused electron beam that is scanned across a rectangular area of the specimen (raster scanning). When the electron beam interacts with the specimen, it loses energy by a variety of mechanisms. The lost energy is converted into alternative forms such as heat, emission of low-energy secondary electrons and high-energy backscattered electrons, light emission (cathodoluminescence) or X-ray emission, which provide signals carrying information about the properties of the specimen surface, such as its topography and composition. The image displayed by an SEM maps the varying intensity of any of these signals into the image in a position corresponding to the position of the beam on the specimen when the signal was generated. In the SEM image of an ant shown at right, the image was constructed from signals produced by a secondary electron detector, the normal or conventional imaging mode in most SEMs.

Generally, the image resolution of an SEM is about an order of magnitude poorer than that of a TEM. However, because the SEM image relies on surface processes rather than transmission, it is able to image bulk samples up to many centimetres in size and (depending on instrument design and settings) has a great depth of field, and so can produce images that are good representations of the three-dimensional shape of the sample. Another advantage of SEM is its variety called environmental scanning electron microscope (ESEM) can produce images of sufficient quality and resolution with the samples being wet or contained in low vacuum or gas. This greatly facilitates imaging biological samples that are unstable in the high vacuum of conventional electron microscopes.

iii). Reflection electron microscope (REM)

In the Reflection Electron Microscope (REM) as in the TEM, an electron beam is incident on a surface but instead of using the transmission (TEM) or secondary electrons (SEM), the reflected beam of elastically scattered electrons is detected. This technique is typically coupled with reflection high energy electron diffraction (RHEED) and reflection high-energy loss spectroscopy (RHELS). Another variation is spin-polarized low-energy electron microscopy (SPLEEM), which is used for looking at the microstructure of magnetic domains.

iv). Scanning transmission electron microscope (STEM)

The STEM rasters a focused incident probe across a specimen that (as with the TEM) has been thinned to facilitate detection of electrons scattered through the specimen. The high resolution of the TEM is thus possible in STEM. The focusing actions (and aberrations) occur before the electrons hit the specimen in the STEM, but afterward in the TEM. The STEMs use of SEM-like beam rastering simplifies annular dark-field imaging, and other analytical techniques, but also means that image data is acquired in serial rather than in parallel fashion. Often TEM can be equipped with the scanning option and then it can function both as TEM and STEM.

Applications:

Electron Microscope is having applications such as Circuit edit, Defect analysis, Failure analysis in Semiconductor and data storage area, Diagnostic electron microscopy, Cryobiology, Protein localization, Electron tomography, Cryo-electron microscopy, Toxicology in Biology and life sciences, Electron beam-induced deposition, Materials qualification, Medical research, Nano prototyping, Nano metrology, Device testing and characterization in Materials research and High-resolution imaging, 2D & 3D micro-characterization, Macro sample to nanometer metrology, Particle detection and characterization, Direct beam-writing fabrication, Dynamic materials experiments, Sample preparation, Forensics, Mining (mineral liberation analysis), Chemical/Petrochemical, Fractography and failure analysis in industries.